http://2009.igem.org/wiki/index.php?title=Special:Contributions&feed=atom&limit=50&target=Jaspervdg2009.igem.org - User contributions [en]2024-03-28T09:54:06ZFrom 2009.igem.orgMediaWiki 1.16.5http://2009.igem.org/Team:Groningen/Brainstorm/ModellingTeam:Groningen/Brainstorm/Modelling2010-02-14T17:06:41Z<p>Jaspervdg: Some small updates.</p>
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<div>{{Team:Groningen/Header}}<br />
[[Category:Team:Groningen/Roles/Modeller]]<br />
<br />
<br />
==Software tools from previous years==<br />
<br />
*RNA folding (secondary structure)<br />
**[https://2008.igem.org/Team:Alberta_NINT/Modeling Alberta 2008], using [http://rna.urmc.rochester.edu/rnastructure.html RNAstructure] and UNAFold (with a front-end), they used both programs (presumably to get an idea of the certainty)<br />
*Molecular/genetic Circuit (?), (small) systems of (non-linear) ODEs<br />
**[https://2008.igem.org/Team:Bologna/Modeling Bologna 2008], using Simulink (Mathworks)<br />
**[https://2008.igem.org/Team:ETH_Zurich/Modeling/Switch_Circuit ETH Zurich 2008], using the SimBiology toolbox in Matlab<br />
**[https://2008.igem.org/Team:iHKU/modeling IHKU 2008]<br />
**(?)[https://2008.igem.org/Team:Istanbul/Modeling Istanbul 2008], using the SimBiology toolbox<br />
**[https://2008.igem.org/Team:LCG-UNAM-Mexico/Modeling LCG-UNAM-Mexico 2008], using the SimBiology toolbox<br />
**[https://2008.igem.org/Team:NTU-Singapore/Modelling/Deterministic_Modeling NTU Singapore 2008], using Simulink, [http://www.sbtoolbox2.org/main.php Systems Biology Toolbox 2] (sensitivity analysis) and [http://www.cellware.org/index.html CellWare] (stochastic analysis)<br />
**[https://2008.igem.org/Team:Purdue/Modeling Purdue 2008], using Excel and Mathcad<br />
**[https://2008.igem.org/Team:TUDelft/Color_modeling TU Delft 2008], using CellDesigner and the [http://www.sys-bio.org/ Synthetic Biology Workbench] for Matlab<br />
**[https://2008.igem.org/Team:Edinburgh/Modelling/Kinetic Edinburgh 2008], using [http://www.copasi.org/tiki-index.php COPASI]<br />
**[https://2008.igem.org/Team:Freiburg/Modeling Freiburg 2008], using Matlab<br />
**[https://2008.igem.org/Team:Johns_Hopkins/Applications Johns Hopkins 2008], using Matlab (for population dynamics of yeast)<br />
**[https://2008.igem.org/Team:Michigan/Project/Modeling Michigan 2008], using Mathematica<br />
**[https://2008.igem.org/Team:UNIPV-Pavia/Modeling Pavia 2008], using Matlab and Simulink<br />
**[https://2008.igem.org/Team:University_of_Ottawa/Modeling Ottawa 2008], using Matlab<br />
**[https://2008.igem.org/Team:University_of_Washington/Modeling Washington 2008], using Mathematica<br />
**[https://2008.igem.org/PHA_Project_Modeling Tsinghua 2008], using Matlab<br />
**[https://2008.igem.org/Team:BCCS-Bristol/Modeling-GRN BCCS-Bristol 2008], Matlab<br />
**[https://2008.igem.org/Team:Groningen/modeling_SingleCell.html Groningen 2008!], using Matlab and some custom tools to construct the models<br />
**[https://2008.igem.org/Team:KULeuven/Model/Overview KULeuven], using Matlab and Celldesigner, site done very decently<br />
**[https://2008.igem.org/Team:Montreal/Modeling Montreal], using Mathematica<br />
**[https://2008.igem.org/Team:Paris/Analysis Paris 2008], using BIOCHAM<br />
**[https://2008.igem.org/Team:UCSF/Modeling UCSF], using Matlab, [[User:Kbover|Klaas Bernd]]: perhaps for growth stages?<br />
**[https://2008.igem.org/Team:Cambridge/Modelling Cambridge], using an unspecified tool<br />
**[https://2008.igem.org/Team:Imperial_College/Dry_Lab Imperial College Londen], using Matlab<br />
**[https://2008.igem.org/Team:Peking_University/Modeling Peking], using SimBiology<br />
*Cell processes<br />
**[https://2008.igem.org/Modeling Calgary 2008], using their own tool (transcription and translation)<br />
**[https://2008.igem.org/Team:Waterloo/Modeling Waterloo 2008], using [http://theileria.ccb.sickkids.ca/CellSim/overview.php Cell++]<br />
*Static genome analysis (?)<br />
**[https://2008.igem.org/Team:ETH_Zurich/Modeling/Genome_Static_Analysis ETH Zurich 2008], using their own tool<br />
*Genome Scale Model (whole cell response)<br />
**[https://2008.igem.org/Team:ETH_Zurich/Modeling/Genome-Scale_Model ETH Zurich 2008], using the [http://gcrg.ucsd.edu/Downloads/Cobra_Toolbox Cobra Toolbox] for Matlab<br />
**?[https://2008.igem.org/Team:Wisconsin/Modeling Wisconsin 2008], using GAMS<br />
*Chemostat simulation<br />
**[https://2008.igem.org/Team:ETH_Zurich/Modeling/Chemostat_Selection ETH Zurich 2008], using their genome scale model data<br />
*Cell movement<br />
**[https://2008.igem.org/Team:iHKU/modeling IHKU 2008], as random walks<br />
**[https://2008.igem.org/Team:University_of_Lethbridge/Modeling Lethbridge 2008], using [http://www.pdn.cam.ac.uk/groups/comp-cell/BCT.html BCT] (a tool to model the chemotaxis pathway of E. Coli?)<br />
**[https://2008.igem.org/Chemotaxis_Modeling Tsinghua 2008], using their own code?<br />
*Group behaviour<br />
**[https://2008.igem.org/Team:BCCS-Bristol/Modeling-Agent_Based BCCS-Bristol 2008], movement of groups of cells, using a home-grown Java tool<br />
**[https://2008.igem.org/Team:Groningen/modeling_Spatial.html Groningen 2008!], spatial interaction<br />
**[https://2008.igem.org/Team:Heidelberg/Modeling Heidelberg], two population distributions and some substance concentrations using custom Matlab code<br />
**[https://2008.igem.org/Team:Montreal/Modeling Montreal], interaction in Repressilator network, using Mathematica<br />
**[https://2008.igem.org/Team:Cambridge/Modelling#Modelling_the_complete_agr-quorum_sensing_system Cambridge], quorum sensing<br />
**[https://2008.igem.org/Team:Imperial_College/Dry_Lab Imperial College Londen], growth curve and motility, using Matlab<br />
*Mutation<br />
**[https://2008.igem.org/Team:Peking_University/Modeling Peking]<br />
<br />
Other potentially interesting software tools:<br />
*[https://2008.igem.org/Team:UC_Berkeley_Tools UC Berkeley's Clotho]<br />
*[http://sbml.org/ SBML], a standard to define models.<br />
*[https://2008.igem.org/Team:KULeuven/Software/Simbiology2LaTeX KU Leuven's Simbiology2LaTeX]<br />
<br />
==Interactive Graphs?==<br />
It might be interesting to use JavaScript to present simulation results. This would allow for some degree of interaction (like resizing graphs, linked views, etc.) and may even make it somewhat easier to use graphs, we'd simply have some on-line repository of simulation results (a spreadsheet for example) and we could select which graphs to use on the Wiki.<br />
<br />
Below an example of a JavaScript generated graph is shown, based on [http://spreadsheets.google.com/pub?key=rRnyFyi-bgqsjT3SdJBdKKw this spreadsheet]. Note that the two views of the data are linked (although at this time both the kind of graph and the link is not optimal) and that it would be possible to create templates for creating these linked graphs. The current demo is based on [http://www.dojotoolkit.org/ the Dojo Toolkit] as it has more advanced charting capabilities at this moment than Google visualization (and it seems to be supported well in different browsers).<br />
<br />
{{GraphHeader}}<br />
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{{graph|Team:Groningen/Graphs/Test}}<br />
{{graph|Team:Groningen/Graphs/Test2}}<br />
<br />
Questions that would have to be resolved include:<br />
<br />
* How can we make this easy to use?<br />
** The graphs can now be defined using a more or less normal Wiki page and allow the use of templates.<br />
* What kinds of plots do we need?<br />
* How flexible do we need it to be? (Layout-wise.)<br />
* Can we make it that flexible? (And still easy to use.)<br />
<!--* Do we want to keep referring to parts of a spreadsheet or do we want to be able to select parts by the parameters used?--><br />
* Can we create a relatively easy way to let the viewer select different data for exploratory purposes? We will likely run more simulations than you would normally graph.<br />
* How to support axis titles?<br />
** Currently done using some custom code (created by someone else and submitted to Dojo's bug tracker).<br />
* ???<br />
<br />
Taking this idea (much) further it would even be possible to run simulations using JavaScript (and charting the results), based on SBML models. However, this would involve much, much more effort than just showing a few interactive plots.<br />
<br />
::Note that we did implement simulations in JavaScript, but based on a function that return the time-derivatives given the current state. In principle this is surprisingly fast (in some cases graphing was the bottle-neck, leading us to subsample the simulated time series for graphing purposes) and it should be relatively easy to adapt to other models. Note that we only used a very simple integration scheme though (so if your model requires a more advanced integration scheme you'll have to program it yourself).<br />
<br />
=={{anchor|ModellingAGeneticCircuit}}Modelling a Genetic Circuit - TODO==<br />
To model a genetic circuit the following must be done (TODO: more detail):<br />
* Determine which genes are involved and how they are regulated???<br />
* Model gene transcription? (How?) Try to avoid this, try going directly to protein.<br />
* Model gene translation? (How?) Try to avoid this, try going directly to protein.<br />
* Model degradation? (How?)<br />
* Model interaction of relevant substances. This requires reaction formulas for all the substances with (known) reaction rates, as well as information on how the substance diffuses (unless it is assumed the model is "well-mixed").<br />
* Link to the world outside the cell and macroscopic effects, like cell density. Note the medium is usually well-known.<br />
* Create a kind of mind map of the processes involved to show how the model could be refined.<br />
* Formulate what aspects of the modelling results are essential. So, for example that some concentration rises as a result of the presence of a substance, or that the bacteria actually float. (Can we use mathematical topology as a criterium?)<br />
<br />
This can be done using one of the following methods:<br />
* One [[Team:Groningen/Glossary#ODE|ordinary differential equation]] per substance involved, reflecting the different reaction formulas and rates.<br />
* If the spatial distribution of substances needs to be taken into account [[Team:Groningen/Glossary#PDE|partial differential equations]] can be used. This is probably not necessary when talking about large numbers of bacteria.<br />
* [[Team:Groningen/Glossary#SSA|Stochastic modelling]] can be used if needed (if we deal with very low concentrations for example).<br />
<br />
Questions:<br />
* What exactly is the role of a kinetic law in modelling a reaction?<br />
** A kinetic law is usually a generic equation describing the rate of a certain class of reactions in terms of the reactant concentrations and some constants. (For example the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]].)<br />
<br />
==Purpose of Modelling==<br />
* Descriptive, it can help describe the system.<br />
* As verification of the design.<br />
* Predictive, it can help predict results to aid in selecting physical parameters. (How many copies of a gene? What concentrations? etc.)<br />
* As tool in designing tests. What tests will give the best discrimination, etc.<br />
<br />
==Literature==<br />
See our [[Team:Groningen/Literature|literature list]] for a full overview of all literature. For our team members that are looking for books on the subject, have a look under code [http://opc.ub.rug.nl/DB=1/SET=2/TTL=1/CLK?IKT=8110&TRM=605B 605B] (Bernoulliborg library, lower floor), as well as 605C/D/E (A and Z also exist but seem to be less interesting) and 610A (and possibly 625, 715).<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:GroningenTeam:Groningen2009-11-16T11:46:10Z<p>Jaspervdg: </p>
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<h1>Heavy metal scavengers<!-- with a vertical gas drive--></h1><br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To battle this problem, a '''purification strategy''', in which arsenic, zinc and copper are removed from water and sediment, was developed. This strategy encompasses a biological device in which <i>E. coli</i> bacteria accumulate metal ions from solutions, after which they '''produce gas vesicles''' and '''start floating'''. This biological device consists of two integrated systems: one for metal uptake and storage, the other for metal induced buoyancy. The uptake and storage system consists of a [[Team:Groningen/Project/Transport|metal transporter]] and [[Team:Groningen/Project/Accumulation|metal binding proteins]] (to reduce toxicity and increase accumulation). The buoyancy system is made up of a [[Team:Groningen/Project/Promoters|metal induced promotor]] in front of a [[Team:Groningen/Project/Vesicle|gas vesicle gene cluster]]. The combination of both systems will enable the efficient cleaning of polluted water and sediment in a biological manner. <br />
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{{Team:Groningen/Footer_Main}}</div>Jaspervdghttp://2009.igem.org/File:GroningenFinalist.pngFile:GroningenFinalist.png2009-11-16T11:45:44Z<p>Jaspervdg: uploaded a new version of "Image:GroningenFinalist.png"</p>
<hr />
<div>We're finalists.</div>Jaspervdghttp://2009.igem.org/Team:GroningenTeam:Groningen2009-11-16T11:45:03Z<p>Jaspervdg: </p>
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<h1>Heavy metal scavengers<!-- with a vertical gas drive--></h1><br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To battle this problem, a '''purification strategy''', in which arsenic, zinc and copper are removed from water and sediment, was developed. This strategy encompasses a biological device in which <i>E. coli</i> bacteria accumulate metal ions from solutions, after which they '''produce gas vesicles''' and '''start floating'''. This biological device consists of two integrated systems: one for metal uptake and storage, the other for metal induced buoyancy. The uptake and storage system consists of a [[Team:Groningen/Project/Transport|metal transporter]] and [[Team:Groningen/Project/Accumulation|metal binding proteins]] (to reduce toxicity and increase accumulation). The buoyancy system is made up of a [[Team:Groningen/Project/Promoters|metal induced promotor]] in front of a [[Team:Groningen/Project/Vesicle|gas vesicle gene cluster]]. The combination of both systems will enable the efficient cleaning of polluted water and sediment in a biological manner. <br />
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{{Team:Groningen/Footer_Main}}</div>Jaspervdghttp://2009.igem.org/Team:GroningenTeam:Groningen2009-11-16T11:42:37Z<p>Jaspervdg: </p>
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<div class="intro"><br />
<h1>Heavy metal scavengers<!-- with a vertical gas drive--></h1><br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To battle this problem, a '''purification strategy''', in which arsenic, zinc and copper are removed from water and sediment, was developed. This strategy encompasses a biological device in which <i>E. coli</i> bacteria accumulate metal ions from solutions, after which they '''produce gas vesicles''' and '''start floating'''. This biological device consists of two integrated systems: one for metal uptake and storage, the other for metal induced buoyancy. The uptake and storage system consists of a [[Team:Groningen/Project/Transport|metal transporter]] and [[Team:Groningen/Project/Accumulation|metal binding proteins]] (to reduce toxicity and increase accumulation). The buoyancy system is made up of a [[Team:Groningen/Project/Promoters|metal induced promotor]] in front of a [[Team:Groningen/Project/Vesicle|gas vesicle gene cluster]]. The combination of both systems will enable the efficient cleaning of polluted water and sediment in a biological manner. <br />
<br><br><br />
<center>{{linkedImage|Enter.png|Team:Groningen/Project}}</center><br />
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{{Team:Groningen/Footer_Main}}</div>Jaspervdghttp://2009.igem.org/Team:GroningenTeam:Groningen2009-11-16T11:42:20Z<p>Jaspervdg: We're finalists!</p>
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<div><html><img style="position:absolute;right:30px;top:30px;" src="/wiki/images/0/02/GroningenFinalist.png" /></html><br />
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<div class="intro"><br />
<h1>Heavy metal scavengers<!-- with a vertical gas drive--></h1><br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To battle this problem, a '''purification strategy''', in which arsenic, zinc and copper are removed from water and sediment, was developed. This strategy encompasses a biological device in which <i>E. coli</i> bacteria accumulate metal ions from solutions, after which they '''produce gas vesicles''' and '''start floating'''. This biological device consists of two integrated systems: one for metal uptake and storage, the other for metal induced buoyancy. The uptake and storage system consists of a [[Team:Groningen/Project/Transport|metal transporter]] and [[Team:Groningen/Project/Accumulation|metal binding proteins]] (to reduce toxicity and increase accumulation). The buoyancy system is made up of a [[Team:Groningen/Project/Promoters|metal induced promotor]] in front of a [[Team:Groningen/Project/Vesicle|gas vesicle gene cluster]]. The combination of both systems will enable the efficient cleaning of polluted water and sediment in a biological manner. <br />
<br><br><br />
<center>{{linkedImage|Enter.png|Team:Groningen/Project}}</center><br />
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{{Team:Groningen/Footer_Main}}</div>Jaspervdghttp://2009.igem.org/File:GroningenFinalist.pngFile:GroningenFinalist.png2009-11-16T11:38:37Z<p>Jaspervdg: We're finalists.</p>
<hr />
<div>We're finalists.</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-22T00:13:29Z<p>Jaspervdg: /* {{anchor|Optimization}}Optimization procedure */</p>
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<div class="intro introduction"><br />
==Characterization==<br />
We have four kinds of parts we would like to characterize: Importers, Accumulators, Sensors and the GVP cluster.<br />
For this we have a number of methods to estimate ''specific parameters'' (detailed below), as well as a ''[[Team:Groningen/Modelling/Characterization#Optimization|stochastic tool to fit our model]]'' to experimental data based on simulated annealing.<br />
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<br />
We have the following parts that we can characterize (RPS stands for Relative Promoter Strength)<br />
{|class="ourtable"<br />
|-style="text-align:left"<br />
!style="width:15%" style="text-align:left"|&nbsp;&nbsp;&nbsp;&nbsp; Input/Output<br />
!style="text-align:left"|Subject<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Importers'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; &Delta;v<sub>max</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
[[Team:Groningen/Literature#Meng2004|Meng 2004]] was able to knock out all efflux of arsenic. If there is no efflux of arsenic the dervative of the accumulation graph is the speed at wich arsenic is pumped inside the cell. The maximum speed would be v5. In such a senario two measurements would be enough to determine the relative promoter strength. One could even determine the reaction rate k6 and GlpF with a simple calculation, since v5 = k6 GlpFT (Vs/Vc). However we do have efflux, not only do we have efflux, but we have efflux that is dependent on the total amount of arsenic inside the cell. Also a portion arsenic gets bound to ArsR. <br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Accumulators'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|<br />
For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):<br />
<pre><br />
Asbound(As(III)in)<br />
= S Bmax As(III)in^n<br />
/ (K^n + As(III)in^n)<br />
</pre><br />
The constants B<sub>max</sub>, K and n can be determined from uptake experiments comparing E. coli with and without fMT expression. Of course this can be done in general by fitting our model to experimental data, if enough data is provided the fit will be tight enough to allow this. However, even without fitting the full model it should be possible to make a fair estimation from equilibrium measurements.{{infoBox|If the total cell volume is much smaller than the volume of the solution it is reasonable to assume a constant import rate. Also, regardless of whether they feature fMT or not, in equilibrium the amount of ArsR is the same, as is the amount of ArsB, leading to the same amount of unbound arsenic being present. This means that any difference in uptake of arsenic is completely due to arsenic being bound to fMT or MBPArsR. By measuring the amount of arsenic in equilibrium in wild-type cells as well as in cells expressing fMT/MBPArsR for several different (inital) concentrations of As(III), at one or more (known) levels of expression, it is possible to determine the constants Bmax, K and n.}}<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Sensors'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; metal(t) &rarr; RPS(t)<br />
|<br />
The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from [[Team:Groningen/Modelling/Arsenic|our model]]. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine <code>&beta;RN &tau;R</code> as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):<br />
<pre><br />
S(max) / S(0) = ars(max) / ars(0)<br />
S(max) / S(0) = arsT / ars(0)<br />
S(max) / S(0) = 1 + ArsR(0)²/KAd²<br />
ArsR(0) = KAd &radic;(S(max)/S(0) - 1)<br />
<br />
0 = &beta;RN ars1(0) - (ln(2)/&tau;R) ArsR(0)<br />
0 = &beta;RN ars1T S(0)/S(max)<br />
- (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN ars1T S(0)/S(max)<br />
= (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN &tau;R = (ln(2)/ars1T) KAd<br />
(S(max)/S(0)) &radic;(S(max)/S(0) - 1)<br />
</pre><br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''GVP cluster'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; GV<br />
|<br />
RPS &rarr; GV<br />
The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.<br />
|-<br />
|}<br />
<br />
==Uptake measurements==<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
<br />
To obtain data for the optimization procedure described above we conducted ICP-MS measurements on our cells containing various devices/parts. To optimize our findings we have conducted measurements both in time and in concentration.<br />
Details on ICP-MS the experiments can be found on our [[Team:Groningen/Protocols|Protocol Page]]. Measurements have been conducted at times and concentrations as indicated in the table on the right. Results can be seen below. <br />
<br />
'''First Uptake Measurement'''<br><br />
In this case we looked at the arsenic uptake of our wildtype and of our wildtype with a lot of pArs promoters with RFP. The raw data can be found at our [[Team:Groningen/Modelling/Downloads| Download Section]]<br />
{|<br />
|[[Image:AsUptakeWildTypeConcentration.png|400px]]||[[Image:AsUptakePArsRFPConcentration.png|400px]]<br />
|-<br />
|[[Image:AsUptakeWildTypeTime.png|400px]]||[[Image:AsUptakePArsRFPTime.png|400px]]<br />
|-<br />
|}<br />
<br />
'''Getting (Vc/Vs) and other conditions'''<br><br />
To effectively determine our constants we need to give our model some extra information. For instance what kind of constructs are inside the cel for a given experiment. Also we need to give the model the volume of cells per liter of fluid. To optain this we use the obtained dry weight and calculate how much wet weight it would have been (assuming dry weight/wet weight = 0.3) and then use the density of ''E. coli'' (1100kg/m<sup>3</sup>) to obtain the cell volume for our sample and eventually the desired volume of cells per liter.<br />
Also we need the absolute value of Arsenic taken up by the cells in the assumption that we have one liter of sample and we know (Vc/Vs). Once we know all these parameters the optimization procedure can start. <br />
<br />
'''Fluorescence Measurements'''<br><br />
Apart from giving our model all the conditions it needs to calculate all the constants by means of the optimization procedure, we have also conducted some fluorescence measurements and made growth curves of our construct with the pArs promoter with RFP. The cells where put into a solution with either no arsenic in it or at a concentration of 100 micromolair. On the left side one can see the graph of the luminance and on right side and on the right side one can see the coresponding grow curves. The raw data of these measurements can again be found under our [[Team:Groningen/Modelling/Downloads|Downloads]]<br />
{|<br />
|[[Image:ArsFluorescence.png|400px]]||[[Image:ArsOD.png|400px]]<br />
|-<br />
|}<br />
Using a formula similar to the formula below{{infoBox|In actuality we did not compute the derivative of the fluorescence and then corrected for the OD, instead we first computed the fluorescence normalized for the OD (correlates with RFP per cell) and then fitted a linear function to the data. This leads to a much more robust fit in the presence of noise and few measurements.}} we where able to derive a RPU of 2.3. This means that on average the ars promoter is 2.3 times more active at 100 micromolarity of arsenic (outside the cell) than if there is no arsenic in the solution. For a detailed calculation I would like to refer to our [[Team:Groningen/Modelling/Downloads|Downloads]] section under the RPU sheet.<br />
{|style=float:center;<br />
|[[Image:RPUcalculation.png|300px]]<br />
|}<br />
<br />
'''Second ICPMS measurement'''<br />
For our second measurement I would like to refer to our [[Team:Groningen/Project/Accumulation|Accumulation]] page. These measerments where higher than expected and they need further analyses before we can use them in tha characterization of our parts.<br />
<br />
=={{anchor|Optimization}}Optimization procedure==<br />
To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved). In the optimizations procedure the ratio between v5 and K5 is kept constant. This is done because this ratio could be determined exactly using the data from the experiments done by [[Team:Groningen/Literature#Meng2004|Meng 2004]] v5 itself is not fixed and may vary. (Note that in the code different experiments and graphs can be enabled/disabled, we have entered data from Kostal, Meng and our first ICP-MS measurements.)<br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|<br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:3600,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:3600,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5',*/'v5','k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.v5/0.11495;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
cSol.v5 = orgC.v5*2;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
c.v5 = orgC.v5*2;<br />
c.k8 = 20;<br />
c.k8_K7 = 4e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
for(var a in mutateFuncs) {<br />
setOutput(a+mode,mutateFuncs[a](c));<br />
}<br />
setOutput('E'+mode,E);<br />
if (dc!=undefined) {<br />
for(var a in dc) {<br />
setOutput(a+mode+'gradient',dc[a]);<br />
}<br />
}<br />
}<br />
<br />
function constructPlot(id) {<br />
var width = 100, height = 100;<br />
var t = document.getElementById(id);<br />
t.minx = Number.NaN;<br />
t.miny = Number.NaN;<br />
t.maxx = Number.NaN;<br />
t.maxy = Number.NaN;<br />
t.points = [];<br />
t.createCaption();<br />
t.style.width = width + 'px';<br />
t.style.width = height + 'px';<br />
t.style.border = 'solid 1px #000';<br />
t.style.borderCollapse = 'collapse';<br />
for(var r=0; r<height; r++) {<br />
var newRow = t.insertRow(0);<br />
for(var c=0; c<width; c++) {<br />
var newCell = newRow.insertCell(0);<br />
newCell.style.width = '1px';<br />
newCell.style.height = '1px';<br />
newCell.style.background = '#fff';<br />
newCell.style.padding = '0px';<br />
}<br />
}<br />
}<br />
<br />
function plotMin(t,x,y,v) {<br />
if (x<0) return;<br />
if (y<0) return;<br />
var regrid = false;<br />
t.points.push({'x':x,'y':y,'v':v});<br />
if (isNaN(t.minx) || x<t.minx) { t.minx = x/1.5; regrid = true; }<br />
if (isNaN(t.maxx) || x>t.maxx) { t.maxx = x*1.5; regrid = true; }<br />
if (isNaN(t.miny) || y<t.miny) { t.miny = y/1.5; regrid = true; }<br />
if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
//alert('regridding' + [x,y,t.minx,t.miny,t.maxx,t.maxy,regrid]);<br />
setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
for(var r=0; r<t.rows.length; r++) {<br />
var row = t.rows[r];<br />
for(var c=0; c<row.cells.length; c++) {<br />
var cell = row.cells[c];<br />
cell.background = '#fff';<br />
}<br />
}<br />
for(var i in t.points) plotMinWork(t,t.points[i].x,t.points[i].y,t.points[i].v);<br />
} else {<br />
plotMinWork(t,x,y,v);<br />
}<br />
}<br />
<br />
function plotMinWork(t,x,y,v) {<br />
var r = Math.floor((y-t.miny)/(t.maxy-t.miny)*t.rows.length);<br />
var c = Math.floor((x-t.minx)/(t.maxx-t.minx)*t.rows[0].cells.length);<br />
var cell = t.rows[r].cells[c];<br />
if (cell.value==undefined || v<cell.value) {<br />
cell.value = v;<br />
cell.style.background = 'rgb('+Math.max(0,100*v)+'%,'+Math.min(100,100*(1-v))+'%,0%)';<br />
}<br />
}<br />
<br />
function setCaption(t,cap) {<br />
if (!t) return;<br />
var caps = t.getElementsByTagName('caption');<br />
if (caps.length>0) {<br />
caps[0].innerHTML = cap;<br />
return;<br />
}<br />
if (t.caption) {<br />
t.caption = cap;<br />
return;<br />
}<br />
}<br />
</script><br />
</html><br />
{|<br />
|<br />
{|id="v5K5plot"<br />
|}<br />
|<br />
{|id="k8K7plot"<br />
|}<br />
|}<br />
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<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
{|<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/GlpF|id=Meng2004Graph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Singh2008|id=Singh2008Graph}}<br />
|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3B|id=Kostal2004fig3BGraph}}--><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2time|id=pSB1A2timeGraph}}<br />
<!--|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPtime|id=pArsRRFPtimeGraph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3A|id=Kostal2004fig3AGraph}}<br />
|- --><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2con|id=pSB1A2conGraph}}<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPcon|id=pArsRRFPconGraph}}--><br />
|}<br />
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<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-22T00:11:39Z<p>Jaspervdg: Let v5 vary.</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div style="float:left" >{{linkedImage|GroningenPrevious.png|Team:Groningen/Modelling/Arsenic}}</div><br />
<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Downloads}}</div><br />
<br />
<div style="clear:both;"></div><br />
<br />
<html><style type="text/css"><br />
.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
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<div class="intro introduction"><br />
==Characterization==<br />
We have four kinds of parts we would like to characterize: Importers, Accumulators, Sensors and the GVP cluster.<br />
For this we have a number of methods to estimate ''specific parameters'' (detailed below), as well as a ''[[Team:Groningen/Modelling/Characterization#Optimization|stochastic tool to fit our model]]'' to experimental data based on simulated annealing.<br />
</div><br />
<br />
We have the following parts that we can characterize (RPS stands for Relative Promoter Strength)<br />
{|class="ourtable"<br />
|-style="text-align:left"<br />
!style="width:15%" style="text-align:left"|&nbsp;&nbsp;&nbsp;&nbsp; Input/Output<br />
!style="text-align:left"|Subject<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Importers'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; &Delta;v<sub>max</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
[[Team:Groningen/Literature#Meng2004|Meng 2004]] was able to knock out all efflux of arsenic. If there is no efflux of arsenic the dervative of the accumulation graph is the speed at wich arsenic is pumped inside the cell. The maximum speed would be v5. In such a senario two measurements would be enough to determine the relative promoter strength. One could even determine the reaction rate k6 and GlpF with a simple calculation, since v5 = k6 GlpFT (Vs/Vc). However we do have efflux, not only do we have efflux, but we have efflux that is dependent on the total amount of arsenic inside the cell. Also a portion arsenic gets bound to ArsR. <br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Accumulators'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|<br />
For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):<br />
<pre><br />
Asbound(As(III)in)<br />
= S Bmax As(III)in^n<br />
/ (K^n + As(III)in^n)<br />
</pre><br />
The constants B<sub>max</sub>, K and n can be determined from uptake experiments comparing E. coli with and without fMT expression. Of course this can be done in general by fitting our model to experimental data, if enough data is provided the fit will be tight enough to allow this. However, even without fitting the full model it should be possible to make a fair estimation from equilibrium measurements.{{infoBox|If the total cell volume is much smaller than the volume of the solution it is reasonable to assume a constant import rate. Also, regardless of whether they feature fMT or not, in equilibrium the amount of ArsR is the same, as is the amount of ArsB, leading to the same amount of unbound arsenic being present. This means that any difference in uptake of arsenic is completely due to arsenic being bound to fMT or MBPArsR. By measuring the amount of arsenic in equilibrium in wild-type cells as well as in cells expressing fMT/MBPArsR for several different (inital) concentrations of As(III), at one or more (known) levels of expression, it is possible to determine the constants Bmax, K and n.}}<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Sensors'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; metal(t) &rarr; RPS(t)<br />
|<br />
The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from [[Team:Groningen/Modelling/Arsenic|our model]]. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine <code>&beta;RN &tau;R</code> as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):<br />
<pre><br />
S(max) / S(0) = ars(max) / ars(0)<br />
S(max) / S(0) = arsT / ars(0)<br />
S(max) / S(0) = 1 + ArsR(0)²/KAd²<br />
ArsR(0) = KAd &radic;(S(max)/S(0) - 1)<br />
<br />
0 = &beta;RN ars1(0) - (ln(2)/&tau;R) ArsR(0)<br />
0 = &beta;RN ars1T S(0)/S(max)<br />
- (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN ars1T S(0)/S(max)<br />
= (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN &tau;R = (ln(2)/ars1T) KAd<br />
(S(max)/S(0)) &radic;(S(max)/S(0) - 1)<br />
</pre><br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''GVP cluster'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; GV<br />
|<br />
RPS &rarr; GV<br />
The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.<br />
|-<br />
|}<br />
<br />
==Uptake measurements==<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
<br />
To obtain data for the optimization procedure described above we conducted ICP-MS measurements on our cells containing various devices/parts. To optimize our findings we have conducted measurements both in time and in concentration.<br />
Details on ICP-MS the experiments can be found on our [[Team:Groningen/Protocols|Protocol Page]]. Measurements have been conducted at times and concentrations as indicated in the table on the right. Results can be seen below. <br />
<br />
'''First Uptake Measurement'''<br><br />
In this case we looked at the arsenic uptake of our wildtype and of our wildtype with a lot of pArs promoters with RFP. The raw data can be found at our [[Team:Groningen/Modelling/Downloads| Download Section]]<br />
{|<br />
|[[Image:AsUptakeWildTypeConcentration.png|400px]]||[[Image:AsUptakePArsRFPConcentration.png|400px]]<br />
|-<br />
|[[Image:AsUptakeWildTypeTime.png|400px]]||[[Image:AsUptakePArsRFPTime.png|400px]]<br />
|-<br />
|}<br />
<br />
'''Getting (Vc/Vs) and other conditions'''<br><br />
To effectively determine our constants we need to give our model some extra information. For instance what kind of constructs are inside the cel for a given experiment. Also we need to give the model the volume of cells per liter of fluid. To optain this we use the obtained dry weight and calculate how much wet weight it would have been (assuming dry weight/wet weight = 0.3) and then use the density of ''E. coli'' (1100kg/m<sup>3</sup>) to obtain the cell volume for our sample and eventually the desired volume of cells per liter.<br />
Also we need the absolute value of Arsenic taken up by the cells in the assumption that we have one liter of sample and we know (Vc/Vs). Once we know all these parameters the optimization procedure can start. <br />
<br />
'''Fluorescence Measurements'''<br><br />
Apart from giving our model all the conditions it needs to calculate all the constants by means of the optimization procedure, we have also conducted some fluorescence measurements and made growth curves of our construct with the pArs promoter with RFP. The cells where put into a solution with either no arsenic in it or at a concentration of 100 micromolair. On the left side one can see the graph of the luminance and on right side and on the right side one can see the coresponding grow curves. The raw data of these measurements can again be found under our [[Team:Groningen/Modelling/Downloads|Downloads]]<br />
{|<br />
|[[Image:ArsFluorescence.png|400px]]||[[Image:ArsOD.png|400px]]<br />
|-<br />
|}<br />
Using a formula similar to the formula below{{infoBox|In actuality we did not compute the derivative of the fluorescence and then corrected for the OD, instead we first computed the fluorescence normalized for the OD (correlates with RFP per cell) and then fitted a linear function to the data. This leads to a much more robust fit in the presence of noise and few measurements.}} we where able to derive a RPU of 2.3. This means that on average the ars promoter is 2.3 times more active at 100 micromolarity of arsenic (outside the cell) than if there is no arsenic in the solution. For a detailed calculation I would like to refer to our [[Team:Groningen/Modelling/Downloads|Downloads]] section under the RPU sheet.<br />
{|style=float:center;<br />
|[[Image:RPUcalculation.png|300px]]<br />
|}<br />
<br />
'''Second ICPMS measurement'''<br />
For our second measurement I would like to refer to our [[Team:Groningen/Project/Accumulation|Accumulation]] page. These measerments where higher than expected and they need further analyses before we can use them in tha characterization of our parts.<br />
<br />
=={{anchor|Optimization}}Optimization procedure==<br />
To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved). In the optimizations procedure the ratio between v5 and K5 is kept constant. This is done because this ratio could be determined exactly using the data from the experiments done by [[Team:Groningen/Literature#Meng2004|Meng 2004]] v5 itself is not fixed and may vary. <br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|<br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:3600,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:3600,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5',*/'v5','k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.v5/0.11495;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
cSol.v5 = orgC.v5*2;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
c.v5 = orgC.v5*2;<br />
c.k8 = 20;<br />
c.k8_K7 = 4e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
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setOutput(a+mode,mutateFuncs[a](c));<br />
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setOutput('E'+mode,E);<br />
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if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
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setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
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{|<br />
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<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Project/PromotersTeam:Groningen/Project/Promoters2009-10-21T23:08:21Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Project/Header|}}<br />
<div style="float:left" >{{linkedImage|GroningenPrevious.png|Team:Groningen/Project/Accumulation}}</div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Project/Vesicle}}</div><br />
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.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
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<div class="intro"><br />
<h1>Promoters</h1><br />
'''A promoter is a part of DNA involved in the regulation of gene transcription by RNA polymerase. In general RNA polymerase tends to bind weakly to a strand of DNA until a suitable promoter is encountered and the binding becomes strong. Promoters are used to express genes of interest in cells in either a constitutive or induced manner. The constitutive promoters are used when a constant expression of enzymes is desired, and the amount of activity can be regulated by choosing from a range of promoters varying from low to high expression. If, however, expression is desired at certain points in time, or growth stage, inducible promoters are the best choice for regulating gene expression. In our system, we want to induce GVP production when the concentration of desired metal in the cells reaches a certain level. By choosing metal sensitive promoters already present in ''E. coli'' cells, the cells contain the necessary components for controlling the promoters, and the promoter sequence has only to be placed in front of the genes of interest.By cloning the ArsR and CueO promotor in front of RFP we have shown that by induction with respectively Arsenite and Copper repression of the promotor is reduced and expression of RFP enhanced. We took the following promoters into consideration:'''<br />
<center><br />
{| cellpadding="30"<br />
|align="center"|[[#Arsenic Induced Promoters|<big>As</big><br>Arsenic Induced Promoters]]<br />
|align="center"|[[#Copper Induced Promoters|<big>Cu</big><br>Copper Induced Promoters]]<br />
|align="center"|[[#Zinc Induced Promoters|<big>Zn</big><br>Zinc Induced Promoters]]<br />
|}<br />
</center><br />
</div><br />
==Arsenic Induced Promoters==<br />
<br />
Because of the similarity to phosphate, sometimes arsenate is mistaken for phosphate, which is how it is introduced into living organisms, including <i>E. coli</i>, by the phosphate uptake system. Other molecules such as As(III) can also be introduced into the cells by various membrane transporters.<br />
<br />
====<i>E. coli</i>====<br />
<br />
Promoter arsRp is associated with the dimer of ArsR for the arsenic induced transcription of genes involved in arsenic efflux (arsR, arsB and arsC, which is present on the genome of <i>E. coli</i> str. K-12 substrain MG1655). The sequence shows the typical -10 and -35 region of the promoter and can be found through the following [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00239 link]. A second region, located at -41.5 from the transcription start site, is thought to bind dimeric ArsR. Upon binding of arsenic, the dimer dissociates and allows the RNA polymerase space to attach itself, and can also be found in the same [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00239 link].<br />
<br />
*ArsR belongs to the ArsR/SmtB family of transcriptional regulators that respond to a variety of metals. ArsR has a helix-turn-helix motif for DNA binding, a metal-binding site, and a dimerization domain. In ArsR the inducer-binding site contains three cysteine residues that bind arsenite and antimonite specifically and with high affinity. Dimerization of ArsR is required for DNA binding and its ability to act as a transcriptional repressor. The dimer recognizes and binds to a 12-2-12 inverted repeat, but the binding of arsenic or antimonite to ArsR causes a conformational change in it, leading to dissociation from DNA and hence derepression (KEGG).<br />
<br />
*ArsR negatively controls the expression of the genes involved in arsenical and antimonite metals resistance, whose expression is induced in the presence of these metals. The protein is autoregulated, because arsR is the first gene in the arsRBC operon that it regulates. Overexpression of ArsR in <i>E. coli</i> has been used for removal of arsenite from contaminated water (KEGG).<br />
<br />
(ArsR)<sub>2</sub>-DNA &rarr; ArsR-Ar + ArsR-Ar + DNA &rarr; Activation of transription<br />
<br />
The presence of all genes and promoters on the chromosome of <i>E. coli</i> makes the use of the arsRp for induction of the GVP cluster relatively straight forward. The promoter sequence of arsRp, with the upstream binding box for ArsR dimer, can either be synthesized completely with the required restriction sites, or acquired using PCR and carefully designed primers. It might even be an option to alter the -10/-35 promoter region for higher or lower transcription of the genes.<br />
<br />
====Cloning strategy====<br />
<br />
The ArsR sensitive promotor was designed by substracting its sequence from the genome database of ''E. Coli'' str K12. <br />
Its binding region was established by Lee and co workers. The promotor region was designed ''in silico'' with its own RBS and the pre and suffix were ''in silico'' cuted with ''Eco''RI and ''Spe''I creating sticky ends. See parts registry {{Part|BBa_K190015}}<br />
<br />
====Results====<br />
The functionality of pArsR (<partinfo>Bba_K190015</partinfo>) was tested by using a test construct, composed of pArsR and RFP on <partinfo>Bba_J61002</partinfo> (Figure 1).<br />
<br />
[[Image:Promoter measurement device.png|200px]]<br />
:Figure 1: The promoter testing device in J61002, where RFP expression is under control of the promoter which is placed in front of it. <br />
<br />
=====Fluorescence of resting cells=====<br />
<br />
The fluorescence of the red fluorescent protein was measured as described in [[Team:Groningen/Protocols#Fluorescence_of_resting_cells_with_J61002-pArsR|protocols]]. Upon induction of the ArsR promoter the expression of RFP increased, as seen in figure 2. From the enhanced fluorescence a value for the relative promoter unit (RPU) was calculated according to [[Team:Groningen/Literature#Kelly2009|Kelly 2009]] (formula 9). Thereby an induction of 2.3 RPU was found, which was in consensus with the promoter activity found for arsenic metal sensitive promoter (used in expression of MTs) (personal communication, Dr. D. Wilcox). The arsenite uptake in ''E. coli'' with J61002-<partinfo>Bba_K190015</partinfo> over time was measured using the [[Team:Groningen/Protocols#Metal_uptake_assay_for_E._coliKostal_2004|arsenite uptake assay]], this was done upon incubation with 10µM NaAsO<sub>2</sub>. This data was multiplied by the following ratio: As(III) uptake upon induction for 1hr with 100µM As(III) devided by As(III) uptake upon induction for with 10 µM As(III). The increasing intracellular concentration is shown in figure 3. <br />
<br />
<center>[[Image:UptakeRPU.png]]</center><br />
:Figure 2: Increase of fluorescence (RFP = 590nm) upon induction of the pArsR promoter with 100 µM As(III). The data was a bit noisy therefore a trendline was calculated and used to calculate the relative promoter unit with. <br />
<br />
<center>[[Image:Uptake100um.png]]</center><br />
:Figure 3: The internal arsenic concentration, calculated from experimental data for ''E. coli'' with J61002-<partinfo>Bba_K190015</partinfo>. The resting cells were incubated with As(III). For further information see text. (The computed fit is <code>(0.152465*x)/(1 + 0.121918*x)</code>.)<br />
<br />
The raw data can be found at [[Team:Groningen/Modelling/Downloads|downloads]].<br />
<br />
=====Fluorescence of growing cells=====<br />
<br />
In order to further characterize the ArsR promotor, measurements were done by inducing cells in the exponential phase. After induction the fluorescence was measured for 22 h. see [[Team:Groningen/Protocols#fluorescence_measurement| protocols]]. The RFP was excited at 580 nm and emission was measured at 600 nm. In order to have a significant high enough signal cells were resuspended at OD<sub>600</sub>=0.5 in half the volume. The cells were induced to an end concentration of 5000, 500, 50, 5 and 0 &micro;M. The fluorescence normalized to the OD<sub>600</sub> is plotted in figure 4. In all measurements {{Part|BBa_J23101|BBa_J23101}} was taken along to serve as a reference.<br />
<br />
<center>[[Image:Promoters-ArsR.png]]</center><br />
:Figure 4: Shows the fluorescence of RFP expressed with the ArsR promotor. The fluorescence is normalized to 1 and p plotted against time. The ArsR promotor is induced to concentrations of 5000, 500, 50, 5 and 0 &micro;M sodium arsenite. <partinfo>Bba_J23101</partinfo> is a constitutive promotor which is used as a reference for asigning promotor strength.<br />
<br />
The fluorescence in figure 4 is normalized to the OD<sub>600</sub> to correct for differences in cell concentration. As can be seen in figure 4 non induced ArsR RFP (0 &micro;M)is already fluorescent at the time of induction, meaning that the promotor is leaking. What figure 4 also shows is that upon induction the fluorescence increases meaning that the promotor although leaking is less suppresed in the presence of Arsenite. The highest increase in fluorescence is upon induction to a concentration of 50 &micro;M arsenite which is as high as 85% of the fluorescence from reference promotor <partinfo>Bba_J23101</partinfo>. Almost all plots show a slight decrease of fluorescence in the beginning due to the recovery of resuspending the cells at 4 &deg;C. Induction to a final concentration of 5000 &micro;M of Arsenite gives after 1 hour already an increase but decreases after 2 hours and shows only a slow increase in fluorescence after 5 hours. Reason for the lower fluorescence intensity of induction to 5000 &micro;M is the poisoning of the cells with Arsenite. The poisoning of the cells is best seen in the OD plotted against time as shown in figure 5. The cells induced to a concentration of 5000 &micro;M Arsenite shows a big decrease in OD between 5 and 22 hours after induction due to Arsenite poisoning.<br />
<br />
<center>[[Image:Promoters-ArsR-OD.png]]</center><br />
:Figure 5: Shows the OD plotted against time of ''E.coli'' with plasmid J61002 containing the pArsR RFP construct.<br />
<br />
===Conclusion===<br />
Both promoter tests, with resting cells and growing cells, show clearly that the pArsR promoter is functional. The negative transcriptional regulator ArsR releases the promoter region upon induction with arsenite. The promoter strength was calculated in relative promoter units, upon induction of resting cells with 100 &micro;M As(III) an increase of 2.3 was found. A disadvantage of the usage of pArsR, also clearly shown by the two measurements, is that the negative regulation is leaky as there is already some RFP expressed without addition of arsenite. The OD<sub>600</sub> measurements of the growing cell measurements showed that concentrations as high as 5000 &micro;M Arsenite are poisonous for '' E. coli'' TOP 10 cells.<br />
<br />
===Modelling===<br />
{{GraphHeader}}<br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
<br />
The three graphs below illustrate the promoter response after induction with arsenic (directly in the cell, with the equivalent of 1 &micro;M in the solution) with and without constitutive expression of ArsR (the first two graphs) and with slower production and degradation of ArsR (the two left graphs). Also, each graph has a line showing the formation of a product behind the ars promoter that does not degrade (and has production rate 1), subtracting the production that would have occurred without induction to show the effect of adding arsenic. Some conclusions:<br />
<br />
* Constitutive expression of ArsR greatly reduces (and slows) the promoter response.<br />
* On the other hand, if we divide the production and degradation rates of ArsR by ten the promoter response is ten times slower, producing ten times as much product.<br />
* In the bottom-right graph the induction is done gradually (the amount of arsenic increases linearly during the first five minutes), showing the high-pass behaviour of the promoter and that this can negatively impact product formation.<br />
<br />
<html><br />
<script type="text/javascript"><br />
addOnloadHook(computePromoterActivation);<br />
<br />
function computePromoterActivation() {<br />
// Set up constants<br />
var maxt = 600;<br />
var c = arsenicModelConstants();<br />
var cNP = {}, cS = {}, cG = {};<br />
c.v5 = 0;<br />
c.k8 = 0;<br />
c.pro = 0;<br />
c.ars2T = 0;<br />
for(var a in c) {<br />
cNP[a] = c[a];<br />
cS[a] = c[a];<br />
cG[a] = c[a];<br />
}<br />
<br />
var Vcell = 1 * 1e-15; // micrometer^3/cell -> liter/cell<br />
var avogadro = 6.02214179e23; // 1/mol<br />
c.pro = 2/(avogadro*Vcell); // 1/cell -> mol/L<br />
cS.tauR *= 10;<br />
cS.beta1 /= 10;<br />
cS.beta3 /= 10;<br />
cG.ars2T = 100*cG.ars1T;<br />
<br />
// Initialize<br />
var x0 = arsenicModelInitialization(c,0);<br />
var xNP0 = arsenicModelInitialization(cNP,0);<br />
var xS0 = arsenicModelInitialization(cS,0);<br />
var x20 = arsenicModelInitialization(c,0);<br />
var xG0 = arsenicModelInitialization(cG,0);<br />
var AsT = 1e-6*c.Vs;<br />
x0.AsinT = AsT/c.Vc;<br />
xNP0.AsinT = AsT/c.Vc;<br />
xS0.AsinT = AsT/c.Vc;<br />
x20.AsinT = 0;<br />
xG0.AsinT = AsT/c.Vc;<br />
<br />
// Simulate<br />
var x = simulate(x0,maxt,function(t,d){return arsenicModelGradient(c,d);});<br />
var xNP = simulate(xNP0,maxt,function(t,d){return arsenicModelGradient(cNP,d);});<br />
var xS = simulate(xS0,maxt*10,function(t,d){return arsenicModelGradient(cS,d);});<br />
var xG = simulate(xG0,maxt,function(t,d){return arsenicModelGradient(cG,d);});<br />
var x2 = simulate(x0,maxt,function(t,d){<br />
var Dx = arsenicModelGradient(c,d);<br />
if (t<maxt/2) Dx.AsinT += (AsT/c.Vc)*2/maxt;<br />
return Dx;<br />
});<br />
<br />
// Output<br />
function convertToSeries(c,x0,x) {<br />
var bAsin, cAsin, ArsR, ars, arsP, arsE;<br />
var arsInt = 0;<br />
var series = [[],[]];<br />
var preTime = -x.time[x._arsF.length-1]/(60*20);<br />
arsE = x0._arsF;<br />
series[0].push({x:preTime,y:100*arsE});<br />
series[0].push({x:0,y:100*arsE});<br />
series[1].push({x:preTime,y:0});<br />
for(var i=0; i<x._arsF.length; i++) {<br />
ars = x._arsF[i];<br />
if (i>0) arsInt += (x.time[i]-x.time[i-1])*(ars+arsP)/2;<br />
series[0].push({x:x.time[i]/60,y:100*ars});<br />
series[1].push({x:x.time[i]/60,y:(arsInt-x.time[i]*arsE)});<br />
arsP = ars;<br />
}<br />
return series;<br />
}<br />
document.getElementById("promoterActivationData").data = {<br />
ars:convertToSeries(c,x0,x),<br />
arsNP:convertToSeries(cNP,xNP0,xNP),<br />
arsS:convertToSeries(cS,xS0,xS),<br />
arsG:convertToSeries(cG,xG0,xG),<br />
ars2:convertToSeries(c,x20,x2)};<br />
var graphNodes = [document.getElementById("promoterActivationGraph"),<br />
document.getElementById("promoterActivationGraphNP"),<br />
document.getElementById("promoterActivationGraphS"),<br />
document.getElementById("promoterActivationGraphG"),<br />
document.getElementById("promoterActivationGraph2")];<br />
for(var i in graphNodes) if (graphNodes[i]) graphNodes[i].refresh();<br />
}<br />
</script><br />
</html><br />
<span id="promoterActivationData"></span><br />
{|<br />
!Wild-type<br />
!+ ArsR overexpression<br />
!+ extra ars promoters<br />
|-<br />
|{{graph|Team:Groningen/Graphs/PromoterActivationNP|promoterActivitationGraphNP}}<br />
|{{graph|Team:Groningen/Graphs/PromoterActivation|promoterActivitationGraph}}<br />
|{{graph|Team:Groningen/Graphs/PromoterActivationG|promoterActivitationGraphG}}<br />
|-<br />
!Slower response<br />
!Gradual induction<br />
|-<br />
|{{graph|Team:Groningen/Graphs/PromoterActivationSlow|promoterActivitationGraphS}}<br />
|{{graph|Team:Groningen/Graphs/PromoterActivation2|promoterActivitationGraph2}}<br />
|}<br />
<br />
===Other organisms===<br />
''Bacillus subtilis''<br />
<br />
In <i>B. subtilis</i>, an ArsR family repressor (ArsR<sub>BS</sub>) responds to As(III) and Sb(III) and regulates the ars operon encoding itself (ArsR), and arsenate reductase (ArsC), an arsenite efflux pump (ArsB) and a protein of unknown function (YqcK). The order in which ArsR<sub>BS</sub> recognises metals is as follows: As(III)>As(V)>Cd(II)~Ag(I).<br />
<br />
A second protein, AseR, negatively regulates itself and AseA, an As(III) efflux pump which contributes to arsenite resistance in cells lacking a functional ars operon. The order in which AseR recognises metals is as follows: As(III)>As(V).<br />
<br />
==Copper Induced Promoters==<br />
<br />
Copper is an essential element that becomes highly cytotoxic when concentrations exceed the capacity of cells to sequester the ion. The toxicity of copper is largely due to its tendency to alternate between its cuprous, Cu(I), and cupric, Cu(II), oxidation states, differentiating copper from other trace metals, such as zinc or nickel. Under aerobic conditions, this redox cycling leads to the generation of highly reactive hydroxyl radicals that readily and efficiently damage biomolecules, such as DNA, proteins, and lipids. Most organisms have specialized mechanisms to deal with dangerous levels of heavy metals, like the production of efflux pumps. These genes are regulated by promoters, which are inducible by the respective metals.<br />
<br />
====<i>E. coli </i>====<br />
<br />
"The intracellular level of copper in ''E. coli'' is controlled by the export of excess copper, but the entire systems of copper uptake and intracellular copper delivery are not fully understood. Two regulatory systems, the<br />
CueR and CusR systems, have been identified to be involved in transcription regulation of the genes for copper<br />
homeostasis (Rensing et al., 2000; Rensing and Grass, 2003). CueR, a MerR-family transcription factor, stimulates<br />
copper-induced transcription of both copA encoding Cu(I)-translocating P-type ATPase pump (exporter), that is the central component for maintenance of the copper homeostasis, and cueO encoding a periplasmic multicopper<br />
oxidase for detoxification (Outten et al., 2000; Petersen and Moller, 2000)." (from Yamamoto K., 2005)<br />
<br />
Promoter cusCp is associated with the two component system CusR and CusS for the copper induced transcription of genes involved in copper efflux (cusC, cusF, cusB and cusA, which is present on the genome of <i>E. coli </i> str. K-12 substrain MG1655). The sequence shows the typical -10 and -35 region of the promoter and can be found through the following [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU0-1821 link]. A second region, located at -53.5 from the transcription start site, is thought to bind CusR. Upon binding of CusR, the RNA polymerase is able to recognize the site and attach itself, and can also be found in the same [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU0-1821 link].<br />
<br />
*CusS, a sensory histidine kinase in a two-component regulatory system with CusR, is able to recognize copper ions, phosphorilate, and form a complex with CusR. It's a 480 amino acid long protein of which the sequence (aa and nt) can be found [http://www.genome.jp/dbget-bin/www_bget?eco+b0570 here] along with other information.<br />
<br />
*CusR, "Cu-sensing regulator", regulates genes related to the copper and silver efflux systems under '''anaerobic growth''' and under '''extreme copper stress''' in aerobic growth . It's a 227 amino acid long protein of which the sequence (aa and nt) can be found [http://www.genome.jp/dbget-bin/www_bget?eco+b0571 here] along with other information. <br />
<br />
Cu &rarr; CusS &rarr; +P &rarr; CusR &rarr; Activation of transription<br />
<br />
The problem so far is the site of detection of copper. The CusS protein senses the external copper concentrations and not the internal. For our project it would be nice to have an internal sensor for the induction of the buoyancy genes, so it will float after uptake. In addition to CusR, three other systems involved in copper resistence are present (CueR, CpxR and YedW). Both CpxR and YedW have the same problem of sensing external copper instead of internal copper, CueR is thought to respond to intracellular concentrations of copper. The choice for CusR over CueR would be based on the frequency of binding sites of both on the genome of <i>E. coli</i> (1 vs. 197 times), which gives CusR more chance of binding to our promoter. However, the idea behind our project is to induce ''gvp'' transcription at a high intracellular concentration, and results in the CueR related promoter.<br />
<br />
====Cloning strategy====<br />
<br />
The CueR CueO sensitive promotor was designed by substracting its sequence from the genome database of ''E. coli'' str K12.It's binding region was established by Yamamoto and co worker. The promotor region was designed in silico with its own RBS and the pre and suffix were ''in silico'' cuted with ''Eco''RI and ''Spe''I creating sticky ends. See parts registry {{Part|BBa_K190024}}<br />
<br />
====Results====<br />
In order characterize the CueO promotor, measurements were done by inducing cells in the exponential phase. After induction the fluorescence was measured for 22 h. see [[Team:Groningen/Protocols#fluorescence_measurement| protocols]]. The RFP was excited at 580 nm and emission was measured at 600 nm. In order to have a significant high enough signal cells were resuspended at OD<sub>600</sub>=0.5 in half the volume. The cells were induced to an end concentration of 5000, 500, 50, 5 and 0 &micro;M. The fluorescence normalized to the OD<sub>600</sub> is plotted in figure 4.In all measurements {{Part|BBa_J23101|BBa_J23101}} was taken along to serve as a reference.<br />
<br />
<center>[[Image:Promoters-CueO.png]]</center><br />
:Figure 6: Shows the fluorescence of RFP expressed with the CueO promotor. The fluorescence is normalized to 1 and p plotted against time. The ArsR promotor is induced to concentration of 5000,500,50,5 and 0 &micro;M CuSO<sub>4</sub>. Bba_J23101 is a constitutive promotor which is used as a reference for asigning promotor strength.<br />
<br />
The fluorescence in figure 6 is normalized to the OD to correct for differences in cell concentration. As can be seen in figure 6 non induced CueO RFP (0&micro;M)shows no fluorescence meaning that the promotor is not leaking. <br />
The Fluorescence for CuSO<sub>4</sub> induced cells shows only slight increase in the order of 0 < 5000 < 5 < 50 < 500<br />
&micro;M CuSO<sub>4</sub>. The cells induced to a concentration of 5000&micro;M CuSO<sub>4</sub> show no increase in fluorescence which could be due to poisoning of the cells by the CuSO<sub>4</sub>. In figure 7 can be seen that the OD of the Copper induced cells is increasing in first 5 hours and then stabilizes or even decreases in case of induction to 5000&micro;M CuSO<sub>4</sub>.<br />
<br />
<center>[[Image:Promoters-CueO-OD.png]]</center><br />
:Figure 7: Shows the OD plotted against time of ''E.coli'' with plasmid J61002 containing the pCueO RFP construct.<br />
<br />
===Conclusion===<br />
The fluorescence measurements of the CueR promotor show that there is no fluorescence without induction of CuSO<sub>4</sub>. Upon induction with CuSO<sub>4</sub> the cells show an increase in RFP fluorescence which keeps increasing over 22 hours after induction.<br />
<br />
===Parts Registry===<br />
<br />
Promoter from the copper-sensitive CusR/CusS two component signal system in <i>E. coli</i> (the <i>CusR/CusS</i> genes are not in parts registry, and are for external Cu concentration as mentioned before).<br />
<br />
'''Abs''': This nucleotide sequence is believed to be able to bind with phosphorylated CusR transcription factor in <i>E. coli</i>. CusR protein is phosphorylated by CusS transmembrane protein in a case of high extracellular concentration of copper ions. After phosphorylation CusR interacts with described DNA sequence and activates the transcription of <i>cusA</i>, Promoter from the copper-sensitive CusR/CusS two component signal system in <i>E. coli</i> (the <i>cusR/cusS</i> genes are not in parts registry, and are for external Cu concentration as mentioned before). <i>CusB</i>, <i>cusC</i> and Promoter from the copper-sensitive CusR/CusS two component signal system in <i>E. coli</i> (the <i>cusR/cusS</i> genes are not in parts registry, and are for external Cu concentration as mentioned before). <i>CusF</i> genes coding the proteins of copper metabolic system were used by Saint-Petersburg Team of 2007 for constructing a copper biosensor system.<br />
*{{part|BBa_I760005}}<br />
*Cu-sensitive promoter <br />
*Part-only sequence (16 bp):<br />
::atgacaaaattgtcat<br />
<br />
====Other organisms====<br />
<br />
''Mycobacterium tuberculosis'' <br><br />
'''Abs.''': Cu(I) binding to the CsoR–DNA complex induces a conformational change in the dimer that decreases its affinity for the DNA [[Team:Groningen/Literature#Liu2006|Liu 2006]].<br />
<br />
''Pseudomonas syringae'' <br><br />
'''Abs.''': The copper resistance (cop) operon promoter (Pcop) of <i>Pseudomonas syringae</i> is copper-inducible, and requires the regulatory genes <i>copR</i> and <i>copS</i>. Primer extension analysis identified the transcriptional initiation site of Pcop 59 bp 5' to the translational start site of <i>copA</i> [[Team:Groningen/Literature#Mills1994|Mills 1994]].<br />
<br />
''Sulfolobus solfataricus'' <br><br />
'''Abs.''': That CopT binds to the copMA promoter at multiple sites, both upstream and downstream of the predicted TATA-BRE site. Copper was found to specifically modulate the affinity of DNA binding by CopT. This study describes a copper-responsive operon in archaea, a new family of archaeal DNA-binding proteins, and supports the idea that this domain plays a prominent role in the archaeal copper response. A model is proposed for copper-responsive transcriptional regulation of the <i>copMA</i> gene cluster [[Team:Groningen/Literature#Ettema2006|Ettema 2006]].<br />
<br />
''Lactococcus lactis'' <br><br />
'''Abs.''': Two regulatory genes (<i>lcoR</i> and <i>lcoS</i>) were identified from a plasmid-borne lactococcal copper resistance determinant and characterized by transcriptional fusion to the promoterless chloramphenicol acetyltransferase gene (<i>cat</i>). The transcription start site involved in copper induction was mapped by primer extension [[Team:Groningen/Literature#Khunajakr1999|Khunajakr 1999]].<br />
<br />
==Zinc Induced Promoters==<br />
<br />
Zinc is essential for the functioning of cells, and must be maintained at certain levels within the cell. However, apart from its function, zinc is also harmful at elevated concentrations. Zinc starvation and zinc toxicity both lead to transcription of a number of recently characterized ''E. coli'' genes that encode Zn(II) uptake or export proteins. (from Outten C.E. et al, 1999)<br />
<br />
ZntR protein found in ''E. coli'', a homologue of MerR, has recently been shown to mediate Zn(II)-responsive regulation of zntA, a gene involved in Zn(II) detoxification. ZntR functions as a zinc receptor that is necessary to activate Zn-responsive transcription at the zntA promoter. ZntR binds in the atypical 20-base pair spacer region of the promoter and distorts the DNA in a manner that is similar to MerR. The addition of Zn(II) to ZntR converts it to a transcriptional activator protein that introduces changes in the DNA conformation. These changes apparently make the promoter a better substrate for RNA polymerase. The ZntR metalloregulatory protein is a direct Zn(II) sensor that catalyzes transcriptional activation of a zinc efflux gene, thus preventing intracellular Zn(II) from exceeding an optimal concentration. (from Outten C.E. et al, 1999)<br />
<br />
The sequence of zntRp has been used to design synthetic oligos ending in biobrick pre- and suffix with EcoRI and SpeI restriction overhangs. The promoter sequence contains the -35 and -10 sequence with the atypical 20-base pair spacer region for binding of ZntR ([http://partsregistry.org/wiki/index.php/Part:BBa_K190016 BBa_K190016]). In addition, the promoter was designed with a RBS found before the zntA gene ([http://partsregistry.org/wiki/index.php/Part:BBa_K190022 BBa_K190022]). The commonly used RBS part ([http://partsregistry.org/wiki/index.php/Part:BBa_B0034 BBa_B0034]) might be to strong and give unwanted leakage of the promoter.<br />
<br />
====Other organisms====<br />
''Bacillus subtilis''<br />
<br />
'''Abs.''': The ''Bacillus subtilis'' cation efflux pump czcD, which mediates resistance against Zn<sup>2+</sup>, Co<sup>2+</sup>, Ni<sup>2+</sup> and Cu<sup>2+</sup>, is regulated by an ArsR-type repressor (CzrABS) as well [[Team:Groningen/Literature#Moore2005|Moore 2005]].<br />
<br />
''Streptococcus pneumoniae''<br />
<br />
'''Abs.''': Activation of the czcD promoter by SczA is shown to proceed by Zn<sup>2+</sup>-dependent binding of SczA to a conserved DNA motif. In the absence of Zn<sup>2+</sup>, SczA binds to a second site in the czcD promoter, thereby fully blocking czcD expression. A metalloregulatory protein belonging to the TetR family<br />
Kloosterman T.G., et al. (O.P. Kuipers), The novel transcriptional regulator SczA mediates protection against Zn<sup>2+</sup> stress by activation of the Zn<sup>2+</sup>-resistance gene czcD in ''Streptococcus pneumoniae'', Molecular Microbiology, 2007, 65(4), 1049–1063. Retrieved from "https://2009.igem.org/Team:Groningen/Project/Promoters" <br />
<br />
<br />
''Staphylococcus aureus''<br />
<br />
'''Abs.''': In ''Staphylococcus aureus'' CzrA, a member of the ArsR/SmtB family of DNA binding proteins, functions as a repressor of the czr operon, that consists of czrA and the gene encoding the CzcD homologue CzrB (Xiong and Jayaswal, 1998; Kuroda et al., 1999; Singh et al., 1999). CzrA-mediated repression is alleviated in the presence of Zn<sup>2+</sup> and Co<sup>2+</sup> (Xiong and Jayaswal, 1998; Kuroda et al., 1999; Singh et al., 1999).<br />
<br />
<br />
<br />
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</html> __NOTOC__ <!-- No empty lines, please! This messes up the layout in some areas. --></div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/ArsenicTeam:Groningen/Modelling/Arsenic2009-10-21T22:24:53Z<p>Jaspervdg: </p>
<hr />
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<div class="intro introduction"><br />
==Detailed Model==<br />
Based on the [[#QuasiSteadyState|quasi-steady-state derivation]] below we have made the simplified version of our model shown below. The simplification is based on two key assumptions (which are also illustrated below, next to the table "Breakdown of core substances"):<br />
<br />
*Binding and unbinding of arsenic to/from the transporters occurs on a much smaller time scale than changes in the concentration of arsenic inside and outside the cell. And similarly, we assume that (un)binding of ArsR to/from the ars promoter is much faster than the production of ArsR (for example).<br />
*The concentration of transporters is insignificant compared to the concentration of arsenic inside and outside the cell.<br />
<br />
This leads to the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation for import, but also some more general equations for export using ArsB and accumulation with ArsR (for example, the Hill equation can be recognized in the activity of the ars promoter). We explicitly state ''relative abundances'' instead of substituting them into the differential equations. This leads to ''clearer and more insightful'' equations and gives ''more freedom'' to define complicated, interdependent ratios between substances.<br />
</div><br />
<br />
The inexperienced viewer may find the following tables and formulas baffling. We would recommend that one would look at the raw model first to gain an understanding of the basic reactions involved then have a look at the steady-state and the quasi steady-state model. It is not mandatory, but it is probably the the best route to get a better understanding of the model as a whole. Also, perhaps first have a look at [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] kinetics before proceeding.<br />
<br />
In contrast to how the quasi-steady-state assumption is normally used we mostly leave the specific states (bound/unbound) of substances intact in the differential equations and explicitly state the relative abundances. This keeps the differential equations shorter and gives more insight into what is actually happening, clearly mapping the "fast" reactions to ratios between substances. This also makes it possible to use quite complicated equations (the Asin and ArsR interdependency is virtually impossible to define using normal methods for example) that would otherwise be unwieldy to handle.<br />
<br />
[[Image:Arsenic_filtering.png|frame|A schematic representation of the processes involved in arsenic filtering (keep in mind that ArsR ''represses'' the expression of the genes behind ars). Note that MBPArsR and fMT are not shown for clarity.<!-- Also, ArsD is not shown here, as it is [[Team:Groningen/BLAST|not present in our E. coli]] and has a role analogous to ArsR.-->]]<br />
<br />
{|class="ourtable"<br />
|+ Reactions<br />
!colspan="2"|Reaction<br />
!Description<br />
!Rate<br />
|-<br />
|colspan="4"|''Transport''<br />
|-<br />
| ||As(III)<sub>ex</sub>T &rarr; As(III)<sub>in</sub>T||Import of arsenic.||(Vc/Vs) v5<sup>&dagger;</sup> As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T)<br />
|-<br />
| ||As(III)<sub>in</sub>T &rarr; As(III)<sub>ex</sub>T||Export of arsenic.|| k8 ArsB<sub>As</sub><br />
|-<br />
| ||style="white-space:nowrap;"|ars1T → ars1T + ArsBT||Production of ArsB.|| βB ars1<br />
|-<br />
| ||ArsBT &rarr; null||Degradation of ArsB|| (ln(2)/τB) ArsB<br />
|-<br />
|colspan="4"|''Accumulation''<br />
|-<br />
| ||ars1T → ars1T + ArsRT||From chromosomal operon.|| βRN ars1<br />
|-<br />
| ||proR → proR + ArsRT||Production of ArsR.|| βR pro<br />
|-<br />
| ||style="white-space:nowrap;"|proM → proM + MBPArsRT||Production of MBPArsR.|| βM pro<br />
|-<br />
| ||proF → proF + fMTT||Production of fMT.|| βF pro<br />
|-<br />
| ||ArsRT → null||Degradation of ArsR.|| (ln(2)/τR) ArsR<br />
|-<br />
| ||MBPArsRT → null||Degradation of MBPArsR.|| (ln(2)/τM) MBPArsR<br />
|-<br />
| ||fMTT → null||Degradation of fMT.|| (ln(2)/τF) fMT<br />
|-<br />
|colspan="4"|''Gas vesicles''<br />
|-<br />
| ||ars2T → ars2T + GV||Transcription + translation.|| βG ars2<br />
|-<br />
| ||GV → null||Degradation of gas vesicles.|| (ln(2)/τG) GV<br />
|}<br />
<br />
{|class="ourtable" style="clear:right;"<br />
|+ Core Substances<br />
!colspan="2"|Name<br />
!Description<br />
!Derivative to time<br />
|-<br />
|colspan="4"|''Extracellular''<br />
|-<br />
| ||As(III)<sub>ex</sub>T || As(III) in the solution. || (Vc/Vs) k8 ArsB<sub>As</sub> - (Vc/Vs) v5<sup>&dagger;</sup> As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T)<br />
|-<br />
|colspan="4"|''Membrane (all naturally occurring, but we plan to bring GlpF to overexpression)''<br />
|-<br />
| ||GlpFT || Importer of As(III) (concentration w.r.t. the exterior of the cell). || (not used directly in model, assumed to be constant)<br />
|-<br />
| ||ArsBT || Exporter of As(III) (concentration w.r.t. the interior of the cell). || βB ars1 - (ln(2)/τB) ArsB<br />
|-<br />
|colspan="4"|''Intracellular (ars2, pro and GV are introduced)''<br />
|-<br />
| ||As(III)<sub>in</sub>T || As(III) (bound and unbound) in the cell. || v5 As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T) - k8 ArsB<sub>As</sub><br />
|-class="estimate"<br />
| ||ars1T || ArsR repressed promoters (bound and unbound) naturally occurring in E. coli. || (concentration is constant = 1.6605nM, one per cell)<br />
|-class="estimate"<br />
| ||ars2T || ArsR repressed promoters in front of gas vesicle genes. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proR || Constitutive promoters in front of arsR. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proM || Constitutive promoters in front of mbp-arsR. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proF || Constitutive promoters in front of fMT. || (concentration is constant = 0-166.05nM)<br />
|-<br />
| ||ArsRT || ArsR in the cell. || βRN ars1 + βR proR - (ln(2)/τR) ArsR<br />
|-<br />
| ||MBPArsRT || MBPArsR in the cell. || βM proM - (ln(2)/τM) MBPArsR<br />
|-<br />
| ||fMTT || fMT in the cell. || βF proF - (ln(2)/τF) fMT<br />
|-<br />
| ||GV || Concentration of gas vesicles. || βG ars2 - (ln(2)/τG) GV<br />
|-style="border:none;"<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Directly from paper.<br />
|class="selfDerived" style="padding:0;"|Based on data from paper.<br />
|class="experimental" style="padding:0;"|Based on experiment.<br />
|class="estimate" style="padding:0;"|Rough estimate.<br />
|class="unknown" style="padding:0;"|Totally unknown.<br />
|}<br />
|}<br />
<div style="text-align:right;font-size:smaller;"><sup>&dagger;</sup> Note that the "constant" v5 depends on the concentration of GlpF transporters in the cell, and this can depend on whether we bring GlpF to overexpression or not. For simplicity the production/degradation of GlpF is not included explicitly in the model, instead we can vary the constant v5 relative to the value found for wild-type E. coli.</div><br />
<br />
{|<br />
|style="vertical-align:top;"|<br />
{|class="ourtable"<br />
|+ Breakdown of core substances<br />
!Core substance<br />
!Component<br />
!Relative abundance<br />
|-<br />
|rowspan="2"|ArsBT<br />
|style="padding-left:0;"|ArsB<br />
|K7<br />
|-<br />
|ArsB<sub>As</sub><br />
|As(III)in<br />
|-<br />
|rowspan="4"|As(III)inT<br />
|style="padding-left:0;"|As(III)in<br />
|1<br />
|-<br />
|ArsR<sub>As</sub><br />
|ArsR / KR<sub>d</sub><br />
|-<br />
|MBPArsR<sub>As</sub><br />
|MBPArsRT / (KM<sub>d</sub> + As(III)in)<br />
|-<br />
|fMT<sub>As</sub><br />
|n<sub>f</sub> fMTT As(III)<sub>in</sub><sup>n<sub>f</sub>-1</sup> / (KF<sub>d</sub><sup>n<sub>f</sub></sup> + As(III)<sub>in</sub><sup>n<sub>f</sub></sup>)<br />
|-<br />
|rowspan="2"|arsT<br />
|style="padding-left:0;"|ars<br />
|KA<sub>d</sub>²<br />
|-<br />
|ArsR<sub>ars</sub><br />
|ArsR²<br />
|-<br />
|rowspan="2"|ars<br />
|style="padding-left:0;"|ars1<br />
|ars1T<br />
|-<br />
|ars2<br />
|ars2T<br />
|-<br />
|rowspan="3"|ArsRT<br />
|style="padding-left:0;"|ArsR<br />
|1<br />
|-<br />
|ArsR<sub>As</sub><br />
|As(III)<sub>in</sub> / KR<sub>d</sub><br />
|-<br />
|ArsR<sub>ars</sub><br />
|2 ArsR ars / KA<sub>d</sub>²<br />
|-<br />
|rowspan="2"|MBPArsRT<br />
|style="padding-left:0;"|MBPArsR<br />
|KM<sub>d</sub><br />
|-<br />
|MBPArsR<sub>As</sub><br />
|As(III)<sub>in</sub><br />
|-<br />
|rowspan="2"|fMTT<br />
|style="padding-left:0;"|fMT<br />
|KF<sub>d</sub><sup>n<sub>f</sub></sup><br />
|-<br />
|fMT<sub>As</sub><br />
|As(III)<sub>in</sub><sup>n<sub>f</sub></sup><br />
|}<br />
|[[Image:Arsenic Model - Substances.png|frame|Circles correspond to core substances. We consider the reactions between the overlapping substances so fast that we model them by determining the ratios between the substances when the reactions between them are in equilibrium. Also, the complexes formed with <strike>ars,</strike> GlpF and ArsB (the small circles) are considered to have such a low concentration that they are of no importance to the concentrations of As(III)in/-ex and ArsR (the large circles).]]<br />
|}<br />
<br />
{|class="ourtable"<br />
|+ Constants<br />
!Name<br />
!Units<br />
!Value<br />
!Description<br />
|-class="unknown"<br />
|k8<br />
|1/s<br />
|<br />
|Reaction rate constant representing how fast ArsB can export arsenic.<br />
|-class="estimate"<br />
|KR<sub>d</sub><br />
|M<br />
|6&micro;M<br />
|Dissociation constant for ArsR and As(III). Assumed to be about an order of magnitude smaller than KD<sub>d</sub> = 60&micro;M, the corresponding constant for the similar protein ArsD from [[Team:Groningen/Literature#Chen1997|Chen1997]].<br />
|-class="estimate"<br />
|KM<sub>d</sub><br />
|M<br />
|6&micro;M<br />
|Dissociation constant for MBPArsR and As(III). We assume this to be roughly equal to KR<sub>d</sub>.<br />
|-class="unknown"<br />
|KF<sub>d</sub><br />
|M<br />
|<br />
|Dissociation constant for fMT and As(III).<br />
|-class="unknown"<br />
|n<sub>f</sub><br />
|<br />
|<br />
|Hill coefficient for the formation of the complex fMTAs. This is related to the number of arsenic ions that bind to fMT.<br />
|-class="fromPaper"<br />
|KA<sub>d</sub><br />
|M<br />
|0.33&micro;M<br />
|Dissociation constants for ArsR and ars.<br />
* KA<sub>d</sub>² = kA<sub>off</sub>/kA<sub>on</sub> = (0.33&micro;M)²? ([[Team:Groningen/Literature#Chen1997|Chen1997]], suspect as the relevant reference doesn't actually seem to give any value for this)<br />
|-class="selfDerived"<br />
|v5<br />
|mol/(s&middot;L)<br />
|3.1863&micro;mol/(s·L)<br />
|Maximum import rate per liter of cells (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]). Note that we have purposefully chosen to write the units as mol/(s&middot;L) instead of M/s, to emphasize the fact that the rate is per liter of ''cells''.<br />
* v5 = k6 GlpFT (Vs/Vc)<br />
|-class="selfDerived"<br />
|K5<br />
|M<br />
|27.718&micro;M<br />
|Concentration at which import reaches half its maximum import rate (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]).<br />
* K5 = (k5off+k6) / k5on<br />
|-class="unknown"<br />
|K7<br />
|M<br />
|<br />
|Concentration at which export reaches half its maximum export rate (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]).<br />
* K7 = (k7off+k8) / k7on<br />
|-class="unknown"<br />
|&tau;B, &tau;R, &tau;G, etc.<br />
|s<br />
|<br />
|Half-lifes (of ArsB, ArsR and GV, respectively). Degradation rate = ln(2)/&tau; {{infoBox|1=If you take just the degradation into account you will have the equation dC/dt = -k*C, which leads to C(t) = C(0) e<sup>-k t</sup>. So if k = ln(2)/&tau; we get C(t) = C(0) e<sup>-ln(2)/&tau; t</sup> = C(0) 2<sup>-t/&tau;</sup>. In other words &tau; is the time it takes for the concentration to half.}}<br />
|-class="unknown"<br />
|&beta;B, &beta;R, etc.<br />
|1/s<br />
|<br />
|Production rates.<br />
* &beta;RN = the production rate for ArsR behind the ars1 promoter<br />
* &beta;B = the production rate for ArsB behind the ars1 promoter<br />
* &beta;G = the production rate for GV behind the ars2 promoter<br />
* &beta;R = the production rate for ArsR behind a constitutive promoter<br />
* &beta;M = the production rate for MBPArsR behind a constitutive promoter<br />
* &beta;F = the production rate for fMT behind a constitutive promoter<br />
|-<br />
|Vs<br />
|L<br />
|<br />
|Volume of solution (excluding cells).<br />
|-<br />
|Vc<br />
|L<br />
|<br />
|Total volume of cells (in solution) (so Vs+Vc is the total volume).<br />
|-style="border:none;"<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Directly from paper.<br />
|class="selfDerived" style="padding:0;"|Based on data from paper.<br />
|class="experimental" style="padding:0;"|Based on experiment.<br />
|class="estimate" style="padding:0;"|Rough estimate.<br />
|class="unknown" style="padding:0;"|Totally unknown.<br />
|}<br />
|}<br />
<br />
<br />
==The raw model==<br />
<html><style type="text/css"></html><br />
.import { background: LightGreen; }<br />
.export { background: LightBlue; }<br />
.accumulation { background: LightPink; }<br />
.production { background: LightGoldenRodYellow; }<br />
<html></style></html><br />
<br />
The following table gives all the reactions that take place inside the cell. You can look at the schematic representation of the processes involved to get a good grasp as how every reaction works to the other. Note that proR, ProM and MBPArsR, ProF and Fmt are not displayed in the figure. This has been done for clarity. These reactions are simple constituative promotor reactions. Once you have an insight in the reactions involved you can have a look at the next table.<br />
<br />
[[Image:Arsenic_filtering.png|frame|A schematic representation of the processes involved in arsenic filtering (keep in mind that ArsR ''represses'' the expression of the genes behind ars). Note that MBPArsR and fMT are not shown for clarity.<!-- Also, ArsD is not shown here, as it is [[Team:Groningen/BLAST|not present in our E. coli]] and has a role analogous to ArsR.-->]]<br />
<br />
{|class="ourtable"<br />
|+ Reactions<br />
!colspan="2"|Reaction<br />
!Description<br />
|-<br />
|colspan="3"|''Transport''{{infoBox|In the reactions below you can see the import of arsenic by GlpF and the export of arsenic by ArsB. Only the degradation of ArsB is taken into acount because the ars operon also produces ArsB, as can be seen in the accumulation section. We assume a constant number of GlpF importers. }}(based on [[Team:Groningen/Literature#Rosen1996|Rosen1996]], [[Team:Groningen/Literature#Meng2004|Meng2004]] and [[Team:Groningen/Literature#Rosen2009|Rosen2009]])<br />
|-<br />
| ||<span class="import">As(III)<sub>ex</sub> + GlpF &harr; GlpF<sub>As</sub></span>||The binding and detachment of rsenic to GlpF on the outside of the cell.||<br />
|-<br />
| ||<span class="import">GlpF<sub>As</sub> &rarr; GlpF + As(III)</span>||The release of arsenic on the inside of the cell by GlpF|| <br />
|-<br />
| ||<span class="export">As(III)<sub>in</sub> + ArsB &harr; ArsB<sub>As</sub></span>||The binding and detachment of arsenic to the Exporter ArsB|| <br />
|-<br />
| ||<span class="export">ArsB<sub>As</sub> &rarr; ArsB + As(III)<sub>ex</sub></span>||The release of the bound arsenic by ArsB on the outside of the cell.|| <br />
|-<br />
| ||<span class="export">ArsB &rarr; null</span> ||The degradation of Ars B||<br />
|-<br />
|colspan="3"|''Accumulation''{{infoBox|In the reactions below you can see the production and degradation of all our accumulation proteins. Two things should be noticed: ArsR represses it's own production and that of the GVP clusters and the ars1 operon does not only produce ArsR but also the exporter ArsB}}(mostly based on [[Team:Groningen/Literature#Chen1997|Chen1997]])<br />
|-<br />
| ||As(III)<sub>in</sub> + ArsR &harr; ArsR<sub>As</sub>||The binding and detachment of arsenic to ArsR||<br />
|-<br />
| ||As(III)<sub>in</sub> + MBPArsR &harr; MBPArsR<sub>As</sub>||The binding and detachment of arsenic to MBPArsR || <br />
|-<br />
| ||n<sub>f</sub> As(III)<sub>in</sub> + fMT &harr; fMT<sub>As</sub>||The binding and detachment of arsenic to fMT || <br />
|-<br />
| ||ars1 + 2 ArsR &harr; ArsR<sub>ars1</sub>||the repression of the promotor of the ars1 operon by 2 arsR molecules||<br />
|-<br />
| ||<span class="production">ars2 + 2 ArsR &harr; ArsR<sub>ars2</sub></span>||the repression of the promotor of the ars1 operon by 2 arsR molecules|| <br />
|-<br />
| ||ars1 &rarr; ars1 + ArsR<span class="export"> + ArsB</span> ||The transcription and translation of the ars1 operon to produce ArsR and ArsB||<br />
|-<br />
| ||proR &rarr; proR + ArsR ||The transcription and translation of the proR operon to produce ArsR||<br />
|-<br />
| ||proM &rarr; proM + MBPArsR ||The transcription and translation of the proM operon to produce MBPArsR||<br />
|-<br />
| ||proF &rarr; proF + fMT ||The transcription and translation of the proF operon to produce fMT||<br />
|-<br />
| ||ArsR &rarr; null ||The degradation of ArsR||<br />
|-<br />
| ||MBPArsR &rarr; null ||The degradation of MBPArsR||<br />
|-<br />
| ||fMT &rarr; null ||The degradation of fMT||<br />
|-<br />
|colspan="3"|''Gas vesicles''{{infoBox|These two reactions give the production and degradation rate of the GVP clusters. Keep in mind that ars2 is repressed by the accumulation protein ArsR. This reaction can be found under accumulation part.}}<br />
|-<br />
| ||ars2 &rarr; ars2<span class="production"> + GV</span> ||The transcription and translation of the ars2 operon to produce GVP clusters wich will make the cell float||<br />
|-<br />
| ||<span class="production">GV &rarr; null</span> ||The degradation of GVP||<br />
|-<br />
|colspan="3"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="estimate" style="padding:0;"|GVP Production related.<br />
|}<br />
|}<br />
<br />
Here you can find the time derivatives for each substance we derived. The constants are explained in the next teble. After one has a full understanding of all the constants and derivatives and and reactions. One can begin the process of simplifying the model and thus one can have a look at the quasi steady-state model and the steady-state model. <br />
<br />
{|class="ourtable"<br />
|+ Core substances<br />
!colspan="2"|substance<br />
!Description<br />
!Derivative to time<br />
|-<br />
|colspan="4"|''Extracellular''<br />
|-<br />
| ||As(III)<sub>ex</sub>||As(III) in the solution||(d/dt) As(III)<sub>ex</sub> = <span class="import">- (d/dt) GlpF<sub>As</sub> - k6 GlpF<sub>As</sub></span><span class="export"> + (Vc/Vs) k8 ArsB<sub>As</sub></span><br />
|-<br />
|colspan="4"|''Membrane'' (all naturally occurring, but we plan to bring GlpF to overexpression)<br />
|-<br />
| ||GlpF||concentration w.r.t. the exterior of the cell||(d/dt) GlpF = <span class="import">- (d/dt) GlpF<sub>As</sub></span><br />
|-<br />
| ||GlpF<sub>As</sub>||concentration w.r.t. the exterior of the cell||(d/dt) GlpF<sub>As</sub> = <span class="import">k5<sub>on</sub> As(III)<sub>ex</sub> GlpF - (k5<sub>off</sub>+k6) GlpF<sub>As</sub></span><br />
|-<br />
| ||ArsB||concentration w.r.t. the interior of the cell||(d/dt) ArsB = <span class="export">- (d/dt) ArsB<sub>As</sub> + &beta;4 ars1 - ln(2)/&tau;B ArsB</span><br />
|-<br />
| ||ArsB<sub>As</sub> ||concentration w.r.t. the interior of the cell||(d/dt) ArsB<sub>As</sub> = <span class="export">k7<sub>on</sub> As(III)<sub>in</sub> ArsB - (k7<sub>off</sub>+k8) ArsB<sub>As</sub></span><br />
|-<br />
|colspan="4"|''Intracellular'' (ars2, pro and GV are introduced)<br />
|-<br />
| ||As(III)<sub>in</sub>||concentration of As(III) inside the cell||(d/dt) As(III)<sub>in</sub> = - (d/dt) ArsR<sub>As</sub> - (d/dt) MBPArsR<sub>As</sub> - n<sub>f</sub> (d/dt) fMT<sub>As</sub><span class="export"> - (d/dt) ArsB<sub>As</sub> - k8 ArsB<sub>As</sub></span><span class="import"> + (Vs/Vc) k6 GlpF<sub>As</sub></span><br />
|-<br />
| ||ars1 {{infoBox|ars1 stands for the promotor in front of the operon which contains the information for the production of the accumulation protein ArsR and the exporter ArsB. It is selfregulatory in the sence that it produces it's own repressor in the form of ArsR}} ||concentration of unbound promoters naturally occurring in <i>E. coli</i>||(d/dt) ars1 = - (d/dt) ArsR<sub>ars1</sub><br />
|-<br />
| ||ars2 {{infoBox|ars2 stands for the promotor in front of the operon which contains the information for the production of Gas Vesicles. Unlike ars 1 it is not selfregulatory, but the if everything goes correctly the production of gas vesicles will only start if there arsenic inside the cell}}||concentration of unbound promoters in front of gas vesicle genes||(d/dt) ars2 = <span class="production">- (d/dt) ArsR<sub>ars2</sub></span><br />
|-<br />
| ||proR ||concentration of constitutive promoters in front of arsR|| (d/dt)proR = 0 in our model<br />
|-<br />
| ||proM ||concentration of constitutive promoters in front of mbp-arsR|| (d/dt)proM = 0 in our model<br />
|-<br />
| ||proF ||concentration of constitutive promoters in front of fMT|| (d/dt)proF = 0 in our model<br />
|-<br />
| ||ArsR {{infoBox|ArsR binds to ars to repress production of the genes they regulate, and binds to As(III) to make it less of a problem for the cell.}}||concentration of the accumulation protein ArsR||(d/dt) ArsR = &beta;RN ars1 + &beta;R proR - (ln(2)/&tau;R) ArsR - (d/dt) ArsR<sub>As</sub> - 2 (d/dt) ArsR<sub>ars1</sub><span class="production"> - 2 (d/dt) ArsR<sub>ars2</sub></span> <br />
|-<br />
| ||ArsR<sub>As</sub> || the concentration of ArsR bound to As(III)||(d/dt) ArsR<sub>As</sub> = kR<sub>on</sub> ArsR As(III)<sub>in</sub> - kR<sub>off</sub> ArsR<sub>As</sub><br />
|-<br />
| ||ArsR<sub>ars1</sub> ||the concentration of ArsR bound to ars1||(d/dt) ArsR<sub>ars1</sub> = kA<sub>on</sub> ArsR&sup2; ars1 - kA<sub>off</sub> ArsR<sub>ars1</sub><br />
|-<br />
| ||ArsR<sub>ars2</sub> ||the concentration of ArsR bound to ars2||(d/dt) ArsR<sub>ars2</sub> = <span class="production">kA<sub>on</sub> ArsR&sup2; ars2 - kA<sub>off</sub> ArsR<sub>ars2</sub></span><br />
|-<br />
| ||MBPArsR {{infoBox|A fusion of maltose binding protein and ArsR. It is more stable than the normal ArsR variant, but it is no longer able to act as a repressor for the ars promotor.}}|| a fusion of maltose binding protein and ArsR||(d/dt) MBPArsR = &beta;M proM - (ln(2)/&tau;M) MBPArsR - (d/dt) MBPArsR<sub>As</sub><br />
|-<br />
| ||MBPArsR<sub>As</sub> ||bound to As(III)||(d/dt) MBPArsR<sub>As</sub> = kM<sub>on</sub> MBPArsR As(III)<sub>in</sub> - kM<sub>off</sub> MBPArsR<sub>As</sub><br />
|-<br />
| ||fMT {{infoBox|It is another binding protein. Unlike it's counterpart it capeble of containing up to five As(III) particles or one As(V) particle }} || Arsenic binding metallotein ||(d/dt) fMT = &beta;F proF - (ln(2)/&tau;F) fMT - (d/dt) fMT<sub>As</sub><br />
|-<br />
| ||fMT<sub>As</sub> ||bound to multiple As(III)||fMT<sub>As</sub> = kF<sub>on</sub> fMT As(III)<sub>in</sub><sup>n<sub>f</sub></sup> - kF<sub>off</sub> fMT<sub>As</sub><br />
|-<br />
| ||ArsR<sub>As</sub> ||bound to As(III)<br />
|-<br />
| ||GV ||concentration of gas vesicles||(d/dt) GV = <span class="production">&beta;G ars2 - ln(2)/&tau;G GV</span><br />
|-<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="estimate" style="padding:0;"|GVP Production related.<br />
|}<br />
|}<br />
<br />
The variables above can be related to each other through the following "reactions" (color coding is continued below to show which parts of the differential equations refer to which groups of reactions):<br />
<br />
<br />
Using the following constants/definitions:<br />
{|class="ourtable"<br />
|-<br />
!Name<br />
!Units<br />
!Description<br />
|-<br />
|kRon, kMon, k5on, etc.<br />
|1/(M&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kAon<br />
|1/(M²&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kFon<br />
|1/(M<sup>n<sub>f</sub></sup>&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kRoff, kMoff, kFoff, kAoff, k5off, etc.<br />
|1/s<br />
|Reaction rate constants for reactions from a complex.<br />
|-<br />
|k6, k8<br />
|1/s<br />
|Reaction rate constants representing how fast transporters transport their cargo to "the other side".<br />
|-<br />
|&tau;B, &tau;R, &tau;M, &tau;F, &tau;G<br />
|s<br />
|Half-lifes (of ArsB, ArsR, MBPArsR, fMT and GV, respectively). Degradation rate = ln(2)/&tau; {{infoBox|1=If you take just the degradation into account you will have the equation dC/dt = -k*C, which leads to C(t) = C(0) e<sup>-k t</sup>. So if k = ln(2)/&tau; we get C(t) = C(0) e<sup>-ln(2)/&tau; t</sup> = C(0) 2<sup>-t/&tau;</sup>. In other words &tau; is the time it takes for the concentration to half.}}<br />
|-<br />
|&beta;RN, &beta;R, etc.<br />
|1/s<br />
|Production rates.<br />
* &beta;RN = the production rate for ArsR behind the ars1 promoter<br />
* &beta;B = the production rate for ArsB behind the ars1 promoter<br />
* &beta;G = the production rate for GV behind the ars2 promoter<br />
* &beta;R = the production rate for ArsR behind a constitutive promoter<br />
* &beta;M = the production rate for MBPArsR behind a constitutive promoter<br />
* &beta;F = the production rate for fMT behind a constitutive promoter<br />
|-<br />
|Vs<br />
|L<br />
|Volume of solution (excluding cells).<br />
|-<br />
|Vc<br />
|L<br />
|Total volume of cells (in solution) (so Vs+Vc is the total volume).<br />
|}<br />
See [[Team:Groningen/Literature#Chen1997|Chen1997]] for the interplay between ArsR and ArsD (the latter has a role similar to ArsR, but we do not treat it, as it is [[Team:Groningen/BLAST|not present in our system]]).<br />
<br />
==Quasi steady state{{anchor|QuasiSteadyState}}==<br />
First of all, we assume the concentration of transporters is quite low compared to the concentration of the transported substances. After all, if this were not the case the transporters would act more like "storage" proteins than transporters (note that this can be even more rigorously justified if, for example, GlpFT<<K5). This leads to:<br />
<br />
<pre><br />
As(III)exT &asymp; As(III)ex<br />
As(III)inT &asymp; As(III)in + ArsRAs + MBPArsRAs + nf fMTAs<br />
</pre><br />
<br />
Also, we assume the binding and unbinding of molecules to the transporters occurs on a much finer time-scale than any actual changes to the concentrations inside and outside the cell. Similarly, within the cell we assume diffusion processes are very fast and binding/unbinding of substances is quite fast compared to the production of proteins. This leads us to assume that the following ratios between substances are constantly in equilibrium:<br />
<br />
{{frame|1=<br />
<div style="text-align:left;"><br />
We use the following when grouping the ars promoters:<br />
<pre><br />
arsT = ars + ArsRars<br />
ars1 / ars1T = ars2 / ars2T<br />
<br />
ars = ars1 + ars2<br />
ars = ars1 (1 + ars2T / ars1T)<br />
ars1 = ars / (1 + ars2T / ars1T)<br />
ars1 = ars ars1T / arsT<br />
<br />
ars2 = ars ars2T / arsT<br />
</pre><br />
</div><br />
}}<br />
<br />
<pre><br />
As(III)ex : GlpFAs &asymp; As(III)ex : 0<br />
GlpF : GlpFAs<br />
ArsB : ArsBAs<br />
As(III)in : ArsRAs : MBPArsRAs : nf fMTAs : ArsBAs &asymp; As(III)in : ArsRAs : MBPArsRAs : nf fMTAs : 0<br />
ArsR : ArsRAs : 2 ArsRars<br />
ars : ArsRars<br />
</pre><br />
<br />
To determine what the unknown ratios are we can set the following derivatives to zero (these are the derivatives of the complexes corresponding to the four overlapping regions in the diagram):<br />
<br />
<pre><br />
0 = (d/dt) GlpFAs = k5on As(III)ex GlpF - (k5off+k6) GlpFAs<br />
0 = (d/dt) ArsBAs = k7on As(III)in ArsB - (k7off+k8) ArsBAs<br />
0 = (d/dt) ArsRars = kAon ArsR² ars - kAoff ArsRars<br />
0 = (d/dt) ArsRAs = kRon ArsR As(III)in - kRoff ArsRAs<br />
0 = (d/dt) MBPArsRAs = kMon MBPArsR As(III)in - kMoff MBPArsRAs<br />
0 = (d/dt) fMTAs = kFon fMT As(III)in^nf - kFoff fMTAs<br />
</pre><br />
<br />
The first two derivates let us determine the ratios between bound and unbound transporters:<br />
<br />
<pre><br />
0 = (d/dt) GlpFAs = k5on As(III)ex GlpF - (k5off+k6) GlpFAs<br />
<br />
k5on As(III)ex GlpF = (k5off+k6) GlpFAs<br />
GlpF = (k5off+k6)/k5on GlpFAs / As(III)ex<br />
GlpF = K5 GlpFAs / As(III)ex<br />
<br />
GlpF : GlpFAs<br />
K5 GlpFAs / As(III)ex : GlpFAs<br />
K5 : As(III)ex<br />
<br />
0 = (d/dt) ArsBAs = k7on As(III)in ArsB - (k7off+k8) ArsBAs<br />
<br />
k7on As(III)in ArsB = (k7off+k8) ArsBAs<br />
ArsB = (k7off+k8)/k7on ArsBAs / As(III)in<br />
ArsB = K7 ArsBAs / As(III)in<br />
<br />
ArsB : ArsBAs<br />
K7 ArsBAs / As(III)in : ArsBAs<br />
K7 : As(III)in<br />
</pre><br />
<br />
The next two differential equations can be used to determine the relative abundances of ArsR and ArsRAs, and ars and ArsRars:<br />
<br />
<pre><br />
0 = (d/dt) ArsRAs = kRon ArsR As(III)in - kRoff ArsRAs<br />
<br />
kRon ArsR As(III)in = kRoff ArsRAs<br />
ArsRAs = kRon/kRoff ArsR As(III)in<br />
ArsRAs = ArsR As(III)in / KRd<br />
<br />
ArsR : ArsRAs<br />
ArsR : ArsR As(III)in / KRd<br />
KRd : As(III)in<br />
<br />
0 = (d/dt) ArsRars = kAon ArsR² ars - kAoff ArsRars<br />
<br />
kAon ArsR² ars = kAoff ArsRars<br />
ArsRars = kAon/kAoff ArsR² ars<br />
ArsRars = ArsR² ars / KAd²<br />
<br />
ArsR : 2 ArsRars<br />
ArsR : 2 ArsR² ars / KAd²<br />
KAd² : 2 ArsR ars<br />
<br />
ars : ArsRars<br />
ars : ArsR² ars / KAd²<br />
KAd² : ArsR²<br />
</pre><br />
<br />
For MBPArsR and fMT we find:<br />
<br />
<pre><br />
0 = (d/dt) MBPArsRAs = kMon MBPArsR As(III)in - kMoff MBPArsRAs<br />
<br />
MBPArsR : MBPArsRAs = KMd : As(III)in<br />
<br />
0 = (d/dt) fMTAs = kFon fMT As(III)in^nf - kFoff fMTAs<br />
<br />
fMT : fMTAs = KFd^nf : As(III)in^nf<br />
</pre><br />
<br />
And finally the relative abundances of arsenic:<br />
<br />
<pre><br />
ArsRAs = ArsR As(III)in / KRd<br />
<br />
As(III)in : ArsRAs : MBPArsRAs : n fMTAs<br />
As(III)in : ArsR As(III)in / KRd : MBPArsRT As(III)in / (KMd+As(III)in) : n fMTT As(III)in^nf / (KFd^nf+As(III)in^nf)<br />
1 : ArsR / KRd : MBPArsRT / (KMd+As(III)in) : n fMTT As(III)in^(nf-1) / (KFd^nf+As(III)in^nf)<br />
</pre><br />
<br />
Summarizing:<br />
<br />
<pre><br />
GlpF : GlpFAs = K5 : As(III)ex<br />
ArsB : ArsBAs = K7 : As(III)in<br />
As(III)in : ArsRAs : MBPArsRAs : n fMTAs &asymp; 1 : ArsR / KRd : MBPArsRT / (KMd+As(III)in) : n fMTT As(III)in^(nf-1) / (KFd^nf+As(III)in^nf)<br />
ars : ArsRars = KAd² : ArsR²<br />
ArsR : ArsRAs : 2 ArsRars &asymp; 1 : As(III)in / KRd : 2 ArsR ars / KAd²<br />
MBPArsR : MBPArsRAs = KMd : As(III)in<br />
fMT : fMTAs = KFd^nf : As(III)in^nf<br />
</pre><br />
<br />
Now we can look at the differential equations for the totals of ArsB (so ArsBT=ArsB+ArsBAs), ArsR, As(III)in and As(III)ex (GlpFT and arsT are assumed to be constant):<br />
<br />
<pre><br />
(d/dt) As(III)exT = (d/dt) As(III)ex + (d/dt) GlpFAs<br />
= - (d/dt) GlpFAs - k6 GlpFAs + (Vc/Vs) k8 ArsBAs + (d/dt) GlpFAs<br />
= (Vc/Vs) k8 ArsBAs - k6 GlpFAs<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 GlpFAs / GlpFT<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 As(III)ex / (K5+As(III)ex)<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 As(III)exT / (K5+As(III)exT)<br />
(d/dt) ArsBT = (d/dt) ArsB + (d/dt) ArsBAs<br />
= - (d/dt) ArsBAs + βB ars1 - ln(2)/τB ArsB + (d/dt) ArsBAs<br />
= βB ars1 - ln(2)/τB ArsB<br />
(d/dt) As(III)inT = -(Vs/Vc) (d/dt) As(III)exT<br />
= v5 As(III)exT / (K5+As(III)exT) - k8 ArsBT As(III)in / (K7+As(III)in)<br />
(d/dt) ArsRT = (d/dt) ArsR + (d/dt) ArsRAs + 2 (d/dt) ArsRars<br />
= βRN ars1 + βR proR - (ln(2)/τR) ArsR - (d/dt) ArsRAs - 2 (d/dt) ArsRars + (d/dt) ArsRAs + 2 (d/dt) ArsRars<br />
= βRN ars1 + βR proR - (ln(2)/τR) ArsR<br />
(d/dt) MBPArsRT = (d/dt) MBPArsR + (d/dt) MBPArsRAs<br />
= βM proM - (ln(2)/τM) MBPArsR<br />
(d/dt) fMTT = (d/dt) fMT + (d/dt) fMTAs<br />
= βF proF - (ln(2)/τF) fMT<br />
</pre><br />
<br />
==Steady state==<br />
By looking at the steady state of the system we can say something about its long-term behaviour. This also makes it easier to analyze relations between variables. To derive the steady state solution we take the quasi steady state solution and simplify it further by setting additional derivatives to zero:<br />
<br />
<pre><br />
0 = (d/dt) ArsBT = βB ars1 - ln(2)/τB ArsB<br />
0 = (d/dt) As(III)inT = v5 As(III)exT / (K5+As(III)exT) - k8 ArsBAs<br />
0 = (d/dt) ArsRT = βRN ars1 + βR pro - (ln(2)/τR) ArsR<br />
0 = (d/dt) MBPArsRT = βM proM - (ln(2)/τM) MBPArsR<br />
0 = (d/dt) fMTT = βF proF - (ln(2)/τF) fMT<br />
0 = (d/dt) GV = βG ars2 - ln(2)/τG GV<br />
</pre><br />
<br />
This directly leads to:<br />
<br />
<pre><br />
0 = βB ars1 - ln(2)/τB ArsB<br />
ArsB = βB (τB/ln(2)) ars1<br />
ArsB = βB (τB/ln(2)) ars1T KAd²/(KAd²+ArsR²)<br />
<br />
0 = βM proM - (ln(2)/τM) MBPArsR<br />
MBPArsR = βM (τM/ln(2)) proM<br />
<br />
0 = βF proF - (ln(2)/τF) fMT<br />
fMT = βF (τF/ln(2)) proF<br />
<br />
0 = βG ars2 - ln(2)/τG GV<br />
GV = βG (τB/ln(2)) ars2<br />
GV = βG (τB/ln(2)) ars2T KAd²/(KAd²+ArsR²)<br />
</pre><br />
<br />
For the intra- and extracellular concentrations we can find the following equation, giving a maximum for As(III)in of <code>K7 v5/(k8 ArsB)</code> (as As(III)exT cannot be negative){{infoBox|Conveniently the function <code>x/(c-x)</code> is non-negative and non-decreasing for x&isin;[0,c&rang;.}}:<br />
<br />
<pre><br />
0 = v5 As(III)exT / (K5+As(III)exT) - k8 ArsBAs<br />
0 = v5 As(III)exT / (K5+As(III)exT) - k8 ArsB As(III)in / K7<br />
0 = v5 As(III)exT - k8 ArsB As(III)in / K7 (K5+As(III)exT)<br />
0 = v5 As(III)exT - k8 ArsB As(III)in As(III)exT / K7 - k8 ArsB As(III)in K5 / K7<br />
0 = As(III)exT (v5 - k8 ArsB As(III)in / K7) - k8 ArsB As(III)in K5 / K7<br />
As(III)exT = k8 ArsB As(III)in K5 / (v5 K7 - k8 ArsB As(III)in)<br />
As(III)exT = K5 As(III)in / (K7 v5/(k8 ArsB) - As(III)in)<br />
</pre><br />
<br />
As we can safely assume arsenic neither disappears into nothingness nor appears from nothingness, we can use this to derive (As(III)T is the total amount of arsenic):<br />
<br />
<pre><br />
As(III)inT = As(III)in (1 + ArsR/KRd + MBPArsR/KMd + fMT As(III)in^(nf-1)/KFd^nf)<br />
<br />
As(III)T = Vs As(III)exT + Vc As(III)inT<br />
0 = Vs As(III)exT + Vc As(III)inT - As(III)T<br />
0 = Vs K5 As(III)in / (K7 v5/(k8 ArsB) - As(III)in) + Vc As(III)in (1 + ArsR/KRd + MBPArsR/KMd + fMT As(III)in^(nf-1)/KFd^nf) - As(III)T<br />
</pre><br />
<br />
As the function on the right-hand side is non-decreasing for <code>As(III)in&isin;[0,K7 v5/(k8 ArsB)&rang;</code> it at most has one zero on this interval (and it has one, as it starts at a negative value and gets arbitrarily large as As(III)in approaches the end of its range). So this zero can safely be found using any number of numerical methods.<br />
<br />
Finally, for ArsR we can find the following third-order equation:<br />
<br />
<pre><br />
0 = βRN ars1 + βR pro - (ln(2)/τR) ArsR<br />
0 = βRN ars1T KAd²/(KAd²+ArsR²) + βR pro - (ln(2)/τR) ArsR<br />
0 = βRN ars1T KAd² + βR pro (KAd²+ArsR²) - (ln(2)/τR) ArsR (KAd²+ArsR²)<br />
0 = βRN ars1T KAd² + βR pro KAd² + βR pro ArsR² - (ln(2)/τR) ArsR KAd² - (ln(2)/τR) ArsR³<br />
0 = (βRN ars1T + βR pro) KAd² - (ln(2)/τR) KAd² ArsR + βR pro ArsR² - (ln(2)/τR) ArsR³<br />
0 = (βRN ars1T + βR pro) (τR/ln(2)) KAd² - KAd² ArsR + βR (τR/ln(2)) pro ArsR² - ArsR³<br />
</pre><br />
<br />
According to Mathematica's solution of <code>Reduce[eq && KAd > 0 && arsT >= 0 && pro >= 0 && &beta;1 > 0 && &beta;3 > 0 && &tau;R > 0, ArsR, Reals]</code> (where eq is the equation shown above) there is only one real solution (examining the discriminant of eq confirms this), so we can solve the equation safely using Newton's (or Halley's) method.<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Ethics/SurveyTeam:Groningen/Ethics/Survey2009-10-21T22:23:10Z<p>Jaspervdg: Survey abstract.</p>
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<div class="intro introduction"><br />
==Survey==<br />
Ethics is an important issue to consider in the new field of synthetic biology. In order to gain more insight into the Dutch public opinion we decided to create a survey. <br />
The results of our survey suggest that in general people in the Netherlands are most concerned about the safety issues, however, they do trust researchers and developers to consider them.<br />
Surprisingly there appears to be no difference in these matters between people familiar with synthetic biology and those unfamiliar with it.<br />
</div><br />
<br />
===Considerations===<br />
The survey contains questions about the ethical issues surrounding synthetic biology and also about the ethical issues surrounding our project.<br />
We wanted to reach a mixed public in order to get an idea of the Dutch public opinion on the ethical issues of synthetic biology and our project. We did a convenience sampling so we handed out our survey among family, friends, secondary school pupils and fellow students. We have chosen for this sample construct because it is not expensive and it is easy to apply. We added a link to our survey on our wiki-website. In an attempt to exclude non-Dutch respondents we included the question “do you live or work in the Netherlands?” to our survey. Since we thought that it might make a difference if the participants already knew what synthetic biology was, we included the question “do you know what synthetic biology is?”. Being religious or not was also thought to possibly influence the opinion of the participant about for instance the playing God issue, so a question about religion was included as well. Just as age and gender could make a difference and therefore questions about that were included. <br />
We wanted to approach the Delphi method for brainstorming, also previous described by [[Team:Groningen/Literature#Zwart, SD, et al.2006|(Zwart, SD, et al.2006)]] in the Netherlands and recently used in the EU synth-ethics meeting, to gain more insights in ethics. Central in this method is the fact that participants can give their opinion anonymously and without consequences. The idea behind it is that if someone can speak freely this will open up the discussion. Although we did not organize a discussion, we did try to mimic this by including an essay question in the survey in which we asked the participants to give other ethical and safety issues surrounding our project. Since the survey is anonymously and we also aimed to ask all kinds of users to fill it out this survey approaches the open discussion method.<br />
The questions are based on the four ethical issues of synthetic biology described by [[Team:Groningen/Literature#Bhutkar, A2005|(Bhutkar, A2005)]], safety, security, playing God and intellectual property. All the respondents were shown a cover letter with information about the aim of the survey. The participants could decide to stop at any moment during the survey. After analyzing the data we send a debriefing to the respondents with the conclusion about our survey. For the confidentiality of the respondents we used the program ‘Examine’. In this program all the participants have a random number as ID. Also we have minimizes the number of people who could see or handle the data. The questions consists mostly of theorems, which were translated to a Likert scale afterwards.<br />
<br />
===Results===<br />
The survey was opened from 11-09-2009 until 07-10-2009 (27 days) and was completed by 262 respondents, 147 male and 115 female. <br />
The educational level of the respondents was mixed. As can be seen in figure 1 the different educational groups are all represented. There is a small bias to the educative level university. So the survey is, however, not a completely representative sample of the Dutch population, but it is still a good suggestion for the Dutch public opinion. <br />
We took this into account when we did the statistical analysis and choose, therefore, to do non-probability tests. We have chosen the ‘Mann-Whitney’ test for two independent samples, by questions with more than two independent groups, we use the ‘Kruskal-Wallis H.’ test. The power of the Mann-Whitney test was determined and appeared to be high enough.<br />
Both procedures are testing equality of population medians among groups. Sometimes if the data looked normal distributed (we have checked this with boxplots), we used an ANOVA two-tailed with the post-hoc ‘Bonferroni’ All test are done with a confidence level of 95% (α=0.05). <br />
<br />
[[Image:Groningen_Figure1Survey.png|400px]]<br />
<br />
Figure 1: Educational level of the respondents of the ethical survey of the iGEM team Groningen 2009<br />
<br />
===Inferential statistics=== <br />
<br />
‘’Difference between different levels of education’’<br />
Grouping the university (biology), university (non-biology) and university (engineering) shows that the data can be biased towards the university level educated respondents. <br />
There, however, does not seem to be a difference in response between the different educational levels towards the ethical issues of our project, one exception being the response towards the risk of bio terrorism. The university level educated respondents see less risk of bio terrorism of our project than do the lower level educated respondents. (p=0,001)<br />
There does also seem to be a significant difference in response to the question “how do you feel about bacteria being manipulated for research” between respondents with educational level secondary school and university (biology) (p=0.014, two-way ANOVA with post-hoc bonferoni). University students are more positive towards manipulating bacteria for research then secondary school pupils. This can also be seen when a correlation test is done. The spearman’s rho correlation test was chosen because we use categorical variables and the data is normal distributed. A (weak) correlation was found (R=0,215 and p=0,001) between level of education and openness towards manipulating bacteria. Respondents with a higher level of education are more positive towards manipulating bacteria.<br />
<br />
<br />
''Difference between religious and not religious''<br />
It was predicted that being religious or not could influence the opinion of the respondents towards the playing God issue of our project. No difference, however, could be detected (p=0.96, two tailed Mann-Withney test). Both religious and non-religious respondents did not thought that using GMO’s for water or sludge cleaning is unethical in the sense that researchers are playing God (figure 2).<br />
<br />
<br />
[[Image:Groningen_Figure2Survey.png|400px]]<br />
<br />
Figure 2: Frequency table of the responses towards the question do you think using GMO’s for water or sludge cleaning unethical in the sense that researchers are playing God against being religious or not.<br />
<br />
''Difference between knowing and not knowing what synthetic biology is''<br />
<br />
Half of the respondents (51,1%) did not know what synthetic biology is, 48,9% of the respondents did. It was hypothesized that there would be a difference between respondents that know what synthetic biology is and those who do not, in how they feel about GMO’s being used in application. This, however, did not appear to be the case form our survey (p=0.236, two-tailed Mann-whitney test). <br />
<br />
''Difference between male and female''<br />
<br />
If male and female respondents were compared there appeared to be a difference how they feel about GMO’s being manipulated for research. Here a one-tailed test has been performed because it was presumed that women are, in general, more caring then men. A significant difference between the genders with a p-value of 0,0005 was found showing that women are more thoughtful about the usage of GMO’s for research then man.<br />
<br />
''Difference between older and younger respondents''<br />
<br />
It was also tested if age make a difference in how the participants feel about the ethical issues of our project. One significant difference was found between participants older than 50 and the group aged between 21 and 30. The older group (>50) appeared to be more afraid of misusage of GMO in cleaning water or sludge for bioterrorism than the younger group (p=0,022) <br />
<br />
<br />
===Descriptive statistics===<br />
<br />
No differences were found between other groups so the following results can be considered the same for all groups.<br />
The respondents were asked what they thought of bacteria being manipulated for research. The majority, 89.7%, answered “good” and only 5,8% answered “not good” because it can be dangerous or researchers are playing God. So making GMO’s does not seem to be considered unethical, using these GMO’s in practice was also not considered unethical, 93.5% was positive about it. Safety for the environment and human health was, however, a concern for 24,4% of the respondents. 69,1% of the respondents found, security and usefulness for society, a condition for the usage of GMO’s. The respondents were more critical about the usage of GMO’s for a specific application, in water or sludge cleaning. A majority of the respondents, 50,8%, thought that the usage of GMO’s can be dangerous for the environment or human health so this should be considered before usage. 29% of the respondents trusted the researchers in considering the safety and make the application more safe. Security of GMO’s for applications in the water and sludge cleaning is an issue that concerns 23,7% and they feel that this deserves some thought. Another 36,6% of the respondents also thought that security is an issue, however, there is always the risk of mis usage. The remaining 33,2% of the respondents did not think security is an issue in this application. Another important ethical issue according to [[Team:Groningen/Literature#Bhutkar, A2005|(Bhutkar, A2005)]], the playing God issue, does not seem to be a concern for the usage of GMO’s in water and sludge cleaning according to the respondents of our survey (92,4%). <br />
The fourth ethical issue, the intellectual property, was also considered for using GMO’s in water and sludge cleaning. Although 26,3% of the respondents thought it should be possible to patent the application of the iGEM team Groningen 2009 because it is important for development the majority (57.3%) of the respondents only agreed with patenting the whole system and not the DNA itself. 11.5% of the respondents were against patenting this system in which GMO’s are used (fig 3).<br />
<br />
[[Image:Groningen_Figure3Survey.png|400px]]<br />
<br />
Figure 3: The four ethical issues, as described by bhutkar, considered for the project of the iGEM team Groningen 2009.<br />
<br />
[[Image:Groningen_Figure4Survey.png|400px]]<br />
<br />
Figure 4: This figure shows what the most important ethical issues is in our project according to our respondents. The four issues, safety (A), security (B), intellectual property (C) and playing God (D) are derived from <br />
<br />
The survey included a question, which ethical issue was considered the most important for our project, two answers could be given. In the above figure it can be seen that most respondents, 40%, thought safety is the most important issue. Also in combination with other issues safety is considered to be very important. Also security is thought to be a risk in water and sludge cleaning, by 30% of the participants. As a second choice safety and security (A and B) are the most chosen answers. This shows that intellectual property and playing God play minor roles in the ethics of our project compared to the risks in safety and security. These are clearly the issues that should be taken into account in a possible application of our project.<br />
<br />
===Conclusion===<br />
The results of our survey suggest that in general people in the Netherlands are most concerned about the safety issues, however, they do trust researchers and developers to consider this in case GMO’s are used in application. Also the majority thinks that there is a security risk by using GMO’s for our project in a possible application. Less educated and older people would indicate a higher security risk than a higher educational level and younger people.<br />
<br />
In general manipulation of bacteria for research is considered good. Women, however, are more thoughtful about it than man. People with a higher level education are more open towards using bacteria for research than do lower level educated people. Unexpectedly we found no difference between people who did know what synthetic biology was and those who did not. So it appears that one is not more anxious about something because of a lack of awareness.<br />
Altogether comparing the four ethical issues of Bhutkar, safety, security, playing God and intellectual property, for synthetic biology in general and our project in particular shows that synthetic biological research is considered ok as long as done carefully and safety and security issues are considered.<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/TeamTeam:Groningen/Team2009-10-21T22:17:35Z<p>Jaspervdg: </p>
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[[Category:Team:Groningen/Disciplines/Project_Management|Team]]<br />
[[Category:Team:Groningen/Roles/Project_Manager|Team]]<br />
<br />
==Our Team At A Glance==<br />
<br />
[[Image:IGEMGroningen_Molen.jpg|400px|thumb|right|[Team:Groningen/Team|Our team!]]<br />
<br />
Welcome to the main page of the iGEM Groningen team! We are an interdisciplinary team of [[Team:Groningen/Team|11 enthusiastic students]] from the [http://www.rug.nl/ University of Groningen] situated in the not-too-big city of [http://portal.groningen.nl/en/startpagina Groningen] in [http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=Groningen&sll=53.281349,6.689459&sspn=0.007261,0.018926&ie=UTF8&z=12&iwloc=A the north of the Netherlands]. You can contact us at '''mailto:igemgroningen@googlegroups.com'''. <br />
<br />
Our team consists of the following student-members:<br />
<br />
* [[User:JolandaWitteveen|Jolanda Witteveen]] (Biomedical Technology): [[:Category:Team:Groningen/Roles/Chair|Chair]], [[:Category:Team:Groningen/Roles/Project_Manager|Project Manager]]<br />
* [[User:svenjurgens|Sven Jurgens]] (Molecular Biology): [[:Category:Team:Groningen/Roles/Treasurer|Treasurer]]<br />
* [[User:Jaspervdg|Jasper van de Gronde]] (Computational Science and Visualization): [[:Category:Team:Groningen/Roles/Configuration_Manager|Configuration Manager]], [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
* [[User:Verhoeven1981|Michael Verhoeven]] (Chemistry): [[:Category:Team:Groningen/Roles/Public_Relations_Officer|PR Officer]]<br />
* [https://2009.igem.org/User:Nienke Nienke Kuipers] (Molecular Biology): [[:Category:Team:Groningen/Roles/Scribe|Minutes secretary]] and Lab manager<br />
* [[User:Jelle|Steven Jelle Meijer]] (Molecular Biology): [[:Category:Team:Groningen/Roles/Facility_Manager|Facility Manager Haren]]<br />
* [[User:Wilfred|Wilfred Poppinga]] (Medical Pharmaceutical Sciences): [[:Category:Team:Groningen/Roles/Chair|Vice Chair]], [[:Category:Team:Groningen/Roles/Treasurer|Treasurer]]<br />
* [https://2009.igem.org/User:Paulschavemaker Paul Schavemaker] (Molecular Life Sciences): [[:Category:Team:Groningen/Roles/Scribe|Minutes secretary]]<br />
* [https://2009.igem.org/User:Frans Frans Bianchi] (Molecular Biology): [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
* [[User:Klaas Bernd Over|Klaas Bernd Over]] (Applied Physics): [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
* [[User:Annelies|Annelies van Keulen]] (Molecular Biology/Psychology): [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
<br />
==Our advisors==<br />
*prof. dr. Oscar Kuipers: [http://molgen.biol.rug.nl/molgen/index.php Molecular Genetics] (Head)<br />
*prof. dr. Jan Kok: [http://molgen.biol.rug.nl/molgen/index.php Molecular Genetics]<br />
*prof. dr. Bert Poolman: Biochemistry; [http://www.centreforsyntheticbiology.eu/ Centre for Synthetic Biology] (Director)<br />
*prof. dr. Roel Bovenberg: Synthetic biology and Cell engineering; Corporate Scientist Biotechnology, [http://www.dsm.com/ DSM]<br />
*dr. Dirk Slotboom: Enzymology <br />
*[https://2008.igem.org/Team:Groningen/team.html iGEM Groningen 2008]. Especially Auke van Heel & Martijn Herber<br />
<br />
<br><br><br />
<br />
==Where to hear from us==<br />
===In the media===<br />
Follow us in '''[[Team:Groningen/Publicity| The News]]'''<br />
<br />
Also follow us on '''[http://twitter.com/igemgroningen Twitter]!'''<br />
<br />
Check out some interesting '''[[Team:Groningen/Videos|Videos]]'''<br />
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Check out some interesting '''[[Team:Groningen/Pictures|Pictures]]'''<br />
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===Presenting===<br />
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*{{todo}} December 11<sup>th</sup> 2009: Meeting @ [http://www.dsm.com/en_US/html/home/dsm_home.cgi DSM] - [http://maps.google.nl/maps?oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&q=delft+DSM&fb=1&gl=nl&hq=DSM&hnear=delft&cid=0,0,8723601113946313921&ei=B_jSSrqHIcTz-QbZsNT7Ag&sa=X&oi=local_result&ct=image&resnum=1&ved=0CAoQnwIwAA Delft]<br />
*{{todo}} November 23<sup>rd</sup> 2009: Meeting @ student societies for [http://www.chemische-binding.nl/ Chemistry] and [http://www.fmf.nl/?file=main.html&lang=.en Math, Physics, Computer Science and Astronomy]<br />
*{{todo}} <b>October 30<sup>th</sup> to November 2<sup>nd</sup> 2009: Presentation @ The [https://2009.igem.org/ iGEM] 2009 [https://2009.igem.org/Jamboree Jamboree] - [http://whereis-beta.mit.edu/?mapterms=stata%20center&zoom=15&lat=42.36161990569666&lng=-71.09055519104004&open=object-32 MIT Stata] and [http://whereis-beta.mit.edu/?mapterms=lobby%2013&zoom=15&lat=42.35993922977393&lng=-71.092529296875&open=object-13 Lobby 13] in Cambridge, MA</b><br />
*{{todo}} October 26<sup>th</sup> 2009: Lecture @ [http://www.hanzeuniversity.eu/home/international Hanze University], Biology & Medical Laboratory Research and Bioinformatics students - room A257 [http://maps.google.nl/maps?q=Zernikeplein+7+Groningen&oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&hq=&hnear=Zernikeplein+7,+9747+Groningen&gl=nl&ei=wwHPSor9A4OF-QaTkL2FAw&sa=X&oi=geocode_result&ct=title&resnum=1 Zernikeplein 11, Groningen] <br />
*{{todo}} October 23<sup>rd</sup> 2009: Update Lecture @ the Bachelor course [http://www.rug.nl/ocasys/fwn/vak/show?code=WLB07010 Genes & Behaviour] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 Haren]<br />
*October 19<sup>th</sup> 2009: [http://www.cs.rug.nl/~biehl/Coll/index.html Colloquium] @ [http://www.rug.nl/informatica/index Institute for Mathematics and Computing Science] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=jGw&resnum=0&q=bernoulliborg%20Groningen%20Nijenborgh%209&um=1&ie=UTF-8&sa=N&tab=wl room 5161.0267 (Bernoulliborg), Groningen]<br />
*October 12<sup>th</sup> 2009: Meeting @ Marine Biology cluster - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 D225, Haren]<br />
* October 7<sup>th</sup> 2009: Lecture @ the Bachelor course [http://www.rug.nl/ocasys/fwn/vak/show?code=WLB07010 Genes & Behaviour] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 D225, Haren]<br />
* October 2<sup>nd</sup> 2009: Lunch meeting @ [http://www2.dhv.com/default.aspx DHV] - [http://maps.google.com/maps?f=q&source=s_q&hl=nl&geocode=&q=Laan+1914+no+35,+Amersfoort&sll=37.0625,-95.677068&sspn=54.357317,79.013672&ie=UTF8&hq=&hnear=Laan+1914+35,+3818+Amersfoort,+Utrecht,+Nederland&ll=52.134107,5.36828&spn=0.010405,0.01929&t=h&z=16&iwloc=r3 Groene zaal DHV, Amersfoort]<br />
* October 1<sup>st</sup> 2009: Lunch meeting @ Life Science student society [http://www.glv-idun.nl/ GLV Idun] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 Groene Zaal, Haren]<br />
*September 29<sup>th</sup> 2009: Meeting @ Applied physics student society [http://www.professorfrancken.nl/ TFV Professor Francken] - [http://maps.google.nl/maps?q=Nijenborgh%204%20NCC%20Complex&oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&hl=nl&ie=UTF-8&sa=N&tab=vl NCC complex VIP Room building 16, Groningen]<br />
*[https://2009.igem.org/Team:Groningen/Notebook/24_September_2009 September 24<sup>th</sup> 2009]: Presentation @ 2nd Programme Day of the [http://www.kluyvercentre.nl/ Kluyver Centre] - [http://maps.google.nl/maps?q=Generaal+Foulkesweg+96+6703+DS+Wageningen&oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&hq=&hnear=Generaal+Foulkesweg+96,+6703+Wageningen&gl=nl&ei=giXDSvfgDcrI-Qa53ojvCw&sa=X&oi=geocode_result&ct=image&resnum=1 Wageningse Berg, Wageningen]<br />
*September 11<sup>th</sup> 2009: Presentation @ [http://www.rug.nl/gbb/studyatgbb/generalcourses/gbbsymposium2009 17th Annual] [http://www.rug.nl/gbb/index GBB] Symposium 2009 - [http://maps.google.nl/maps?oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&q=Hampshire+hotel+Groningen+Radesingel+50,+9711+EK+Groningen&fb=1&gl=nl&hq=Hampshire+hotel&hnear=Groningen+Radesingel+50,+9711+EK+Groningen&cid=0,0,5400363645623663183&ei=eybDSq-jNojj-Qbz1PXuCw&sa=X&oi=local_result&ct=image&resnum=1 Hampshire hotel, Groningen]</div><br />
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{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/LiteratureTeam:Groningen/Literature2009-10-21T22:08:01Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
<div style="float:left" >{{linkedImage|GroningenPrevious.png|Team:Groningen/Glossary}}</div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Protocols}}</div><br />
<br />
[[Category:Team:Groningen]]<br />
<br />
==Literature==<br />
Buoyancy related literature:<br />
*Buoyant density: [[Team:Groningen/Literature#Poole1977|Poole 1977]], [[Team:Groningen/Literature#Bylund1991|Bylund 1991]], '''[[Team:Groningen/Literature#Baldwin1995|Baldwin 1995]]'''<br />
*Gas vesicles: [[Team:Groningen/Literature#Bowen1965|Bowen 1965]], [[Team:Groningen/Literature#Walsby1979|Walsby 1979]], '''[[Team:Groningen/Literature#Walsby1994|Walsby 1994]]''', '''[[Team:Groningen/Literature#Li1998|Li 1998]]''', [[Team:Groningen/Literature#Sivertsen2008|Sivertsen 2008]], [[Team:Groningen/Literature#Holland2009|Holland 2009]]<br />
<br />
Other methods of arsenic purification.<br />
*General information about the subject:[[Team:Groningen/Literature#Frankenberger2001|Frankenberger 2001]],[[Team:Groningen/Literature#Stephan Hug|Stephan Hug]],[[Team:Groningen/Literature#Wlckramaslnghe2004|Wlckramaslnghe 2004]],[[Team:Groningen/Literature#Dong2008|Dong 2008]],'''[[Team:Groningen/Literature#EPA2000|EPA 2000]]''',<br />
*Ion exchange and Membranes:[[Team:Groningen/Literature#Oehmen2006|Oehmen 2006]],<br />
*Nanomaterials:[[Team:Groningen/Literature#Hristovski2007|Hristovski 2007]],[[Team:Groningen/Literature#Martinson2009|Martinson 2009]],[[Team:Groningen/Literature#Chang2009|Chang 2009]],<br />
*Precipitative Processes:[[Team:Groningen/Literature#Raje2005|Raje 2005]],<br />
<br />
Our metal related literature by subject:<br />
{|border="1" <br />
!<br />
!<br />
!Cu<br />
!Zn<br />
!As<br />
!Cd<br />
!Sb<br />
!Hg<br />
|-<br />
!rowspan="2" |Importers<br />
!GlpF<br />
|<br />
|<br />
|'''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Rosen2009|Rosen 2009]]<br />
|<br />
|'''[[Team:Groningen/Literature#Meng2004|Meng 2004]]'''<br />
|<br />
|-<br />
!{{part|BBa_K190018|HmtA}}<br />
|[[Team:Groningen/Literature#Lewinson2009|Lewinson 2009]]<br />
|[[Team:Groningen/Literature#Lewinson2009|Lewinson 2009]]<br />
|<br />
|<br />
|<br />
|-<br />
!rowspan="1" |Exporters<br />
!ArsB<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Tisa1989|Tisa 1989]], [[Team:Groningen/Literature#Carlin1995|Carlin 1995]],<br />
[[Team:Groningen/Literature#Dey1995|Dey 1995]] [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|[[Team:Groningen/Literature#Tisa1989|Tisa 1989]], [[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|-<br />
!rowspan="6" |Accumulators<br />
!ArsR<br />
|<br />
|<br />
||[[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Chen1997|Chen 1997]]''', '''[[Team:Groningen/Literature#Kostal2004|Kostal 2004]]''', [[Team:Groningen/Literature#Rensing2005|Rensing 2005]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
||[[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
<br />
|<br />
|-<br />
!ArsD<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Chen1997|Chen 1997]], [[Team:Groningen/Literature#Lin2007-1|Lin 2007-1/2]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|[[Team:Groningen/Literature#Chen1997|Chen 1997]], [[Team:Groningen/Literature#Lin2007-1|Lin 2007-1/2]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|-<br />
!SmtA<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]], [[Team:Groningen/Literature#Turner1995|Turner 1995]], [[Team:Groningen/Literature#Robinson2001|Robinson 2001]], [[Team:Groningen/Literature#Blindauer2002|Blindauer 2002]]<br />
|<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|-<br />
!MymT<br />
|[[Team:Groningen/Literature#Gold2008|Gold 2008]]<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
!MT<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Morris1999|Morris 1999]],[[Team:Groningen/Literature#Ngu2006|Ngu 2006]],[[Team:Groningen/Literature#Singh2008|Singh 2008]], [[Team:Groningen/Literature#Merrifield2004|Merrifield 2004]], [[Team:Groningen/Literature#Ngu2009|Ngu 2009]]<br />
|[[Team:Groningen/Literature#Deng2007|Deng 2007]]<br />
|<br />
|[[Team:Groningen/Literature#Chen1998|Chen1998]]<br />
|-<br />
!Unclassified<br />
|[[Team:Groningen/Literature#Brady1994|Brady 1994]]<br />
|[[Team:Groningen/Literature#Chang1998|Chang 1998]], [[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]<br />
|<br />
|[[Team:Groningen/Literature#Brady1994|Brady 1994]], [[Team:Groningen/Literature#Chang1998|Chang 1998]], <br />
|<br />
|[[Team:Groningen/Literature#Deng2008|Deng 2008]]<br />
|-<br />
!rowspan="1" |Promoters<br />
!<br />
|[[Team:Groningen/Literature#Mills1994|Mills 1994 ]], [[Team:Groningen/Literature#Khunajakr1999 |Khunajakr 1999]], [[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore 2005]], [[Team:Groningen/Literature#Ettema2006 |Ettema2006 ]], [[Team:Groningen/Literature#Liu2006|Liu 2006]], [[Team:Groningen/Literature#Liu2008|Liu 2008]], [[Team:Groningen/Literature#Catini2008|Catini 2008]], [[Team:Groningen/Literature#Nawapan2009|Nawapan 2009]]<br />
|[[Team:Groningen/Literature#Thelwell1998|Thelwell 1998]], [[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore2005]], [[Team:Groningen/Literature#Hirose2006 |Hirose 2006]], [[Team:Groningen/Literature#Kloosterman2008|Kloosterman 2008]]<br />
|[[Team:Groningen/Literature#Summers2009 |Summers 2009]]<br />
|[[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore 2005]]<br />
|<br />
|<br />
|}<br />
<br />
;Alon 2007 {{anchor|Alon2007}}<br />
:{{star}} Uri Alon (2007). ''Introduction to systems biology: design principles of biological circuits'' Chapman & Hall/CRC. ISBN 978-1-58488-642-6<br />
<br />
;Baldwin 1995 {{anchor|Baldwin1995}}<br />
:W.W. Baldwin, Richard Myer, Nicole Powell, ''et al'' (August 1995). "[http://www.springerlink.com/content/nu1lkduf3w89fmd8 Buoyant density of Escherichia coli is determined solely by the osmolarity of the culture medium]". ''Archives of Microbiology'' '''164(2)''': 155-157<br />
<br />
;Beltramini 1981 {{anchor| Beltramini1981}}<br />
:M. Beltramini and K. Lerch (1981). "[http://www.ncbi.nlm.nih.gov/pubmed/6453726 Luminescence Properties of ''Neurospora'' Copper Metallothionein]". ''FEBS Letters'' '''127(2)''': 201-203<br />
<br />
;Beyer 2004 {{anchor|Beyer2004}}<br />
:Andreas Beyer, Jens Hollunder, Heinz-Peter Nasheuer and Thomas Wilhelm (August 2004). "[http://dx.doi.org/10.1074/mcp.M400099-MCP200 Post-transcriptional Expression Regulation in the Yeast Saccharomyces cerevisiae on a Genomic Scale]". ''Molecular & Cellular Proteomics'' '''3''': 1083-1092<br />
<br />
;Bhutkar, A2005{{anchor|Bhutkar, A2005}}<br />
:Bhutkar, A(2005). '[http://www.ncbi.nlm.nih.gov/pubmed/16538811?dopt=Abstract Synthetic Biology: Navigating the Challenges Ahead]".''The journal of Biolaw and Business. '' '''2(8)''':<br />
<br />
;Blancato 2006 {{anchor|Blancato2006}}<br />
:Blancato VS, Magni C, Lolkema JS. (October 2006). "[http://dx.doi.org/doi:10.1016/j.jmb.2009.02.015 Functional characterization and Me ion specificity of a Ca-citrate transporter from Enterococcus faecalis]". ''FEBS journal'' '''273(22)''': 5121-5130<br />
<br />
;Blindauer 2002 {{anchor|Blindauer2002}}<br />
:Claudia A. Blindauer, Mark D. Harrison, Andrea K. Robinson, ''et al'' (2002). "[http://dx.doi.org/10.1046/j.1365-2958.2002.03109.x Multiple bacteria encode metallothioneins and SmtA-like zinc fingers]". ''Molecular Microbiology'' '''45(5)''': 1421-1432<br />
<br />
;Blindauer 2001 {{anchor|Blindauer2001}}<br />
:Blindauer CA, Harrison MD, ''et al'' (2001). "[http://www.ncbi.nlm.nih.gov/pubmed/11493688 A metallothionein containing a zinc finger within a four-metal cluster protects a bacterium from zinc toxicity.]". '' Proc Natl Acad Sci USA. '' '''98(17)''': ):9593-9598<br />
<br />
;Bowen 1965 {{anchor|Bowen1965}}<br />
:C.C. Bowen and T.E. Jensen ( March 1965). "[http://dx.doi.org/10.1126/science.147.3664.1460 Blue-Green Algae: Fine Structure of the Gas Vacuoles]". ''Science '' '''147(3664)''': 1460 - 1462<br />
<br />
;Busenlehner 2003 {{anchor|Busenlehner2003}}<br />
:Busenlehner L.S., Pennella M.A. & Giedroc D.P., (June 2003) "[http://dx.doi.org/10.1155/2006/837139 The SmtB/ArsR family of metalloregulatory transcriptional repressors: structural insights into prokaryotic metal resistance]". ''FEMS Microbiology Reviews, '''2003''', 27, 131-143.<br />
<br />
;Brady 1994 {{anchor|Brady1994}}<br />
:Brady D, Rose PD, Duncan JR. (1994). "[http://www.ncbi.nlm.nih.gov/pubmed/18618649 The use of hollow fiber cross-flow microfiltration in bioaccumulation and continuous removal of heavy metals from solution by Saccharomyces cerevisiae.]". '' Biotechnol Bioeng. '' '''44(11)''':1362-1366<br />
<br />
;Bylund 1991 {{anchor|Bylund1991}}<br />
:J.E. Bylund, M.A. Haines, K. Walsh, ''et al'' (September 1991). "[http://jb.asm.org/cgi/content/abstract/173/17/5396 Buoyant density studies of several mecillinam-resistant and division mutants of Escherichia coli]". ''Journal of Bacteriology'' '''173(17):''' 5396-5402<br />
<br />
;Cadosch 2008 {{anchor|Cadosch2008}}<br />
:Cadosch D, Meagher J, Gautschi OP, Filgueira L. (December 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/19133293 Uptake and intracellular distribution of various metal ions in human monocyte-derived dendritic cells detected by Newport Green DCF diacetate ester]". '' Journal Neurosci Methods.'' '''178(1)''':182-187<br />
<br />
;Catini 2008 {{anchor|Catini2008}}<br />
:Cantini F., Banci L. & Solioz M., (October 2008) "[http://dx.doi.org/10.1042/BJ20081713 The copper-responsive repressor CopR of Lactococcus lactis is a ‘winged helix’ protein]". ''Biochem. J., '''2009''', 417, 493–499.<br />
<br />
;Carlin 1995 {{anchor|Carlin1995}}<br />
:Arthur Carlin, Weiping Shi, Saibal Dey and Barry P. Rosen (February 1995). "[http://www.ncbi.nlm.nih.gov/pubmed/7860609 The ars Operon of Escherichia coli Confers Arsenical and Antimonial Resistance]". ''Journal of Bacteriology'' '''177(4)''': 981-986<br />
<br />
;Chen 1997 {{anchor|Chen1997}}<br />
:{{star}} Yanxiang Chen and Barry P. Rosen (May 1997). "[http://www.ncbi.nlm.nih.gov/pubmed/9162059 Metalloregulatory Properties of the ArsD Repressor]". ''The Journal of Biological Chemistry'' '''272(22)''': 14257-14262<br />
<br />
;Chen 1997-2 {{anchor|Chen1997-2}}<br />
:Chen S, Wilson DB. (1997). "[http://www.ncbi.nlm.nih.gov/pubmed/9342882 Genetic engineering of bacteria and their potential for Hg2+ bioremediation] ". ''Biodegradation'' '''8(2)''': 97-103<br />
<br />
;Chen 1998 {{anchor|Chen1998}}<br />
:Chen S, Kim E, Shuler ML, Wilson DB. (1998). "[http://www.ncbi.nlm.nih.gov/pubmed/9758654 Hg2+ removal by genetically engineered Escherichia coli in a hollow fiber bioreactor]". ''Biotechnol Prog. '' '''14(5)''':667-671<br />
<br />
;Chen 2008 {{anchor|Chen2008}}<br />
:Chen P.R. & He C., (March 2008) "[http://dx.doi.org/10.1016/j.cbpa.2007.12.010 Selective recognition of metal ions by metalloregulatory proteins'', ''Current Opinion in Chemical Biology]". '''2008''', 12, 214–221.<br />
<br />
;Chang 1998 {{anchor|Chang1998}}<br />
:Chang CC, Liao WF, Huang PC. (1998). "[http://www.ncbi.nlm.nih.gov/pubmed/9579658 Cysteine contributions to metal binding preference for Zn/Cd in the beta-domain of metallothionein]". '' Protein Eng.'' '''11(1)''':42-46<br />
<br />
;Chang 2009 {{anchor|Chang2009}}<br />
:Yoon-Young Chang, Seung-Mok Lee, Jae-Kyu Yang, (August 2009). "[http://dx.doi.org/10.1016/j.colsurfa.2009.06.017 Removal of As(III) and As(V) by natural and synthetic metal oxides]". ''Colloids and Surfaces A: Physicochemical and Engineering Aspects'' '''346(1-3)''': 202-207<br />
<br />
;Chopra, PK, A2006{{anchor|Chopra, PK, A2006}}<br />
:Chopra, PK, A(2006). "[http://www.ncbi.nlm.nih.gov/pubmed/17274769?dopt=Abstract Engineering life through Synthetic Biology]".''In silico Biology. '' '''0038(6)''':<br />
<br />
;Cleland, CE, et al.2002{{anchor|Cleland, CE, et al.2002}}<br />
:Cleland, CE, et al.(2002). "[http://www.springerlink.com/content/hl14401v6rq7010r/ Defining 'life']".''Origins of Life and Evolution of the Biosphere. '' '''4(32)''':387-393<br />
<br />
;Deng 2003 {{anchor|Deng2003}}<br />
:Deng X, Li QB, Lu YH, Sun DH, Huang YL, Chen XR. (2003). "[http://www.ncbi.nlm.nih.gov/pubmed/12727263 Bioaccumulation of nickel from aqueous solutions by genetically engineered Escherichia coli.]". '' Water Res.'' '''37(10)''':2505-2511<br />
<br />
;Deng 2007 {{anchor|Deng2007}}<br />
:Deng X, Yi XE, Liu G. (2007). "[http://www.ncbi.nlm.nih.gov/pubmed/16890348 Cadmium removal from aqueous solution by gene-modified Escherichia coli JM109]". '' Journal Hazard Mater. '' '''139(2)''':340-344<br />
<br />
;Deng 2008 {{anchor|Deng2008}}<br />
:Deng X, Hu ZL, Yi XE. (May 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/17920767 Continuous treatment process of mercury removal from aqueous solution by growing recombinant E. coli cells and modeling study]". '' Journal Hazard Mater. '' '''153(1-2)''':487-492<br />
<br />
;Deplazes, A2009{{anchor|Deplazes, A2009}}<br />
:Deplazes, A(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19415076?dopt=Abstract Piecing together a puzzle An exposition of synthetic biology]".''Embo Reports. '' '''5(10)''':428-432<br />
<br />
;Dey 1995 {{anchor|Dey1995}}<br />
:Saibal Dey, Barry P. Rosen (1995). "[http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=176602 Dual Mode of Energy Coupling by the Oxyanion Translocating ArsB Protein]". ''JOURNAL OF BACTERIOLOGY'' '''177(2)''': 385–389<br />
<br />
;Dong 2008 {{anchor|Dong2008}}<br />
:Dong, Liangjie (December 2008). "[http://www.freepatentsonline.com/y2008/0311288.html Methods and Compositions for Removal of Arsenic and Heavy Metals From Water]". ''United States Patent Application 20080311288 Kind Code:A1 <br />
''<br />
<br />
;EPA 2000 {{anchor|EPA2000}}<br />
:Environmental Protection Agency (December 2000). "[http://www.epa.gov/safewater Technologies and Costs for Removal of Arsenic from Drinking Water]". ''EPA 815-R-00-028'' <br />
<br />
;Ettema 2006 {{anchor|Ettema2006}}<br />
:Thijs J. G. Ettema, Arie B. Brinkman ''et al'' (2006). "[http://dx.doi.org/10.1099/mic.0.28724-0 Molecular characterization of a conserved archaeal copper resistance (cop) gene cluster and its copper-responsive regulator in Sulfolobus solfataricus P2]". ''Microbiology '''152''': 1969-1979<br />
<br />
;Fowler 1987 {{anchor|Fowler1987}}<br />
:Fowler BA. (1987). "[http://www.ncbi.nlm.nih.gov/pubmed/3297654 Intracellular compartmentation of metals in aquatic organisms: roles in mechanisms of cell injury]". '' Environ Health Perspect.'' '''7(1)''': 121-128<br />
<br />
;Fosmire 1990 {{anchor|Fosmire1990}}<br />
:Fosmire GA. (1990). "[http://www.ncbi.nlm.nih.gov/pubmed/2407097 Zinc toxicity]". ''American Society for Clinical Nutrition.'' '''5l''': 225-227<br />
<br />
;Frankenberger 2001 {{anchor|Frankenberger2001}}<br />
:William T. Frankenberger Jr. (2001). ''Environmental Chemistry of Arsenic'', Marcel Dekker, New York, NY, 404 pp. ISBN 0-8247-0676-5<br />
<br />
;Fu, DX, et al.2000{{anchor|Fu, DX, et al.2000}}<br />
:Fu, DX, et al.(2000). "[http://www.ncbi.nlm.nih.gov./pubmed/11039922?dopt=Abstract Structure of a glycerol-conducting channel and the basis for its selectivity]".''Science. '' '''5491(290)''':481-486<br />
<br />
;Gilchrist 2007 {{anchor|Gilchrist2007}}<br />
:Michael A. Gilchrist (2007). "[http://dx.doi.org/10.1093/molbev/msm169 Combining Models of Protein Translation and Population Genetics to Predict Protein Production Rates from Codon Usage Patterns]". ''Molecular Biology and Evolution'' '''24(11)''': 2362-2372<br />
<br />
;Gold 2008 {{anchor|Gold2008}}<br />
:Gold B, Deng H, ''et al''(2008). "[http://www.ncbi.nlm.nih.gov/pubmed/18724363 Identification of a copper-binding metallothionein in pathogenic mycobacteria]". ''Nat Chem Biol.'' '''4(10)''': 609-616<br />
<br />
;Goudar 1999 {{anchor|Goudar1999}}<br />
:Chetan T. Goudara, Jagadeesh R. Sonnadb and Ronald G. Duggleby (January 1999). "[http://dx.doi.org/10.1016/S0167-4838(98)00247-7 Parameter estimation using a direct solution of the integrated Michaelis-Menten equation]". ''Biochimica et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology'' '''1429(2)''': 377-383<br />
<br />
;Guven 2007 {{anchor|Guven2007}}<br />
:Basak Guven and Alan Howarda (September 2007). "[http://dx.doi.org/doi:10.1016/j.ecolmodel.2007.03.024 Identifying the critical parameters of a cyanobacterial growth and movement model by using generalised sensitivity analysis]". ''Ecological Modelling'' '''207(1)''': 11-21<br />
<br />
;Heller, KB, et al.1980{{anchor|Heller, KB, et al.1980}}<br />
:Heller, KB, et al.(1980). "[http://www.ncbi.nlm.nih.gov/pubmed/6998951?dopt=Abstract Substrate-Specificity and Transport-Properties of the Glycerol Facilitator of Escherichia-Coli]".''Journal of Bacteriology. '' '''1(144)''':274-278<br />
<br />
;Hirose 2006 {{anchor|Hirose2006}}<br />
:Hirose K, Ezaki B, Tong L Nakashima S, ''et al'' (August 2005) "[http://dx.doi.org/10.1016/j.toxlet.2005.11.008 Diamide stress induces a metallothionein BmtA through a repressor BxmR and is modulated by Zn-inducible BmtA in the cyanobacterium Oscillatoria brevis]". ''Toxicology Letters, '''2006''', 163, 250–256.<br />
<br />
;Hoefnagel 2002 {{anchor|Hoefnagel2002}}<br />
:M.H.N. Hoefnagel, A. van der Burgt, D.E. Martens, ''et al'' (March 2002). "[http://dx.doi.org/10.1023/A:1020313409954 Time Dependent Responses of Glycolytic Intermediates in a Detailed Glycolytic Model of ''Lactococcus Lactis'' During Glucose Run-Out Experiments]". ''Molecular Biology Reports'' '''29''': 157-161<br />
<br />
;Holland 2009 {{anchor|Holland2009}}<br />
:Daryl P. Holland, Anthony E. Walsby (January 2009). "[http://dx.doi.org/10.1016/j.mimet.2009.02.005 Digital recordings of gas-vesicle collapse used to measure turgor pressure and cell–water relations of cyanobacterial cells ]". ''Journal of Microbiological Methods'' '''77''': 214-224<br />
<br />
;Hristovski 2007 {{anchor|Hristovski2007}}<br />
:Kiril Hristovski, Andrew Baumgardner, Paul Westerhoff, (August 2007). "[http://dx.doi.org/10.1016/j.jhazmat.2007.01.017 Selecting metal oxide nanomaterials for arsenic removal in fixed bed columns: From nanopowders to aggregated nanoparticle media]". Journal of Hazardous Materials'' '''147(1-2)''': 265-274 <br />
<br />
;Kao 2008 {{anchor|Kao2008}}<br />
:Kao WC, Huang CC, Chang JS (October 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/18313216 Biosorption of nickel, chromium and zinc by MerP-expressing recombinant Escherichia coli.]". '' J Hazard Mater.'' '''158(1)''': 100-106<br />
<br />
;Kelle, A2009{{anchor|Kelle, A2009}}<br />
:Kelle, A(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19636299?dopt=Abstract Synthetic biology and biosecurity From low levels of awareness to a comprehensive strategy]".''Embo Reports. '' 10)''':S23-S27<br />
<br />
;Kelly 2009 {{anchor|Kelly2009}}<br />
:Jason R. Kelly, Adam J. Rubin, Joseph H. Davis, ''et al'' (March 2009). "[http://dx.doi.org/10.1186/1754-1611-3-4 Measuring the activity of BioBrick promoters using an in vivo reference standard]". ''Journal of Biological Engineering'' '''3''': 4<br />
<br />
;Khunajakr 1999 {{anchor|Khunajakr1999}}<br />
:Nongpanga Khunajakr, Chun-Qiang Liu ''et al'' (March 1999). "[http://dx.doi.org/10.1016/S0378-1119(98)00395-3 A plasmid-encoded two-component regulatory system involved in copper-inducible transcription in Lactococcus lactis]". ''Gene'''229(1-1)''': 229-235<br />
<br />
;Klaassen 1994 {{anchor|Klaassen1994}}<br />
:Klaassen, Curtis D., Supratim Choudhuri, James M. McKim, Jr., Lois D. Lehman-McKeeman, and William C. Kershaw (1994). [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1567434/ "In Vitro and In Vivo Studies on the Degradation of Metallothionein"]. ''Environ. Health Perspect'' '''102(3)''': 141-146.<br />
<br />
;Kloosterman 2008 {{anchor|Kloosterman2008}}<br />
:Tomas G. Kloosterman, Robert M. Witwicki ''et al'' (2008). "[http://dx.doi.org/10.1128/JB.00307-08 Opposite Effects of Mn2+ and Zn2+ on PsaR-Mediated Expression of the Virulence Genes pcpA, prtA, and psaBCA of Streptococcus pneumonia]". ''J Bacterio'''190(15)''': 5382–5393<br />
<br />
;Kostal 2004 {{anchor|Kostal2004}}<br />
:{{star}} Jan Kostal, Rosanna Yang, Cindy H. Wu, ''et al'' (August 2004). "[http://dx.doi.org/10.1128/AEM.70.8.4582-4587.2004 Enhanced Arsenic Accumulation in Engineered Bacterial Cells Expressing ArsR]". ''Applied and Environmental Microbiology'' 70(8): 4582–4587<br />
<br />
;Lewinson 2009 {{anchor|Lewinson2009}}<br />
:Lewinson O, Lee AT, Rees DC. (2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19264958 A P-type ATPase importer that discriminates between essential and toxic transition metals]". '' PNAS'' 106(12): 4677-4682<br />
<br />
;Li 1998 {{anchor|Li1998}}<br />
:{{star}} Ning Li and Maura C. Cannon (May 1998). "Gas Vesicle Genes Identified in Bacillus megaterium and Functional Expression in Escherichia coli". ''Journal of Bacteriology'' '''180(9)''': 2450–2458<br />
<br />
;Lin 2007-1 {{anchor|Lin2007-1}}<br />
:Yung-Feng Lin, Jianbo Yang and Barry P. Rosen (April 2007). "[http://dx.doi.org/10.1074/jbc.M700886200 ArsD Residues Cys12, Cys13, and Cys18 Form an As(III)-binding Site Required for Arsenic Metallochaperone Activity]". ''The Journal of Biological Chemistry'' '''282(23)''': 16783–16791<br />
<br />
;Lin 2007-2 {{anchor|Lin2007-2}}<br />
:Yung-Feng Lin, Jianbo Yang and Barry P. Rosen (December 2007). "[http://dx.doi.org/10.1007/s10863-007-9113-y ArsD: an As(III) metallochaperone for the ArsAB As(III)-translocating ATPase]". ''Journal of Bioenergetics and Biomembranes'' '''39''': 453-458<br />
<br />
;Liu 2004 {{anchor|Liu2004}}<br />
:Tong Liu, Susumu Nakashima ''et al'' (April 2004) "[http://dx.doi.org/10.1074/jbc.M310560200 A Novel Cyanobacterial SmtB/ArsR Family Repressor Regulates the Expression of a CPx-ATPase and a Metallothionein in Response to Both Cu(I)/Ag(I) and Zn(II)/Cd(II)]". ''The Journal of Biological Chemistry, '''2004''', Vol. 279, No. 17, 17810–17818.<br />
<br />
;Liu 2006 {{anchor|Liu2006}}<br />
:Tong Liu Arati Ramesh ''et al''(December 2006). "[http://dx.doi.org/10.1038/nchembio844 CsoR is a novel Mycobacterium tuberculosis copper-sensing transcriptional regulator]". ''Nature Chemical Biology'' '''3''': 60-68<br />
<br />
;Liu 2008 {{anchor|Liu2008}}<br />
:Tong Liu, Xiaohua Chen, Zhen Ma, ''et al'' (September 2008) "[http://dx.doi.org/10.1021/bi801313y A CuI-sensing ArsR family Metal Sensor Protein with a Relaxed Metal Selectivity Profile]". ''Biochemistry, '''2008''', 47(40), 10564–10575.<br />
<br />
; Lundstrom (2006) {{anchor|Lundstom2006}}<br />
:Lundstrom, K. (2006). “[http://www.springerlink.com/content/23783l53l616238t/ Structural genomics for membrane proteins]” ''Cell. Mol. Life Sci.'' '''63: 2597–2607'''.<br />
<br />
;Martinson 2009 {{anchor|Martinson2009}}<br />
:Carol A. Martinson, K.J. Reddy, (August 2009). "[http://dx.doi.org/10.1016/j.jcis.2009.04.075 Adsorption of arsenic(III) and arsenic(V) by cupric oxide nanoparticles]". ''Journal of Colloid and Interface Science'' '''336(2)''': 406-411<br />
<br />
;Meng, YL, et al.2004{{anchor|Meng, YL, et al.2004}}{{anchor|Meng2004}}:Meng, YL, et al.(2004). ” [http://dx.doi.org/10.1074/jbc.M400037200 As(III) and Sb(III) uptake by G1pF and efflux by ArsB in Escherichia coli]".''Journal of Biological Chemistry. '' '''18(279)''':18334-18341<br />
<br />
;Merrifield 2004 {{anchor| Merrifield2004}}<br />
:M. E. Merrifield, T. Ngu, M. J. Stillman ''et al'' (September 2004). "[http://www.ncbi.nlm.nih.gov/pubmed/15464992 Arsenic binding to <i>Fucus vesiculosus</i> metallothionein.]". ''Biochemical and Biophysical Research Communications'' '''324 :''' 127–132<br />
<br />
;Mills 1994 {{anchor|Mills1994}}<br />
:Scott D. Mills Chun-Keun Lim and Donald A. Cooksey (1994). "[http://dx.doi.org/10.1007/BF00286685 Purification and characterization of CopR, a transcriptional activator protein that binds to a conserved domain (cop box) in copper- inducible promoters of Pseudomonas syringae]". ''Molecular and General Genetics MGG '''244(4)''': 1432-1874<br />
<br />
;Mindlin, SZ, et al.2002{{anchor|Mindlin, SZ, et al.2002}}:Mindlin, SZ, et al.(2002). "[http://dx.doi.org/10.1023/A:1015353402657 Horizontal transfer of mercury resistance genes in environmental bacterial populations]".''Molecular Biology. '' '''2(36)''':160-170<br />
<br />
;Moore 2005 {{anchor|Moore2005}}<br />
:Charles M. Moore, Ahmed Gaballa ''et al'' (May 2005). "[http://dx.doi.org/10.1111/j.1365-2958.2005.04642.x Genetic and physiological responses of Bacillus subtilis to metal ion stress]". ''Molecular Microbiology'''57(1)''': 27-40<br />
<br />
;Morris 1999 {{anchor| Morris1999}}<br />
:C.A. Morris, B. Nicolaus, V. Sampson ''et al'' (March 1999). "[http://www.ncbi.nlm.nih.gov/pubmed/10024535 Identification and characterization of a recombinant metallothionein protein from a marine alga, <i>Fucus vesiculosus</i>]". '' The Biochemical journal'' '''338(2):''' 553-560<br />
<br />
;Nawapan 2009 {{anchor|Nawapan2009}}<br />
:Sirikan Nawapan, Nisanart Charoenlap ''et al'' (August 2009). "[http://dx.doi.org/10.1046/10.1128/JB.00384-09 Functional and Expression Analyses of the cop Operon, Required for Copper Resistance in Agrobacterium tumefaciens]". ''American Society for Microbiology '''191(16)''': 5159-5168<br />
<br />
;Neves 1999 {{anchor|Neves1999}}<br />
:Ana Rute Neves, Ana Ramos, Marta C. Nunes, ''et al'' (1999). "[http://dx.doi.org/10.1002/(SICI)1097-0290(19990720)64%3A2%3C200%3A%3AAID-BIT9%3E3.0.CO%3B2-K In vivo nuclear magnetic resonance studies of glycolytic kinetics in ''Lactococcus lactis'']". ''Biotechnology and Bioengineering'' '''64''': 200-212<br />
<br />
;Ngu 2006 {{anchor|Ngu2006}}<br />
:Thanh T. Ngu, M. Stillman (April 2006). "[http://dx.doi.org/10.1021/ja062914c Arsenic Binding to Human Metallothionein]". ''J. Am. Chem. Soc'' '''128 (38)''': 12473–12483<br />
<br />
;Ngu 2009 {{anchor|Ngu2009}}<br />
:Thanh T. Ngu, J. A. Lee ''et al''. (April 2009). "[http://dx.doi.org/10.1021/bi9007462 Arsenic Metalation of Seaweed ''Fucus vesiculosus'' Metallothionein: The importance of the Interdomain Linker in Metallothionein]". ''Biochemistry'' '''48''': 8806–8816<br />
<br />
;Nicholls, H2008{{anchor|Nicholls, H2008}}<br />
:Nicholls, H(2008). "[http://dx.doi.org/10.1016/S0140-6736(08)61881-4 Synthetic biology]".''Lancet. '' S45-S49<br />
<br />
;Nouri, A, et al.2009{{anchor|Nouri, A, et al.2009}}<br />
:Nouri, A, et al.(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19270668?dopt=Abstract Proliferation-resistant biotechnology: an approach to improve biological security]".''Nature Biotechnology. '' '''3(27)''':234-236<br />
<br />
;Oehmen 2006 {{anchor|Oehmen2006}}<br />
:Adrian Oehmen, Rui Viegas, Svetlozar Velizarov, ''et al'' (November 2006). "[http://dx.doi.org/10.1016/j.desal.2006.03.091 Removal of heavy metals from drinking water supplies through the ion exchange membrane bioreactor]". ''Desalination'' '''199(1-3)''': 405-407 <br />
<br />
;Outten 2000 {{anchor|Outten2000}}<br />
:F. Wayne Outten, Caryn E. Outten, Jeremy Hale and Thomas V. O’Halloran (October 2000). "[http://dx.doi.org/10.1074/jbc.M006508200 Transcriptional Activation of an ''Escherichia coli'' Copper Efflux Regulon by the Chromosomal MerR Homologue, CueR]". ''The Journal of Biological Chemistry'' '''275(40)''': 31024-31029<br />
<br />
;Pennella 2005 {{anchor|Pennella2005}}<br />
:Pennella M.A. & Giedroc D.P., (August 2005) "[http://dx.doi.org/10.1007/s10534-005-3716-8 Structural determinants of metal selectivity in prokaryotic metal-responsive transcriptional regulator]". ''BioMetals, '''2005''', 18, 413–428.<br />
<br />
;Poole 1977 {{anchor|Poole1977}}<br />
:R.K. Poole (1977). "[http://mic.sgmjournals.org/cgi/content/abstract/98/1/177 Fluctuations in Buoyant Density during the Cell Cycle of Escherichia coli K12]". ''Journal of General Microbiology'' '''98''': 177-186<br />
<br />
;Porquet, A, et al.2007{{anchor|Porquet, A, et al.2007}}<br />
:Porquet, A, et al.(2007). “[http://www.ncbi.nlm.nih.gov./pubmed/17713961?dopt=Abstract Structural evidence of the similarity of Sb(OH)(3) and As(OH)(3) with glycerol: Implications for their uptake]".''Chemical Research in Toxicology. '' '''9(20)''':1269-1276<br />
<br />
;Raje 2005 {{anchor|Raje2005}}<br />
:N. Raje,* K. K. Swain (April 2005). "[http://dx.doi.org/10.1023/A:1015812517214 Purification of arsenic contaminated ground water using hydrated manganese dioxide]". ''Journal of Radioanalytical and Nuclear Chemistry'' '''253(1)''': 77-80<br />
<br />
;Rawlings 1994 {{anchor| Rawlings1994}}<br />
:RAWLINGS, D E. and KUSANO, T (1994). “[http://mmbr.asm.org/cgi/reprint/58/1/39?view=long&pmid=8177170 Molecular Genetics of Thiobacillus ferrooxidans]”. ‘’MICROBIOLOGICAL REVIEWS’’, ‘’’58 (1): 39-55’’’<br />
<br />
;Rensing 2005 {{anchor|Rensing2005}}<br />
:Christopher Rensing (June 2005). "[http://dx.doi.org/10.1128/JB.187.12.3909-3912.2005 Form and Function in Metal-Dependent Transcriptional Regulation: Dawn of the Enlightenment]". ''Journal of Bacteriology'' '''187(12)''': 3909–3912<br />
<br />
;Robinson 2001 {{anchor|Robinson2001}}<br />
:Nigel J. Robinson, Simon K. Whitehall and Jennifer S. Cavet (2001). "[http://www.ncbi.nlm.nih.gov/pubmed/11407113 Microbial Metallothioneins]". ''Advances in Microbial Physiology'' '''44''': 183-213<br />
<br />
;Rosen 1996 {{anchor|Rosen1996}}<br />
:Barry P. Rosen (August 1996). "[http://dx.doi.org/10.1007/s007750050053 Bacterial resistance to heavy metals and metalloids]". ''Journal of Biological Inorganic Chemistry'' '''1(4)''': 273-277<br />
<br />
;Rosen, BR, et al.2009{{anchor|Rosen, BR, et al.2009}}{{anchor|Rosen2009}}<br />
:Rosen, BR, et al.(2009). “[http://dx.doi.org/10.1007/s007750050053 Transport pathways for arsenic and selenium: A minireview]".''Environment International. '' '''3(35)''':512-515<br />
<br />
;Samuel, GN, et al.2009{{anchor|Samuel, GN, et al.2009}}<br />
:Samuel, GN, et al.(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19079130?dopt=Abstract Managing the unimaginable Regulatory responses to the challenges posed by synthetic biology and synthetic genomics]".''Embo Reports. '' '''1(10)''':7-11<br />
<br />
;Schmidt, M 2008 {{anchor|Schmidt2008}}<br />
:Schmidt, M (2008). "[http://dx.doi.org/10.1007/s11693-008-9018-z Diffusion of synthetic biology: a challenge to biosafety]", ''Syst Synth Biol.''<br />
<br />
;Schwartz 2008 {{anchor|Schwartz2008}}<br />
:Russel Schwartz (2008). ''Biological modeling and simulation: a survey of practical models, algorithms, and numerical methods'' MIT Press. ISBN 978-0-262-19584-3<br />
<br />
;Serrano, L2007{{anchor|Serrano, L2007}}<br />
:Serrano, L(2007). "[http://www.ncbi.nlm.nih.gov/pubmed/18091727?dopt=Abstract Synthetic biology: promises and challenges]".''Molecular Systems Biology. '' 3)''':<br />
<br />
;Shi 1992 {{anchor|Shi1992}}<br />
:Jianguo Shi, William P. Lindsay, James W. Huckle (June 1992). "[http://dx.doi.org/10.1016/0014-5793(92)80509-F Cyanobacterial metallothionein gene expressed in Escherichia coli: Metal-binding properties of the expressed protein]". ''FEBS Letters'' '''303(2-3)''': 159-163<br />
<br />
;Singh 2008 {{anchor|Singh2008}}<br />
:Shailendra Singh, Ashok Mulchandani, Wilfred Chen (February 2008). "[http://dx.doi.org/10.1128/AEM.02871-07 Highly Selective and Rapid Arsenic Removal by Metabolically Engineered Escherichia coli Cells Expressing Fucus vesiculosus Metallothionein]". ''MICROBIOLOGY'' '''74(9)''': 2924–2927<br />
<br />
;Sivertsen 2008 {{anchor|Sivertsen2008}}<br />
:Astrid C. Sivertsen, Marvin J. Bayro, ''et al'' ( april 2008). "[http://dx.doi.org/doi:10.1016/j.jmb.2009.02.015 Solid-State NMR Evidence for Inequivalent GvpA Subunits in Gas Vesicles]". ''Journal of Molecular Biology'' '''387(4)''': 1032-1039<br />
<br />
;Stephan Hug {{anchor|Stephan Hug}}<br />
:Stephan Hug. "[http://www.eawag.ch/publications/eawagnews/www_en49/en49e_ihv_web.html Arsenic Contamination of Ground Water: Disastrous Consequences in Bangladesh]". ''EAWAG news'' '''49(e)''': 18-20<br />
<br />
;Stephenson, JR, et al.1996 {{anchor|Stephenson, JR, et al.1996}}:Stephenson, JR, et al.(1996). "[http://dx.doi.org/10.1002 Release of genetically modified micro-organisms into the environment]".''Journal of Chemical Technology and Biotechnology. '' '''1(65)''':5-14<br />
<br />
;Summers 2009 {{anchor|Summers2009}}<br />
:Anne O. Summers (April 2009). "[http://dx.doi.org/10.1016/j.mib.2009.02.003 Damage control: regulating defenses against toxic metals and metalloids]". ''Current Opinion in Microbiology'' '''12(2)''': 138-144<br />
<br />
;Suzuki 1998 {{anchor|Suzuki1998}}<br />
:Katsuhisa Suzukia, Norio Wakaob, Tetsuya Kimuraa, Kazuo Sakkaa and Kunio Ohmiya (February 1998). "[http://dx.doi.org/10.1016/S0922-338X(98)80016-0 Metalloregulatory properties of the ArsR and ArsD repressors of ''Acidiphilium multivorum'' AIU 301]". ''Journal of Fermentation and Bioengineering'' '''85(6)''': 623-626<br />
<br />
;Thelwell 1998 {{anchor|Thelwell1998}}<br />
:Thelwell C., Robinson N.J. & Turner-Cavet J.S., "[http://dx.doi.org/10.1073/pnas.95.18.10728 An SmtB-like repressor from Synechocystis PCC 6803 regulates a zinc exporter]". ''Proc. Natl. Acad. Sci. USA, '''1998''', Vol. 95, 10728–10733.<br />
<br />
;Tisa 1989 {{anchor|Tisa1989}}<br />
:Louis S. Tisa and Barry P. Rosen (January 1990). "[http://www.ncbi.nlm.nih.gov/pubmed/1688427 Molecular characterization of an anion pump. The ArsB protein is the membrane anchor for the ArsA protein]". ''The journal of biological chemistry'' '''265(1)''': 190-194<br />
<br />
;Turner 1995 {{anchor|Turner1995}}<br />
:Jennifer S. Turner, Nigel J. Robinson and Amit Gupta (March 1995). "[http://dx.doi.org/10.1007/BF01569937 Construction of Zn<sup>2+</sup>/Cd<sup>2+</sup>-tolerant cyanobacteria with a modified metallothionein divergon: Further analysis of the function and regulation of ''smt'']". ''Journal of Industrial Microbiology and Biotechnology'' '''14(3-4)''': 259-264<br />
<br />
;Walsby 1979 {{anchor|Walsby1979}}<br />
:A.E. Walsby (April 1979). "[http://dx.doi.org/10.1016/0022-2836(79)90281-X Average thickness of the gas vesicle wall in Anabaena flos-aquae]". ''Journal of Molecular Biology'' '''129(2)''': 279-285<br />
<br />
;Walsby 1994 {{anchor|Walsby1994}}<br />
:A.E. Walsby (March 1994). "[http://www.ncbi.nlm.nih.gov/pubmed/8177173 Gas Vesicles]". ''Microbiological reviews'' '''58(1)''': 94-144<br />
<br />
;Wlckramaslnghe 2004 {{anchor|Wlckramaslnghe2004}}<br />
:S.R. Wlckramaslnghe, Binbing Han, J. Zimbron, ''et al'' (October 2004). "[http://dx.doi.org/10.1016/j.desal.2004.03.013 Arsenic removal by coagulation and filtration: comparison of groundwaters from the United States and Bangladesh]". ''Desalination'' '''169(3)''': 231-244 <br />
<br />
;Xu 1996 {{anchor|Xu1996}}<br />
:Chun Xu, Weiping Shi and Barry P. Rosen (February 1996). "[http://dx.doi.org/10.1074/jbc.271.5.2427 The Chromosomal ''arsR'' Gene of ''Escherichia coli'' Encodes a ''trans''-acting Metalloregulatory Protein]". ''The Journal of Biological Chemistry'' '''271(5)''': 2427-2432<br />
<br />
;Yamamoto 2005 {{anchor|Yamamoto2005}}<br />
:Kaneyoshi Yamamoto and Akira Ishihama (2005). "[http://dx.doi.org/10.1111/j.1365-2958.2005.04532.x Transcriptional response of ''Escherichia coli'' to external copper]". ''Molecular Microbiology'' '''56(1)''': 215-227<br />
<br />
;Zwart, SD, et al.2006{{anchor|Zwart, SD, et al.2006}}:Zwart, SD, et al.(2006). "[http://dx.doi.org/10.1007/s11948-006-0063-2 network approach for distinguishing ethical issues in research and development]".''Science and Engineering Ethics. '' '''4(12)''':663-684<br />
<br />
<br />
<br />
Miscellaneous:<br />
* [http://ginkgobioworks.com/cgi/primer.cgi Primer design Bioworks]<br />
* [http://openwetware.org/wiki/The_BioBricks_Foundation:Standards/Technical/Measurement Promotor measurement]<br />
* [http://openwetware.org/wiki/Main_Page OpenWetWare]<br />
* [http://www.hgsc.bcm.tmc.edu/projects/microbial/microbial-detail.xsp?project_id=105 E. coli DH10B genome] (with BLAST)<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/LiteratureTeam:Groningen/Literature2009-10-21T22:07:34Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
<div style="float:left" >{{linkedImage|GroningenPrevious.png|Team:Groningen/Glossary}}</div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Protocols}}</div><br />
<br />
[[Category:Team:Groningen]]<br />
<br />
==Literature==<br />
Buoyancy related literature:<br />
*Buoyant density: [[Team:Groningen/Literature#Poole1977|Poole 1977]], [[Team:Groningen/Literature#Bylund1991|Bylund 1991]], '''[[Team:Groningen/Literature#Baldwin1995|Baldwin 1995]]'''<br />
*Gas vesicles: [[Team:Groningen/Literature#Bowen1965|Bowen 1965]], [[Team:Groningen/Literature#Walsby1979|Walsby 1979]], '''[[Team:Groningen/Literature#Walsby1994|Walsby 1994]]''', '''[[Team:Groningen/Literature#Li1998|Li 1998]]''', [[Team:Groningen/Literature#Sivertsen2008|Sivertsen 2008]], [[Team:Groningen/Literature#Holland2009|Holland 2009]]<br />
<br />
Ohter methods of arsenic purification.<br />
*General information about the subject:[[Team:Groningen/Literature#Frankenberger2001|Frankenberger 2001]],[[Team:Groningen/Literature#Stephan Hug|Stephan Hug]],[[Team:Groningen/Literature#Wlckramaslnghe2004|Wlckramaslnghe 2004]],[[Team:Groningen/Literature#Dong2008|Dong 2008]],'''[[Team:Groningen/Literature#EPA2000|EPA 2000]]''',<br />
*Ion exchange and Membranes:[[Team:Groningen/Literature#Oehmen2006|Oehmen 2006]],<br />
*Nanomaterials:[[Team:Groningen/Literature#Hristovski2007|Hristovski 2007]],[[Team:Groningen/Literature#Martinson2009|Martinson 2009]],[[Team:Groningen/Literature#Chang2009|Chang 2009]],<br />
*Precipitative Processes:[[Team:Groningen/Literature#Raje2005|Raje 2005]],<br />
<br />
Our metal related literature by subject:<br />
{|border="1" <br />
!<br />
!<br />
!Cu<br />
!Zn<br />
!As<br />
!Cd<br />
!Sb<br />
!Hg<br />
|-<br />
!rowspan="2" |Importers<br />
!GlpF<br />
|<br />
|<br />
|'''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Rosen2009|Rosen 2009]]<br />
|<br />
|'''[[Team:Groningen/Literature#Meng2004|Meng 2004]]'''<br />
|<br />
|-<br />
!{{part|BBa_K190018|HmtA}}<br />
|[[Team:Groningen/Literature#Lewinson2009|Lewinson 2009]]<br />
|[[Team:Groningen/Literature#Lewinson2009|Lewinson 2009]]<br />
|<br />
|<br />
|<br />
|-<br />
!rowspan="1" |Exporters<br />
!ArsB<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Tisa1989|Tisa 1989]], [[Team:Groningen/Literature#Carlin1995|Carlin 1995]],<br />
[[Team:Groningen/Literature#Dey1995|Dey 1995]] [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|[[Team:Groningen/Literature#Tisa1989|Tisa 1989]], [[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|-<br />
!rowspan="6" |Accumulators<br />
!ArsR<br />
|<br />
|<br />
||[[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Chen1997|Chen 1997]]''', '''[[Team:Groningen/Literature#Kostal2004|Kostal 2004]]''', [[Team:Groningen/Literature#Rensing2005|Rensing 2005]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
||[[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
<br />
|<br />
|-<br />
!ArsD<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Chen1997|Chen 1997]], [[Team:Groningen/Literature#Lin2007-1|Lin 2007-1/2]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|[[Team:Groningen/Literature#Chen1997|Chen 1997]], [[Team:Groningen/Literature#Lin2007-1|Lin 2007-1/2]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|-<br />
!SmtA<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]], [[Team:Groningen/Literature#Turner1995|Turner 1995]], [[Team:Groningen/Literature#Robinson2001|Robinson 2001]], [[Team:Groningen/Literature#Blindauer2002|Blindauer 2002]]<br />
|<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|-<br />
!MymT<br />
|[[Team:Groningen/Literature#Gold2008|Gold 2008]]<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
!MT<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Morris1999|Morris 1999]],[[Team:Groningen/Literature#Ngu2006|Ngu 2006]],[[Team:Groningen/Literature#Singh2008|Singh 2008]], [[Team:Groningen/Literature#Merrifield2004|Merrifield 2004]], [[Team:Groningen/Literature#Ngu2009|Ngu 2009]]<br />
|[[Team:Groningen/Literature#Deng2007|Deng 2007]]<br />
|<br />
|[[Team:Groningen/Literature#Chen1998|Chen1998]]<br />
|-<br />
!Unclassified<br />
|[[Team:Groningen/Literature#Brady1994|Brady 1994]]<br />
|[[Team:Groningen/Literature#Chang1998|Chang 1998]], [[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]<br />
|<br />
|[[Team:Groningen/Literature#Brady1994|Brady 1994]], [[Team:Groningen/Literature#Chang1998|Chang 1998]], <br />
|<br />
|[[Team:Groningen/Literature#Deng2008|Deng 2008]]<br />
|-<br />
!rowspan="1" |Promoters<br />
!<br />
|[[Team:Groningen/Literature#Mills1994|Mills 1994 ]], [[Team:Groningen/Literature#Khunajakr1999 |Khunajakr 1999]], [[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore 2005]], [[Team:Groningen/Literature#Ettema2006 |Ettema2006 ]], [[Team:Groningen/Literature#Liu2006|Liu 2006]], [[Team:Groningen/Literature#Liu2008|Liu 2008]], [[Team:Groningen/Literature#Catini2008|Catini 2008]], [[Team:Groningen/Literature#Nawapan2009|Nawapan 2009]]<br />
|[[Team:Groningen/Literature#Thelwell1998|Thelwell 1998]], [[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore2005]], [[Team:Groningen/Literature#Hirose2006 |Hirose 2006]], [[Team:Groningen/Literature#Kloosterman2008|Kloosterman 2008]]<br />
|[[Team:Groningen/Literature#Summers2009 |Summers 2009]]<br />
|[[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore 2005]]<br />
|<br />
|<br />
|}<br />
<br />
;Alon 2007 {{anchor|Alon2007}}<br />
:{{star}} Uri Alon (2007). ''Introduction to systems biology: design principles of biological circuits'' Chapman & Hall/CRC. ISBN 978-1-58488-642-6<br />
<br />
;Baldwin 1995 {{anchor|Baldwin1995}}<br />
:W.W. Baldwin, Richard Myer, Nicole Powell, ''et al'' (August 1995). "[http://www.springerlink.com/content/nu1lkduf3w89fmd8 Buoyant density of Escherichia coli is determined solely by the osmolarity of the culture medium]". ''Archives of Microbiology'' '''164(2)''': 155-157<br />
<br />
;Beltramini 1981 {{anchor| Beltramini1981}}<br />
:M. Beltramini and K. Lerch (1981). "[http://www.ncbi.nlm.nih.gov/pubmed/6453726 Luminescence Properties of ''Neurospora'' Copper Metallothionein]". ''FEBS Letters'' '''127(2)''': 201-203<br />
<br />
;Beyer 2004 {{anchor|Beyer2004}}<br />
:Andreas Beyer, Jens Hollunder, Heinz-Peter Nasheuer and Thomas Wilhelm (August 2004). "[http://dx.doi.org/10.1074/mcp.M400099-MCP200 Post-transcriptional Expression Regulation in the Yeast Saccharomyces cerevisiae on a Genomic Scale]". ''Molecular & Cellular Proteomics'' '''3''': 1083-1092<br />
<br />
;Bhutkar, A2005{{anchor|Bhutkar, A2005}}<br />
:Bhutkar, A(2005). '[http://www.ncbi.nlm.nih.gov/pubmed/16538811?dopt=Abstract Synthetic Biology: Navigating the Challenges Ahead]".''The journal of Biolaw and Business. '' '''2(8)''':<br />
<br />
;Blancato 2006 {{anchor|Blancato2006}}<br />
:Blancato VS, Magni C, Lolkema JS. (October 2006). "[http://dx.doi.org/doi:10.1016/j.jmb.2009.02.015 Functional characterization and Me ion specificity of a Ca-citrate transporter from Enterococcus faecalis]". ''FEBS journal'' '''273(22)''': 5121-5130<br />
<br />
;Blindauer 2002 {{anchor|Blindauer2002}}<br />
:Claudia A. Blindauer, Mark D. Harrison, Andrea K. Robinson, ''et al'' (2002). "[http://dx.doi.org/10.1046/j.1365-2958.2002.03109.x Multiple bacteria encode metallothioneins and SmtA-like zinc fingers]". ''Molecular Microbiology'' '''45(5)''': 1421-1432<br />
<br />
;Blindauer 2001 {{anchor|Blindauer2001}}<br />
:Blindauer CA, Harrison MD, ''et al'' (2001). "[http://www.ncbi.nlm.nih.gov/pubmed/11493688 A metallothionein containing a zinc finger within a four-metal cluster protects a bacterium from zinc toxicity.]". '' Proc Natl Acad Sci USA. '' '''98(17)''': ):9593-9598<br />
<br />
;Bowen 1965 {{anchor|Bowen1965}}<br />
:C.C. Bowen and T.E. Jensen ( March 1965). "[http://dx.doi.org/10.1126/science.147.3664.1460 Blue-Green Algae: Fine Structure of the Gas Vacuoles]". ''Science '' '''147(3664)''': 1460 - 1462<br />
<br />
;Busenlehner 2003 {{anchor|Busenlehner2003}}<br />
:Busenlehner L.S., Pennella M.A. & Giedroc D.P., (June 2003) "[http://dx.doi.org/10.1155/2006/837139 The SmtB/ArsR family of metalloregulatory transcriptional repressors: structural insights into prokaryotic metal resistance]". ''FEMS Microbiology Reviews, '''2003''', 27, 131-143.<br />
<br />
;Brady 1994 {{anchor|Brady1994}}<br />
:Brady D, Rose PD, Duncan JR. (1994). "[http://www.ncbi.nlm.nih.gov/pubmed/18618649 The use of hollow fiber cross-flow microfiltration in bioaccumulation and continuous removal of heavy metals from solution by Saccharomyces cerevisiae.]". '' Biotechnol Bioeng. '' '''44(11)''':1362-1366<br />
<br />
;Bylund 1991 {{anchor|Bylund1991}}<br />
:J.E. Bylund, M.A. Haines, K. Walsh, ''et al'' (September 1991). "[http://jb.asm.org/cgi/content/abstract/173/17/5396 Buoyant density studies of several mecillinam-resistant and division mutants of Escherichia coli]". ''Journal of Bacteriology'' '''173(17):''' 5396-5402<br />
<br />
;Cadosch 2008 {{anchor|Cadosch2008}}<br />
:Cadosch D, Meagher J, Gautschi OP, Filgueira L. (December 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/19133293 Uptake and intracellular distribution of various metal ions in human monocyte-derived dendritic cells detected by Newport Green DCF diacetate ester]". '' Journal Neurosci Methods.'' '''178(1)''':182-187<br />
<br />
;Catini 2008 {{anchor|Catini2008}}<br />
:Cantini F., Banci L. & Solioz M., (October 2008) "[http://dx.doi.org/10.1042/BJ20081713 The copper-responsive repressor CopR of Lactococcus lactis is a ‘winged helix’ protein]". ''Biochem. J., '''2009''', 417, 493–499.<br />
<br />
;Carlin 1995 {{anchor|Carlin1995}}<br />
:Arthur Carlin, Weiping Shi, Saibal Dey and Barry P. Rosen (February 1995). "[http://www.ncbi.nlm.nih.gov/pubmed/7860609 The ars Operon of Escherichia coli Confers Arsenical and Antimonial Resistance]". ''Journal of Bacteriology'' '''177(4)''': 981-986<br />
<br />
;Chen 1997 {{anchor|Chen1997}}<br />
:{{star}} Yanxiang Chen and Barry P. Rosen (May 1997). "[http://www.ncbi.nlm.nih.gov/pubmed/9162059 Metalloregulatory Properties of the ArsD Repressor]". ''The Journal of Biological Chemistry'' '''272(22)''': 14257-14262<br />
<br />
;Chen 1997-2 {{anchor|Chen1997-2}}<br />
:Chen S, Wilson DB. (1997). "[http://www.ncbi.nlm.nih.gov/pubmed/9342882 Genetic engineering of bacteria and their potential for Hg2+ bioremediation] ". ''Biodegradation'' '''8(2)''': 97-103<br />
<br />
;Chen 1998 {{anchor|Chen1998}}<br />
:Chen S, Kim E, Shuler ML, Wilson DB. (1998). "[http://www.ncbi.nlm.nih.gov/pubmed/9758654 Hg2+ removal by genetically engineered Escherichia coli in a hollow fiber bioreactor]". ''Biotechnol Prog. '' '''14(5)''':667-671<br />
<br />
;Chen 2008 {{anchor|Chen2008}}<br />
:Chen P.R. & He C., (March 2008) "[http://dx.doi.org/10.1016/j.cbpa.2007.12.010 Selective recognition of metal ions by metalloregulatory proteins'', ''Current Opinion in Chemical Biology]". '''2008''', 12, 214–221.<br />
<br />
;Chang 1998 {{anchor|Chang1998}}<br />
:Chang CC, Liao WF, Huang PC. (1998). "[http://www.ncbi.nlm.nih.gov/pubmed/9579658 Cysteine contributions to metal binding preference for Zn/Cd in the beta-domain of metallothionein]". '' Protein Eng.'' '''11(1)''':42-46<br />
<br />
;Chang 2009 {{anchor|Chang2009}}<br />
:Yoon-Young Chang, Seung-Mok Lee, Jae-Kyu Yang, (August 2009). "[http://dx.doi.org/10.1016/j.colsurfa.2009.06.017 Removal of As(III) and As(V) by natural and synthetic metal oxides]". ''Colloids and Surfaces A: Physicochemical and Engineering Aspects'' '''346(1-3)''': 202-207<br />
<br />
;Chopra, PK, A2006{{anchor|Chopra, PK, A2006}}<br />
:Chopra, PK, A(2006). "[http://www.ncbi.nlm.nih.gov/pubmed/17274769?dopt=Abstract Engineering life through Synthetic Biology]".''In silico Biology. '' '''0038(6)''':<br />
<br />
;Cleland, CE, et al.2002{{anchor|Cleland, CE, et al.2002}}<br />
:Cleland, CE, et al.(2002). "[http://www.springerlink.com/content/hl14401v6rq7010r/ Defining 'life']".''Origins of Life and Evolution of the Biosphere. '' '''4(32)''':387-393<br />
<br />
;Deng 2003 {{anchor|Deng2003}}<br />
:Deng X, Li QB, Lu YH, Sun DH, Huang YL, Chen XR. (2003). "[http://www.ncbi.nlm.nih.gov/pubmed/12727263 Bioaccumulation of nickel from aqueous solutions by genetically engineered Escherichia coli.]". '' Water Res.'' '''37(10)''':2505-2511<br />
<br />
;Deng 2007 {{anchor|Deng2007}}<br />
:Deng X, Yi XE, Liu G. (2007). "[http://www.ncbi.nlm.nih.gov/pubmed/16890348 Cadmium removal from aqueous solution by gene-modified Escherichia coli JM109]". '' Journal Hazard Mater. '' '''139(2)''':340-344<br />
<br />
;Deng 2008 {{anchor|Deng2008}}<br />
:Deng X, Hu ZL, Yi XE. (May 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/17920767 Continuous treatment process of mercury removal from aqueous solution by growing recombinant E. coli cells and modeling study]". '' Journal Hazard Mater. '' '''153(1-2)''':487-492<br />
<br />
;Deplazes, A2009{{anchor|Deplazes, A2009}}<br />
:Deplazes, A(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19415076?dopt=Abstract Piecing together a puzzle An exposition of synthetic biology]".''Embo Reports. '' '''5(10)''':428-432<br />
<br />
;Dey 1995 {{anchor|Dey1995}}<br />
:Saibal Dey, Barry P. Rosen (1995). "[http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=176602 Dual Mode of Energy Coupling by the Oxyanion Translocating ArsB Protein]". ''JOURNAL OF BACTERIOLOGY'' '''177(2)''': 385–389<br />
<br />
;Dong 2008 {{anchor|Dong2008}}<br />
:Dong, Liangjie (December 2008). "[http://www.freepatentsonline.com/y2008/0311288.html Methods and Compositions for Removal of Arsenic and Heavy Metals From Water]". ''United States Patent Application 20080311288 Kind Code:A1 <br />
''<br />
<br />
;EPA 2000 {{anchor|EPA2000}}<br />
:Environmental Protection Agency (December 2000). "[http://www.epa.gov/safewater Technologies and Costs for Removal of Arsenic from Drinking Water]". ''EPA 815-R-00-028'' <br />
<br />
;Ettema 2006 {{anchor|Ettema2006}}<br />
:Thijs J. G. Ettema, Arie B. Brinkman ''et al'' (2006). "[http://dx.doi.org/10.1099/mic.0.28724-0 Molecular characterization of a conserved archaeal copper resistance (cop) gene cluster and its copper-responsive regulator in Sulfolobus solfataricus P2]". ''Microbiology '''152''': 1969-1979<br />
<br />
;Fowler 1987 {{anchor|Fowler1987}}<br />
:Fowler BA. (1987). "[http://www.ncbi.nlm.nih.gov/pubmed/3297654 Intracellular compartmentation of metals in aquatic organisms: roles in mechanisms of cell injury]". '' Environ Health Perspect.'' '''7(1)''': 121-128<br />
<br />
;Fosmire 1990 {{anchor|Fosmire1990}}<br />
:Fosmire GA. (1990). "[http://www.ncbi.nlm.nih.gov/pubmed/2407097 Zinc toxicity]". ''American Society for Clinical Nutrition.'' '''5l''': 225-227<br />
<br />
;Frankenberger 2001 {{anchor|Frankenberger2001}}<br />
:William T. Frankenberger Jr. (2001). ''Environmental Chemistry of Arsenic'', Marcel Dekker, New York, NY, 404 pp. ISBN 0-8247-0676-5<br />
<br />
;Fu, DX, et al.2000{{anchor|Fu, DX, et al.2000}}<br />
:Fu, DX, et al.(2000). "[http://www.ncbi.nlm.nih.gov./pubmed/11039922?dopt=Abstract Structure of a glycerol-conducting channel and the basis for its selectivity]".''Science. '' '''5491(290)''':481-486<br />
<br />
;Gilchrist 2007 {{anchor|Gilchrist2007}}<br />
:Michael A. Gilchrist (2007). "[http://dx.doi.org/10.1093/molbev/msm169 Combining Models of Protein Translation and Population Genetics to Predict Protein Production Rates from Codon Usage Patterns]". ''Molecular Biology and Evolution'' '''24(11)''': 2362-2372<br />
<br />
;Gold 2008 {{anchor|Gold2008}}<br />
:Gold B, Deng H, ''et al''(2008). "[http://www.ncbi.nlm.nih.gov/pubmed/18724363 Identification of a copper-binding metallothionein in pathogenic mycobacteria]". ''Nat Chem Biol.'' '''4(10)''': 609-616<br />
<br />
;Goudar 1999 {{anchor|Goudar1999}}<br />
:Chetan T. Goudara, Jagadeesh R. Sonnadb and Ronald G. Duggleby (January 1999). "[http://dx.doi.org/10.1016/S0167-4838(98)00247-7 Parameter estimation using a direct solution of the integrated Michaelis-Menten equation]". ''Biochimica et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology'' '''1429(2)''': 377-383<br />
<br />
;Guven 2007 {{anchor|Guven2007}}<br />
:Basak Guven and Alan Howarda (September 2007). "[http://dx.doi.org/doi:10.1016/j.ecolmodel.2007.03.024 Identifying the critical parameters of a cyanobacterial growth and movement model by using generalised sensitivity analysis]". ''Ecological Modelling'' '''207(1)''': 11-21<br />
<br />
;Heller, KB, et al.1980{{anchor|Heller, KB, et al.1980}}<br />
:Heller, KB, et al.(1980). "[http://www.ncbi.nlm.nih.gov/pubmed/6998951?dopt=Abstract Substrate-Specificity and Transport-Properties of the Glycerol Facilitator of Escherichia-Coli]".''Journal of Bacteriology. '' '''1(144)''':274-278<br />
<br />
;Hirose 2006 {{anchor|Hirose2006}}<br />
:Hirose K, Ezaki B, Tong L Nakashima S, ''et al'' (August 2005) "[http://dx.doi.org/10.1016/j.toxlet.2005.11.008 Diamide stress induces a metallothionein BmtA through a repressor BxmR and is modulated by Zn-inducible BmtA in the cyanobacterium Oscillatoria brevis]". ''Toxicology Letters, '''2006''', 163, 250–256.<br />
<br />
;Hoefnagel 2002 {{anchor|Hoefnagel2002}}<br />
:M.H.N. Hoefnagel, A. van der Burgt, D.E. Martens, ''et al'' (March 2002). "[http://dx.doi.org/10.1023/A:1020313409954 Time Dependent Responses of Glycolytic Intermediates in a Detailed Glycolytic Model of ''Lactococcus Lactis'' During Glucose Run-Out Experiments]". ''Molecular Biology Reports'' '''29''': 157-161<br />
<br />
;Holland 2009 {{anchor|Holland2009}}<br />
:Daryl P. Holland, Anthony E. Walsby (January 2009). "[http://dx.doi.org/10.1016/j.mimet.2009.02.005 Digital recordings of gas-vesicle collapse used to measure turgor pressure and cell–water relations of cyanobacterial cells ]". ''Journal of Microbiological Methods'' '''77''': 214-224<br />
<br />
;Hristovski 2007 {{anchor|Hristovski2007}}<br />
:Kiril Hristovski, Andrew Baumgardner, Paul Westerhoff, (August 2007). "[http://dx.doi.org/10.1016/j.jhazmat.2007.01.017 Selecting metal oxide nanomaterials for arsenic removal in fixed bed columns: From nanopowders to aggregated nanoparticle media]". Journal of Hazardous Materials'' '''147(1-2)''': 265-274 <br />
<br />
;Kao 2008 {{anchor|Kao2008}}<br />
:Kao WC, Huang CC, Chang JS (October 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/18313216 Biosorption of nickel, chromium and zinc by MerP-expressing recombinant Escherichia coli.]". '' J Hazard Mater.'' '''158(1)''': 100-106<br />
<br />
;Kelle, A2009{{anchor|Kelle, A2009}}<br />
:Kelle, A(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19636299?dopt=Abstract Synthetic biology and biosecurity From low levels of awareness to a comprehensive strategy]".''Embo Reports. '' 10)''':S23-S27<br />
<br />
;Kelly 2009 {{anchor|Kelly2009}}<br />
:Jason R. Kelly, Adam J. Rubin, Joseph H. Davis, ''et al'' (March 2009). "[http://dx.doi.org/10.1186/1754-1611-3-4 Measuring the activity of BioBrick promoters using an in vivo reference standard]". ''Journal of Biological Engineering'' '''3''': 4<br />
<br />
;Khunajakr 1999 {{anchor|Khunajakr1999}}<br />
:Nongpanga Khunajakr, Chun-Qiang Liu ''et al'' (March 1999). "[http://dx.doi.org/10.1016/S0378-1119(98)00395-3 A plasmid-encoded two-component regulatory system involved in copper-inducible transcription in Lactococcus lactis]". ''Gene'''229(1-1)''': 229-235<br />
<br />
;Klaassen 1994 {{anchor|Klaassen1994}}<br />
:Klaassen, Curtis D., Supratim Choudhuri, James M. McKim, Jr., Lois D. Lehman-McKeeman, and William C. Kershaw (1994). [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1567434/ "In Vitro and In Vivo Studies on the Degradation of Metallothionein"]. ''Environ. Health Perspect'' '''102(3)''': 141-146.<br />
<br />
;Kloosterman 2008 {{anchor|Kloosterman2008}}<br />
:Tomas G. Kloosterman, Robert M. Witwicki ''et al'' (2008). "[http://dx.doi.org/10.1128/JB.00307-08 Opposite Effects of Mn2+ and Zn2+ on PsaR-Mediated Expression of the Virulence Genes pcpA, prtA, and psaBCA of Streptococcus pneumonia]". ''J Bacterio'''190(15)''': 5382–5393<br />
<br />
;Kostal 2004 {{anchor|Kostal2004}}<br />
:{{star}} Jan Kostal, Rosanna Yang, Cindy H. Wu, ''et al'' (August 2004). "[http://dx.doi.org/10.1128/AEM.70.8.4582-4587.2004 Enhanced Arsenic Accumulation in Engineered Bacterial Cells Expressing ArsR]". ''Applied and Environmental Microbiology'' 70(8): 4582–4587<br />
<br />
;Lewinson 2009 {{anchor|Lewinson2009}}<br />
:Lewinson O, Lee AT, Rees DC. (2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19264958 A P-type ATPase importer that discriminates between essential and toxic transition metals]". '' PNAS'' 106(12): 4677-4682<br />
<br />
;Li 1998 {{anchor|Li1998}}<br />
:{{star}} Ning Li and Maura C. Cannon (May 1998). "Gas Vesicle Genes Identified in Bacillus megaterium and Functional Expression in Escherichia coli". ''Journal of Bacteriology'' '''180(9)''': 2450–2458<br />
<br />
;Lin 2007-1 {{anchor|Lin2007-1}}<br />
:Yung-Feng Lin, Jianbo Yang and Barry P. Rosen (April 2007). "[http://dx.doi.org/10.1074/jbc.M700886200 ArsD Residues Cys12, Cys13, and Cys18 Form an As(III)-binding Site Required for Arsenic Metallochaperone Activity]". ''The Journal of Biological Chemistry'' '''282(23)''': 16783–16791<br />
<br />
;Lin 2007-2 {{anchor|Lin2007-2}}<br />
:Yung-Feng Lin, Jianbo Yang and Barry P. Rosen (December 2007). "[http://dx.doi.org/10.1007/s10863-007-9113-y ArsD: an As(III) metallochaperone for the ArsAB As(III)-translocating ATPase]". ''Journal of Bioenergetics and Biomembranes'' '''39''': 453-458<br />
<br />
;Liu 2004 {{anchor|Liu2004}}<br />
:Tong Liu, Susumu Nakashima ''et al'' (April 2004) "[http://dx.doi.org/10.1074/jbc.M310560200 A Novel Cyanobacterial SmtB/ArsR Family Repressor Regulates the Expression of a CPx-ATPase and a Metallothionein in Response to Both Cu(I)/Ag(I) and Zn(II)/Cd(II)]". ''The Journal of Biological Chemistry, '''2004''', Vol. 279, No. 17, 17810–17818.<br />
<br />
;Liu 2006 {{anchor|Liu2006}}<br />
:Tong Liu Arati Ramesh ''et al''(December 2006). "[http://dx.doi.org/10.1038/nchembio844 CsoR is a novel Mycobacterium tuberculosis copper-sensing transcriptional regulator]". ''Nature Chemical Biology'' '''3''': 60-68<br />
<br />
;Liu 2008 {{anchor|Liu2008}}<br />
:Tong Liu, Xiaohua Chen, Zhen Ma, ''et al'' (September 2008) "[http://dx.doi.org/10.1021/bi801313y A CuI-sensing ArsR family Metal Sensor Protein with a Relaxed Metal Selectivity Profile]". ''Biochemistry, '''2008''', 47(40), 10564–10575.<br />
<br />
; Lundstrom (2006) {{anchor|Lundstom2006}}<br />
:Lundstrom, K. (2006). “[http://www.springerlink.com/content/23783l53l616238t/ Structural genomics for membrane proteins]” ''Cell. Mol. Life Sci.'' '''63: 2597–2607'''.<br />
<br />
;Martinson 2009 {{anchor|Martinson2009}}<br />
:Carol A. Martinson, K.J. Reddy, (August 2009). "[http://dx.doi.org/10.1016/j.jcis.2009.04.075 Adsorption of arsenic(III) and arsenic(V) by cupric oxide nanoparticles]". ''Journal of Colloid and Interface Science'' '''336(2)''': 406-411<br />
<br />
;Meng, YL, et al.2004{{anchor|Meng, YL, et al.2004}}{{anchor|Meng2004}}:Meng, YL, et al.(2004). ” [http://dx.doi.org/10.1074/jbc.M400037200 As(III) and Sb(III) uptake by G1pF and efflux by ArsB in Escherichia coli]".''Journal of Biological Chemistry. '' '''18(279)''':18334-18341<br />
<br />
;Merrifield 2004 {{anchor| Merrifield2004}}<br />
:M. E. Merrifield, T. Ngu, M. J. Stillman ''et al'' (September 2004). "[http://www.ncbi.nlm.nih.gov/pubmed/15464992 Arsenic binding to <i>Fucus vesiculosus</i> metallothionein.]". ''Biochemical and Biophysical Research Communications'' '''324 :''' 127–132<br />
<br />
;Mills 1994 {{anchor|Mills1994}}<br />
:Scott D. Mills Chun-Keun Lim and Donald A. Cooksey (1994). "[http://dx.doi.org/10.1007/BF00286685 Purification and characterization of CopR, a transcriptional activator protein that binds to a conserved domain (cop box) in copper- inducible promoters of Pseudomonas syringae]". ''Molecular and General Genetics MGG '''244(4)''': 1432-1874<br />
<br />
;Mindlin, SZ, et al.2002{{anchor|Mindlin, SZ, et al.2002}}:Mindlin, SZ, et al.(2002). "[http://dx.doi.org/10.1023/A:1015353402657 Horizontal transfer of mercury resistance genes in environmental bacterial populations]".''Molecular Biology. '' '''2(36)''':160-170<br />
<br />
;Moore 2005 {{anchor|Moore2005}}<br />
:Charles M. Moore, Ahmed Gaballa ''et al'' (May 2005). "[http://dx.doi.org/10.1111/j.1365-2958.2005.04642.x Genetic and physiological responses of Bacillus subtilis to metal ion stress]". ''Molecular Microbiology'''57(1)''': 27-40<br />
<br />
;Morris 1999 {{anchor| Morris1999}}<br />
:C.A. Morris, B. Nicolaus, V. Sampson ''et al'' (March 1999). "[http://www.ncbi.nlm.nih.gov/pubmed/10024535 Identification and characterization of a recombinant metallothionein protein from a marine alga, <i>Fucus vesiculosus</i>]". '' The Biochemical journal'' '''338(2):''' 553-560<br />
<br />
;Nawapan 2009 {{anchor|Nawapan2009}}<br />
:Sirikan Nawapan, Nisanart Charoenlap ''et al'' (August 2009). "[http://dx.doi.org/10.1046/10.1128/JB.00384-09 Functional and Expression Analyses of the cop Operon, Required for Copper Resistance in Agrobacterium tumefaciens]". ''American Society for Microbiology '''191(16)''': 5159-5168<br />
<br />
;Neves 1999 {{anchor|Neves1999}}<br />
:Ana Rute Neves, Ana Ramos, Marta C. Nunes, ''et al'' (1999). "[http://dx.doi.org/10.1002/(SICI)1097-0290(19990720)64%3A2%3C200%3A%3AAID-BIT9%3E3.0.CO%3B2-K In vivo nuclear magnetic resonance studies of glycolytic kinetics in ''Lactococcus lactis'']". ''Biotechnology and Bioengineering'' '''64''': 200-212<br />
<br />
;Ngu 2006 {{anchor|Ngu2006}}<br />
:Thanh T. Ngu, M. Stillman (April 2006). "[http://dx.doi.org/10.1021/ja062914c Arsenic Binding to Human Metallothionein]". ''J. Am. Chem. Soc'' '''128 (38)''': 12473–12483<br />
<br />
;Ngu 2009 {{anchor|Ngu2009}}<br />
:Thanh T. Ngu, J. A. Lee ''et al''. (April 2009). "[http://dx.doi.org/10.1021/bi9007462 Arsenic Metalation of Seaweed ''Fucus vesiculosus'' Metallothionein: The importance of the Interdomain Linker in Metallothionein]". ''Biochemistry'' '''48''': 8806–8816<br />
<br />
;Nicholls, H2008{{anchor|Nicholls, H2008}}<br />
:Nicholls, H(2008). "[http://dx.doi.org/10.1016/S0140-6736(08)61881-4 Synthetic biology]".''Lancet. '' S45-S49<br />
<br />
;Nouri, A, et al.2009{{anchor|Nouri, A, et al.2009}}<br />
:Nouri, A, et al.(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19270668?dopt=Abstract Proliferation-resistant biotechnology: an approach to improve biological security]".''Nature Biotechnology. '' '''3(27)''':234-236<br />
<br />
;Oehmen 2006 {{anchor|Oehmen2006}}<br />
:Adrian Oehmen, Rui Viegas, Svetlozar Velizarov, ''et al'' (November 2006). "[http://dx.doi.org/10.1016/j.desal.2006.03.091 Removal of heavy metals from drinking water supplies through the ion exchange membrane bioreactor]". ''Desalination'' '''199(1-3)''': 405-407 <br />
<br />
;Outten 2000 {{anchor|Outten2000}}<br />
:F. Wayne Outten, Caryn E. Outten, Jeremy Hale and Thomas V. O’Halloran (October 2000). "[http://dx.doi.org/10.1074/jbc.M006508200 Transcriptional Activation of an ''Escherichia coli'' Copper Efflux Regulon by the Chromosomal MerR Homologue, CueR]". ''The Journal of Biological Chemistry'' '''275(40)''': 31024-31029<br />
<br />
;Pennella 2005 {{anchor|Pennella2005}}<br />
:Pennella M.A. & Giedroc D.P., (August 2005) "[http://dx.doi.org/10.1007/s10534-005-3716-8 Structural determinants of metal selectivity in prokaryotic metal-responsive transcriptional regulator]". ''BioMetals, '''2005''', 18, 413–428.<br />
<br />
;Poole 1977 {{anchor|Poole1977}}<br />
:R.K. Poole (1977). "[http://mic.sgmjournals.org/cgi/content/abstract/98/1/177 Fluctuations in Buoyant Density during the Cell Cycle of Escherichia coli K12]". ''Journal of General Microbiology'' '''98''': 177-186<br />
<br />
;Porquet, A, et al.2007{{anchor|Porquet, A, et al.2007}}<br />
:Porquet, A, et al.(2007). “[http://www.ncbi.nlm.nih.gov./pubmed/17713961?dopt=Abstract Structural evidence of the similarity of Sb(OH)(3) and As(OH)(3) with glycerol: Implications for their uptake]".''Chemical Research in Toxicology. '' '''9(20)''':1269-1276<br />
<br />
;Raje 2005 {{anchor|Raje2005}}<br />
:N. Raje,* K. K. Swain (April 2005). "[http://dx.doi.org/10.1023/A:1015812517214 Purification of arsenic contaminated ground water using hydrated manganese dioxide]". ''Journal of Radioanalytical and Nuclear Chemistry'' '''253(1)''': 77-80<br />
<br />
;Rawlings 1994 {{anchor| Rawlings1994}}<br />
:RAWLINGS, D E. and KUSANO, T (1994). “[http://mmbr.asm.org/cgi/reprint/58/1/39?view=long&pmid=8177170 Molecular Genetics of Thiobacillus ferrooxidans]”. ‘’MICROBIOLOGICAL REVIEWS’’, ‘’’58 (1): 39-55’’’<br />
<br />
;Rensing 2005 {{anchor|Rensing2005}}<br />
:Christopher Rensing (June 2005). "[http://dx.doi.org/10.1128/JB.187.12.3909-3912.2005 Form and Function in Metal-Dependent Transcriptional Regulation: Dawn of the Enlightenment]". ''Journal of Bacteriology'' '''187(12)''': 3909–3912<br />
<br />
;Robinson 2001 {{anchor|Robinson2001}}<br />
:Nigel J. Robinson, Simon K. Whitehall and Jennifer S. Cavet (2001). "[http://www.ncbi.nlm.nih.gov/pubmed/11407113 Microbial Metallothioneins]". ''Advances in Microbial Physiology'' '''44''': 183-213<br />
<br />
;Rosen 1996 {{anchor|Rosen1996}}<br />
:Barry P. Rosen (August 1996). "[http://dx.doi.org/10.1007/s007750050053 Bacterial resistance to heavy metals and metalloids]". ''Journal of Biological Inorganic Chemistry'' '''1(4)''': 273-277<br />
<br />
;Rosen, BR, et al.2009{{anchor|Rosen, BR, et al.2009}}{{anchor|Rosen2009}}<br />
:Rosen, BR, et al.(2009). “[http://dx.doi.org/10.1007/s007750050053 Transport pathways for arsenic and selenium: A minireview]".''Environment International. '' '''3(35)''':512-515<br />
<br />
;Samuel, GN, et al.2009{{anchor|Samuel, GN, et al.2009}}<br />
:Samuel, GN, et al.(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19079130?dopt=Abstract Managing the unimaginable Regulatory responses to the challenges posed by synthetic biology and synthetic genomics]".''Embo Reports. '' '''1(10)''':7-11<br />
<br />
;Schmidt, M 2008 {{anchor|Schmidt2008}}<br />
:Schmidt, M (2008). "[http://dx.doi.org/10.1007/s11693-008-9018-z Diffusion of synthetic biology: a challenge to biosafety]", ''Syst Synth Biol.''<br />
<br />
;Schwartz 2008 {{anchor|Schwartz2008}}<br />
:Russel Schwartz (2008). ''Biological modeling and simulation: a survey of practical models, algorithms, and numerical methods'' MIT Press. ISBN 978-0-262-19584-3<br />
<br />
;Serrano, L2007{{anchor|Serrano, L2007}}<br />
:Serrano, L(2007). "[http://www.ncbi.nlm.nih.gov/pubmed/18091727?dopt=Abstract Synthetic biology: promises and challenges]".''Molecular Systems Biology. '' 3)''':<br />
<br />
;Shi 1992 {{anchor|Shi1992}}<br />
:Jianguo Shi, William P. Lindsay, James W. Huckle (June 1992). "[http://dx.doi.org/10.1016/0014-5793(92)80509-F Cyanobacterial metallothionein gene expressed in Escherichia coli: Metal-binding properties of the expressed protein]". ''FEBS Letters'' '''303(2-3)''': 159-163<br />
<br />
;Singh 2008 {{anchor|Singh2008}}<br />
:Shailendra Singh, Ashok Mulchandani, Wilfred Chen (February 2008). "[http://dx.doi.org/10.1128/AEM.02871-07 Highly Selective and Rapid Arsenic Removal by Metabolically Engineered Escherichia coli Cells Expressing Fucus vesiculosus Metallothionein]". ''MICROBIOLOGY'' '''74(9)''': 2924–2927<br />
<br />
;Sivertsen 2008 {{anchor|Sivertsen2008}}<br />
:Astrid C. Sivertsen, Marvin J. Bayro, ''et al'' ( april 2008). "[http://dx.doi.org/doi:10.1016/j.jmb.2009.02.015 Solid-State NMR Evidence for Inequivalent GvpA Subunits in Gas Vesicles]". ''Journal of Molecular Biology'' '''387(4)''': 1032-1039<br />
<br />
;Stephan Hug {{anchor|Stephan Hug}}<br />
:Stephan Hug. "[http://www.eawag.ch/publications/eawagnews/www_en49/en49e_ihv_web.html Arsenic Contamination of Ground Water: Disastrous Consequences in Bangladesh]". ''EAWAG news'' '''49(e)''': 18-20<br />
<br />
;Stephenson, JR, et al.1996 {{anchor|Stephenson, JR, et al.1996}}:Stephenson, JR, et al.(1996). "[http://dx.doi.org/10.1002 Release of genetically modified micro-organisms into the environment]".''Journal of Chemical Technology and Biotechnology. '' '''1(65)''':5-14<br />
<br />
;Summers 2009 {{anchor|Summers2009}}<br />
:Anne O. Summers (April 2009). "[http://dx.doi.org/10.1016/j.mib.2009.02.003 Damage control: regulating defenses against toxic metals and metalloids]". ''Current Opinion in Microbiology'' '''12(2)''': 138-144<br />
<br />
;Suzuki 1998 {{anchor|Suzuki1998}}<br />
:Katsuhisa Suzukia, Norio Wakaob, Tetsuya Kimuraa, Kazuo Sakkaa and Kunio Ohmiya (February 1998). "[http://dx.doi.org/10.1016/S0922-338X(98)80016-0 Metalloregulatory properties of the ArsR and ArsD repressors of ''Acidiphilium multivorum'' AIU 301]". ''Journal of Fermentation and Bioengineering'' '''85(6)''': 623-626<br />
<br />
;Thelwell 1998 {{anchor|Thelwell1998}}<br />
:Thelwell C., Robinson N.J. & Turner-Cavet J.S., "[http://dx.doi.org/10.1073/pnas.95.18.10728 An SmtB-like repressor from Synechocystis PCC 6803 regulates a zinc exporter]". ''Proc. Natl. Acad. Sci. USA, '''1998''', Vol. 95, 10728–10733.<br />
<br />
;Tisa 1989 {{anchor|Tisa1989}}<br />
:Louis S. Tisa and Barry P. Rosen (January 1990). "[http://www.ncbi.nlm.nih.gov/pubmed/1688427 Molecular characterization of an anion pump. The ArsB protein is the membrane anchor for the ArsA protein]". ''The journal of biological chemistry'' '''265(1)''': 190-194<br />
<br />
;Turner 1995 {{anchor|Turner1995}}<br />
:Jennifer S. Turner, Nigel J. Robinson and Amit Gupta (March 1995). "[http://dx.doi.org/10.1007/BF01569937 Construction of Zn<sup>2+</sup>/Cd<sup>2+</sup>-tolerant cyanobacteria with a modified metallothionein divergon: Further analysis of the function and regulation of ''smt'']". ''Journal of Industrial Microbiology and Biotechnology'' '''14(3-4)''': 259-264<br />
<br />
;Walsby 1979 {{anchor|Walsby1979}}<br />
:A.E. Walsby (April 1979). "[http://dx.doi.org/10.1016/0022-2836(79)90281-X Average thickness of the gas vesicle wall in Anabaena flos-aquae]". ''Journal of Molecular Biology'' '''129(2)''': 279-285<br />
<br />
;Walsby 1994 {{anchor|Walsby1994}}<br />
:A.E. Walsby (March 1994). "[http://www.ncbi.nlm.nih.gov/pubmed/8177173 Gas Vesicles]". ''Microbiological reviews'' '''58(1)''': 94-144<br />
<br />
;Wlckramaslnghe 2004 {{anchor|Wlckramaslnghe2004}}<br />
:S.R. Wlckramaslnghe, Binbing Han, J. Zimbron, ''et al'' (October 2004). "[http://dx.doi.org/10.1016/j.desal.2004.03.013 Arsenic removal by coagulation and filtration: comparison of groundwaters from the United States and Bangladesh]". ''Desalination'' '''169(3)''': 231-244 <br />
<br />
;Xu 1996 {{anchor|Xu1996}}<br />
:Chun Xu, Weiping Shi and Barry P. Rosen (February 1996). "[http://dx.doi.org/10.1074/jbc.271.5.2427 The Chromosomal ''arsR'' Gene of ''Escherichia coli'' Encodes a ''trans''-acting Metalloregulatory Protein]". ''The Journal of Biological Chemistry'' '''271(5)''': 2427-2432<br />
<br />
;Yamamoto 2005 {{anchor|Yamamoto2005}}<br />
:Kaneyoshi Yamamoto and Akira Ishihama (2005). "[http://dx.doi.org/10.1111/j.1365-2958.2005.04532.x Transcriptional response of ''Escherichia coli'' to external copper]". ''Molecular Microbiology'' '''56(1)''': 215-227<br />
<br />
;Zwart, SD, et al.2006{{anchor|Zwart, SD, et al.2006}}:Zwart, SD, et al.(2006). "[http://dx.doi.org/10.1007/s11948-006-0063-2 network approach for distinguishing ethical issues in research and development]".''Science and Engineering Ethics. '' '''4(12)''':663-684<br />
<br />
<br />
<br />
Miscellaneous:<br />
* [http://ginkgobioworks.com/cgi/primer.cgi Primer design Bioworks]<br />
* [http://openwetware.org/wiki/The_BioBricks_Foundation:Standards/Technical/Measurement Promotor measurement]<br />
* [http://openwetware.org/wiki/Main_Page OpenWetWare]<br />
* [http://www.hgsc.bcm.tmc.edu/projects/microbial/microbial-detail.xsp?project_id=105 E. coli DH10B genome] (with BLAST)<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/LiteratureTeam:Groningen/Literature2009-10-21T22:06:45Z<p>Jaspervdg: Some more references and tweaks to the layout.</p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
<div style="float:left" >{{linkedImage|GroningenPrevious.png|Team:Groningen/Glossary}}</div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Protocols}}</div><br />
<br />
[[Category:Team:Groningen]]<br />
<br />
==Literature==<br />
Buoyancy related literature:<br />
*Buoyant density: [[Team:Groningen/Literature#Poole1977|Poole 1977]], [[Team:Groningen/Literature#Bylund1991|Bylund 1991]], '''[[Team:Groningen/Literature#Baldwin1995|Baldwin 1995]]'''<br />
*Gas vesicles: [[Team:Groningen/Literature#Bowen1965|Bowen 1965]], [[Team:Groningen/Literature#Walsby1979|Walsby 1979]], '''[[Team:Groningen/Literature#Walsby1994|Walsby 1994]]''', '''[[Team:Groningen/Literature#Li1998|Li 1998]]''', [[Team:Groningen/Literature#Sivertsen2008|Sivertsen 2008]], [[Team:Groningen/Literature#Holland2009|Holland 2009]]<br />
<br />
Ohter methods of arsenic purification.<br />
*General information about the subject:[[Team:Groningen/Literature#Frankenberger2001|Frankenberger 2001]],[[Team:Groningen/Literature#Stephan Hug|Stephan Hug]],[[Team:Groningen/Literature#Wlckramaslnghe2004|Wlckramaslnghe 2004]],[[Team:Groningen/Literature#Dong2008|Dong 2008]],'''[[Team:Groningen/Literature#EPA2000|EPA 2000]]''',<br />
*Ion exchange and Membranes:[[Team:Groningen/Literature#Oehmen2006|Oehmen 2006]],<br />
*Nanomaterials:[[Team:Groningen/Literature#Hristovski2007|Hristovski 2007]],[[Team:Groningen/Literature#Martinson2009|Martinson 2009]],[[Team:Groningen/Literature#Chang2009|Chang 2009]],<br />
*Precipitative Processes:[[Team:Groningen/Literature#Raje2005|Raje 2005]],<br />
<br />
Our metal related literature by subject:<br />
{|border="1" <br />
!<br />
!<br />
!Cu<br />
!Zn<br />
!As<br />
!Cd<br />
!Sb<br />
!Hg<br />
|-<br />
!rowspan="2" |Importers<br />
!GlpF<br />
|<br />
|<br />
|'''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Rosen2009|Rosen 2009]]<br />
|<br />
|'''[[Team:Groningen/Literature#Meng2004|Meng 2004]]'''<br />
|<br />
|-<br />
!{{part|BBa_K190018|HmtA}}<br />
|[[Team:Groningen/Literature#Lewinson2009|Lewinson 2009]]<br />
|[[Team:Groningen/Literature#Lewinson2009|Lewinson 2009]]<br />
|<br />
|<br />
|<br />
|-<br />
!rowspan="1" |Exporters<br />
!ArsB<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Tisa1989|Tisa 1989]], [[Team:Groningen/Literature#Carlin1995|Carlin 1995]],<br />
[[Team:Groningen/Literature#Dey1995|Dey 1995]] [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|[[Team:Groningen/Literature#Tisa1989|Tisa 1989]], [[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Meng2004|Meng 2004]]''', [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|-<br />
!rowspan="6" |Accumulators<br />
!ArsR<br />
|<br />
|<br />
||[[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], '''[[Team:Groningen/Literature#Chen1997|Chen 1997]]''', '''[[Team:Groningen/Literature#Kostal2004|Kostal 2004]]''', [[Team:Groningen/Literature#Rensing2005|Rensing 2005]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
||[[Team:Groningen/Literature#Carlin1995|Carlin 1995]], [[Team:Groningen/Literature#Rosen1996|Rosen 1996]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
<br />
|<br />
|-<br />
!ArsD<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Chen1997|Chen 1997]], [[Team:Groningen/Literature#Lin2007-1|Lin 2007-1/2]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|[[Team:Groningen/Literature#Chen1997|Chen 1997]], [[Team:Groningen/Literature#Lin2007-1|Lin 2007-1/2]], [[Team:Groningen/Literature#Summers2009|Summers 2009]]<br />
|<br />
|-<br />
!SmtA<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]], [[Team:Groningen/Literature#Turner1995|Turner 1995]], [[Team:Groningen/Literature#Robinson2001|Robinson 2001]], [[Team:Groningen/Literature#Blindauer2002|Blindauer 2002]]<br />
|<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|<br />
|[[Team:Groningen/Literature#Shi1992|Shi 1992]]<br />
|-<br />
!MymT<br />
|[[Team:Groningen/Literature#Gold2008|Gold 2008]]<br />
|<br />
|<br />
|<br />
|<br />
|<br />
|-<br />
!MT<br />
|<br />
|<br />
|[[Team:Groningen/Literature#Morris1999|Morris 1999]],[[Team:Groningen/Literature#Ngu2006|Ngu 2006]],[[Team:Groningen/Literature#Singh2008|Singh 2008]], [[Team:Groningen/Literature#Merrifield2004|Merrifield 2004]], [[Team:Groningen/Literature#Ngu2009|Ngu 2009]]<br />
|[[Team:Groningen/Literature#Deng2007|Deng 2007]]<br />
|<br />
|[[Team:Groningen/Literature#Chen1998|Chen1998]]<br />
|-<br />
!Unclassified<br />
|[[Team:Groningen/Literature#Brady1994|Brady 1994]]<br />
|[[Team:Groningen/Literature#Chang1998|Chang 1998]], [[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]<br />
|<br />
|[[Team:Groningen/Literature#Brady1994|Brady 1994]], [[Team:Groningen/Literature#Chang1998|Chang 1998]], <br />
|<br />
|[[Team:Groningen/Literature#Deng2008|Deng 2008]]<br />
|-<br />
!rowspan="1" |Promoters<br />
!<br />
|[[Team:Groningen/Literature#Mills1994|Mills 1994 ]], [[Team:Groningen/Literature#Khunajakr1999 |Khunajakr 1999]], [[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore 2005]], [[Team:Groningen/Literature#Ettema2006 |Ettema2006 ]], [[Team:Groningen/Literature#Liu2006|Liu 2006]], [[Team:Groningen/Literature#Liu2008|Liu 2008]], [[Team:Groningen/Literature#Catini2008|Catini 2008]], [[Team:Groningen/Literature#Nawapan2009|Nawapan 2009]]<br />
|[[Team:Groningen/Literature#Thelwell1998|Thelwell 1998]], [[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore2005]], [[Team:Groningen/Literature#Hirose2006 |Hirose 2006]], [[Team:Groningen/Literature#Kloosterman2008|Kloosterman 2008]]<br />
|[[Team:Groningen/Literature#Summers2009 |Summers 2009]]<br />
|[[Team:Groningen/Literature#Liu2004|Liu 2004]], [[Team:Groningen/Literature#Moore2005|Moore 2005]]<br />
|<br />
|<br />
|}<br />
<br />
;Alon 2007 {{anchor|Alon2007}}<br />
:{{star}} Uri Alon (2007). ''Introduction to systems biology: design principles of biological circuits'' Chapman & Hall/CRC. ISBN 978-1-58488-642-6<br />
<br />
;Baldwin 1995 {{anchor|Baldwin1995}}<br />
:W.W. Baldwin, Richard Myer, Nicole Powell, ''et al'' (August 1995). "[http://www.springerlink.com/content/nu1lkduf3w89fmd8 Buoyant density of Escherichia coli is determined solely by the osmolarity of the culture medium]". ''Archives of Microbiology'' '''164(2)''': 155-157<br />
<br />
;Beltramini 1981 {{anchor| Beltramini1981}}<br />
:M. Beltramini and K. Lerch (1981). "[http://www.ncbi.nlm.nih.gov/pubmed/6453726 Luminescence Properties of ''Neurospora'' Copper Metallothionein]". ''FEBS Letters'' '''127(2)''': 201-203<br />
<br />
;Beyer 2004 {{anchor|Beyer2004}}<br />
:Andreas Beyer, Jens Hollunder, Heinz-Peter Nasheuer and Thomas Wilhelm (August 2004). "[http://dx.doi.org/10.1074/mcp.M400099-MCP200 Post-transcriptional Expression Regulation in the Yeast Saccharomyces cerevisiae on a Genomic Scale]". ''Molecular & Cellular Proteomics'' '''3''': 1083-1092<br />
<br />
;Bhutkar, A2005{{anchor|Bhutkar, A2005}}<br />
:Bhutkar, A(2005). '[http://www.ncbi.nlm.nih.gov/pubmed/16538811?dopt=Abstract Synthetic Biology: Navigating the Challenges Ahead]".''The journal of Biolaw and Business. '' '''2(8)''':<br />
<br />
;Blancato 2006 {{anchor|Blancato2006}}<br />
:Blancato VS, Magni C, Lolkema JS. (October 2006). "[http://dx.doi.org/doi:10.1016/j.jmb.2009.02.015 Functional characterization and Me ion specificity of a Ca-citrate transporter from Enterococcus faecalis]". ''FEBS journal'' '''273(22)''': 5121-5130<br />
<br />
;Blindauer 2002 {{anchor|Blindauer2002}}<br />
:Claudia A. Blindauer, Mark D. Harrison, Andrea K. Robinson, ''et al'' (2002). "[http://dx.doi.org/10.1046/j.1365-2958.2002.03109.x Multiple bacteria encode metallothioneins and SmtA-like zinc fingers]". ''Molecular Microbiology'' '''45(5)''': 1421-1432<br />
<br />
;Blindauer 2001 {{anchor|Blindauer2001}}<br />
:Blindauer CA, Harrison MD, ''et al'' (2001). "[http://www.ncbi.nlm.nih.gov/pubmed/11493688 A metallothionein containing a zinc finger within a four-metal cluster protects a bacterium from zinc toxicity.]". '' Proc Natl Acad Sci USA. '' '''98(17)''': ):9593-9598<br />
<br />
;Bowen 1965 {{anchor|Bowen1965}}<br />
:C.C. Bowen and T.E. Jensen ( March 1965). "[http://dx.doi.org/10.1126/science.147.3664.1460 Blue-Green Algae: Fine Structure of the Gas Vacuoles]". ''Science '' '''147(3664)''': 1460 - 1462<br />
<br />
;Busenlehner 2003 {{anchor|Busenlehner2003}}<br />
:Busenlehner L.S., Pennella M.A. & Giedroc D.P., (June 2003) "[http://dx.doi.org/10.1155/2006/837139 The SmtB/ArsR family of metalloregulatory transcriptional repressors: structural insights into prokaryotic metal resistance]". ''FEMS Microbiology Reviews, '''2003''', 27, 131-143.<br />
<br />
;Brady 1994 {{anchor|Brady1994}}<br />
:Brady D, Rose PD, Duncan JR. (1994). "[http://www.ncbi.nlm.nih.gov/pubmed/18618649 The use of hollow fiber cross-flow microfiltration in bioaccumulation and continuous removal of heavy metals from solution by Saccharomyces cerevisiae.]". '' Biotechnol Bioeng. '' '''44(11)''':1362-1366<br />
<br />
;Bylund 1991 {{anchor|Bylund1991}}<br />
:J.E. Bylund, M.A. Haines, K. Walsh, ''et al'' (September 1991). "[http://jb.asm.org/cgi/content/abstract/173/17/5396 Buoyant density studies of several mecillinam-resistant and division mutants of Escherichia coli]". ''Journal of Bacteriology'' '''173(17):''' 5396-5402<br />
<br />
;Cadosch 2008 {{anchor|Cadosch2008}}<br />
:Cadosch D, Meagher J, Gautschi OP, Filgueira L. (December 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/19133293 Uptake and intracellular distribution of various metal ions in human monocyte-derived dendritic cells detected by Newport Green DCF diacetate ester]". '' Journal Neurosci Methods.'' '''178(1)''':182-187<br />
<br />
;Catini 2008 {{anchor|Catini2008}}<br />
:Cantini F., Banci L. & Solioz M., (October 2008) "[http://dx.doi.org/10.1042/BJ20081713 The copper-responsive repressor CopR of Lactococcus lactis is a ‘winged helix’ protein]". ''Biochem. J., '''2009''', 417, 493–499.<br />
<br />
;Carlin 1995 {{anchor|Carlin1995}}<br />
:Arthur Carlin, Weiping Shi, Saibal Dey and Barry P. Rosen (February 1995). "[http://www.ncbi.nlm.nih.gov/pubmed/7860609 The ars Operon of Escherichia coli Confers Arsenical and Antimonial Resistance]". ''Journal of Bacteriology'' '''177(4)''': 981-986<br />
<br />
;Chen 1997 {{anchor|Chen1997}}<br />
:{{star}} Yanxiang Chen and Barry P. Rosen (May 1997). "[http://www.ncbi.nlm.nih.gov/pubmed/9162059 Metalloregulatory Properties of the ArsD Repressor]". ''The Journal of Biological Chemistry'' '''272(22)''': 14257-14262<br />
<br />
;Chen 1997-2 {{anchor|Chen1997-2}}<br />
:Chen S, Wilson DB. (1997). "[http://www.ncbi.nlm.nih.gov/pubmed/9342882 Genetic engineering of bacteria and their potential for Hg2+ bioremediation] ". ''Biodegradation'' '''8(2)''': 97-103<br />
<br />
;Chen 1998 {{anchor|Chen1998}}<br />
:Chen S, Kim E, Shuler ML, Wilson DB. (1998). "[http://www.ncbi.nlm.nih.gov/pubmed/9758654 Hg2+ removal by genetically engineered Escherichia coli in a hollow fiber bioreactor]". ''Biotechnol Prog. '' '''14(5)''':667-671<br />
<br />
;Chen 2008 {{anchor|Chen2008}}<br />
:Chen P.R. & He C., (March 2008) "[http://dx.doi.org/10.1016/j.cbpa.2007.12.010 Selective recognition of metal ions by metalloregulatory proteins'', ''Current Opinion in Chemical Biology]". '''2008''', 12, 214–221.<br />
<br />
;Chang 1998 {{anchor|Chang1998}}<br />
:Chang CC, Liao WF, Huang PC. (1998). "[http://www.ncbi.nlm.nih.gov/pubmed/9579658 Cysteine contributions to metal binding preference for Zn/Cd in the beta-domain of metallothionein]". '' Protein Eng.'' '''11(1)''':42-46<br />
<br />
;Chang 2009 {{anchor|Chang2009}}<br />
:Yoon-Young Chang, Seung-Mok Lee, Jae-Kyu Yang, (August 2009). "[http://dx.doi.org/10.1016/j.colsurfa.2009.06.017 Removal of As(III) and As(V) by natural and synthetic metal oxides]". ''Colloids and Surfaces A: Physicochemical and Engineering Aspects'' '''346(1-3)''': 202-207<br />
<br />
;Chopra, PK, A2006{{anchor|Chopra, PK, A2006}}<br />
:Chopra, PK, A(2006). "[http://www.ncbi.nlm.nih.gov/pubmed/17274769?dopt=Abstract Engineering life through Synthetic Biology]".''In silico Biology. '' '''0038(6)''':<br />
<br />
;Cleland, CE, et al.2002{{anchor|Cleland, CE, et al.2002}}<br />
:Cleland, CE, et al.(2002). "[http://www.springerlink.com/content/hl14401v6rq7010r/ Defining 'life']".''Origins of Life and Evolution of the Biosphere. '' '''4(32)''':387-393<br />
<br />
;Deng 2003 {{anchor|Deng2003}}<br />
:Deng X, Li QB, Lu YH, Sun DH, Huang YL, Chen XR. (2003). "[http://www.ncbi.nlm.nih.gov/pubmed/12727263 Bioaccumulation of nickel from aqueous solutions by genetically engineered Escherichia coli.]". '' Water Res.'' '''37(10)''':2505-2511<br />
<br />
;Deng 2007 {{anchor|Deng2007}}<br />
:Deng X, Yi XE, Liu G. (2007). "[http://www.ncbi.nlm.nih.gov/pubmed/16890348 Cadmium removal from aqueous solution by gene-modified Escherichia coli JM109]". '' Journal Hazard Mater. '' '''139(2)''':340-344<br />
<br />
;Deng 2008 {{anchor|Deng2008}}<br />
:Deng X, Hu ZL, Yi XE. (May 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/17920767 Continuous treatment process of mercury removal from aqueous solution by growing recombinant E. coli cells and modeling study]". '' Journal Hazard Mater. '' '''153(1-2)''':487-492<br />
<br />
;Deplazes, A2009{{anchor|Deplazes, A2009}}<br />
:Deplazes, A(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19415076?dopt=Abstract Piecing together a puzzle An exposition of synthetic biology]".''Embo Reports. '' '''5(10)''':428-432<br />
<br />
;Dey 1995 {{anchor|Dey1995}}<br />
:Saibal Dey, Barry P. Rosen (1995). "[http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=176602 Dual Mode of Energy Coupling by the Oxyanion Translocating ArsB Protein]". ''JOURNAL OF BACTERIOLOGY'' '''177(2)''': 385–389<br />
<br />
;Dong 2008 {{anchor|Dong2008}}<br />
:Dong, Liangjie (December 2008). "[http://www.freepatentsonline.com/y2008/0311288.html Methods and Compositions for Removal of Arsenic and Heavy Metals From Water]". ''United States Patent Application 20080311288 Kind Code:A1 <br />
''<br />
<br />
;EPA 2000 {{anchor|EPA2000}}<br />
:Environmental Protection Agency (December 2000). "[http://www.epa.gov/safewater Technologies and Costs for Removal of Arsenic from Drinking Water]". ''EPA 815-R-00-028'' <br />
<br />
;Ettema 2006 {{anchor|Ettema2006}}<br />
:Thijs J. G. Ettema, Arie B. Brinkman ''et al'' (2006). "[http://dx.doi.org/10.1099/mic.0.28724-0 Molecular characterization of a conserved archaeal copper resistance (cop) gene cluster and its copper-responsive regulator in Sulfolobus solfataricus P2]". ''Microbiology '''152''': 1969-1979<br />
<br />
;Fowler 1987 {{anchor|Fowler1987}}<br />
:Fowler BA. (1987). "[http://www.ncbi.nlm.nih.gov/pubmed/3297654 Intracellular compartmentation of metals in aquatic organisms: roles in mechanisms of cell injury]". '' Environ Health Perspect.'' '''7(1)''': 121-128<br />
<br />
;Fosmire 1990 {{anchor|Fosmire1990}}<br />
:Fosmire GA. (1990). "[http://www.ncbi.nlm.nih.gov/pubmed/2407097 Zinc toxicity]". ''American Society for Clinical Nutrition.'' '''5l''': 225-227<br />
<br />
;Frankenberger 2001 {{anchor|Frankenberger2001}}<br />
:William T. Frankenberger Jr. (2001). ''Environmental Chemistry of Arsenic'', Marcel Dekker, New York, NY, 404 pp. ISBN 0-8247-0676-5<br />
<br />
;Fu, DX, et al.2000{{anchor|Fu, DX, et al.2000}}<br />
:Fu, DX, et al.(2000). "[http://www.ncbi.nlm.nih.gov./pubmed/11039922?dopt=Abstract Structure of a glycerol-conducting channel and the basis for its selectivity]".''Science. '' '''5491(290)''':481-486<br />
<br />
;Gilchrist 2007 {{anchor|Gilchrist2007}}<br />
:Michael A. Gilchrist (2007). "[http://dx.doi.org/10.1093/molbev/msm169 Combining Models of Protein Translation and Population Genetics to Predict Protein Production Rates from Codon Usage Patterns]". ''Molecular Biology and Evolution'' '''24(11)''': 2362-2372<br />
<br />
;Gold 2008 {{anchor|Gold2008}}<br />
:Gold B, Deng H, ''et al''(2008). "[http://www.ncbi.nlm.nih.gov/pubmed/18724363 Identification of a copper-binding metallothionein in pathogenic mycobacteria]". ''Nat Chem Biol.'' '''4(10)''': 609-616<br />
<br />
;Goudar 1999 {{anchor|Goudar1999}}<br />
:Chetan T. Goudara, Jagadeesh R. Sonnadb and Ronald G. Duggleby (January 1999). "[http://dx.doi.org/10.1016/S0167-4838(98)00247-7 Parameter estimation using a direct solution of the integrated Michaelis-Menten equation]". ''Biochimica et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology'' '''1429(2)''': 377-383<br />
<br />
;Guven 2007 {{anchor|Guven2007}}<br />
:Basak Guven and Alan Howarda (September 2007). "[http://dx.doi.org/doi:10.1016/j.ecolmodel.2007.03.024 Identifying the critical parameters of a cyanobacterial growth and movement model by using generalised sensitivity analysis]". ''Ecological Modelling'' '''207(1)''': 11-21<br />
<br />
;Heller, KB, et al.1980{{anchor|Heller, KB, et al.1980}}<br />
:Heller, KB, et al.(1980). "[http://www.ncbi.nlm.nih.gov/pubmed/6998951?dopt=Abstract Substrate-Specificity and Transport-Properties of the Glycerol Facilitator of Escherichia-Coli]".''Journal of Bacteriology. '' '''1(144)''':274-278<br />
<br />
;Hirose 2006 {{anchor|Hirose2006}}<br />
:Hirose K, Ezaki B, Tong L Nakashima S, ''et al'' (August 2005) "[http://dx.doi.org/10.1016/j.toxlet.2005.11.008 Diamide stress induces a metallothionein BmtA through a repressor BxmR and is modulated by Zn-inducible BmtA in the cyanobacterium Oscillatoria brevis]". ''Toxicology Letters, '''2006''', 163, 250–256.<br />
<br />
;Hoefnagel 2002 {{anchor|Hoefnagel2002}}<br />
:M.H.N. Hoefnagel, A. van der Burgt, D.E. Martens, ''et al'' (March 2002). "[http://dx.doi.org/10.1023/A:1020313409954 Time Dependent Responses of Glycolytic Intermediates in a Detailed Glycolytic Model of ''Lactococcus Lactis'' During Glucose Run-Out Experiments]". ''Molecular Biology Reports'' '''29''': 157-161<br />
<br />
;Holland 2009 {{anchor|Holland2009}}<br />
:Daryl P. Holland, Anthony E. Walsby (January 2009). "[http://dx.doi.org/10.1016/j.mimet.2009.02.005 Digital recordings of gas-vesicle collapse used to measure turgor pressure and cell–water relations of cyanobacterial cells ]". ''Journal of Microbiological Methods'' '''77''': 214-224<br />
<br />
;Hristovski 2007 {{anchor|Hristovski2007}}<br />
:Kiril Hristovski, Andrew Baumgardner, Paul Westerhoff, (August 2007). "[http://dx.doi.org/10.1016/j.jhazmat.2007.01.017 Selecting metal oxide nanomaterials for arsenic removal in fixed bed columns: From nanopowders to aggregated nanoparticle media]". Journal of Hazardous Materials'' '''147(1-2)''': 265-274 <br />
<br />
;Kao 2008 {{anchor|Kao2008}}<br />
:Kao WC, Huang CC, Chang JS (October 2008). "[http://www.ncbi.nlm.nih.gov/pubmed/18313216 Biosorption of nickel, chromium and zinc by MerP-expressing recombinant Escherichia coli.]". '' J Hazard Mater.'' '''158(1)''': 100-106<br />
<br />
;Kelle, A2009{{anchor|Kelle, A2009}}<br />
:Kelle, A(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19636299?dopt=Abstract Synthetic biology and biosecurity From low levels of awareness to a comprehensive strategy]".''Embo Reports. '' 10)''':S23-S27<br />
<br />
;Kelly 2009 {{anchor|Kelly2009}}<br />
:Jason R. Kelly, Adam J. Rubin, Joseph H. Davis, ''et al'' (March 2009). "[http://dx.doi.org/10.1186/1754-1611-3-4 Measuring the activity of BioBrick promoters using an in vivo reference standard]". ''Journal of Biological Engineering'' '''3''': 4<br />
<br />
;Khunajakr 1999 {{anchor|Khunajakr1999}}<br />
:Nongpanga Khunajakr, Chun-Qiang Liu ''et al'' (March 1999). "[http://dx.doi.org/10.1016/S0378-1119(98)00395-3 A plasmid-encoded two-component regulatory system involved in copper-inducible transcription in Lactococcus lactis]". ''Gene'''229(1-1)''': 229-235<br />
<br />
;Klaassen 1994 {{anchor|Klaassen1994}}<br />
:Klaassen, Curtis D., Supratim Choudhuri, James M. McKim, Jr., Lois D. Lehman-McKeeman, and William C. Kershaw (1994). [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1567434/ "In Vitro and In Vivo Studies on the Degradation of Metallothionein"]. ''Environ. Health Perspect'' '''102(3)''': 141-146.<br />
<br />
;Kloosterman 2008 {{anchor|Kloosterman2008}}<br />
:Tomas G. Kloosterman, Robert M. Witwicki ''et al'' (2008). "[http://dx.doi.org/10.1128/JB.00307-08 Opposite Effects of Mn2+ and Zn2+ on PsaR-Mediated Expression of the Virulence Genes pcpA, prtA, and psaBCA of Streptococcus pneumonia]". ''J Bacterio'''190(15)''': 5382–5393<br />
<br />
;Kostal 2004 {{anchor|Kostal2004}}<br />
:{{star}} Jan Kostal, Rosanna Yang, Cindy H. Wu, ''et al'' (August 2004). "[http://dx.doi.org/10.1128/AEM.70.8.4582-4587.2004 Enhanced Arsenic Accumulation in Engineered Bacterial Cells Expressing ArsR]". ''Applied and Environmental Microbiology'' 70(8): 4582–4587<br />
<br />
;Lewinson 2009 {{anchor|Lewinson2009}}<br />
:Lewinson O, Lee AT, Rees DC. (2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19264958 A P-type ATPase importer that discriminates between essential and toxic transition metals]". '' PNAS'' 106(12): 4677-4682<br />
<br />
;Li 1998 {{anchor|Li1998}}<br />
:{{star}} Ning Li and Maura C. Cannon (May 1998). "Gas Vesicle Genes Identified in Bacillus megaterium and Functional Expression in Escherichia coli". ''Journal of Bacteriology'' '''180(9)''': 2450–2458<br />
<br />
;Lin 2007-1 {{anchor|Lin2007-1}}<br />
:Yung-Feng Lin, Jianbo Yang and Barry P. Rosen (April 2007). "[http://dx.doi.org/10.1074/jbc.M700886200 ArsD Residues Cys12, Cys13, and Cys18 Form an As(III)-binding Site Required for Arsenic Metallochaperone Activity]". ''The Journal of Biological Chemistry'' '''282(23)''': 16783–16791<br />
<br />
;Lin 2007-2 {{anchor|Lin2007-2}}<br />
:Yung-Feng Lin, Jianbo Yang and Barry P. Rosen (December 2007). "[http://dx.doi.org/10.1007/s10863-007-9113-y ArsD: an As(III) metallochaperone for the ArsAB As(III)-translocating ATPase]". ''Journal of Bioenergetics and Biomembranes'' '''39''': 453-458<br />
<br />
;Liu 2004 {{anchor|Liu2004}}<br />
:Tong Liu, Susumu Nakashima ''et al'' (April 2004) "[http://dx.doi.org/10.1074/jbc.M310560200 A Novel Cyanobacterial SmtB/ArsR Family Repressor Regulates the Expression of a CPx-ATPase and a Metallothionein in Response to Both Cu(I)/Ag(I) and Zn(II)/Cd(II)]". ''The Journal of Biological Chemistry, '''2004''', Vol. 279, No. 17, 17810–17818.<br />
<br />
;Liu 2006 {{anchor|Liu2006}}<br />
:Tong Liu Arati Ramesh ''et al''(December 2006). "[http://dx.doi.org/10.1038/nchembio844 CsoR is a novel Mycobacterium tuberculosis copper-sensing transcriptional regulator]". ''Nature Chemical Biology'' '''3''': 60-68<br />
<br />
;Liu 2008 {{anchor|Liu2008}}<br />
:Tong Liu, Xiaohua Chen, Zhen Ma, ''et al'' (September 2008) "[http://dx.doi.org/10.1021/bi801313y A CuI-sensing ArsR family Metal Sensor Protein with a Relaxed Metal Selectivity Profile]". ''Biochemistry, '''2008''', 47(40), 10564–10575.<br />
<br />
; Lundstrom (2006) {{anchor|Lundstom2006}}<br />
:Lundstrom, K. (2006). “[http://www.springerlink.com/content/23783l53l616238t/ Structural genomics for membrane proteins]” ''Cell. Mol. Life Sci.'' '''63: 2597–2607'''.<br />
<br />
;Martinson 2009 {{anchor|Martinson2009}}<br />
:Carol A. Martinson, K.J. Reddy, (August 2009). "[http://dx.doi.org/10.1016/j.jcis.2009.04.075 Adsorption of arsenic(III) and arsenic(V) by cupric oxide nanoparticles]". ''Journal of Colloid and Interface Science'' '''336(2)''': 406-411<br />
<br />
;Meng, YL, et al.2004{{anchor|Meng, YL, et al.2004}}{{anchor|Meng2004}}:Meng, YL, et al.(2004). ” [http://dx.doi.org/10.1074/jbc.M400037200 As(III) and Sb(III) uptake by G1pF and efflux by ArsB in Escherichia coli]".''Journal of Biological Chemistry. '' '''18(279)''':18334-18341<br />
<br />
;Merrifield 2004 {{anchor| Merrifield2004}}<br />
:M. E. Merrifield, T. Ngu, M. J. Stillman ''et al'' (September 2004). "[http://www.ncbi.nlm.nih.gov/pubmed/15464992 Arsenic binding to <i>Fucus vesiculosus</i> metallothionein.]". ''Biochemical and Biophysical Research Communications'' '''324 :''' 127–132<br />
<br />
;Mills 1994 {{anchor|Mills1994}}<br />
:Scott D. Mills Chun-Keun Lim and Donald A. Cooksey (1994). "[http://dx.doi.org/10.1007/BF00286685 Purification and characterization of CopR, a transcriptional activator protein that binds to a conserved domain (cop box) in copper- inducible promoters of Pseudomonas syringae]". ''Molecular and General Genetics MGG '''244(4)''': 1432-1874<br />
<br />
;Mindlin, SZ, et al.2002{{anchor|Mindlin, SZ, et al.2002}}:Mindlin, SZ, et al.(2002). "[http://dx.doi.org/10.1023/A:1015353402657 Horizontal transfer of mercury resistance genes in environmental bacterial populations]".''Molecular Biology. '' '''2(36)''':160-170<br />
<br />
;Moore 2005 {{anchor|Moore2005}}<br />
:Charles M. Moore, Ahmed Gaballa ''et al'' (May 2005). "[http://dx.doi.org/10.1111/j.1365-2958.2005.04642.x Genetic and physiological responses of Bacillus subtilis to metal ion stress]". ''Molecular Microbiology'''57(1)''': 27-40<br />
<br />
;Morris 1999 {{anchor| Morris1999}}<br />
:C.A. Morris, B. Nicolaus, V. Sampson ''et al'' (March 1999). "[http://www.ncbi.nlm.nih.gov/pubmed/10024535 Identification and characterization of a recombinant metallothionein protein from a marine alga, <i>Fucus vesiculosus</i>]". '' The Biochemical journal'' '''338(2):''' 553-560<br />
<br />
;Nawapan 2009 {{anchor|Nawapan2009}}<br />
:Sirikan Nawapan, Nisanart Charoenlap ''et al'' (August 2009). "[http://dx.doi.org/10.1046/10.1128/JB.00384-09 Functional and Expression Analyses of the cop Operon, Required for Copper Resistance in Agrobacterium tumefaciens]". ''American Society for Microbiology '''191(16)''': 5159-5168<br />
<br />
;Neves 1999 {{anchor|Neves1999}}<br />
:Ana Rute Neves, Ana Ramos, Marta C. Nunes, ''et al'' (1999). "[http://dx.doi.org/10.1002/(SICI)1097-0290(19990720)64%3A2%3C200%3A%3AAID-BIT9%3E3.0.CO%3B2-K In vivo nuclear magnetic resonance studies of glycolytic kinetics in ''Lactococcus lactis'']". ''Biotechnology and Bioengineering'' '''64''': 200-212<br />
<br />
;Ngu 2006 {{anchor|Ngu2006}}<br />
:Thanh T. Ngu, M. Stillman (April 2006). "[http://dx.doi.org/10.1021/ja062914c Arsenic Binding to Human Metallothionein]". ''J. Am. Chem. Soc'' '''128 (38)''': 12473–12483<br />
<br />
;Ngu 2009 {{anchor|Ngu2009}}<br />
:Thanh T. Ngu, J. A. Lee ''et al''. (April 2009). "[http://dx.doi.org/10.1021/bi9007462 Arsenic Metalation of Seaweed ''Fucus vesiculosus'' Metallothionein: The importance of the Interdomain Linker in Metallothionein]". ''Biochemistry'' '''48''': 8806–8816<br />
<br />
;Nicholls, H2008{{anchor|Nicholls, H2008}}<br />
:Nicholls, H(2008). "[http://dx.doi.org/10.1016/S0140-6736(08)61881-4 Synthetic biology]".''Lancet. '' S45-S49<br />
<br />
;Nouri, A, et al.2009{{anchor|Nouri, A, et al.2009}}<br />
:Nouri, A, et al.(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19270668?dopt=Abstract Proliferation-resistant biotechnology: an approach to improve biological security]".''Nature Biotechnology. '' '''3(27)''':234-236<br />
<br />
;Oehmen 2006 {{anchor|Oehmen2006}}<br />
:Adrian Oehmen, Rui Viegas, Svetlozar Velizarov, ''et al'' (November 2006). "[http://dx.doi.org/10.1016/j.desal.2006.03.091 Removal of heavy metals from drinking water supplies through the ion exchange membrane bioreactor]". ''Desalination'' '''199(1-3)''': 405-407 <br />
<br />
;Outten 2000 {{anchor|Outten2000}}<br />
:F. Wayne Outten, Caryn E. Outten, Jeremy Hale and Thomas V. O’Halloran (October 2000). "[http://dx.doi.org/10.1074/jbc.M006508200 Transcriptional Activation of an ''Escherichia coli'' Copper Efflux Regulon by the Chromosomal MerR Homologue, CueR]". ''The Journal of Biological Chemistry'' '''275(40)''': 31024-31029<br />
<br />
;Pennella 2005 {{anchor|Pennella2005}}<br />
:Pennella M.A. & Giedroc D.P., (August 2005) "[http://dx.doi.org/10.1007/s10534-005-3716-8 Structural determinants of metal selectivity in prokaryotic metal-responsive transcriptional regulator]". ''BioMetals, '''2005''', 18, 413–428.<br />
<br />
;Poole 1977 {{anchor|Poole1977}}<br />
:R.K. Poole (1977). "[http://mic.sgmjournals.org/cgi/content/abstract/98/1/177 Fluctuations in Buoyant Density during the Cell Cycle of Escherichia coli K12]". ''Journal of General Microbiology'' '''98''': 177-186<br />
<br />
;Porquet, A, et al.2007{{anchor|Porquet, A, et al.2007}}<br />
:Porquet, A, et al.(2007). “[http://www.ncbi.nlm.nih.gov./pubmed/17713961?dopt=Abstract Structural evidence of the similarity of Sb(OH)(3) and As(OH)(3) with glycerol: Implications for their uptake]".''Chemical Research in Toxicology. '' '''9(20)''':1269-1276<br />
<br />
;Raje 2005 {{anchor|Raje2005}}<br />
:N. Raje,* K. K. Swain (April 2005). "[http://dx.doi.org/10.1023/A:1015812517214 Purification of arsenic contaminated ground water using hydrated manganese dioxide]". ''Journal of Radioanalytical and Nuclear Chemistry'' '''253(1)''': 77-80<br />
<br />
;Rawlings 1994 {{anchor| Rawlings1994}}<br />
:RAWLINGS, D E. and KUSANO, T (1994). “[http://mmbr.asm.org/cgi/reprint/58/1/39?view=long&pmid=8177170 Molecular Genetics of Thiobacillus ferrooxidans]”. ‘’MICROBIOLOGICAL REVIEWS’’, ‘’’58 (1): 39-55’’’<br />
<br />
;Rensing 2005 {{anchor|Rensing2005}}<br />
:Christopher Rensing (June 2005). "[http://dx.doi.org/10.1128/JB.187.12.3909-3912.2005 Form and Function in Metal-Dependent Transcriptional Regulation: Dawn of the Enlightenment]". ''Journal of Bacteriology'' '''187(12)''': 3909–3912<br />
<br />
;Robinson 2001 {{anchor|Robinson2001}}<br />
:Nigel J. Robinson, Simon K. Whitehall and Jennifer S. Cavet (2001). "[http://www.ncbi.nlm.nih.gov/pubmed/11407113 Microbial Metallothioneins]". ''Advances in Microbial Physiology'' '''44''': 183-213<br />
<br />
;Rosen 1996 {{anchor|Rosen1996}}<br />
:Barry P. Rosen (August 1996). "[http://dx.doi.org/10.1007/s007750050053 Bacterial resistance to heavy metals and metalloids]". ''Journal of Biological Inorganic Chemistry'' '''1(4)''': 273-277<br />
<br />
;Rosen, BR, et al.2009{{anchor|Rosen, BR, et al.2009}}{{anchor|Rosen2009}}<br />
:Rosen, BR, et al.(2009). “[http://dx.doi.org/10.1007/s007750050053 Transport pathways for arsenic and selenium: A minireview]".''Environment International. '' '''3(35)''':512-515<br />
<br />
;Samuel, GN, et al.2009{{anchor|Samuel, GN, et al.2009}}<br />
:Samuel, GN, et al.(2009). "[http://www.ncbi.nlm.nih.gov/pubmed/19079130?dopt=Abstract Managing the unimaginable Regulatory responses to the challenges posed by synthetic biology and synthetic genomics]".''Embo Reports. '' '''1(10)''':7-11<br />
<br />
;Schmidt, M 2008 {{anchor|Schmidt2008}}<br />
:Schmidt, M (2008). "[http://dx.doi.org/10.1007/s11693-008-9018-z Diffusion of synthetic biology: a challenge to biosafety]", ''Syst Synth Biol.''<br />
<br />
;Schwartz 2008 {{anchor|Schwartz2008}}<br />
:Russel Schwartz (2008). ''Biological modeling and simulation: a survey of practical models, algorithms, and numerical methods'' MIT Press. ISBN 978-0-262-19584-3<br />
<br />
;Serrano, L2007{{anchor|Serrano, L2007}}<br />
:Serrano, L(2007). "[http://www.ncbi.nlm.nih.gov/pubmed/18091727?dopt=Abstract Synthetic biology: promises and challenges]".''Molecular Systems Biology. '' 3)''':<br />
<br />
;Shi 1992 {{anchor|Shi1992}}<br />
:Jianguo Shi, William P. Lindsay, James W. Huckle (June 1992). "[http://dx.doi.org/10.1016/0014-5793(92)80509-F Cyanobacterial metallothionein gene expressed in Escherichia coli: Metal-binding properties of the expressed protein]". ''FEBS Letters'' '''303(2-3)''': 159-163<br />
<br />
;Singh 2008 {{anchor|Singh2008}}<br />
:Shailendra Singh, Ashok Mulchandani, Wilfred Chen (February 2008). "[http://dx.doi.org/10.1128/AEM.02871-07 Highly Selective and Rapid Arsenic Removal by Metabolically Engineered Escherichia coli Cells Expressing Fucus vesiculosus Metallothionein]". ''MICROBIOLOGY'' '''74(9)''': 2924–2927<br />
<br />
;Sivertsen 2008 {{anchor|Sivertsen2008}}<br />
:Astrid C. Sivertsen, Marvin J. Bayro, ''et al'' ( april 2008). "[http://dx.doi.org/doi:10.1016/j.jmb.2009.02.015 Solid-State NMR Evidence for Inequivalent GvpA Subunits in Gas Vesicles]". ''Journal of Molecular Biology'' '''387(4)''': 1032-1039<br />
<br />
;Stephan Hug {{anchor|Stephan Hug}}<br />
:Stephan Hug. "[http://www.eawag.ch/publications/eawagnews/www_en49/en49e_ihv_web.html Arsenic Contamination of Ground Water: Disastrous Consequences in Bangladesh]". ''EAWAG news'' '''49(e)''': 18-20<br />
<br />
;Stephenson, JR, et al.1996 {{anchor|Stephenson, JR, et al.1996}}:Stephenson, JR, et al.(1996). "[http://dx.doi.org/10.1002 Release of genetically modified micro-organisms into the environment]".''Journal of Chemical Technology and Biotechnology. '' '''1(65)''':5-14<br />
<br />
;Summers 2009 {{anchor|Summers2009}}<br />
:Anne O. Summers (April 2009). "[http://dx.doi.org/10.1016/j.mib.2009.02.003 Damage control: regulating defenses against toxic metals and metalloids]". ''Current Opinion in Microbiology'' '''12(2)''': 138-144<br />
<br />
;Suzuki 1998 {{anchor|Suzuki1998}}<br />
:Katsuhisa Suzukia, Norio Wakaob, Tetsuya Kimuraa, Kazuo Sakkaa and Kunio Ohmiya (February 1998). "[http://dx.doi.org/10.1016/S0922-338X(98)80016-0 Metalloregulatory properties of the ArsR and ArsD repressors of ''Acidiphilium multivorum'' AIU 301]". ''Journal of Fermentation and Bioengineering'' '''85(6)''': 623-626<br />
<br />
;Thelwell 1998 {{anchor|Thelwell1998}}<br />
:Thelwell C., Robinson N.J. & Turner-Cavet J.S., "[http://dx.doi.org/10.1073/pnas.95.18.10728 An SmtB-like repressor from Synechocystis PCC 6803 regulates a zinc exporter]". ''Proc. Natl. Acad. Sci. USA, '''1998''', Vol. 95, 10728–10733.<br />
<br />
;Tisa 1989 {{anchor|Tisa1989}}<br />
:Louis S. Tisa and Barry P. Rosen (January 1990). "[http://www.ncbi.nlm.nih.gov/pubmed/1688427 Molecular characterization of an anion pump. The ArsB protein is the membrane anchor for the ArsA protein]". ''The journal of biological chemistry'' '''265(1)''': 190-194<br />
<br />
;Turner 1995 {{anchor|Turner1995}}<br />
:Jennifer S. Turner, Nigel J. Robinson and Amit Gupta (March 1995). "[http://dx.doi.org/10.1007/BF01569937 Construction of Zn<sup>2+</sup>/Cd<sup>2+</sup>-tolerant cyanobacteria with a modified metallothionein divergon: Further analysis of the function and regulation of ''smt'']". ''Journal of Industrial Microbiology and Biotechnology'' '''14(3-4)''': 259-264<br />
<br />
;Walsby 1979 {{anchor|Walsby1979}}<br />
:A.E. Walsby (April 1979). "[http://dx.doi.org/10.1016/0022-2836(79)90281-X Average thickness of the gas vesicle wall in Anabaena flos-aquae]". ''Journal of Molecular Biology'' '''129(2)''': 279-285<br />
<br />
;Walsby 1994 {{anchor|Walsby1994}}<br />
:A.E. Walsby (March 1994). "[http://www.ncbi.nlm.nih.gov/pubmed/8177173 Gas Vesicles]". ''Microbiological reviews'' '''58(1)''': 94-144<br />
<br />
;Wlckramaslnghe 2004 {{anchor|Wlckramaslnghe2004}}<br />
:S.R. Wlckramaslnghe, Binbing Han, J. Zimbron, ''et al'' (October 2004). "[http://dx.doi.org/10.1016/j.desal.2004.03.013 Arsenic removal by coagulation and filtration: comparison of<br />
groundwaters from the United States and Bangladesh]". ''Desalination'' '''169(3)''': 231-244 <br />
<br />
;Xu 1996 {{anchor|Xu1996}}<br />
:Chun Xu, Weiping Shi and Barry P. Rosen (February 1996). "[http://dx.doi.org/10.1074/jbc.271.5.2427 The Chromosomal ''arsR'' Gene of ''Escherichia coli'' Encodes a ''trans''-acting Metalloregulatory Protein]". ''The Journal of Biological Chemistry'' '''271(5)''': 2427-2432<br />
<br />
;Yamamoto 2005 {{anchor|Yamamoto2005}}<br />
:Kaneyoshi Yamamoto and Akira Ishihama (2005). "[http://dx.doi.org/10.1111/j.1365-2958.2005.04532.x Transcriptional response of ''Escherichia coli'' to external copper]". ''Molecular Microbiology'' '''56(1)''': 215-227<br />
<br />
;Zwart, SD, et al.2006{{anchor|Zwart, SD, et al.2006}}:Zwart, SD, et al.(2006). "[http://dx.doi.org/10.1007/s11948-006-0063-2 network approach for distinguishing ethical issues in research and development]".''Science and Engineering Ethics. '' '''4(12)''':663-684<br />
<br />
<br />
<br />
Miscellaneous:<br />
* [http://ginkgobioworks.com/cgi/primer.cgi Primer design Bioworks]<br />
* [http://openwetware.org/wiki/The_BioBricks_Foundation:Standards/Technical/Measurement Promotor measurement]<br />
* [http://openwetware.org/wiki/Main_Page OpenWetWare]<br />
* [http://www.hgsc.bcm.tmc.edu/projects/microbial/microbial-detail.xsp?project_id=105 E. coli DH10B genome] (with BLAST)<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:GroningenTeam:Groningen2009-10-21T21:42:36Z<p>Jaspervdg: Moved abstract up a little.</p>
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<h1>Heavy metal scavengers<!-- with a vertical gas drive--></h1><br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To battle this problem, a '''purification strategy''', in which arsenic, zinc and copper are removed from water and sediment, was developed. This strategy encompasses a biological device in which <i>E. coli</i> bacteria accumulate metal ions from solutions, after which they '''produce gas vesicles''' and '''start floating'''. This biological device consists of two integrated systems: one for metal uptake and storage, the other for metal induced buoyancy. The uptake and storage system consists of a [[Team:Groningen/Project/Transport|metal transporter]] and [[Team:Groningen/Project/Accumulation|metal binding proteins]] (to reduce toxicity and increase accumulation). The buoyancy system is made up of a [[Team:Groningen/Project/Promoters|metal induced promotor]] in front of a [[Team:Groningen/Project/Vesicle|gas vesicle gene cluster]]. The combination of both systems will enable the efficient cleaning of polluted water and sediment in a biological manner. <br />
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{{Team:Groningen/Footer_Main}}</div>Jaspervdghttp://2009.igem.org/Team:GroningenTeam:Groningen2009-10-21T21:41:07Z<p>Jaspervdg: Moved twitter stuff and counters to team page.</p>
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<h1>Heavy metal scavengers<!-- with a vertical gas drive--></h1><br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To battle this problem, a '''purification strategy''', in which arsenic, zinc and copper are removed from water and sediment, was developed. This strategy encompasses a biological device in which <i>E. coli</i> bacteria accumulate metal ions from solutions, after which they '''produce gas vesicles''' and '''start floating'''. This biological device consists of two integrated systems: one for metal uptake and storage, the other for metal induced buoyancy. The uptake and storage system consists of a [[Team:Groningen/Project/Transport|metal transporter]] and [[Team:Groningen/Project/Accumulation|metal binding proteins]] (to reduce toxicity and increase accumulation). The buoyancy system is made up of a [[Team:Groningen/Project/Promoters|metal induced promotor]] in front of a [[Team:Groningen/Project/Vesicle|gas vesicle gene cluster]]. The combination of both systems will enable the efficient cleaning of polluted water and sediment in a biological manner. <br />
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{{Team:Groningen/Footer_Main}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/TeamTeam:Groningen/Team2009-10-21T21:40:33Z<p>Jaspervdg: Moved twitter stuff and counters to team page.</p>
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[[Category:Team:Groningen/Disciplines/Project_Management|Team]]<br />
[[Category:Team:Groningen/Roles/Project_Manager|Team]]<br />
<br />
==Our Team At A Glance==<br />
<br />
[[Image:IGEMGroningen_Molen.jpg|400px|thumb|right|[Team:Groningen/Team|Our team!]]<br />
<br />
Welcome to the main page of the iGEM Groningen team! We are an interdisciplinary team of [[Team:Groningen/Team|11 enthusiastic students]] from the [http://www.rug.nl/ University of Groningen] situated in the not-too-big city of [http://portal.groningen.nl/en/startpagina Groningen] in [http://maps.google.com/maps?f=q&source=s_q&hl=en&geocode=&q=Groningen&sll=53.281349,6.689459&sspn=0.007261,0.018926&ie=UTF8&z=12&iwloc=A the north of the Netherlands]. You can contact us at '''igemgroningen@googlegroups.com'''. <br />
<br />
Our team consists of the following student-members:<br />
<br />
* [[User:JolandaWitteveen|Jolanda Witteveen]] (Biomedical Technology): [[:Category:Team:Groningen/Roles/Chair|Chair]], [[:Category:Team:Groningen/Roles/Project_Manager|Project Manager]]<br />
* [[User:svenjurgens|Sven Jurgens]] (Molecular Biology): [[:Category:Team:Groningen/Roles/Treasurer|Treasurer]]<br />
* [[User:Jaspervdg|Jasper van de Gronde]] (Computational Science and Visualization): [[:Category:Team:Groningen/Roles/Configuration_Manager|Configuration Manager]], [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
* [[User:Verhoeven1981|Michael Verhoeven]] (Chemistry): [[:Category:Team:Groningen/Roles/Public_Relations_Officer|PR Officer]]<br />
* [https://2009.igem.org/User:Nienke Nienke Kuipers] (Molecular Biology): [[:Category:Team:Groningen/Roles/Scribe|Minutes secretary]] and Lab manager<br />
* [[User:Jelle|Steven Jelle Meijer]] (Molecular Biology): [[:Category:Team:Groningen/Roles/Facility_Manager|Facility Manager Haren]]<br />
* [[User:Wilfred|Wilfred Poppinga]] (Medical Pharmaceutical Sciences): [[:Category:Team:Groningen/Roles/Chair|Vice Chair]], [[:Category:Team:Groningen/Roles/Treasurer|Treasurer]]<br />
* [https://2009.igem.org/User:Paulschavemaker Paul Schavemaker] (Molecular Life Sciences): [[:Category:Team:Groningen/Roles/Scribe|Minutes secretary]]<br />
* [https://2009.igem.org/User:Frans Frans Bianchi] (Molecular Biology): [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
* [[User:Klaas Bernd Over|Klaas Bernd Over]] (Applied Physics): [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
* [[User:Annelies|Annelies van Keulen]] (Molecular Biology/Psychology): [[:Category:Team:Groningen/Roles/Modeller|Modeller]]<br />
<br />
==Our advisors==<br />
*prof. dr. Oscar Kuipers: [http://molgen.biol.rug.nl/molgen/index.php Molecular Genetics] (Head)<br />
*prof. dr. Jan Kok: [http://molgen.biol.rug.nl/molgen/index.php Molecular Genetics]<br />
*prof. dr. Bert Poolman: Biochemistry; [http://www.centreforsyntheticbiology.eu/ Centre for Synthetic Biology] (Director)<br />
*prof. dr. Roel Bovenberg: Synthetic biology and Cell engineering; Corporate Scientist Biotechnology, [http://www.dsm.com/ DSM]<br />
*dr. Dirk Slotboom: Enzymology <br />
*[https://2008.igem.org/Team:Groningen/team.html iGEM Groningen 2008]. Especially Auke van Heel & Martijn Herber<br />
<br />
<br><br><br />
<br />
==Where to hear from us==<br />
===In the media===<br />
Follow us in '''[[Team:Groningen/Publicity| The News]]'''<br />
<br />
Also follow us on '''[http://twitter.com/igemgroningen Twitter]!'''<br />
<br />
Check out some interesting '''[[Team:Groningen/Videos|Videos]]'''<br />
<br />
Check out some interesting '''[[Team:Groningen/Pictures|Pictures]]'''<br />
<br />
===Presenting===<br />
{|<br />
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*{{todo}} December 11<sup>th</sup> 2009: Meeting @ [http://www.dsm.com/en_US/html/home/dsm_home.cgi DSM] - [http://maps.google.nl/maps?oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&q=delft+DSM&fb=1&gl=nl&hq=DSM&hnear=delft&cid=0,0,8723601113946313921&ei=B_jSSrqHIcTz-QbZsNT7Ag&sa=X&oi=local_result&ct=image&resnum=1&ved=0CAoQnwIwAA Delft]<br />
*{{todo}} November 23<sup>rd</sup> 2009: Meeting @ student societies for [http://www.chemische-binding.nl/ Chemistry] and [http://www.fmf.nl/?file=main.html&lang=.en Math, Physics, Computer Science and Astronomy]<br />
*{{todo}} <b>October 30<sup>th</sup> to November 2<sup>nd</sup> 2009: Presentation @ The [https://2009.igem.org/ iGEM] 2009 [https://2009.igem.org/Jamboree Jamboree] - [http://whereis-beta.mit.edu/?mapterms=stata%20center&zoom=15&lat=42.36161990569666&lng=-71.09055519104004&open=object-32 MIT Stata] and [http://whereis-beta.mit.edu/?mapterms=lobby%2013&zoom=15&lat=42.35993922977393&lng=-71.092529296875&open=object-13 Lobby 13] in Cambridge, MA</b><br />
*{{todo}} October 26<sup>th</sup> 2009: Lecture @ [http://www.hanzeuniversity.eu/home/international Hanze University], Biology & Medical Laboratory Research and Bioinformatics students - room A257 [http://maps.google.nl/maps?q=Zernikeplein+7+Groningen&oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&hq=&hnear=Zernikeplein+7,+9747+Groningen&gl=nl&ei=wwHPSor9A4OF-QaTkL2FAw&sa=X&oi=geocode_result&ct=title&resnum=1 Zernikeplein 11, Groningen] <br />
*{{todo}} October 23<sup>rd</sup> 2009: Update Lecture @ the Bachelor course [http://www.rug.nl/ocasys/fwn/vak/show?code=WLB07010 Genes & Behaviour] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 Haren]<br />
*October 19<sup>th</sup> 2009: [http://www.cs.rug.nl/~biehl/Coll/index.html Colloquium] @ [http://www.rug.nl/informatica/index Institute for Mathematics and Computing Science] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=jGw&resnum=0&q=bernoulliborg%20Groningen%20Nijenborgh%209&um=1&ie=UTF-8&sa=N&tab=wl room 5161.0267 (Bernoulliborg), Groningen]<br />
*October 12<sup>th</sup> 2009: Meeting @ Marine Biology cluster - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 D225, Haren]<br />
* October 7<sup>th</sup> 2009: Lecture @ the Bachelor course [http://www.rug.nl/ocasys/fwn/vak/show?code=WLB07010 Genes & Behaviour] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 D225, Haren]<br />
* October 2<sup>nd</sup> 2009: Lunch meeting @ [http://www2.dhv.com/default.aspx DHV] - [http://maps.google.com/maps?f=q&source=s_q&hl=nl&geocode=&q=Laan+1914+no+35,+Amersfoort&sll=37.0625,-95.677068&sspn=54.357317,79.013672&ie=UTF8&hq=&hnear=Laan+1914+35,+3818+Amersfoort,+Utrecht,+Nederland&ll=52.134107,5.36828&spn=0.010405,0.01929&t=h&z=16&iwloc=r3 Groene zaal DHV, Amersfoort]<br />
* October 1<sup>st</sup> 2009: Lunch meeting @ Life Science student society [http://www.glv-idun.nl/ GLV Idun] - [http://maps.google.nl/maps?hl=nl&client=firefox-a&rls=org.mozilla:nl:official&hs=7wv&q=Haren+groningen&um=1&ie=UTF-8&hq=&hnear=Haren&gl=nl&ei=CSXDSsXoLJTc-Qbd7IXvCw&sa=X&oi=geocode_result&ct=image&resnum=1 Groene Zaal, Haren]<br />
*September 29<sup>th</sup> 2009: Meeting @ Applied physics student society [http://www.professorfrancken.nl/ TFV Professor Francken] - [http://maps.google.nl/maps?q=Nijenborgh%204%20NCC%20Complex&oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&hl=nl&ie=UTF-8&sa=N&tab=vl NCC complex VIP Room building 16, Groningen]<br />
*[https://2009.igem.org/Team:Groningen/Notebook/24_September_2009 September 24<sup>th</sup> 2009]: Presentation @ 2nd Programme Day of the [http://www.kluyvercentre.nl/ Kluyver Centre] - [http://maps.google.nl/maps?q=Generaal+Foulkesweg+96+6703+DS+Wageningen&oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&hq=&hnear=Generaal+Foulkesweg+96,+6703+Wageningen&gl=nl&ei=giXDSvfgDcrI-Qa53ojvCw&sa=X&oi=geocode_result&ct=image&resnum=1 Wageningse Berg, Wageningen]<br />
*September 11<sup>th</sup> 2009: Presentation @ [http://www.rug.nl/gbb/studyatgbb/generalcourses/gbbsymposium2009 17th Annual] [http://www.rug.nl/gbb/index GBB] Symposium 2009 - [http://maps.google.nl/maps?oe=utf-8&rls=org.mozilla:nl:official&client=firefox-a&um=1&ie=UTF-8&q=Hampshire+hotel+Groningen+Radesingel+50,+9711+EK+Groningen&fb=1&gl=nl&hq=Hampshire+hotel&hnear=Groningen+Radesingel+50,+9711+EK+Groningen&cid=0,0,5400363645623663183&ei=eybDSq-jNojj-Qbz1PXuCw&sa=X&oi=local_result&ct=image&resnum=1 Hampshire hotel, Groningen]</div><br />
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{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-21T20:12:06Z<p>Jaspervdg: Linked to individual modelling sections.</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div style="clear:both;"></div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right;" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Arsenic}}</div><br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
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<div class="intro introduction"><br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|<span style="font-weight:normal;">Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line. For one thing, this makes it easier to '''explore''' the model, up to the point that even non-modellers are able to explore the model.</span>]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible ''interactively'' available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
</div><br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*'''Analysis''' of results. Using data from uptake experiments, promoter measurements and TEM pictures we can [[Team:Groningen/Modelling/Characterization|estimate further constants]] and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Models==<br />
Our modelling results can be viewed on our project pages, including our '''interactive''' calculators and graphs:<br />
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<li class="transport"></html>[[Team:Groningen/Project/Transport#Modelling|Transport]]<html></li><br />
<li class="accumulation"></html>[[Team:Groningen/Project/Accumulation#Modelling|Accumulation]]<html></li><br />
<li class="promoters"></html>[[Team:Groningen/Project/Promoters#Modelling|Metal-sensitive Promoters]]<html></li><br />
<li class="vesicles"></html>[[Team:Groningen/Project/Vesicle#Modelling|Gas Vesicles]]<html></li><br />
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Most of the modelling sections are based on our ODE model:<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Project/TransportTeam:Groningen/Project/Transport2009-10-21T20:09:51Z<p>Jaspervdg: /* Modelling uptake GlpF */ Anchor</p>
<hr />
<div>{{Team:Groningen/Project/Header|}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Project/Accumulation}}</div><br />
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<div class="intro"><br />
<h1>Transport</h1><br />
'''To isolate heavy metals from the environment we require uptake systems. So far we found several different mechanisms to create such a system. We investigated three kinds of metal uptake:'''<br />
*Metal transporters, Membrane proteins that transport the metal from the environment (<i>i.e.</i> wastewater) to the cytoplasm<br />
**Uncoupled<br />
**Coupled with 'helper' compounds<br />
*Metal binding proteins in the periplasm<br />
<br />
'''We have investigated several systems to determine which are suitable for the final design. The following systems are under consideration:'''<br />
<br />
*Arsenite uptake via GlpF<br />
*Copper/zinc uptake via HmtA<br />
*Heavy metal uptake coupled to citrate via ''ef''CitH ''bs''CitM <br />
*Periplasmic accumulation of heavy metals via Mer Operon.<br />
<br />
'''We chose to focus on GlpF and HmtA, the final device was made with GlpF for arsenate purification. '''<br />
<br><br><br><br />
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<br />
<br />
==Arsenite uptake via GlpF==<br />
<!--[[Image:GlpF.jpeg|200px|thumb|right|73As(III) and 125Sb(III) uptake into cells of E. coli is facilitated by the aquaglyceroporin channel GlpF.]]--><br />
<br />
===GlpF===<br />
<br />
====Introduction====<br />
GlpF is an aquaglycerol porin of E.coli which facilitates not only glycerol import, but also arsenic (As) and antimone (Sb) import [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000]]), [[Team:Groningen/Literature#Meng, YL, et al.2004|(Meng, YL, et al.2004]]), [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007]]), [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009)]] . It has homologues in other organisms; Fps1p has shown to facilitate arsenic import in yeast and AQP9 is the mammalian homologue [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007]]), [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009)]] .<br />
The GlpF aquaglycerol porin is a membrane protein with a symmetric arrangement of four independent GlpF channels. One monomer of this tetramer GlpF porin consists of six transmembrane and two half membrane-spanning α-helices that form a right-handed helical bundle around the channel. The channel has a diameter of ~15Å at the periplasmid end, which constricts towards a diameter of ~3.8Å at the beginning of a 28 Å long selective channel that ends at the cytoplasmic end [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000)]].<br />
The GlpF is a stereospecific channel that is thought to be more selective on molecular size than on chemical structure [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000]], [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]] . It does allow transport of a variance of non-charged compounds ranging from polyhydric alcohols, glycerol being one of them, arsenic to antimone [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000]]), [[Team:Groningen/Literature#Meng, YL, et al.2004|(Meng, YL, et al.2004]]), [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007)]], [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009]]), [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]]. Carbon sugars and ions are shown to be unable to be transported by GlpF [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]]. At physiological pH arsenic and antimone are not present in their ionic state but rather as As(OH)3 and Sb(OH)3 [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009)]]. These elements show a charge distribution similar to glycerol and a smaller but comparable volume. The structural similarities are thought to be the reason for the possibility of these elements to enter the cell by GlpF [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007)]], GlpF facilitates transport of these compounds down there gradient (inside or outside the cell).<br />
If GlpF behaves as a nonsaturable transporter, a transport rate of 1umol of glycerol is transported per minute per mgr of cell protein [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]].<br />
<br />
====Cloning strategy====<br />
This part has been obtained from the genome of ''E.coli'' 356 in two steps with PCR. First the whole gene was obtained from the genome by using PCR and in the second step an ''EcoR''1 restiction site was removed.<br />
The GlpF PCR product was restricted with ''Xba''I and ''Pst''I and a psB1AC3 vector with a pMed promotor was restricted with ''Spe''I and ''Pst''I. The restriction products were ligated. This resulted in a psB1AC3 vector with a promotor and GlpF.<br />
[[Image:RestictioLigationGlpF.JPG]]<br />
<br />
====Results====<br />
The ability of GlpF (overexpressed under IPTG induction) to transport As(III) was tested by an arsenite uptake [https://2009.igem.org/Team:Groningen/Protocols assay]. Also the full accumulation device (<partinfo>BBa_K190038</partinfo>) was tested using this assay. '''Data and analysis can be found [https://2009.igem.org/Team:Groningen/Project/Accumulation here]. <br />
'''<br />
<br />
[[Image:Growth_WT.gif|310px|left]]<br />
[[Image:Growth GlpF.gif|310px|left]]<br />
[[Image:Growth GlpF fMT.gif|310px|left]]<br />
<br />
The graphs above represent the result of the membrane protein [https://2009.igem.org/Team:Groningen/Protocols#Death_assay assay]. The lines in the graphs represent the average optical density of a construct over time. The graph on the left show that increased As(III) levels inhibit growth and, that as more As(III) is added the lower the plateau is. <br />
<br />
The middle graph is from the pLac GlpF construct. The curves are less steep in the log phase compared to WT because of the protein expresion by IPTG induction. In the absence of As(III) the plateau level equals the WT. If arsenite is present the plateaus are lower (OD<sub>600</sub> <0.8) compared to WT. This is due to As(III) uptake by GlpF. <br />
<br />
In the graph on the right we see the curves of low constitutively expressed GlpF and fMT and it shows a similar slope in the log phase compared to pLac GlpF due to protein expression and like WT 0 μM As(III) it has its plateau over OD<sub>600</sub> 0.9. If arsenite is present the plateaus are lower (OD<sub>600</sub> <0.8) compared to WT. This is due to As(III) uptake by GlpF. Here the reduced growth is also an indicator for arsenite uptake. It is difficult to see if fMT has an effect because this assay can not show where the arsenite is and how fMT interferes with the cells detoxificatoin.<br />
<br />
==={{anchor|Modelling}}Modelling uptake GlpF===<br />
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The import of As(III) via GlpF is modelled as a simple import reaction with [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten kinetics]], in part because this makes it easy to specify, but also because we only have very high level data. The following allows a comparison with the data acquired from figure 1B from [[Team:Groningen/Literature#Meng2004|Meng 2004]].<br />
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<table style="border-collapse:collapse;background:none;"><tr><br />
<td style="border-right:1px solid #9c9;padding-right:1em;"><br />
<dl><br />
<dt>Initial values</dt><br />
<dd><br />
As(III)<sub>ex</sub> = <input type="text" id="As3exInitial" value="9.15164271986822"/> &micro;M<br/><br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(10&micro;M &middot; 1mL / 1.092mL)<br />
</dd><br />
<dt>Volumes</dt><br />
<dd><br />
V<sub>total</sub> = <input type="text" id="Vtotal" value="1.1"/> mL<br/><br />
V<sub>cells</sub> = <input type="text" id="Vcells" value="0.0073"/> mL<br/><br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(0.1ml &middot; 80mg/mL / 1100mg/mL) </html>{{infoBox|E. coli has a density of approximately 1100mg/mL, see [[Team:Groningen/Project/Vesicle|our gas vesicle page]] for more information.}}<html><br />
</dd><br />
<dt>Kinetic Constants</dt><br />
<dd><br />
<nobr>v5 = <input type="text" id="v5" value="3.1862846729357852"/> &micro;mol/(s&middot;L)</nobr><br/><br />
K5 = <input type="text" id="K5" value="27.71808199428998"/> &micro;M<br/><br />
</dd><br />
</dl><br />
<br />
<button onClick="computeGlpFTransport()">Compute</button><br/><br />
</td><br />
<br />
<td style="padding-left:1em;"><br />
<div id="glpFTransportError" style="color:red"></div><br />
</html>{{graph|Team:Groningen/Graphs/GlpFTransport|id=glpFTransportGraph}}<html><br />
</td><br />
</tr></table><br />
</div><br />
<script type="text/javascript"><br />
<br />
//The graph already initializes itself (and we don't do any other computations).<br />
//addOnloadHook(computeGlpFTransport);<br />
<br />
function computeGlpFTransport() {<br />
document.getElementById('glpFTransportGraph').refresh();<br />
}<br />
</script><br />
</html><br />
<br />
To determine the constants v5 and K5 we performed the following steps:<br />
<br />
# '''Read the wild-type line in figure 1B''' of [[Team:Groningen/Literature#Meng2004|Meng 2004]] by pasting it in a drawing program and aligning/scaling the axes and then manually determining the coordinates of each data point.<br />
# '''Converted to units of concentration''' using the data in Meng 2004 and [http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi the CCDB] (assuming that the cells are resting/non-growing), see our [http://spreadsheets.google.com/pub?key=t4gilzCbEaCFAvpEVWUE_zQ Google Docs spreadsheet]. Here we disregarded the fact that the measurements were made by taking out 0.1mL samples, as this does not change the concentrations. Specifically (note that uptake is in nmol/mg):<br />
#* uptake<sub>total</sub> (nmol) = uptake &middot; 8mg &middot; 0.3 {{infoBox|The ratio between dry and wet weight is 0.3 (see the [http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi CCDB]).}}<br />
#* As(III)<sub>ex</sub> (&micro;M=nmol/mL) = (10nmol/mL &middot; 1mL - uptake<sub>total</sub>) / (1.1-0.0073)mL {{infoBox|1=The experiment started with 1mL of a 10&micro;M=10nmol/mL solution of As(III). After adding the cells the total volume of the solution was 1.1mL, and 0.0073mL is an estimate of the total volume of cells in the solution, see below.}}<br />
# '''Fit the Michaelis-Menten equation''' to find the constants v5 and K5 in Mathematica (see [http://igemgroningen.googlecode.com/svn/trunk/buoyant/Models/Meng2004%20Figure%201B.nb the Mathematica notebook in SVN]) using the method from [[Team:Groningen/Literature#Goudar1999|Goudar 1999]] (a least squares fit of a closed-form solution of the differential equation).<br />
<br />
{{GraphHeader}}<br />
<br />
<br><br />
<br />
===Missing information/To Do===<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*<del>Q:Eliminate BioBrick restriction sites</del><br />
*<del>Q: What does the ars operon of our <i>E. coli</i> look like? Do we have both ArsA and ArsB? (And what about ArsR and ArsD?)</del> A: We only have ArsRBC, see [[Team:Groningen/BLAST|our BLAST results]].<br />
<br />
<br><br />
<br />
===Additional sources===<br />
<br><br />
* [[Team:Groningen/Literature#Meng2004|Meng 2004]] (As(III) and Sb(III) Uptake by GlpF and Efflux by ArsB in Escherichia coli)<br />
* [[Team:Groningen/Literature#Rosen2009|Rosen 2009]] (Transport pathways for arsenic and selenium: A minireview)<br />
*[[Team:Groningen/Literature#Porquet, A, et al.2007|Porquet, A, et al.2007]] (structural similarity between As(OH)3 and glycerol)<br />
* [[Team:Groningen/Literature#Fu, DX, et al.2000|Fu, DX, et al.2000]] (Structure of the GlpF channel)<br />
*[[Team:Groningen/Literature#Heller, KB, et al.1980|Heller, KB, et al.1980]] (Glycerol transport properties of GlpF)<br />
<br />
==Copper/zinc uptake via HmtA==<br />
<br />
===HmtA===<br />
====Introduction====<br />
HmtA(heavy metal transporter A) from <i>Pseudomonas aeruginosa</i> [http://www.ncbi.nlm.nih.gov/protein/81857196 Q9I147] is a P-type ATPase importer. This membrane protein mediates the uptake of copper (Cu) and zinc (Zn) and was functionally expressed in ''E. coli'' ([http://www.ncbi.nlm.nih.gov/pubmed/19264958 Lewinson 2009]). We want to use this membrane protein to accumulate copper and zinc into the cells. we believe this ATP-driven pump is capable of generating an elevated intracellular concentration of these compounds enabling the harvesting of copper and zinc from the medium.<br />
<br />
====Cloning strategy====<br />
There are several restriction sites to be modified from [https://static.igem.org/mediawiki/2009/8/85/PBAD-HmtA-ClonemanagerFile.zip Lewinson's] pBAD construct. A vector with amp resistance with L-arabinose inducible HmtA-6HIS. The restriction sites have been silently mutated maintaining the amino acid sequence.<br />
We will create these mutations via PCR than digest the old methylated template and clone the product into competent cells.<br />
<br />
====Results==== <br />
[[Image:HmtA_SDS_gel.jpg|200px|thumb|right|[Team:Groningen/Team|HmtA-6HIS on SDS-page]]<br />
So far we have cloned HmtA as a biobrick without EcoRI site in the coding region into the iGEM vector. Unfortunately a mutation occurred at base 103 from the start of the orf. By a point mutation c to t in the first nucleotide of the codon changed arginine 35 to a Cysteine. We do not know the effects but we suspect it might have a great influence due to the very reactive side chain of Cysteine, eventhough it is not in the channel itself based on [http://www.cbs.dtu.dk/services/TMHMM/ TMHMM] predictions which indicate trans membrane helices of a protein. Further cloning is expected to be unsuccessful because the iPTG induced clones grow even slightly better than the empty vector control. This is most likely cause by the missing pLAC-RBS in front of the gene. There was no positive controle with the L-arabinose inducable HmtA-6His in pBAD. We did do expression experiments with the pBAD construct to purified the membrane protein as quality controle. result shown in the figure on the right.<br />
<br />
==Heavy metal uptake coupled to citrate via ''ef''CitH ''bs''CitM==<br />
<br />
Force feeding of the heavy metals into the cell is possible when citrate is the only available carbon source. Citrate in complex with heavy metals can be translocated over the membrane into the cell via citrate transporters.<br />
This can be a very efficient strategy to accumulate vast ammounts of heavy metals.<br />
The two membrane proteins are CitM from ''Bacillus subtilis'' studied by [http://www.ncbi.nlm.nih.gov/pubmed/11053381 B.P Krom]. <i>Bs</i>CitM can transport citrate in complex with Mg<sup>2+</sup>, Ni<sup>2+</sup>, Mn<sup>2+</sup>, Co<sup>2+</sup>, and Zn<sup>2+</sup>. <br />
The other is CitH from ''Enterococcus faecalis'' described by [http://www.ncbi.nlm.nih.gov/pubmed/17042778 V.S Blancato]. <i>Ef</i>CitH catalyzes translocation of the citrate in complex with Ca<sup>2+</sup>, Sr<sup>2+</sup> Mn<sup>2+</sup> Mn<sup>2+</sup> Cd<sup>2+</sup> and Pb<sup>2+</sup>.<br />
<br />
<br />
===Additional sources===<br />
<br />
More information on this topic can be found in:<br />
<br />
Bastiaan Krom. Citrate transporters of <i>Bacillus subtilis</i> PhD thesis. [[http://dissertations.ub.rug.nl/faculties/science/2002/b.p.krom/ Dissertation Groningen]]<br />
<br />
Jessica B. Warner. Regulation and expression of the metal citrate transporter CitM PhD thesis. [[http://dissertations.ub.rug.nl/faculties/science/2002/j.b.warner/ Dissertation Groningen]]<br />
<br />
==Periplasmic accumulation of heavy metals via Mer Operon==<br />
Periplasmic accumulation of heavy metals via Mer proteins enables the harvesting of heavy metals from the medium by binding the cytosolic and periplasmic metals to metallothionein and transporting the metal-protein complex into the periplasm.<br />
The MerR family consists of different proteins for one specific metal (<i>i.e.</i><br />
PbrR (lead), CueR (copper), ZntR (zinc), MerR (mercury), ArsR (arsenic), CadR (cadmium)).<br />
<br />
As the cells die after uptake of Mg (and induction of the Mer transporter), this system is not very well usable for our project. The dead cells will not produce the gas vesicles (it may be used however by having the gas vesicles consitutively expressed), thereby bouyancy may be a problem ([[Team:Groningen/Literature#Pennella2005|Pennella 2005]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]).<br />
<br />
===Missing information/To Do===<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*Eliminate BioBrick restriction sites<br />
<br />
==Planning and requirements==<br />
<br />
* '''Modelling:'''<br />
** Import speed<br />
** Amount <br />
** Max<br />
* '''Lab:'''<br />
** HmtA<br />
*** Zn/Cu alone<br />
*** B-type ATPase (could be use if there is a ATP shortage?)<br />
** CitM (probably not used)<br />
*** Divalent ions<br />
*** Citrate around<br />
*** Citrate can bind metals that are already bound.<br />
** Measurements (both for the "normal" cell and the cell with overexpression of the transporter)<br />
*** Transporter, on/off mechanism, up to what concentration (in the cell) does it still have metal uptake.<br />
*** Measure concentration of metal. difference between begin and end concentrations of metal outside the cell.<br />
*** How fast does it transport metal in/out the cell.<br />
**** Set up tests with (initial) extracellular concentrations of about <sup>1</sup>/<sub>3</sub>K (25% of V<sub>max</sub>), K (50% of V<sub>max</sub>), 3K (75% of V<sub>max</sub>) and 10mM (99.7% of V<sub>max</sub>, corresponding to extremely polluted water), and a control with no arsenic. Obviously, more tests is better. In general a desired fraction of V<sub>max</sub> at the initial concentration can be attained by using an initial concentration of x/(1-x) times K.<br />
**** Determine "final" (steady-state) concentration of As(III) in the solution and in the cells. (Concentration over time is even better!)<br />
**** This means that the total volume of the cells (and the solution) has to be determined. Possibly through looking at the dry weight (without arsenic!).<br />
**** By manipulating the equation for the derivative of As(III) in equilibrium, As(III) can be expressed as a function of As(III)<sub>ex</sub> (given the V and K constants). We can try to fill in the computed V and K constants for GlpF and then use a least squares fit to estimate the V and K constants for ArsB.<br />
**** '''NOTE:''' Interestingly [[Team:Groningen/Literature#Kostal2004|Kostal 2004]] already did an experiment like this with cells that overexpressed ArsR. We're looking at analysing these results under the assumption that overexpressing ArsR only gives a constant factor more accumulation (for 1-100&microM As(III)), but it would be very nice to do this ourselves for unmodified cells to determine whether this is indeed true (and to determine the factor).<br />
<br />
==Export of arsenicum via Ars operon==<br />
<br />
GlpF is the importer of arsenicum. After arsenicum enters the cell, in response the Ars operon produces ArsR. At the same time, ArsB is also produced by Ars operon. This happens because the Ars operon contains three open reading frames: the first is ArsR, second ArsB and the last one is ArsC. ArsB is the exporter of arsenicum. The ars operon is located on the chromosomal DNA of E. coli.<br />
For more information see: [http://biocyc.org/ECOLI/NEW-IMAGE?type=GENE-IN-CHROM-BROWSER&object=EG12235 biocyc].<br />
<br />
[[Image:ArsRBC_operon.PNG|600px]]<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
{{Team:Groningen/Project/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/ArsenicTeam:Groningen/Modelling/Arsenic2009-10-21T20:02:07Z<p>Jaspervdg: A bit about our approach and formatting the "abstract"</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div style="clear:both;"></div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Characterization}}</div><br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
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<div class="intro introduction"><br />
==Detailed Model==<br />
Based on the [[#QuasiSteadyState|quasi-steady-state derivation]] below we have made the simplified version of our model shown below. The simplification is based on two key assumptions (which are also illustrated below, next to the table "Breakdown of core substances"):<br />
<br />
*Binding and unbinding of arsenic to/from the transporters occurs on a much smaller time scale than changes in the concentration of arsenic inside and outside the cell. And similarly, we assume that (un)binding of ArsR to/from the ars promoter is much faster than the production of ArsR (for example).<br />
*The concentration of transporters is insignificant compared to the concentration of arsenic inside and outside the cell.<br />
<br />
This leads to the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation for import, but also some more general equations for export using ArsB and accumulation with ArsR (for example, the Hill equation can be recognized in the activity of the ars promoter). We explicitly state ''relative abundances'' instead of substituting them into the differential equations. This leads to ''clearer and more insightful'' equations and gives ''more freedom'' to define complicated, interdependent ratios between substances.<br />
</div><br />
<br />
The inexperienced viewer may find the following tables and formulas baffling. We would recommend that one would look at the raw model first to gain an understanding of the basic reactions involved then have a look at the steady-state and the quasi steady-state model. It is not mandatory, but it is probably the the best route to get a better understanding of the model as a whole. Also, perhaps first have a look at [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] kinetics before proceeding.<br />
<br />
In contrast to how the quasi-steady-state assumption is normally used we mostly leave the specific states (bound/unbound) of substances intact in the differential equations and explicitly state the relative abundances. This keeps the differential equations shorter and gives more insight into what is actually happening, clearly mapping the "fast" reactions to ratios between substances. This also makes it possible to use quite complicated equations (the Asin and ArsR interdependency is virtually impossible to define using normal methods for example) that would otherwise be unwieldy to handle.<br />
<br />
[[Image:Arsenic_filtering.png|frame|A schematic representation of the processes involved in arsenic filtering (keep in mind that ArsR ''represses'' the expression of the genes behind ars). Note that MBPArsR and fMT are not shown for clarity.<!-- Also, ArsD is not shown here, as it is [[Team:Groningen/BLAST|not present in our E. coli]] and has a role analogous to ArsR.-->]]<br />
<br />
{|class="ourtable"<br />
|+ Reactions<br />
!colspan="2"|Reaction<br />
!Description<br />
!Rate<br />
|-<br />
|colspan="4"|''Transport''<br />
|-<br />
| ||As(III)<sub>ex</sub>T &rarr; As(III)<sub>in</sub>T||Import of arsenic.||(Vc/Vs) v5<sup>&dagger;</sup> As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T)<br />
|-<br />
| ||As(III)<sub>in</sub>T &rarr; As(III)<sub>ex</sub>T||Export of arsenic.|| k8 ArsB<sub>As</sub><br />
|-<br />
| ||style="white-space:nowrap;"|ars1T → ars1T + ArsBT||Production of ArsB.|| βB ars1<br />
|-<br />
| ||ArsBT &rarr; null||Degradation of ArsB|| (ln(2)/τB) ArsB<br />
|-<br />
|colspan="4"|''Accumulation''<br />
|-<br />
| ||ars1T → ars1T + ArsRT||From chromosomal operon.|| βRN ars1<br />
|-<br />
| ||proR → proR + ArsRT||Production of ArsR.|| βR pro<br />
|-<br />
| ||style="white-space:nowrap;"|proM → proM + MBPArsRT||Production of MBPArsR.|| βM pro<br />
|-<br />
| ||proF → proF + fMTT||Production of fMT.|| βF pro<br />
|-<br />
| ||ArsRT → null||Degradation of ArsR.|| (ln(2)/τR) ArsR<br />
|-<br />
| ||MBPArsRT → null||Degradation of MBPArsR.|| (ln(2)/τM) MBPArsR<br />
|-<br />
| ||fMTT → null||Degradation of fMT.|| (ln(2)/τF) fMT<br />
|-<br />
|colspan="4"|''Gas vesicles''<br />
|-<br />
| ||ars2T → ars2T + GV||Transcription + translation.|| βG ars2<br />
|-<br />
| ||GV → null||Degradation of gas vesicles.|| (ln(2)/τG) GV<br />
|}<br />
<br />
{|class="ourtable" style="clear:right;"<br />
|+ Core Substances<br />
!colspan="2"|Name<br />
!Description<br />
!Derivative to time<br />
|-<br />
|colspan="4"|''Extracellular''<br />
|-<br />
| ||As(III)<sub>ex</sub>T || As(III) in the solution. || (Vc/Vs) k8 ArsB<sub>As</sub> - (Vc/Vs) v5<sup>&dagger;</sup> As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T)<br />
|-<br />
|colspan="4"|''Membrane (all naturally occurring, but we plan to bring GlpF to overexpression)''<br />
|-<br />
| ||GlpFT || Importer of As(III) (concentration w.r.t. the exterior of the cell). || (not used directly in model, assumed to be constant)<br />
|-<br />
| ||ArsBT || Exporter of As(III) (concentration w.r.t. the interior of the cell). || βB ars1 - (ln(2)/τB) ArsB<br />
|-<br />
|colspan="4"|''Intracellular (ars2, pro and GV are introduced)''<br />
|-<br />
| ||As(III)<sub>in</sub>T || As(III) (bound and unbound) in the cell. || v5 As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T) - k8 ArsB<sub>As</sub><br />
|-class="estimate"<br />
| ||ars1T || ArsR repressed promoters (bound and unbound) naturally occurring in E. coli. || (concentration is constant = 1.6605nM, one per cell)<br />
|-class="estimate"<br />
| ||ars2T || ArsR repressed promoters in front of gas vesicle genes. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proR || Constitutive promoters in front of arsR. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proM || Constitutive promoters in front of mbp-arsR. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proF || Constitutive promoters in front of fMT. || (concentration is constant = 0-166.05nM)<br />
|-<br />
| ||ArsRT || ArsR in the cell. || βRN ars1 + βR proR - (ln(2)/τR) ArsR<br />
|-<br />
| ||MBPArsRT || MBPArsR in the cell. || βM proM - (ln(2)/τM) MBPArsR<br />
|-<br />
| ||fMTT || fMT in the cell. || βF proF - (ln(2)/τF) fMT<br />
|-<br />
| ||GV || Concentration of gas vesicles. || βG ars2 - (ln(2)/τG) GV<br />
|-style="border:none;"<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Directly from paper.<br />
|class="selfDerived" style="padding:0;"|Based on data from paper.<br />
|class="experimental" style="padding:0;"|Based on experiment.<br />
|class="estimate" style="padding:0;"|Rough estimate.<br />
|class="unknown" style="padding:0;"|Totally unknown.<br />
|}<br />
|}<br />
<div style="text-align:right;font-size:smaller;"><sup>&dagger;</sup> Note that the "constant" v5 depends on the concentration of GlpF transporters in the cell, and this can depend on whether we bring GlpF to overexpression or not. For simplicity the production/degradation of GlpF is not included explicitly in the model, instead we can vary the constant v5 relative to the value found for wild-type E. coli.</div><br />
<br />
{|<br />
|style="vertical-align:top;"|<br />
{|class="ourtable"<br />
|+ Breakdown of core substances<br />
!Core substance<br />
!Component<br />
!Relative abundance<br />
|-<br />
|rowspan="2"|ArsBT<br />
|style="padding-left:0;"|ArsB<br />
|K7<br />
|-<br />
|ArsB<sub>As</sub><br />
|As(III)in<br />
|-<br />
|rowspan="4"|As(III)inT<br />
|style="padding-left:0;"|As(III)in<br />
|1<br />
|-<br />
|ArsR<sub>As</sub><br />
|ArsR / KR<sub>d</sub><br />
|-<br />
|MBPArsR<sub>As</sub><br />
|MBPArsRT / (KM<sub>d</sub> + As(III)in)<br />
|-<br />
|fMT<sub>As</sub><br />
|n<sub>f</sub> fMTT As(III)<sub>in</sub><sup>n<sub>f</sub>-1</sup> / (KF<sub>d</sub><sup>n<sub>f</sub></sup> + As(III)<sub>in</sub><sup>n<sub>f</sub></sup>)<br />
|-<br />
|rowspan="2"|arsT<br />
|style="padding-left:0;"|ars<br />
|KA<sub>d</sub>²<br />
|-<br />
|ArsR<sub>ars</sub><br />
|ArsR²<br />
|-<br />
|rowspan="2"|ars<br />
|style="padding-left:0;"|ars1<br />
|ars1T<br />
|-<br />
|ars2<br />
|ars2T<br />
|-<br />
|rowspan="3"|ArsRT<br />
|style="padding-left:0;"|ArsR<br />
|1<br />
|-<br />
|ArsR<sub>As</sub><br />
|As(III)<sub>in</sub> / KR<sub>d</sub><br />
|-<br />
|ArsR<sub>ars</sub><br />
|2 ArsR ars / KA<sub>d</sub>²<br />
|-<br />
|rowspan="2"|MBPArsRT<br />
|style="padding-left:0;"|MBPArsR<br />
|KM<sub>d</sub><br />
|-<br />
|MBPArsR<sub>As</sub><br />
|As(III)<sub>in</sub><br />
|-<br />
|rowspan="2"|fMTT<br />
|style="padding-left:0;"|fMT<br />
|KF<sub>d</sub><sup>n<sub>f</sub></sup><br />
|-<br />
|fMT<sub>As</sub><br />
|As(III)<sub>in</sub><sup>n<sub>f</sub></sup><br />
|}<br />
|[[Image:Arsenic Model - Substances.png|frame|Circles correspond to core substances. We consider the reactions between the overlapping substances so fast that we model them by determining the ratios between the substances when the reactions between them are in equilibrium. Also, the complexes formed with <strike>ars,</strike> GlpF and ArsB (the small circles) are considered to have such a low concentration that they are of no importance to the concentrations of As(III)in/-ex and ArsR (the large circles).]]<br />
|}<br />
<br />
{|class="ourtable"<br />
|+ Constants<br />
!Name<br />
!Units<br />
!Value<br />
!Description<br />
|-class="unknown"<br />
|k8<br />
|1/s<br />
|<br />
|Reaction rate constant representing how fast ArsB can export arsenic.<br />
|-class="estimate"<br />
|KR<sub>d</sub><br />
|M<br />
|6&micro;M<br />
|Dissociation constant for ArsR and As(III). Assumed to be about an order of magnitude smaller than KD<sub>d</sub> = 60&micro;M, the corresponding constant for the similar protein ArsD from [[Team:Groningen/Literature#Chen1997|Chen1997]].<br />
|-class="estimate"<br />
|KM<sub>d</sub><br />
|M<br />
|6&micro;M<br />
|Dissociation constant for MBPArsR and As(III). We assume this to be roughly equal to KR<sub>d</sub>.<br />
|-class="unknown"<br />
|KF<sub>d</sub><br />
|M<br />
|<br />
|Dissociation constant for fMT and As(III).<br />
|-class="unknown"<br />
|n<sub>f</sub><br />
|<br />
|<br />
|Hill coefficient for the formation of the complex fMTAs. This is related to the number of arsenic ions that bind to fMT.<br />
|-class="fromPaper"<br />
|KA<sub>d</sub><br />
|M<br />
|0.33&micro;M<br />
|Dissociation constants for ArsR and ars.<br />
* KA<sub>d</sub>² = kA<sub>off</sub>/kA<sub>on</sub> = (0.33&micro;M)²? ([[Team:Groningen/Literature#Chen1997|Chen1997]], suspect as the relevant reference doesn't actually seem to give any value for this)<br />
|-class="selfDerived"<br />
|v5<br />
|mol/(s&middot;L)<br />
|3.1863&micro;mol/(s·L)<br />
|Maximum import rate per liter of cells (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]). Note that we have purposefully chosen to write the units as mol/(s&middot;L) instead of M/s, to emphasize the fact that the rate is per liter of ''cells''.<br />
* v5 = k6 GlpFT (Vs/Vc)<br />
|-class="selfDerived"<br />
|K5<br />
|M<br />
|27.718&micro;M<br />
|Concentration at which import reaches half its maximum import rate (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]).<br />
* K5 = (k5off+k6) / k5on<br />
|-class="unknown"<br />
|K7<br />
|M<br />
|<br />
|Concentration at which export reaches half its maximum export rate (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]).<br />
* K7 = (k7off+k8) / k7on<br />
|-class="unknown"<br />
|&tau;B, &tau;R, &tau;G, etc.<br />
|s<br />
|<br />
|Half-lifes (of ArsB, ArsR and GV, respectively). Degradation rate = ln(2)/&tau; {{infoBox|1=If you take just the degradation into account you will have the equation dC/dt = -k*C, which leads to C(t) = C(0) e<sup>-k t</sup>. So if k = ln(2)/&tau; we get C(t) = C(0) e<sup>-ln(2)/&tau; t</sup> = C(0) 2<sup>-t/&tau;</sup>. In other words &tau; is the time it takes for the concentration to half.}}<br />
|-class="unknown"<br />
|&beta;B, &beta;R, etc.<br />
|1/s<br />
|<br />
|Production rates.<br />
* &beta;RN = the production rate for ArsR behind the ars1 promoter<br />
* &beta;B = the production rate for ArsB behind the ars1 promoter<br />
* &beta;G = the production rate for GV behind the ars2 promoter<br />
* &beta;R = the production rate for ArsR behind a constitutive promoter<br />
* &beta;M = the production rate for MBPArsR behind a constitutive promoter<br />
* &beta;F = the production rate for fMT behind a constitutive promoter<br />
|-<br />
|Vs<br />
|L<br />
|<br />
|Volume of solution (excluding cells).<br />
|-<br />
|Vc<br />
|L<br />
|<br />
|Total volume of cells (in solution) (so Vs+Vc is the total volume).<br />
|-style="border:none;"<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Directly from paper.<br />
|class="selfDerived" style="padding:0;"|Based on data from paper.<br />
|class="experimental" style="padding:0;"|Based on experiment.<br />
|class="estimate" style="padding:0;"|Rough estimate.<br />
|class="unknown" style="padding:0;"|Totally unknown.<br />
|}<br />
|}<br />
<br />
<br />
==The raw model==<br />
<html><style type="text/css"></html><br />
.import { background: LightGreen; }<br />
.export { background: LightBlue; }<br />
.accumulation { background: LightPink; }<br />
.production { background: LightGoldenRodYellow; }<br />
<html></style></html><br />
<br />
The following table gives all the reactions that take place inside the cell. You can look at the schematic representation of the processes involved to get a good grasp as how every reaction works to the other. Note that proR, ProM and MBPArsR, ProF and Fmt are not displayed in the figure. This has been done for clarity. These reactions are simple constituative promotor reactions. Once you have an insight in the reactions involved you can have a look at the next table.<br />
<br />
[[Image:Arsenic_filtering.png|frame|A schematic representation of the processes involved in arsenic filtering (keep in mind that ArsR ''represses'' the expression of the genes behind ars). Note that MBPArsR and fMT are not shown for clarity.<!-- Also, ArsD is not shown here, as it is [[Team:Groningen/BLAST|not present in our E. coli]] and has a role analogous to ArsR.-->]]<br />
<br />
{|class="ourtable"<br />
|+ Reactions<br />
!colspan="2"|Reaction<br />
!Description<br />
|-<br />
|colspan="3"|''Transport''{{infoBox|In the reactions below you can see the import of arsenic by GlpF and the export of arsenic by ArsB. Only the degradation of ArsB is taken into acount because the ars operon also produces ArsB, as can be seen in the accumulation section. We assume a constant number of GlpF importers. }}(based on [[Team:Groningen/Literature#Rosen1996|Rosen1996]], [[Team:Groningen/Literature#Meng2004|Meng2004]] and [[Team:Groningen/Literature#Rosen2009|Rosen2009]])<br />
|-<br />
| ||<span class="import">As(III)<sub>ex</sub> + GlpF &harr; GlpF<sub>As</sub></span>||The binding and detachment of rsenic to GlpF on the outside of the cell.||<br />
|-<br />
| ||<span class="import">GlpF<sub>As</sub> &rarr; GlpF + As(III)</span>||The release of arsenic on the inside of the cell by GlpF|| <br />
|-<br />
| ||<span class="export">As(III)<sub>in</sub> + ArsB &harr; ArsB<sub>As</sub></span>||The binding and detachment of arsenic to the Exporter ArsB|| <br />
|-<br />
| ||<span class="export">ArsB<sub>As</sub> &rarr; ArsB + As(III)<sub>ex</sub></span>||The release of the bound arsenic by ArsB on the outside of the cell.|| <br />
|-<br />
| ||<span class="export">ArsB &rarr; null</span> ||The degradation of Ars B||<br />
|-<br />
|colspan="3"|''Accumulation''{{infoBox|In the reactions below you can see the production and degradation of all our accumulation proteins. Two things should be noticed: ArsR represses it's own production and that of the GVP clusters and the ars1 operon does not only produce ArsR but also the exporter ArsB}}(mostly based on [[Team:Groningen/Literature#Chen1997|Chen1997]])<br />
|-<br />
| ||As(III)<sub>in</sub> + ArsR &harr; ArsR<sub>As</sub>||The binding and detachment of arsenic to ArsR||<br />
|-<br />
| ||As(III)<sub>in</sub> + MBPArsR &harr; MBPArsR<sub>As</sub>||The binding and detachment of arsenic to MBPArsR || <br />
|-<br />
| ||n<sub>f</sub> As(III)<sub>in</sub> + fMT &harr; fMT<sub>As</sub>||The binding and detachment of arsenic to fMT || <br />
|-<br />
| ||ars1 + 2 ArsR &harr; ArsR<sub>ars1</sub>||the repression of the promotor of the ars1 operon by 2 arsR molecules||<br />
|-<br />
| ||<span class="production">ars2 + 2 ArsR &harr; ArsR<sub>ars2</sub></span>||the repression of the promotor of the ars1 operon by 2 arsR molecules|| <br />
|-<br />
| ||ars1 &rarr; ars1 + ArsR<span class="export"> + ArsB</span> ||The transcription and translation of the ars1 operon to produce ArsR and ArsB||<br />
|-<br />
| ||proR &rarr; proR + ArsR ||The transcription and translation of the proR operon to produce ArsR||<br />
|-<br />
| ||proM &rarr; proM + MBPArsR ||The transcription and translation of the proM operon to produce MBPArsR||<br />
|-<br />
| ||proF &rarr; proF + fMT ||The transcription and translation of the proF operon to produce fMT||<br />
|-<br />
| ||ArsR &rarr; null ||The degradation of ArsR||<br />
|-<br />
| ||MBPArsR &rarr; null ||The degradation of MBPArsR||<br />
|-<br />
| ||fMT &rarr; null ||The degradation of fMT||<br />
|-<br />
|colspan="3"|''Gas vesicles''{{infoBox|These two reactions give the production and degradation rate of the GVP clusters. Keep in mind that ars2 is repressed by the accumulation protein ArsR. This reaction can be found under accumulation part.}}<br />
|-<br />
| ||ars2 &rarr; ars2<span class="production"> + GV</span> ||The transcription and translation of the ars2 operon to produce GVP clusters wich will make the cell float||<br />
|-<br />
| ||<span class="production">GV &rarr; null</span> ||The degradation of GVP||<br />
|-<br />
|colspan="3"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="estimate" style="padding:0;"|GVP Production related.<br />
|}<br />
|}<br />
<br />
Here you can find the time derivatives for each substance we derived. The constants are explained in the next teble. After one has a full understanding of all the constants and derivatives and and reactions. One can begin the process of simplifying the model and thus one can have a look at the quasi steady-state model and the steady-state model. <br />
<br />
{|class="ourtable"<br />
|+ Core substances<br />
!colspan="2"|substance<br />
!Description<br />
!Derivative to time<br />
|-<br />
|colspan="4"|''Extracellular''<br />
|-<br />
| ||As(III)<sub>ex</sub>||As(III) in the solution||(d/dt) As(III)<sub>ex</sub> = <span class="import">- (d/dt) GlpF<sub>As</sub> - k6 GlpF<sub>As</sub></span><span class="export"> + (Vc/Vs) k8 ArsB<sub>As</sub></span><br />
|-<br />
|colspan="4"|''Membrane'' (all naturally occurring, but we plan to bring GlpF to overexpression)<br />
|-<br />
| ||GlpF||concentration w.r.t. the exterior of the cell||(d/dt) GlpF = <span class="import">- (d/dt) GlpF<sub>As</sub></span><br />
|-<br />
| ||GlpF<sub>As</sub>||concentration w.r.t. the exterior of the cell||(d/dt) GlpF<sub>As</sub> = <span class="import">k5<sub>on</sub> As(III)<sub>ex</sub> GlpF - (k5<sub>off</sub>+k6) GlpF<sub>As</sub></span><br />
|-<br />
| ||ArsB||concentration w.r.t. the interior of the cell||(d/dt) ArsB = <span class="export">- (d/dt) ArsB<sub>As</sub> + &beta;4 ars1 - ln(2)/&tau;B ArsB</span><br />
|-<br />
| ||ArsB<sub>As</sub> ||concentration w.r.t. the interior of the cell||(d/dt) ArsB<sub>As</sub> = <span class="export">k7<sub>on</sub> As(III)<sub>in</sub> ArsB - (k7<sub>off</sub>+k8) ArsB<sub>As</sub></span><br />
|-<br />
|colspan="4"|''Intracellular'' (ars2, pro and GV are introduced)<br />
|-<br />
| ||As(III)<sub>in</sub>||concentration of As(III) inside the cell||(d/dt) As(III)<sub>in</sub> = - (d/dt) ArsR<sub>As</sub> - (d/dt) MBPArsR<sub>As</sub> - n<sub>f</sub> (d/dt) fMT<sub>As</sub><span class="export"> - (d/dt) ArsB<sub>As</sub> - k8 ArsB<sub>As</sub></span><span class="import"> + (Vs/Vc) k6 GlpF<sub>As</sub></span><br />
|-<br />
| ||ars1 {{infoBox|ars1 stands for the promotor in front of the operon which contains the information for the production of the accumulation protein ArsR and the exporter ArsB. It is selfregulatory in the sence that it produces it's own repressor in the form of ArsR}} ||concentration of unbound promoters naturally occurring in <i>E. coli</i>||(d/dt) ars1 = - (d/dt) ArsR<sub>ars1</sub><br />
|-<br />
| ||ars2 {{infoBox|ars2 stands for the promotor in front of the operon which contains the information for the production of Gas Vesicles. Unlike ars 1 it is not selfregulatory, but the if everything goes correctly the production of gas vesicles will only start if there arsenic inside the cell}}||concentration of unbound promoters in front of gas vesicle genes||(d/dt) ars2 = <span class="production">- (d/dt) ArsR<sub>ars2</sub></span><br />
|-<br />
| ||proR ||concentration of constitutive promoters in front of arsR|| (d/dt)proR = 0 in our model<br />
|-<br />
| ||proM ||concentration of constitutive promoters in front of mbp-arsR|| (d/dt)proM = 0 in our model<br />
|-<br />
| ||proF ||concentration of constitutive promoters in front of fMT|| (d/dt)proF = 0 in our model<br />
|-<br />
| ||ArsR {{infoBox|ArsR binds to ars to repress production of the genes they regulate, and binds to As(III) to make it less of a problem for the cell.}}||concentration of the accumulation protein ArsR||(d/dt) ArsR = &beta;RN ars1 + &beta;R proR - (ln(2)/&tau;R) ArsR - (d/dt) ArsR<sub>As</sub> - 2 (d/dt) ArsR<sub>ars1</sub><span class="production"> - 2 (d/dt) ArsR<sub>ars2</sub></span> <br />
|-<br />
| ||ArsR<sub>As</sub> || the concentration of ArsR bound to As(III)||(d/dt) ArsR<sub>As</sub> = kR<sub>on</sub> ArsR As(III)<sub>in</sub> - kR<sub>off</sub> ArsR<sub>As</sub><br />
|-<br />
| ||ArsR<sub>ars1</sub> ||the concentration of ArsR bound to ars1||(d/dt) ArsR<sub>ars1</sub> = kA<sub>on</sub> ArsR&sup2; ars1 - kA<sub>off</sub> ArsR<sub>ars1</sub><br />
|-<br />
| ||ArsR<sub>ars2</sub> ||the concentration of ArsR bound to ars2||(d/dt) ArsR<sub>ars2</sub> = <span class="production">kA<sub>on</sub> ArsR&sup2; ars2 - kA<sub>off</sub> ArsR<sub>ars2</sub></span><br />
|-<br />
| ||MBPArsR {{infoBox|A fusion of maltose binding protein and ArsR. It is more stable than the normal ArsR variant, but it is no longer able to act as a repressor for the ars promotor.}}|| a fusion of maltose binding protein and ArsR||(d/dt) MBPArsR = &beta;M proM - (ln(2)/&tau;M) MBPArsR - (d/dt) MBPArsR<sub>As</sub><br />
|-<br />
| ||MBPArsR<sub>As</sub> ||bound to As(III)||(d/dt) MBPArsR<sub>As</sub> = kM<sub>on</sub> MBPArsR As(III)<sub>in</sub> - kM<sub>off</sub> MBPArsR<sub>As</sub><br />
|-<br />
| ||fMT {{infoBox|It is another binding protein. Unlike it's counterpart it capeble of containing up to five As(III) particles or one As(V) particle }} || Arsenic binding metallotein ||(d/dt) fMT = &beta;F proF - (ln(2)/&tau;F) fMT - (d/dt) fMT<sub>As</sub><br />
|-<br />
| ||fMT<sub>As</sub> ||bound to multiple As(III)||fMT<sub>As</sub> = kF<sub>on</sub> fMT As(III)<sub>in</sub><sup>n<sub>f</sub></sup> - kF<sub>off</sub> fMT<sub>As</sub><br />
|-<br />
| ||ArsR<sub>As</sub> ||bound to As(III)<br />
|-<br />
| ||GV ||concentration of gas vesicles||(d/dt) GV = <span class="production">&beta;G ars2 - ln(2)/&tau;G GV</span><br />
|-<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="estimate" style="padding:0;"|GVP Production related.<br />
|}<br />
|}<br />
<br />
The variables above can be related to each other through the following "reactions" (color coding is continued below to show which parts of the differential equations refer to which groups of reactions):<br />
<br />
<br />
Using the following constants/definitions:<br />
{|class="ourtable"<br />
|-<br />
!Name<br />
!Units<br />
!Description<br />
|-<br />
|kRon, kMon, k5on, etc.<br />
|1/(M&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kAon<br />
|1/(M²&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kFon<br />
|1/(M<sup>n<sub>f</sub></sup>&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kRoff, kMoff, kFoff, kAoff, k5off, etc.<br />
|1/s<br />
|Reaction rate constants for reactions from a complex.<br />
|-<br />
|k6, k8<br />
|1/s<br />
|Reaction rate constants representing how fast transporters transport their cargo to "the other side".<br />
|-<br />
|&tau;B, &tau;R, &tau;M, &tau;F, &tau;G<br />
|s<br />
|Half-lifes (of ArsB, ArsR, MBPArsR, fMT and GV, respectively). Degradation rate = ln(2)/&tau; {{infoBox|1=If you take just the degradation into account you will have the equation dC/dt = -k*C, which leads to C(t) = C(0) e<sup>-k t</sup>. So if k = ln(2)/&tau; we get C(t) = C(0) e<sup>-ln(2)/&tau; t</sup> = C(0) 2<sup>-t/&tau;</sup>. In other words &tau; is the time it takes for the concentration to half.}}<br />
|-<br />
|&beta;RN, &beta;R, etc.<br />
|1/s<br />
|Production rates.<br />
* &beta;RN = the production rate for ArsR behind the ars1 promoter<br />
* &beta;B = the production rate for ArsB behind the ars1 promoter<br />
* &beta;G = the production rate for GV behind the ars2 promoter<br />
* &beta;R = the production rate for ArsR behind a constitutive promoter<br />
* &beta;M = the production rate for MBPArsR behind a constitutive promoter<br />
* &beta;F = the production rate for fMT behind a constitutive promoter<br />
|-<br />
|Vs<br />
|L<br />
|Volume of solution (excluding cells).<br />
|-<br />
|Vc<br />
|L<br />
|Total volume of cells (in solution) (so Vs+Vc is the total volume).<br />
|}<br />
See [[Team:Groningen/Literature#Chen1997|Chen1997]] for the interplay between ArsR and ArsD (the latter has a role similar to ArsR, but we do not treat it, as it is [[Team:Groningen/BLAST|not present in our system]]).<br />
<br />
==Quasi steady state{{anchor|QuasiSteadyState}}==<br />
First of all, we assume the concentration of transporters is quite low compared to the concentration of the transported substances. After all, if this were not the case the transporters would act more like "storage" proteins than transporters (note that this can be even more rigorously justified if, for example, GlpFT<<K5). This leads to:<br />
<br />
<pre><br />
As(III)exT &asymp; As(III)ex<br />
As(III)inT &asymp; As(III)in + ArsRAs + MBPArsRAs + nf fMTAs<br />
</pre><br />
<br />
Also, we assume the binding and unbinding of molecules to the transporters occurs on a much finer time-scale than any actual changes to the concentrations inside and outside the cell. Similarly, within the cell we assume diffusion processes are very fast and binding/unbinding of substances is quite fast compared to the production of proteins. This leads us to assume that the following ratios between substances are constantly in equilibrium:<br />
<br />
{{frame|1=<br />
<div style="text-align:left;"><br />
We use the following when grouping the ars promoters:<br />
<pre><br />
arsT = ars + ArsRars<br />
ars1 / ars1T = ars2 / ars2T<br />
<br />
ars = ars1 + ars2<br />
ars = ars1 (1 + ars2T / ars1T)<br />
ars1 = ars / (1 + ars2T / ars1T)<br />
ars1 = ars ars1T / arsT<br />
<br />
ars2 = ars ars2T / arsT<br />
</pre><br />
</div><br />
}}<br />
<br />
<pre><br />
As(III)ex : GlpFAs &asymp; As(III)ex : 0<br />
GlpF : GlpFAs<br />
ArsB : ArsBAs<br />
As(III)in : ArsRAs : MBPArsRAs : nf fMTAs : ArsBAs &asymp; As(III)in : ArsRAs : MBPArsRAs : nf fMTAs : 0<br />
ArsR : ArsRAs : 2 ArsRars<br />
ars : ArsRars<br />
</pre><br />
<br />
To determine what the unknown ratios are we can set the following derivatives to zero (these are the derivatives of the complexes corresponding to the four overlapping regions in the diagram):<br />
<br />
<pre><br />
0 = (d/dt) GlpFAs = k5on As(III)ex GlpF - (k5off+k6) GlpFAs<br />
0 = (d/dt) ArsBAs = k7on As(III)in ArsB - (k7off+k8) ArsBAs<br />
0 = (d/dt) ArsRars = kAon ArsR² ars - kAoff ArsRars<br />
0 = (d/dt) ArsRAs = kRon ArsR As(III)in - kRoff ArsRAs<br />
0 = (d/dt) MBPArsRAs = kMon MBPArsR As(III)in - kMoff MBPArsRAs<br />
0 = (d/dt) fMTAs = kFon fMT As(III)in^nf - kFoff fMTAs<br />
</pre><br />
<br />
The first two derivates let us determine the ratios between bound and unbound transporters:<br />
<br />
<pre><br />
0 = (d/dt) GlpFAs = k5on As(III)ex GlpF - (k5off+k6) GlpFAs<br />
<br />
k5on As(III)ex GlpF = (k5off+k6) GlpFAs<br />
GlpF = (k5off+k6)/k5on GlpFAs / As(III)ex<br />
GlpF = K5 GlpFAs / As(III)ex<br />
<br />
GlpF : GlpFAs<br />
K5 GlpFAs / As(III)ex : GlpFAs<br />
K5 : As(III)ex<br />
<br />
0 = (d/dt) ArsBAs = k7on As(III)in ArsB - (k7off+k8) ArsBAs<br />
<br />
k7on As(III)in ArsB = (k7off+k8) ArsBAs<br />
ArsB = (k7off+k8)/k7on ArsBAs / As(III)in<br />
ArsB = K7 ArsBAs / As(III)in<br />
<br />
ArsB : ArsBAs<br />
K7 ArsBAs / As(III)in : ArsBAs<br />
K7 : As(III)in<br />
</pre><br />
<br />
The next two differential equations can be used to determine the relative abundances of ArsR and ArsRAs, and ars and ArsRars:<br />
<br />
<pre><br />
0 = (d/dt) ArsRAs = kRon ArsR As(III)in - kRoff ArsRAs<br />
<br />
kRon ArsR As(III)in = kRoff ArsRAs<br />
ArsRAs = kRon/kRoff ArsR As(III)in<br />
ArsRAs = ArsR As(III)in / KRd<br />
<br />
ArsR : ArsRAs<br />
ArsR : ArsR As(III)in / KRd<br />
KRd : As(III)in<br />
<br />
0 = (d/dt) ArsRars = kAon ArsR² ars - kAoff ArsRars<br />
<br />
kAon ArsR² ars = kAoff ArsRars<br />
ArsRars = kAon/kAoff ArsR² ars<br />
ArsRars = ArsR² ars / KAd²<br />
<br />
ArsR : 2 ArsRars<br />
ArsR : 2 ArsR² ars / KAd²<br />
KAd² : 2 ArsR ars<br />
<br />
ars : ArsRars<br />
ars : ArsR² ars / KAd²<br />
KAd² : ArsR²<br />
</pre><br />
<br />
For MBPArsR and fMT we find:<br />
<br />
<pre><br />
0 = (d/dt) MBPArsRAs = kMon MBPArsR As(III)in - kMoff MBPArsRAs<br />
<br />
MBPArsR : MBPArsRAs = KMd : As(III)in<br />
<br />
0 = (d/dt) fMTAs = kFon fMT As(III)in^nf - kFoff fMTAs<br />
<br />
fMT : fMTAs = KFd^nf : As(III)in^nf<br />
</pre><br />
<br />
And finally the relative abundances of arsenic:<br />
<br />
<pre><br />
ArsRAs = ArsR As(III)in / KRd<br />
<br />
As(III)in : ArsRAs : MBPArsRAs : n fMTAs<br />
As(III)in : ArsR As(III)in / KRd : MBPArsRT As(III)in / (KMd+As(III)in) : n fMTT As(III)in^nf / (KFd^nf+As(III)in^nf)<br />
1 : ArsR / KRd : MBPArsRT / (KMd+As(III)in) : n fMTT As(III)in^(nf-1) / (KFd^nf+As(III)in^nf)<br />
</pre><br />
<br />
Summarizing:<br />
<br />
<pre><br />
GlpF : GlpFAs = K5 : As(III)ex<br />
ArsB : ArsBAs = K7 : As(III)in<br />
As(III)in : ArsRAs : MBPArsRAs : n fMTAs &asymp; 1 : ArsR / KRd : MBPArsRT / (KMd+As(III)in) : n fMTT As(III)in^(nf-1) / (KFd^nf+As(III)in^nf)<br />
ars : ArsRars = KAd² : ArsR²<br />
ArsR : ArsRAs : 2 ArsRars &asymp; 1 : As(III)in / KRd : 2 ArsR ars / KAd²<br />
MBPArsR : MBPArsRAs = KMd : As(III)in<br />
fMT : fMTAs = KFd^nf : As(III)in^nf<br />
</pre><br />
<br />
Now we can look at the differential equations for the totals of ArsB (so ArsBT=ArsB+ArsBAs), ArsR, As(III)in and As(III)ex (GlpFT and arsT are assumed to be constant):<br />
<br />
<pre><br />
(d/dt) As(III)exT = (d/dt) As(III)ex + (d/dt) GlpFAs<br />
= - (d/dt) GlpFAs - k6 GlpFAs + (Vc/Vs) k8 ArsBAs + (d/dt) GlpFAs<br />
= (Vc/Vs) k8 ArsBAs - k6 GlpFAs<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 GlpFAs / GlpFT<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 As(III)ex / (K5+As(III)ex)<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 As(III)exT / (K5+As(III)exT)<br />
(d/dt) ArsBT = (d/dt) ArsB + (d/dt) ArsBAs<br />
= - (d/dt) ArsBAs + βB ars1 - ln(2)/τB ArsB + (d/dt) ArsBAs<br />
= βB ars1 - ln(2)/τB ArsB<br />
(d/dt) As(III)inT = -(Vs/Vc) (d/dt) As(III)exT<br />
= v5 As(III)exT / (K5+As(III)exT) - k8 ArsBT As(III)in / (K7+As(III)in)<br />
(d/dt) ArsRT = (d/dt) ArsR + (d/dt) ArsRAs + 2 (d/dt) ArsRars<br />
= βRN ars1 + βR proR - (ln(2)/τR) ArsR - (d/dt) ArsRAs - 2 (d/dt) ArsRars + (d/dt) ArsRAs + 2 (d/dt) ArsRars<br />
= βRN ars1 + βR proR - (ln(2)/τR) ArsR<br />
(d/dt) MBPArsRT = (d/dt) MBPArsR + (d/dt) MBPArsRAs<br />
= βM proM - (ln(2)/τM) MBPArsR<br />
(d/dt) fMTT = (d/dt) fMT + (d/dt) fMTAs<br />
= βF proF - (ln(2)/τF) fMT<br />
</pre><br />
<br />
==Steady state==<br />
By looking at the steady state of the system we can say something about its long-term behaviour. This also makes it easier to analyze relations between variables. To derive the steady state solution we take the quasi steady state solution and simplify it further by setting additional derivatives to zero:<br />
<br />
<pre><br />
0 = (d/dt) ArsBT = βB ars1 - ln(2)/τB ArsB<br />
0 = (d/dt) As(III)inT = v5 As(III)exT / (K5+As(III)exT) - k8 ArsBAs<br />
0 = (d/dt) ArsRT = βRN ars1 + βR pro - (ln(2)/τR) ArsR<br />
0 = (d/dt) MBPArsRT = βM proM - (ln(2)/τM) MBPArsR<br />
0 = (d/dt) fMTT = βF proF - (ln(2)/τF) fMT<br />
0 = (d/dt) GV = βG ars2 - ln(2)/τG GV<br />
</pre><br />
<br />
This directly leads to:<br />
<br />
<pre><br />
0 = βB ars1 - ln(2)/τB ArsB<br />
ArsB = βB (τB/ln(2)) ars1<br />
ArsB = βB (τB/ln(2)) ars1T KAd²/(KAd²+ArsR²)<br />
<br />
0 = βM proM - (ln(2)/τM) MBPArsR<br />
MBPArsR = βM (τM/ln(2)) proM<br />
<br />
0 = βF proF - (ln(2)/τF) fMT<br />
fMT = βF (τF/ln(2)) proF<br />
<br />
0 = βG ars2 - ln(2)/τG GV<br />
GV = βG (τB/ln(2)) ars2<br />
GV = βG (τB/ln(2)) ars2T KAd²/(KAd²+ArsR²)<br />
</pre><br />
<br />
For the intra- and extracellular concentrations we can find the following equation, giving a maximum for As(III)in of <code>K7 v5/(k8 ArsB)</code> (as As(III)exT cannot be negative){{infoBox|Conveniently the function <code>x/(c-x)</code> is non-negative and non-decreasing for x&isin;[0,c&rang;.}}:<br />
<br />
<pre><br />
0 = v5 As(III)exT / (K5+As(III)exT) - k8 ArsBAs<br />
0 = v5 As(III)exT / (K5+As(III)exT) - k8 ArsB As(III)in / K7<br />
0 = v5 As(III)exT - k8 ArsB As(III)in / K7 (K5+As(III)exT)<br />
0 = v5 As(III)exT - k8 ArsB As(III)in As(III)exT / K7 - k8 ArsB As(III)in K5 / K7<br />
0 = As(III)exT (v5 - k8 ArsB As(III)in / K7) - k8 ArsB As(III)in K5 / K7<br />
As(III)exT = k8 ArsB As(III)in K5 / (v5 K7 - k8 ArsB As(III)in)<br />
As(III)exT = K5 As(III)in / (K7 v5/(k8 ArsB) - As(III)in)<br />
</pre><br />
<br />
As we can safely assume arsenic neither disappears into nothingness nor appears from nothingness, we can use this to derive (As(III)T is the total amount of arsenic):<br />
<br />
<pre><br />
As(III)inT = As(III)in (1 + ArsR/KRd + MBPArsR/KMd + fMT As(III)in^(nf-1)/KFd^nf)<br />
<br />
As(III)T = Vs As(III)exT + Vc As(III)inT<br />
0 = Vs As(III)exT + Vc As(III)inT - As(III)T<br />
0 = Vs K5 As(III)in / (K7 v5/(k8 ArsB) - As(III)in) + Vc As(III)in (1 + ArsR/KRd + MBPArsR/KMd + fMT As(III)in^(nf-1)/KFd^nf) - As(III)T<br />
</pre><br />
<br />
As the function on the right-hand side is non-decreasing for <code>As(III)in&isin;[0,K7 v5/(k8 ArsB)&rang;</code> it at most has one zero on this interval (and it has one, as it starts at a negative value and gets arbitrarily large as As(III)in approaches the end of its range). So this zero can safely be found using any number of numerical methods.<br />
<br />
Finally, for ArsR we can find the following third-order equation:<br />
<br />
<pre><br />
0 = βRN ars1 + βR pro - (ln(2)/τR) ArsR<br />
0 = βRN ars1T KAd²/(KAd²+ArsR²) + βR pro - (ln(2)/τR) ArsR<br />
0 = βRN ars1T KAd² + βR pro (KAd²+ArsR²) - (ln(2)/τR) ArsR (KAd²+ArsR²)<br />
0 = βRN ars1T KAd² + βR pro KAd² + βR pro ArsR² - (ln(2)/τR) ArsR KAd² - (ln(2)/τR) ArsR³<br />
0 = (βRN ars1T + βR pro) KAd² - (ln(2)/τR) KAd² ArsR + βR pro ArsR² - (ln(2)/τR) ArsR³<br />
0 = (βRN ars1T + βR pro) (τR/ln(2)) KAd² - KAd² ArsR + βR (τR/ln(2)) pro ArsR² - ArsR³<br />
</pre><br />
<br />
According to Mathematica's solution of <code>Reduce[eq && KAd > 0 && arsT >= 0 && pro >= 0 && &beta;1 > 0 && &beta;3 > 0 && &tau;R > 0, ArsR, Reals]</code> (where eq is the equation shown above) there is only one real solution (examining the discriminant of eq confirms this), so we can solve the equation safely using Newton's (or Halley's) method.<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-21T19:53:04Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div style="clear:both;"></div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Downloads}}</div><br />
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<div class="intro introduction"><br />
==Characterization==<br />
We have four kinds of parts we would like to characterize: Importers, Accumulators, Sensors and the GVP cluster.<br />
For this we have a number of methods to estimate ''specific parameters'' (detailed below), as well as a ''[[Team:Groningen/Modelling/Characterization#Optimization|stochastic tool to fit our model]]'' to experimental data based on simulated annealing.<br />
</div><br />
<br />
We have the following parts that we can characterize (RPS stands for Relative Promoter Strength)<br />
{|class="ourtable"<br />
|-style="text-align:left"<br />
!style="width:15%" style="text-align:left"|&nbsp;&nbsp;&nbsp;&nbsp; Input/Output<br />
!style="text-align:left"|Subject<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Importers'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; &Delta;v<sub>max</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
[[Team:Groningen/Literature#Meng2004|Meng 2004]] was able to knock out all efflux of arsenic. If there is no efflux of arsenic the dervative of the accumulation graph is the speed at wich arsenic is pumped inside the cell. The maximum speed would be v5. In such a senario two measurements would be enough to determine the relative promoter strength. One could even determine the reaction rate k6 and GlpF with a simple calculation, since v5 = k6 GlpFT (Vs/Vc). However we do have efflux, not only do we have efflux, but we have efflux that is dependent on the total amount of arsenic inside the cell. Also a portion arsenic gets bound to ArsR. <br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Accumulators'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|<br />
For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):<br />
<pre><br />
Asbound(As(III)in)<br />
= S Bmax As(III)in^n<br />
/ (K^n + As(III)in^n)<br />
</pre><br />
The constants B<sub>max</sub>, K and n can be determined from uptake experiments comparing E. coli with and without fMT expression. Of course this can be done in general by fitting our model to experimental data, if enough data is provided the fit will be tight enough to allow this. However, even without fitting the full model it should be possible to make a fair estimation from equilibrium measurements.{{infoBox|If the total cell volume is much smaller than the volume of the solution it is reasonable to assume a constant import rate. Also, regardless of whether they feature fMT or not, in equilibrium the amount of ArsR is the same, as is the amount of ArsB, leading to the same amount of unbound arsenic being present. This means that any difference in uptake of arsenic is completely due to arsenic being bound to fMT or MBPArsR. By measuring the amount of arsenic in equilibrium in wild-type cells as well as in cells expressing fMT/MBPArsR for several different (inital) concentrations of As(III), at one or more (known) levels of expression, it is possible to determine the constants Bmax, K and n.}}<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Sensors'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; metal(t) &rarr; RPS(t)<br />
|<br />
The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from [[Team:Groningen/Modelling/Arsenic|our model]]. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine <code>&beta;RN &tau;R</code> as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):<br />
<pre><br />
S(max) / S(0) = ars(max) / ars(0)<br />
S(max) / S(0) = arsT / ars(0)<br />
S(max) / S(0) = 1 + ArsR(0)²/KAd²<br />
ArsR(0) = KAd &radic;(S(max)/S(0) - 1)<br />
<br />
0 = &beta;RN ars1(0) - (ln(2)/&tau;R) ArsR(0)<br />
0 = &beta;RN ars1T S(0)/S(max)<br />
- (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN ars1T S(0)/S(max)<br />
= (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN &tau;R = (ln(2)/ars1T) KAd<br />
(S(max)/S(0)) &radic;(S(max)/S(0) - 1)<br />
</pre><br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''GVP cluster'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; GV<br />
|<br />
RPS &rarr; GV<br />
The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.<br />
|-<br />
|}<br />
<br />
==Uptake measurements==<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
<br />
To obtain data for the optimization procedure described above we conducted ICP-MS measurements on our cells containing various devices/parts. To optimize our findings we have conducted measurements both in time and in concentration.<br />
Details on ICP-MS the experiments can be found on our [[Team:Groningen/Protocols|Protocol Page]]. Measurements have been conducted at times and concentrations as indicated in the table on the right. Results can be seen below. <br />
<br />
'''First Uptake Measurement'''<br><br />
In this case we looked at the arsenic uptake of our wildtype and of our wildtype with a lot of pArs promoters with RFP. The raw data can be found at our [[Team:Groningen/Modelling/Downloads| Download Section]]<br />
{|<br />
|[[Image:AsUptakeWildTypeConcentration.png|400px]]||[[Image:AsUptakePArsRFPConcentration.png|400px]]<br />
|-<br />
|[[Image:AsUptakeWildTypeTime.png|400px]]||[[Image:AsUptakePArsRFPTime.png|400px]]<br />
|-<br />
|}<br />
<br />
'''Getting (Vc/Vs) and other conditions'''<br><br />
To effectively determine our constants we need to give our model some extra information. For instance what kind of constructs are inside the cel for a given experiment. Also we need to give the model the volume of cells per liter of fluid. To optain this we use the obtained dry weight and calculate how much wet weight it would have been (assuming dry weight/wet weight = 0.3) and then use the density of ''E. coli'' (1100kg/m<sup>3</sup>) to obtain the cell volume for our sample and eventually the desired volume of cells per liter.<br />
Also we need the absolute value of Arsenic taken up by the cells in the assumption that we have one liter of sample and we know (Vc/Vs). Once we know all these parameters the optimization procedure can start. <br />
<br />
'''Fluorescence Measurements'''<br><br />
Apart from giving our model all the conditions it needs to calculate all the constants by means of the optimization procedure, we have also conducted some fluorescence measurements and made growth curves of our construct with the pArs promoter with RFP. The cells where put into a solution with either no arsenic in it or at a concentration of 100 micromolair. On the left side one can see the graph of the luminance and on right side and on the right side one can see the coresponding grow curves. The raw data of these measurements can again be found under our [[Team:Groningen/Modelling/Downloads|Downloads]]<br />
{|<br />
|[[Image:ArsFluorescence.png|400px]]||[[Image:ArsOD.png|400px]]<br />
|-<br />
|}<br />
Using a formula similar to the formula below{{infoBox|In actuality we did not compute the derivative of the fluorescence and then corrected for the OD, instead we first computed the fluorescence normalized for the OD (correlates with RFP per cell) and then fitted a linear function to the data. This leads to a much more robust fit in the presence of noise and few measurements.}} we where able to derive a RPU of 2.3. This means that on average the ars promoter is 2.3 times more active at 100 micromolarity of arsenic (outside the cell) than if there is no arsenic in the solution. For a detailed calculation I would like to refer to our [[Team:Groningen/Modelling/Downloads|Downloads]] section under the RPU sheet.<br />
{|style=float:center;<br />
|[[Image:RPUcalculation.png|300px]]<br />
|}<br />
<br />
'''Second ICPMS measurement'''<br />
For our second measurement I would like to refer to our [[Team:Groningen/Project/Accumulation|Accumulation]] page. These measerments where higher than expected and they need further analyses before we can use them in tha characterization of our parts.<br />
<br />
=={{anchor|Optimization}}Optimization procedure==<br />
To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved).<br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
<!--|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|--><br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:Infinity,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:Infinity,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5','v5',*/'k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {//v5: function(v){return v.v5;},<br />
//K5: function(v){return v.v5/v.v5_K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
//cSol.v5 = orgC.v5;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
//c.v5 = orgC.v5;<br />
c.k8 = 10;<br />
c.k8_K7 = 2e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
for(var a in mutateFuncs) {<br />
setOutput(a+mode,mutateFuncs[a](c));<br />
}<br />
setOutput('E'+mode,E);<br />
if (dc!=undefined) {<br />
for(var a in dc) {<br />
setOutput(a+mode+'gradient',dc[a]);<br />
}<br />
}<br />
}<br />
<br />
function constructPlot(id) {<br />
var width = 100, height = 100;<br />
var t = document.getElementById(id);<br />
t.minx = Number.NaN;<br />
t.miny = Number.NaN;<br />
t.maxx = Number.NaN;<br />
t.maxy = Number.NaN;<br />
t.points = [];<br />
t.createCaption();<br />
t.style.width = width + 'px';<br />
t.style.width = height + 'px';<br />
t.style.border = 'solid 1px #000';<br />
t.style.borderCollapse = 'collapse';<br />
for(var r=0; r<height; r++) {<br />
var newRow = t.insertRow(0);<br />
for(var c=0; c<width; c++) {<br />
var newCell = newRow.insertCell(0);<br />
newCell.style.width = '1px';<br />
newCell.style.height = '1px';<br />
newCell.style.background = '#fff';<br />
newCell.style.padding = '0px';<br />
}<br />
}<br />
}<br />
<br />
function plotMin(t,x,y,v) {<br />
if (x<0) return;<br />
if (y<0) return;<br />
var regrid = false;<br />
t.points.push({'x':x,'y':y,'v':v});<br />
if (isNaN(t.minx) || x<t.minx) { t.minx = x/1.5; regrid = true; }<br />
if (isNaN(t.maxx) || x>t.maxx) { t.maxx = x*1.5; regrid = true; }<br />
if (isNaN(t.miny) || y<t.miny) { t.miny = y/1.5; regrid = true; }<br />
if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
//alert('regridding' + [x,y,t.minx,t.miny,t.maxx,t.maxy,regrid]);<br />
setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
for(var r=0; r<t.rows.length; r++) {<br />
var row = t.rows[r];<br />
for(var c=0; c<row.cells.length; c++) {<br />
var cell = row.cells[c];<br />
cell.background = '#fff';<br />
}<br />
}<br />
for(var i in t.points) plotMinWork(t,t.points[i].x,t.points[i].y,t.points[i].v);<br />
} else {<br />
plotMinWork(t,x,y,v);<br />
}<br />
}<br />
<br />
function plotMinWork(t,x,y,v) {<br />
var r = Math.floor((y-t.miny)/(t.maxy-t.miny)*t.rows.length);<br />
var c = Math.floor((x-t.minx)/(t.maxx-t.minx)*t.rows[0].cells.length);<br />
var cell = t.rows[r].cells[c];<br />
if (cell.value==undefined || v<cell.value) {<br />
cell.value = v;<br />
cell.style.background = 'rgb('+Math.max(0,100*v)+'%,'+Math.min(100,100*(1-v))+'%,0%)';<br />
}<br />
}<br />
<br />
function setCaption(t,cap) {<br />
if (!t) return;<br />
var caps = t.getElementsByTagName('caption');<br />
if (caps.length>0) {<br />
caps[0].innerHTML = cap;<br />
return;<br />
}<br />
if (t.caption) {<br />
t.caption = cap;<br />
return;<br />
}<br />
}<br />
</script><br />
</html><br />
{|<br />
|<br />
{|id="v5K5plot"<br />
|}<br />
|<br />
{|id="k8K7plot"<br />
|}<br />
|}<br />
<br />
<!-- Model graphs start here --><br />
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{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-21T19:52:14Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div style="clear:both;"></div><br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right;" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Arsenic}}</div><br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
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<div class="intro introduction"><br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|<span style="font-weight:normal;">Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line. For one thing, this makes it easier to '''explore''' the model, up to the point that even non-modellers are able to explore the model.</span>]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible ''interactively'' available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
</div><br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*'''Analysis''' of results. Using data from uptake experiments, promoter measurements and TEM pictures we can [[Team:Groningen/Modelling/Characterization|estimate further constants]] and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-21T19:50:27Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right;clear:both;" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Arsenic}}</div><br />
<br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
<br />
<html><style type="text/css"><br />
.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
</style></html><br />
<div class="intro introduction"><br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|<span style="font-weight:normal;">Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line. For one thing, this makes it easier to '''explore''' the model, up to the point that even non-modellers are able to explore the model.</span>]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible ''interactively'' available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
</div><br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*'''Analysis''' of results. Using data from uptake experiments, promoter measurements and TEM pictures we can [[Team:Groningen/Modelling/Characterization|estimate further constants]] and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-21T19:49:50Z<p>Jaspervdg: Made introduction "yellow"</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Arsenic}}</div><br />
<br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
<br />
<html><style type="text/css"><br />
.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
</style></html><br />
<div class="intro introduction"><br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|<span style="font-weight:normal;">Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line. For one thing, this makes it easier to '''explore''' the model, up to the point that even non-modellers are able to explore the model.</span>]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible ''interactively'' available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
</div><br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*'''Analysis''' of results. Using data from uptake experiments, promoter measurements and TEM pictures we can [[Team:Groningen/Modelling/Characterization|estimate further constants]] and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-21T19:42:37Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Downloads}}</div><br />
<br />
<html><style type="text/css"><br />
.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
</style></html><br />
<div class="intro introduction" style="clear:both;"><br />
==Characterization==<br />
We have four kinds of parts we would like to characterize: Importers, Accumulators, Sensors and the GVP cluster.<br />
For this we have a number of methods to estimate ''specific parameters'' (detailed below), as well as a ''[[Team:Groningen/Modelling/Characterization#Optimization|stochastic tool to fit our model]]'' to experimental data based on simulated annealing.<br />
</div><br />
<br />
We have the following parts that we can characterize (RPS stands for Relative Promoter Strength)<br />
{|class="ourtable"<br />
|-style="text-align:left"<br />
!style="width:15%" style="text-align:left"|&nbsp;&nbsp;&nbsp;&nbsp; Input/Output<br />
!style="text-align:left"|Subject<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Importers'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; &Delta;v<sub>max</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
[[Team:Groningen/Literature#Meng2004|Meng 2004]] was able to knock out all efflux of arsenic. If there is no efflux of arsenic the dervative of the accumulation graph is the speed at wich arsenic is pumped inside the cell. The maximum speed would be v5. In such a senario two measurements would be enough to determine the relative promoter strength. One could even determine the reaction rate k6 and GlpF with a simple calculation, since v5 = k6 GlpFT (Vs/Vc). However we do have efflux, not only do we have efflux, but we have efflux that is dependent on the total amount of arsenic inside the cell. Also a portion arsenic gets bound to ArsR. <br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Accumulators'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|<br />
For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):<br />
<pre><br />
Asbound(As(III)in)<br />
= S Bmax As(III)in^n<br />
/ (K^n + As(III)in^n)<br />
</pre><br />
The constants B<sub>max</sub>, K and n can be determined from uptake experiments comparing E. coli with and without fMT expression. Of course this can be done in general by fitting our model to experimental data, if enough data is provided the fit will be tight enough to allow this. However, even without fitting the full model it should be possible to make a fair estimation from equilibrium measurements.{{infoBox|If the total cell volume is much smaller than the volume of the solution it is reasonable to assume a constant import rate. Also, regardless of whether they feature fMT or not, in equilibrium the amount of ArsR is the same, as is the amount of ArsB, leading to the same amount of unbound arsenic being present. This means that any difference in uptake of arsenic is completely due to arsenic being bound to fMT or MBPArsR. By measuring the amount of arsenic in equilibrium in wild-type cells as well as in cells expressing fMT/MBPArsR for several different (inital) concentrations of As(III), at one or more (known) levels of expression, it is possible to determine the constants Bmax, K and n.}}<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Sensors'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; metal(t) &rarr; RPS(t)<br />
|<br />
The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from [[Team:Groningen/Modelling/Arsenic|our model]]. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine <code>&beta;RN &tau;R</code> as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):<br />
<pre><br />
S(max) / S(0) = ars(max) / ars(0)<br />
S(max) / S(0) = arsT / ars(0)<br />
S(max) / S(0) = 1 + ArsR(0)²/KAd²<br />
ArsR(0) = KAd &radic;(S(max)/S(0) - 1)<br />
<br />
0 = &beta;RN ars1(0) - (ln(2)/&tau;R) ArsR(0)<br />
0 = &beta;RN ars1T S(0)/S(max)<br />
- (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN ars1T S(0)/S(max)<br />
= (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN &tau;R = (ln(2)/ars1T) KAd<br />
(S(max)/S(0)) &radic;(S(max)/S(0) - 1)<br />
</pre><br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''GVP cluster'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; GV<br />
|<br />
RPS &rarr; GV<br />
The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.<br />
|-<br />
|}<br />
<br />
==Uptake measurements==<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
<br />
To obtain data for the optimization procedure described above we conducted ICP-MS measurements on our cells containing various devices/parts. To optimize our findings we have conducted measurements both in time and in concentration.<br />
Details on ICP-MS the experiments can be found on our [[Team:Groningen/Protocols|Protocol Page]]. Measurements have been conducted at times and concentrations as indicated in the table on the right. Results can be seen below. <br />
<br />
'''First Uptake Measurement'''<br><br />
In this case we looked at the arsenic uptake of our wildtype and of our wildtype with a lot of pArs promoters with RFP. The raw data can be found at our [[Team:Groningen/Modelling/Downloads| Download Section]]<br />
{|<br />
|[[Image:AsUptakeWildTypeConcentration.png|400px]]||[[Image:AsUptakePArsRFPConcentration.png|400px]]<br />
|-<br />
|[[Image:AsUptakeWildTypeTime.png|400px]]||[[Image:AsUptakePArsRFPTime.png|400px]]<br />
|-<br />
|}<br />
<br />
'''Getting (Vc/Vs) and other conditions'''<br><br />
To effectively determine our constants we need to give our model some extra information. For instance what kind of constructs are inside the cel for a given experiment. Also we need to give the model the volume of cells per liter of fluid. To optain this we use the obtained dry weight and calculate how much wet weight it would have been (assuming dry weight/wet weight = 0.3) and then use the density of ''E. coli'' (1100kg/m<sup>3</sup>) to obtain the cell volume for our sample and eventually the desired volume of cells per liter.<br />
Also we need the absolute value of Arsenic taken up by the cells in the assumption that we have one liter of sample and we know (Vc/Vs). Once we know all these parameters the optimization procedure can start. <br />
<br />
'''Fluorescence Measurements'''<br><br />
Apart from giving our model all the conditions it needs to calculate all the constants by means of the optimization procedure, we have also conducted some fluorescence measurements and made growth curves of our construct with the pArs promoter with RFP. The cells where put into a solution with either no arsenic in it or at a concentration of 100 micromolair. On the left side one can see the graph of the luminance and on right side and on the right side one can see the coresponding grow curves. The raw data of these measurements can again be found under our [[Team:Groningen/Modelling/Downloads|Downloads]]<br />
{|<br />
|[[Image:ArsFluorescence.png|400px]]||[[Image:ArsOD.png|400px]]<br />
|-<br />
|}<br />
Using a formula similar to the formula below{{infoBox|In actuality we did not compute the derivative of the fluorescence and then corrected for the OD, instead we first computed the fluorescence normalized for the OD (correlates with RFP per cell) and then fitted a linear function to the data. This leads to a much more robust fit in the presence of noise and few measurements.}} we where able to derive a RPU of 2.3. This means that on average the ars promoter is 2.3 times more active at 100 micromolarity of arsenic (outside the cell) than if there is no arsenic in the solution. For a detailed calculation I would like to refer to our [[Team:Groningen/Modelling/Downloads|Downloads]] section under the RPU sheet.<br />
{|style=float:center;<br />
|[[Image:RPUcalculation.png|300px]]<br />
|}<br />
<br />
'''Second ICPMS measurement'''<br />
For our second measurement I would like to refer to our [[Team:Groningen/Project/Accumulation|Accumulation]] page. These measerments where higher than expected and they need further analyses before we can use them in tha characterization of our parts.<br />
<br />
=={{anchor|Optimization}}Optimization procedure==<br />
To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved).<br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
<!--|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|--><br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:Infinity,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:Infinity,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5','v5',*/'k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {//v5: function(v){return v.v5;},<br />
//K5: function(v){return v.v5/v.v5_K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
//cSol.v5 = orgC.v5;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
//c.v5 = orgC.v5;<br />
c.k8 = 10;<br />
c.k8_K7 = 2e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
for(var a in mutateFuncs) {<br />
setOutput(a+mode,mutateFuncs[a](c));<br />
}<br />
setOutput('E'+mode,E);<br />
if (dc!=undefined) {<br />
for(var a in dc) {<br />
setOutput(a+mode+'gradient',dc[a]);<br />
}<br />
}<br />
}<br />
<br />
function constructPlot(id) {<br />
var width = 100, height = 100;<br />
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t.createCaption();<br />
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t.style.width = height + 'px';<br />
t.style.border = 'solid 1px #000';<br />
t.style.borderCollapse = 'collapse';<br />
for(var r=0; r<height; r++) {<br />
var newRow = t.insertRow(0);<br />
for(var c=0; c<width; c++) {<br />
var newCell = newRow.insertCell(0);<br />
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newCell.style.height = '1px';<br />
newCell.style.background = '#fff';<br />
newCell.style.padding = '0px';<br />
}<br />
}<br />
}<br />
<br />
function plotMin(t,x,y,v) {<br />
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if (y<0) return;<br />
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t.points.push({'x':x,'y':y,'v':v});<br />
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if (isNaN(t.maxx) || x>t.maxx) { t.maxx = x*1.5; regrid = true; }<br />
if (isNaN(t.miny) || y<t.miny) { t.miny = y/1.5; regrid = true; }<br />
if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
//alert('regridding' + [x,y,t.minx,t.miny,t.maxx,t.maxy,regrid]);<br />
setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
for(var r=0; r<t.rows.length; r++) {<br />
var row = t.rows[r];<br />
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var cell = row.cells[c];<br />
cell.background = '#fff';<br />
}<br />
}<br />
for(var i in t.points) plotMinWork(t,t.points[i].x,t.points[i].y,t.points[i].v);<br />
} else {<br />
plotMinWork(t,x,y,v);<br />
}<br />
}<br />
<br />
function plotMinWork(t,x,y,v) {<br />
var r = Math.floor((y-t.miny)/(t.maxy-t.miny)*t.rows.length);<br />
var c = Math.floor((x-t.minx)/(t.maxx-t.minx)*t.rows[0].cells.length);<br />
var cell = t.rows[r].cells[c];<br />
if (cell.value==undefined || v<cell.value) {<br />
cell.value = v;<br />
cell.style.background = 'rgb('+Math.max(0,100*v)+'%,'+Math.min(100,100*(1-v))+'%,0%)';<br />
}<br />
}<br />
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}<br />
}<br />
</script><br />
</html><br />
{|<br />
|<br />
{|id="v5K5plot"<br />
|}<br />
|<br />
{|id="k8K7plot"<br />
|}<br />
|}<br />
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<!-- Model graphs start here --><br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
{|<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/GlpF|id=Meng2004Graph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Singh2008|id=Singh2008Graph}}<br />
|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3B|id=Kostal2004fig3BGraph}}--><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2time|id=pSB1A2timeGraph}}<br />
<!--|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPtime|id=pArsRRFPtimeGraph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3A|id=Kostal2004fig3AGraph}}<br />
|- --><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2con|id=pSB1A2conGraph}}<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPcon|id=pArsRRFPconGraph}}--><br />
|}<br />
<!-- Don't forget to update the refreshGraphs function above! --><br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-21T19:37:16Z<p>Jaspervdg: Some tweaks to our characterization page.</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Downloads}}</div><br />
<br />
<div class="intro introduction"><br />
==Characterization==<br />
We have four kinds of parts we would like to characterize: Importers, Accumulators, Sensors and the GVP cluster.<br />
For this we have a number of methods to estimate '''specific parameters''' (detailed below), as well as a '''[[#Optimization|stochastic tool to fit our model]]''' to experimental data based on simulated annealing.<br />
</div><br />
<br />
We have the following parts that we can characterize (RPS stands for Relative Promoter Strength)<br />
{|class="ourtable"<br />
|-style="text-align:left"<br />
!style="width:15%" style="text-align:left"|&nbsp;&nbsp;&nbsp;&nbsp; Input/Output<br />
!style="text-align:left"|Subject<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Importers'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; &Delta;v<sub>max</sub> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
[[Team:Groningen/Literature#Meng2004|Meng 2004]] was able to knock out all efflux of arsenic. If there is no efflux of arsenic the dervative of the accumulation graph is the speed at wich arsenic is pumped inside the cell. The maximum speed would be v5. In such a senario two measurements would be enough to determine the relative promoter strength. One could even determine the reaction rate k6 and GlpF with a simple calculation, since v5 = k6 GlpFT (Vs/Vc). However we do have efflux, not only do we have efflux, but we have efflux that is dependent on the total amount of arsenic inside the cell. Also a portion arsenic gets bound to ArsR. <br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Accumulators'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|<br />
For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):<br />
<pre><br />
Asbound(As(III)in)<br />
= S Bmax As(III)in^n<br />
/ (K^n + As(III)in^n)<br />
</pre><br />
The constants B<sub>max</sub>, K and n can be determined from uptake experiments comparing E. coli with and without fMT expression. Of course this can be done in general by fitting our model to experimental data, if enough data is provided the fit will be tight enough to allow this. However, even without fitting the full model it should be possible to make a fair estimation from equilibrium measurements.{{infoBox|If the total cell volume is much smaller than the volume of the solution it is reasonable to assume a constant import rate. Also, regardless of whether they feature fMT or not, in equilibrium the amount of ArsR is the same, as is the amount of ArsB, leading to the same amount of unbound arsenic being present. This means that any difference in uptake of arsenic is completely due to arsenic being bound to fMT or MBPArsR. By measuring the amount of arsenic in equilibrium in wild-type cells as well as in cells expressing fMT/MBPArsR for several different (inital) concentrations of As(III), at one or more (known) levels of expression, it is possible to determine the constants Bmax, K and n.}}<br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''Sensors'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; metal(t) &rarr; RPS(t)<br />
|<br />
The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from [[Team:Groningen/Modelling/Arsenic|our model]]. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine <code>&beta;RN &tau;R</code> as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):<br />
<pre><br />
S(max) / S(0) = ars(max) / ars(0)<br />
S(max) / S(0) = arsT / ars(0)<br />
S(max) / S(0) = 1 + ArsR(0)²/KAd²<br />
ArsR(0) = KAd &radic;(S(max)/S(0) - 1)<br />
<br />
0 = &beta;RN ars1(0) - (ln(2)/&tau;R) ArsR(0)<br />
0 = &beta;RN ars1T S(0)/S(max)<br />
- (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN ars1T S(0)/S(max)<br />
= (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN &tau;R = (ln(2)/ars1T) KAd<br />
(S(max)/S(0)) &radic;(S(max)/S(0) - 1)<br />
</pre><br />
|-<br />
|||!style="width:15%" style="text-align:left"|'''GVP cluster'''<br />
|-<br />
|&nbsp;&nbsp;&nbsp;&nbsp; RPS &rarr; GV<br />
|<br />
RPS &rarr; GV<br />
The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.<br />
|-<br />
|}<br />
<br />
==Uptake measurements==<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
<br />
To obtain data for the optimization procedure described above we conducted ICP-MS measurements on our cells containing various devices/parts. To optimize our findings we have conducted measurements both in time and in concentration.<br />
Details on ICP-MS the experiments can be found on our [[Team:Groningen/Protocols|Protocol Page]]. Measurements have been conducted at times and concentrations as indicated in the table on the right. Results can be seen below. <br />
<br />
'''First Uptake Measurement'''<br><br />
In this case we looked at the arsenic uptake of our wildtype and of our wildtype with a lot of pArs promoters with RFP. The raw data can be found at our [[Team:Groningen/Modelling/Downloads| Download Section]]<br />
{|<br />
|[[Image:AsUptakeWildTypeConcentration.png|400px]]||[[Image:AsUptakePArsRFPConcentration.png|400px]]<br />
|-<br />
|[[Image:AsUptakeWildTypeTime.png|400px]]||[[Image:AsUptakePArsRFPTime.png|400px]]<br />
|-<br />
|}<br />
<br />
'''Getting (Vc/Vs) and other conditions'''<br><br />
To effectively determine our constants we need to give our model some extra information. For instance what kind of constructs are inside the cel for a given experiment. Also we need to give the model the volume of cells per liter of fluid. To optain this we use the obtained dry weight and calculate how much wet weight it would have been (assuming dry weight/wet weight = 0.3) and then use the density of ''E. coli'' (1100kg/m<sup>3</sup>) to obtain the cell volume for our sample and eventually the desired volume of cells per liter.<br />
Also we need the absolute value of Arsenic taken up by the cells in the assumption that we have one liter of sample and we know (Vc/Vs). Once we know all these parameters the optimization procedure can start. <br />
<br />
'''Fluorescence Measurements'''<br><br />
Apart from giving our model all the conditions it needs to calculate all the constants by means of the optimization procedure, we have also conducted some fluorescence measurements and made growth curves of our construct with the pArs promoter with RFP. The cells where put into a solution with either no arsenic in it or at a concentration of 100 micromolair. On the left side one can see the graph of the luminance and on right side and on the right side one can see the coresponding grow curves. The raw data of these measurements can again be found under our [[Team:Groningen/Modelling/Downloads|Downloads]]<br />
{|<br />
|[[Image:ArsFluorescence.png|400px]]||[[Image:ArsOD.png|400px]]<br />
|-<br />
|}<br />
Using a formula similar to the formula below{{infoBox|In actuality we did not compute the derivative of the fluorescence and then corrected for the OD, instead we first computed the fluorescence normalized for the OD (correlates with RFP per cell) and then fitted a linear function to the data. This leads to a much more robust fit in the presence of noise and few measurements.}} we where able to derive a RPU of 2.3. This means that on average the ars promoter is 2.3 times more active at 100 micromolarity of arsenic (outside the cell) than if there is no arsenic in the solution. For a detailed calculation I would like to refer to our [[Team:Groningen/Modelling/Downloads|Downloads]] section under the RPU sheet.<br />
{|style=float:center;<br />
|[[Image:RPUcalculation.png|300px]]<br />
|}<br />
<br />
'''Second ICPMS measurement'''<br />
For our second measurement I would like to refer to our [[Team:Groningen/Project/Accumulation|Accumulation]] page. These measerments where higher than expected and they need further analyses before we can use them in tha characterization of our parts.<br />
<br />
=={{anchor|Optimization}}Optimization procedure==<br />
To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved).<br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
<!--|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|--><br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:Infinity,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:Infinity,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promoters.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5','v5',*/'k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {//v5: function(v){return v.v5;},<br />
//K5: function(v){return v.v5/v.v5_K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
//cSol.v5 = orgC.v5;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
//c.v5 = orgC.v5;<br />
c.k8 = 10;<br />
c.k8_K7 = 2e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
for(var a in mutateFuncs) {<br />
setOutput(a+mode,mutateFuncs[a](c));<br />
}<br />
setOutput('E'+mode,E);<br />
if (dc!=undefined) {<br />
for(var a in dc) {<br />
setOutput(a+mode+'gradient',dc[a]);<br />
}<br />
}<br />
}<br />
<br />
function constructPlot(id) {<br />
var width = 100, height = 100;<br />
var t = document.getElementById(id);<br />
t.minx = Number.NaN;<br />
t.miny = Number.NaN;<br />
t.maxx = Number.NaN;<br />
t.maxy = Number.NaN;<br />
t.points = [];<br />
t.createCaption();<br />
t.style.width = width + 'px';<br />
t.style.width = height + 'px';<br />
t.style.border = 'solid 1px #000';<br />
t.style.borderCollapse = 'collapse';<br />
for(var r=0; r<height; r++) {<br />
var newRow = t.insertRow(0);<br />
for(var c=0; c<width; c++) {<br />
var newCell = newRow.insertCell(0);<br />
newCell.style.width = '1px';<br />
newCell.style.height = '1px';<br />
newCell.style.background = '#fff';<br />
newCell.style.padding = '0px';<br />
}<br />
}<br />
}<br />
<br />
function plotMin(t,x,y,v) {<br />
if (x<0) return;<br />
if (y<0) return;<br />
var regrid = false;<br />
t.points.push({'x':x,'y':y,'v':v});<br />
if (isNaN(t.minx) || x<t.minx) { t.minx = x/1.5; regrid = true; }<br />
if (isNaN(t.maxx) || x>t.maxx) { t.maxx = x*1.5; regrid = true; }<br />
if (isNaN(t.miny) || y<t.miny) { t.miny = y/1.5; regrid = true; }<br />
if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
//alert('regridding' + [x,y,t.minx,t.miny,t.maxx,t.maxy,regrid]);<br />
setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
for(var r=0; r<t.rows.length; r++) {<br />
var row = t.rows[r];<br />
for(var c=0; c<row.cells.length; c++) {<br />
var cell = row.cells[c];<br />
cell.background = '#fff';<br />
}<br />
}<br />
for(var i in t.points) plotMinWork(t,t.points[i].x,t.points[i].y,t.points[i].v);<br />
} else {<br />
plotMinWork(t,x,y,v);<br />
}<br />
}<br />
<br />
function plotMinWork(t,x,y,v) {<br />
var r = Math.floor((y-t.miny)/(t.maxy-t.miny)*t.rows.length);<br />
var c = Math.floor((x-t.minx)/(t.maxx-t.minx)*t.rows[0].cells.length);<br />
var cell = t.rows[r].cells[c];<br />
if (cell.value==undefined || v<cell.value) {<br />
cell.value = v;<br />
cell.style.background = 'rgb('+Math.max(0,100*v)+'%,'+Math.min(100,100*(1-v))+'%,0%)';<br />
}<br />
}<br />
<br />
function setCaption(t,cap) {<br />
if (!t) return;<br />
var caps = t.getElementsByTagName('caption');<br />
if (caps.length>0) {<br />
caps[0].innerHTML = cap;<br />
return;<br />
}<br />
if (t.caption) {<br />
t.caption = cap;<br />
return;<br />
}<br />
}<br />
</script><br />
</html><br />
{|<br />
|<br />
{|id="v5K5plot"<br />
|}<br />
|<br />
{|id="k8K7plot"<br />
|}<br />
|}<br />
<br />
<!-- Model graphs start here --><br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
{|<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/GlpF|id=Meng2004Graph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Singh2008|id=Singh2008Graph}}<br />
|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3B|id=Kostal2004fig3BGraph}}--><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2time|id=pSB1A2timeGraph}}<br />
<!--|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPtime|id=pArsRRFPtimeGraph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3A|id=Kostal2004fig3AGraph}}<br />
|- --><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2con|id=pSB1A2conGraph}}<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPcon|id=pArsRRFPconGraph}}--><br />
|}<br />
<!-- Don't forget to update the refreshGraphs function above! --><br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Project/AccumulationTeam:Groningen/Project/Accumulation2009-10-21T19:09:48Z<p>Jaspervdg: Layout fix.</p>
<hr />
<div>{{Team:Groningen/Project/Header|}}<br />
<div title="Arsie Says UP TO METAL SENSITIVE PROMOTORS" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Project/Promoters}}</div><br />
<br />
<div class="introduction"><br />
<br />
{|style="clear:both"<br />
|<html><style type="text/css"><br />
.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
</style></html><br />
<div class="intro"><br />
=Accumulation=<br />
Once heavy metals have entered the cell, it is crucial to keep them there. As these metals are toxic to cell survival in critical amounts, evolution has provided us with biological detoxicification proteins such as [http://en.wikipedia.org/wiki/Metallothionein metallothioneins]. These proteins can aid us in our quest to accumulate a variety of heavy metals as they bind to a wide range of metals including cadmium, zinc, mercury, copper, arsenic, silver, coordinated in metal-thiolates. The metal chelating proteins are cloned in a synthetic operon with a metal specific transporter to make up the accumulation device. For arcummulation of arsenite fMT and ArsR used, which were characterized by our model. Enhanced arsenite uptake by ''E. coli'' fMT could not be determined by the arsenite uptake assay, where the internal arsenic concentration was measured by ICP-MS. <br />
</div><br />
|}<br />
</div><br />
<br />
==Metallothioneins==<br />
Metallothioneins are a class of low molecular-weight metal-binding proteins (<10kDa) rich in cysteines residues(~30%). The contain a conserved cys-x-cys or cys-x-his motif which coordinates metal binding, as can be seen in figure 1. They are capable of binding a variety of heavy metals (e.g. Zn, Cu, Cd, Hg, As) with high avidity (Kb), they are ''in vivo'' used as a defense against oxidative stress by chelating metals. This proteins do also have a function in storing, detoxify and distributing metals throughout the cell ([[Team:Groningen/Literature#Merrifield2004|Merrifield 2004]], [[Team:Groningen/Literature#Gold2008|Gold 2008]]). These proteins have readily been used to create cell based systems for purification of contaminated water ([[Team:Groningen/Literature#Chen1998|Chen 1998]], [[Team:Groningen/Literature#Brady1994|Brady 1994]]). In addition to their wide application possibilities, they also have the capacity to carry multiple metal ions at one time, in contrast to some other metalloproteins that carry them one-on-one ([[Team:Groningen/Literature#Chang1998|Chang 1998]]).<br />
Many forms of metallothioneins are known and their affinity for different metals has been investigated on several occasions, such as for cadmium ([[Team:Groningen/Literature#Deng2007|Deng 2007]]), arsenic ([[Team:Groningen/Literature#Ngu2006|Ngu 2006]], [[Team:Groningen/Literature#Kostal2004|Kostal 2004]], [[Team:Groningen/Literature#Singh2008|Singh 2008]]), mercury ([[Team:Groningen/Literature#Chen1998|Chen 1998]], [[Team:Groningen/Literature#Chen1998|Chen 1997-2]], [[Team:Groningen/Literature#Deng2008|Deng 2008]]), nickel ([[Team:Groningen/Literature#Deng2003|Deng 2003]]) or a combination of metals ([[Team:Groningen/Literature#Chang1998|Chang 1998]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]).<br />
Metal-protein complexes can be quantified using a fluorescent molecule ([[Team:Groningen/Literature#Cadosch2008 |Cadosch 2008]]) but Cu(I) binding to metallothioneins in metal thiolates, was shown to cause a concentration dependant increase in luminescence. These Cu(I) binding metallothioneins were shown to give rise to a Stokes shift of approximately 300nm upon excitation at 280nm ([[Team:Groningen/Literature#Beltramini1981|Beltramini 1981]], [[Team:Groningen/Literature#Gold2008|Gold 2008]]). <br />
<br />
<br />
<center>[[Image:800px-Zinc finger rendered.png|250px]] </center><br />
:Figure 1: Zinc finger protein, consisting of a α-helix and an anti-parallel β-sheet. The zinc atom (green) is bound by two histidines and two cysteins.<br />
<br />
==Cloning strategy==<br />
In order to have a functional accumulation device, the cDNA of a metallothionein (MT) will be amplified using [http://en.wikipedia.org/wiki/PCR PCR] and cloned into <partinfo>pSB1A2</partinfo>, also a corresponding metal-ion transporter was amplified by PCR and cloned behind the MT. Both will expressed by one promoter (constitutive or lactose inducible). In this way the bacterium will take up the metal-ion and consecutively the metal-ion will be sequestered by the MT. When this device is combined with the [[Team:Groningen/Project/Vesicle#Cloning_strategy|floating device]], the bacteria will start floating when a certain threshold of intracellular metal concentration is reached, because the negative regulator of the buoyancy device will be released and the gas vesicle cluster can be transcribed.<br />
<br />
[[Image:Accumulation device.PNG]]<br />
:Figure 2: Cloning strategy for the metal accumulation device. A promoter taken from <partinfo>J61002</partinfo> will be cloned in front of a metallothionein and a metal transporter in a <partinfo>pSB1A2</partinfo> vector. This device will be combined with the floating device.<br />
<br />
===Practical note===<br />
MTs are degraded intracellular inside lysozymes, especially when they are in the apo/non-bound state ([[Team:Groningen/Literature#Gold2008|Gold 2008]]), for bacteria the degradation rate is not known, but for <br />
mammalian MT this can be estimated around 0.8nmol apo-MT/mg protein/min ([[Team:Groningen/Literature#Klaassen1994|Klaassen 1994]]). This can be avoided by adding metal-salts (ZnCl, CuCl) to cells expressing the protein.<br />
<br />
==Metals==<br />
===Arsenic===<br />
For the accumulation of arsenic some MTs are possible, like rh-MT (human MT) ([[Team:Groningen/Literature#Ngu2006 |Ngu 2006]]) and fMT (the seaweed species ''Fucus vesiculosis'') both binding As(III). The oxidized version of arsenic (As (V)) can also be bound by the metallothioneins but with lower affinity ([[Team:Groningen/Literature#Singh2008 |Singh 2008]]), another way As(V) is proposed to be accumulated is by conversion of As(V) to As(III) by the arsenate reductase and subsequent bound to the metallothionein or ArsR. rh-MT is known to bind 6x As(III) per molecule, fMT binds 5x As(III). No extra quantitative information is known from literature.<br />
====ArsR====<br />
ArsR is a trans-acting repressor that senses environmental As(III)and regulates the chromosomal ars operon. The ArsR protein has a specific binding site for As(III) and discriminates effectively against other metals like: phosphate, cadmium, sulfate and cobalt. The affinity of ArsR for As(III) is very high 10<sup>-15</sup>M of AS(III) can induce the promotor. The specific binding site spans 33 nucleotides in the promotor region including the putative -35 promotor element. When ArsR was purified, its size corresponded to that of a homodimer, bound to promoter DNA. Because of the high affinity of ArsR for As(III) the protein could be used for arsenic remediation. Chen and co-workers overexpressed ArsR in <i>E. coli</i> JM109 cells and found that the specific AS(III) content was 13-fold higher than the control without ArsR expression. High level expression of ArsR appeared to be toxic as a 3-fold reduction in cell density was observed. It has been shown that fusion partners reduce the toxicity of overexpression. Originally, Chen and co-workers made a fusion between ArsR and ELP (elastin protein), which is build out of VPGVG repeats. Because making a ArsR ELP153 fusion is very time consuming, we choose to make a fusion between MBP (maltose binding protein) and ArsR ([[Team:Groningen/Literature#Chen1998|Chen 1998]]).<br />
<BR><br />
Also see the [https://2009.igem.org/Team:Groningen/Project/Promoters|Metal sensitive promoters]. <br />
As ordering rh-MT was not successful, we try to use fMT for accumulation of As(III) and use ArsR to regulate the expression of the GVP cluster behind the ArsR regulated promoter.<br />
<br />
=====Results=====<br />
<br />
The fusion protein MBP-ArsR was built by creating giving the reverse primer of the MBP and the Forward primer of the ArsR a mutual restriction site SacI. The linker region was designed in such a way that it contained a Tev cleavage site, containing a SacI restriction site and a string of alanine residues to facilitate folding. The fusion protein has been succesfully cloned into the psb1AC3 vector creating biobrick {{part|BBa_K190027}}, but further attempts to add a promotor and rbs failed. Due to time the MBP-ArsR fusion protein has not been equipped with a promotor and so overexpression could not be established.<br />
<br />
===fMT===<br />
The <i>Fucus</i> [[Team:Groningen/Glossary#Metallothionein|Metallothionein]] (fMT) was isolated from the [http://en.wikipedia.org/wiki/Seaweed macroalgae] [http://en.wikipedia.org/wiki/Fucus_vesiculosus <i>Fucus vesiculosus</i> ]([[Team:Groningen/Literature#Morris1999|Morris 1999]]). It consists of 67 amino acid residues and has 16 cysteine residues, a high cysteine content is a key feature of MT. Another characteristic is the lack of aromatic residues is also seen in fMT where it only has one, tryptophan. Two domains containing cysteine residues are presumed to be involved in the metal binding function. Unusual in fMT is the presence of a 14 amino acid linker region between the two putative metal-binding domains which contains no cysteine residues. Plant MTs show this feature with about 40 residues, where vertebrate MTs only have three residues ([[Team:Groningen/Literature#Morris1999|Morris 1999]]). Being a MT fMT binds a multitude of metal ions, 6 Cd<sup>2+</sup> ions or 5 As<sup>3+</sup> ions in a sequential order, facilitated by the elongated linker domain ([[Team:Groningen/Literature#Ngu2009|Ngu 2009]]). The organisms from which fMT was first isolated are known to have the ability to survive in highly metal polluted water and with it having been expressed in ''E. coli'' previously ([[Team:Groningen/Literature#Singh2008|Singh 2008]]) it was an ideal choice to use as an arsenic sequestering protein.<br />
<br />
<br />
====Results====<br />
Arsenite uptake [[Team:Groningen/Protocols|assays]] were done to determine the As(III) accumulation of ''E. coli'' WT and fMT / GlpF overexpression strains. The concentration was measured by [[Team:Groningen/Protocols|ICP-MS]]. <br />
<br />
The arsenic uptake in ''E. coli'' WT (figure 3) as measured during this project (by [http://www.rikilt.wur.nl/NL/ RIKILT], Wageningen University), was compared with the uptake of ''E. coli'' with ArsR overexpression (described by [[Team:Groningen/Literature#Kostal2004|Kostal 2004]], see figure 3). This shows that the arsenic uptake in ''E. coli'' WT behaves similar but has lower final As(III) uptake yield. The difference is about 10% in the standard mode, but a higher extracellular arsenic concentration seems to be needed to saturate the uptake of arsenic in ''E. coli'' WT compared to ''E. coli'' with ArsR overexpression. This can be seen by comparing the transition point to saturation in figure 3, which are respectively around 50µM As(III) and around 20µM. <br />
<br />
[[Image:As uptake in E coli ArsR overexp - Kostal 2004.PNG]]<br />
:Figure 3: Uptake of As(III) by ''E. coli'' WT (containing pSB1A2-pLac)<br />
<br />
There is a relatively large difference between the data generated by measuring the arsenic concentration with ICP-MS in the standard mode and measuring in the collusion cell technology mode (CCT mode). The difference between these two techniques is that in the standard mode it is possible that multi-atomic compounds lead to interference with the arsenic (mw = 75) peak, like argon-chloride (Ar = 40 + Cl = 35 (75%) or 37(25%)). Because 25% of this compound is found in the mw = 77 peak, a correction factor may be calculated to correct for this, the ICP-MS software (Thermo) automatically corrects for Ar-Cl interference. It uses the amount of Krypton and Selenium for this correction. In the CCT all multi-atomic compounds are supposed to be decomposed, therefore no interference will be found in this mode. But a disadvantage of this mode is that the resolution is 10x lower than the standard mode, leading to a smaller signal-to-noise ratio. Because of this, we decided to use the standard mode (corrected for interference) to determine the arsenic accumulation by ''E. coli''.<br />
<br />
A second arsenic measurement was performed (by [http://www.vwa.nl/portal/page?_pageid=119,1639634&_dad=portal&_schema=PORTAL Food and Consumer Product Safety Authority], Groningen) using ''E. coli'' WT and ''E. coli'' containing the [accumulation device] (<partinfo>BBa_K190038</partinfo>) and the different parts ([[Team:Groningen/Project/Transport#Arsenite uptake via GlpF|GlpF]] (<partinfo>BBa_K190028</partinfo>) and [[Team:Groningen/Project/Accumulation#Arsenic|fMT]] (<partinfo>BBa_K190019</partinfo>)). The data was measured in the standard mode and the calculated arsenic imported by the cells is shown in figure 4.<br />
<br />
[[Image:As_uptake_in_WT_fMT_GlpF_ArsR.PNG]]<br />
:Figure 4: Uptake of As(III) by ''E. coli'' WT, and the strains containing the different parts of the accumulation device. As a control the arsenic uptake of ''E. coli'' with ArsR overexpression (as described by [[Team:Groningen/Literature#Kostal2004|Kostal 2004]]) is also shown.<br />
<br />
The curves in this figure show that there is no difference between the arsenic uptake by ''E. coli'' WT and by ''E. coli'' plus (parts of) the accumulation device. As a second observation, it can be seen that the uptake of arsenic in measured here is higher than found before (figure 3). A ratio of 2-3x was found for the WT strains (pSB1A2 and pArsR-RFP). These two differences will be discussed below. fMT shows exceptionally low arsenite uptake, this may be caused by incidentally "burning" the already dried cells at ~100;deg&C.<br />
<br />
The raw data can be found at [https://2009.igem.org/Team:Groningen/Modelling/Downloads| downloads].<br />
<br />
====Discussion====<br />
Between the two data sets there are a few differences, first there seems to be no difference between arsenic uptake in WT and ''E. coli'' with the accumulation device (or parts of this). Secondly, the data of arsenic uptake by ''E. coli'' WT could was not reproducible and the last data set showed a arsenic uptake which was even higher for ''E. coli'' WT than the ''E. coli'' ArsR overexpression strain. <br />
<br />
*Why is there no difference between the ''E. coli'' WT and the ''E. coli'' with accumulation device?<br />
This can be caused by non-functional expression of one of the genes (fMT or GlpF) or both. For membrane proteins it is known that functional overexpression is harder than for cytoplasmic proteins ([[Team:Groningen/Literature#Lundstom2006|Lundstom 2006]]). This could be tested by doing As(III) uptake/binding experiments with purified proteins, but this requires protein purification which could be facilitated by the addition of a his-tag (not present yet). The function of the transporter can be tested by measuring the uptake in membrane vesicles and that of the accumulation protein can be tested by measuring metal binding for instance by isothermal titration calorimetry. Otherwise the proteins may not be produced at all, this should be tested by protein purification or sds-page. Another possibility is that these proteins cannot be produced by ‘’E. coli’’ at once, though functional expression was already proven by Singh ''et al.'' ([[Team:Groningen/Literature#Singh2008|Singh 2008]]).<br />
<br />
*Non reproducible concentrations of arsenic, imported by ''E. coli'' WT, which can be seen as there is a large difference (2-3x) in arsenic uptake determined from the first and the second measurement. All data from the second ICP-MS arsenic determination, were also unexpectedly higher than was found in literature ([[Team:Groningen/Literature#Kostal2004|Kostal 2004]], [[Team:Groningen/Literature#Singh2008|Singh 2008]]). This discrepancy may be caused by one of the following reasons.<br />
During the second arsenic uptake assay the time between the incubation and washing the cells was decreased to the minimum though during the first assay there was some time for the cells to export the As(III) via there exporter ArsB. This may have caused the lower uptake yield of arsenic in the first data set. Also there was a difference in cell concentration, in the second assay this was 2.5 times higher. It is presumably that with a higher cell concentration the uptake rate is slower but a saturating incubation time (>1hr) might cause that the equilibrium of arsenite concentration in/outside the cell is reached faster. After destruction of the samples of the first data set, the samples did not become a clear solution but a suspension containing white flakes. These were removed by centrifugation, but this seems to indicate incomplete destruction. This was not seen for the second samples, therefore an increased arsenite concentration may be measured as arsenite bound to the white flakes is not measured. <br />
It also might be, that during the second arsenite uptake assay the cells were washed less properly causing the concentration to become way higher than the first measurement. A more acidic buffer used for washing the cells is probably more efficient in removing metal ions than the TB74S buffer (pH 7.4), but as this protocol was the same as described by [[Team:Groningen/Literature#Kostal2004|Kostal 2004]], this should be a major problem. The expected increase in arsenic concentration should be linear with the external arsenite concentration, but this was not seen (figure 4), a clear saturation curve was seen. <br />
A plausible cause is that there was a mistake in the calculations, a correction factor which was forgotten to correct for. Another plausible cause is that the concentration is higher because the measured concentration was for some samples 5 times higher than the calibration range. It might be that linear extrapolation is not correct. This can cause the structural increased arsenic uptake. <br />
<br />
*Other considerations:<br />
-Metal buffer interactions, causing a lower free-As(III) concentration surrounding the cell suspension.<br />
-Arsenic oxidation in aerobic conditions to As(V), this equilibrium may change over hours, so if the stock solution is enriched with As(V) it may take hours before it is changed to As(III) again. <br />
- Binding of other metal ions to the metallothionein causing competition for arsenite binding to fMT. Possible metal ions can be: Copper(I) or other metal ions present in the undefined LB medium. A requiry is that the metal ion should bind stronger or as strong to the MT as arsenite, which binds less strongly to MT than Zn(II) for instance or Cu(I).<br />
<br />
====Conclusion====<br />
{{todo}}<br />
<br />
==Modelling==<br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
===Arsenic - ArsR===<br />
<br />
Below you can calculate how many grams of arsenic will be taken out of the water per cubic meter of cells. This extra weight raises the density of the cell and therefore lowers its capacity for buoyancy. Our preliminary results look very promising. Even under the assumption that the weight of the metal is added to the weight of the cells, without increasing their volume, we could add up to a hundred times the currently computed weight without having a large effect on the required fraction of gas vesicles (it will only go up from about 12.2% to 12.7%).<br />
<br />
At this moment we use four different variables:<br />
<br />
# Molecular weight of arsenic. Source: [http://en.wikipedia.org/wiki/Arsenic Arsenic page on Wikipedia]<br />
# Millimol arsenic per kg of cell dryweight (note that this is equivalent to nmol/mg). Source: [[Team:Groningen/Literature#Kostal2004|Kostal 2004]]<br />
# The proportion between the weight of a dry cell and a wet cell. Source: [http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi CCDB Database]<br />
# Cell density. Source: see our [[Team:Groningen/Project/Vesicle|gas vesicle page]].<br />
<br />
{|<br />
|style="vertical-align:top;"|<html><br />
<div style="background:#efe;border:1px solid #9c9;padding:1em;"><br />
<table style="border-collapse:collapse;background:none;"><tr><br />
<td style="border-right:1px solid #9c9;padding-right:1em;"><br />
aw<sub>As(III)</sub> = <input type="text" id="awAs" value="74.92"/> g/mol<br/><br />
<nobr>n<sub>As(III)</sub> / M<sub>cell(dry)</sub> = <input type="text" id="cAs" value="2"/> millimole/kg</nobr><br/> <!-- Reasonable estimate --><br />
M<sub>cell(dry)</sub> / M<sub>cell(wet)</sub> = <input type="text" id="Mcelldrywet" value="0.3"/><br/><br />
&rho;<sub>cell</sub> = <input type="text" id="rhocell" value="1100"/> kg/m<sup>3</sup><br/> <!-- Reasonable estimate --><br />
<br />
<button onClick="computeArsenicWeight()">Compute</button><br/><br />
</td><br />
<br />
<td style="padding-left:1em;"><br />
<div id="arsenicError" style="color:red"></div><br />
<nobr>As(III) intake per volume of cells</nobr><br/><br />
<nobr> = <span id="Aspercellvolume"></span> g/m<sup>3</sup></nobr><br/><br />
<nobr> = <span id="molAspercellvolume"></span> &micro;mol/liter</nobr><br/><br />
</td><br />
</tr></table><br />
</div><br />
<script type="text/javascript"><br />
<br />
addOnloadHook(computeArsenicWeight);<br />
<br />
function computeArsenicWeight() {<br />
// Intermediates (mostly useful for debugging)<br />
var arsenicErrorNode = document.getElementById("arsenicError");<br />
arsenicErrorNode.innerHTML = '';<br />
<br />
// Read inputs<br />
var awAs = getInput('awAs'); // g/mol<br />
var cAs = getInput('cAs') * 1e-3; // mmol/kg -> mol/kg<br />
var Mcelldrywet = getInput('Mcelldrywet'); // kg/kg<br />
var rhocell = getInput('rhocell'); // kg/m^3<br />
<br />
// Compute density(/-ies)<br />
try {<br />
var Aspercellvolume = awAs * cAs * Mcelldrywet * rhocell;<br />
var molAspercellvolume = cAs * Mcelldrywet * rhocell * 1e3;<br />
// 1e-3 to convert from /m^3 to /L and 1e6 to convert from mole to micromole<br />
} catch(err) {<br />
arsenicErrorNode.innerHTML = err.message;<br />
}<br />
<br />
// Set outputs<br />
setOutput('Aspercellvolume', Aspercellvolume);<br />
setOutput('molAspercellvolume', molAspercellvolume);<br />
}<br />
</script><br />
</html><br />
|style="vertical-align:top;"|<pre><br />
<br />
As per cell volume = awAs * nAs(III) /<br />
Mcell(dry) * Mcelldrywet * rhocell<br />
mol As per cell volume = nAs(III) / <br />
Mcell(dry) * Mcelldrywet * rhocell<br />
<br />
</pre><br />
|}<br />
<br />
[[Image:Arsenic_accumulation.png|frame]]<br />
<br />
At a lower level arsenic accumulation can be described using reactions between ArsR, As(III) and the ars promoter. As shown in the figure on the right, a number of different substances(/complexes) are involved. For our purposes it is especially important to determine what fraction of As(III) is unbound, if more As(III) is bound we can accumulate more.<br />
<br />
In addition to binding to As(III), ArsR can repress Ars, creating a negative feedback loop. In effect this regulates the production of ArsR based on the As(III) concentration ([[Team:Groningen/Literature#Chen1997|Chen 1997]]). In the <i>E. coli</i> top 10 there is only ars promoter present on the genome to produce ArsR (see [[Team:Groningen/BLAST|BLAST]] results). There are plasmids which produce both ArsR and ArsD, but these are not used in this project. We intend to introduce instead a constitutive promoter (pro), which produces just ArsR, in order to bind as much As(III) as possible.<br />
<br />
The calculator below tries to compute the ratio between bound and unbound arsenic, specifically As(III), in the cell.<br />
See our [[Team:Groningen/Modelling/Arsenic|Modelling]] page for detailed information on the constants/variables used and a derivation of the formulas. Note that the computations currently involve slightly more variables/constants than strictly necessary.<br />
<br />
<html><br />
<table style="background:#efe;border:1px solid #9c9;padding:1em;"><tr><td><br />
<table style="border-collapse:collapse;background:none;"><tr><br />
<td style="border-right:1px solid #9c9;padding-right:1em;"><br />
<dl><br />
<dt>Dissociation constants</dt><br />
<dd><br />
KR<sub>d</sub> (ArsR<sub>As</sub>) = <input type="text" id="K1d" value="6"/> &micro;M (??)<br/><br />
<nobr>KA<sub>d</sub> (ArsR<sub>ars</sub>) = <input type="text" id="K3d" value="0.33"/> &micro;M (</html>[[Team:Groningen/Literature#Chen1997|Chen1997]]<html>)</nobr><br/><br />
KM<sub>d</sub> (MBPArsR<sub>As</sub>) = <input type="text" id="KMd" value="6"/> &micro;M (???)<br/><br />
KF<sub>d</sub> (fMTArsR<sub>As</sub>) = <input type="text" id="KFd" value="6"/> &micro;M (???)<br/><br />
n<sub>f</sub> = <input type="text" id="nf" value="3"/> (???)<br/><br />
</dd><br />
<dt>Half-lifes</dt><br />
<dd><br />
&tau;R (ArsR) = <input type="text" id="tauR" value="0.1"/> min (???)<br/><br />
&tau;M (MBPArsR) = <input type="text" id="tauM" value="0.1"/> min (???)<br/><br />
&tau;F (fMT) = <input type="text" id="tauF" value="0.1"/> min (???)<br/><br />
</dd><br />
<dt>Production rates of the promoters</dt><br />
<dd><br />
<nobr>&beta;RN (ars1 &rarr; ArsR) = <input type="text" id="beta1" value="100"/> 1/second (???)</nobr><br/><br />
<nobr>&beta;R (proR &rarr; ArsR) = <input type="text" id="beta3" value="100"/> 1/second (???)</nobr><br/><br />
<nobr>&beta;M (proM &rarr; MBPArsR) = <input type="text" id="betaM" value="26.6"/> 1/second (???)</nobr><br/><br />
<nobr>&beta;F (proF &rarr; fMT) = <input type="text" id="betaF" value="200"/> 1/second (???)</nobr><br/><br />
</dd><br />
<!--As(III) = <input type="text" id="As3Concentration" value="10"/> &micro;M<br/>--><br />
<dt>Promoter concentrations<dt><br />
<dd><br />
ars1<sub>total</sub> = <input type="text" id="ars1TPerCell" value="1"/> per cell<br/><br />
<nobr>proR = <input type="text" id="proRPerCell" value="0"/> per cell (??)</nobr><br/><br />
<nobr>proM = <input type="text" id="proMPerCell" value="100"/> per cell (??)</nobr><br/><br />
<nobr>proF = <input type="text" id="proFPerCell" value="0"/> per cell (??)</nobr><br/><br />
V<sub>cell</sub> = <input type="text" id="Vcell" value="1"/> &micro;m<sup>3</sup> </html><br />
([http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi| CCBD])<html><br />
<br />
</dd><br />
</dl><br />
<br />
<button onClick="computeArsenicEquilibrium()">Compute</button><br/><br />
</td><br />
<br />
<td style="padding-left:1em;"><br />
<div id="arsenicEquilibriumError" style="color:red"></div><br />
<dl><br />
<dt>ArsR</dt><br />
<dd><br />
ars / ars<sub>total</sub> = <span id="arsFraction"></span><br/><br />
ArsR = <span id="ArsR"></span> &micro;M<br/><br />
<!--ArsR<sub>total</sub> = <span id="ArsRT"></span> &micro;M<br/>--><br />
</dd><br />
<dt>"Accumulation factor"</dt><br />
<dd><br />
<!--As(III)<sub>total</sub> = <span id="AsinT"></span> &micro;M<br/>--><br />
As(III)<sub>total</sub>/As(III) = <span id="AsinTfactor"></span><br/><br />
</dd><br />
</dl><br />
</html><br />
<span id="accumulationFactorData"></span><br />
{{graph|Team:Groningen/Graphs/AccumulationFactor|id=accumulationFactorGraph}}<br />
(For constants other than the ones on the left the [[Team:Groningen/Modelling/Arsenic.js|default values]] are used.)<br />
<html><br />
</td><br />
</tr></table><br />
</td></tr></table><br />
<script type="text/javascript"><br />
<br />
addOnloadHook(computeArsenicEquilibrium);<br />
<br />
function computeArsenicEquilibrium() {<br />
// Intermediates (mostly useful for debugging)<br />
var errorNode = document.getElementById("arsenicEquilibriumError");<br />
errorNode.innerHTML = '';<br />
<br />
// Read inputs<br />
var c = arsenicModelConstants();<br />
c.AsT = 0;<br />
c.K1d = getInput('K1d') * 1e-6; // micromolar -> molar<br />
c.K3d2 = Math.pow(getInput('K3d') * 1e-6,2); // micromolar -> molar<br />
c.KMd = getInput('KMd') * 1e-6; // micromolar -> molar<br />
c.KFd = getInput('KFd') * 1e-6; // micromolar -> molar<br />
c.nf = getInput('nf') * 1e-6; // micromolar -> molar<br />
c.tauR = getInput('tauR') * 60; // minutes -> seconds<br />
c.tauM = getInput('tauM') * 60; // minutes -> seconds<br />
c.tauF = getInput('tauF') * 60; // minutes -> seconds<br />
c.beta1 = getInput('beta1'); // 1/second<br />
c.beta3 = getInput('beta3'); // 1/second<br />
c.betaM = getInput('betaM'); // 1/second<br />
c.betaF = getInput('betaF'); // 1/second<br />
var avogadro = 6.02214179e23; // 1/mol<br />
var Vcell = getInput('Vcell') * 1e-15; // micrometer^3/cell -> liter/cell<br />
c.ars1T = getInput('ars1TPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
c.ars2T = 0;<br />
c.pro = getInput('proRPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
c.proM = getInput('proMPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
c.proF = getInput('proFPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
<br />
// Compute density(/-ies)<br />
try {<br />
var x = arsenicModelEquilibrium(c);<br />
var ArsR = x._ArsR;<br />
var arsFraction = x._arsF;<br />
var AsinTfactor = 1 + ArsR/c.K1d;<br />
} catch(err) {<br />
errorNode.innerHTML = err.message;<br />
}<br />
<br />
// Set intermediates if they exist<br />
setOutput('arsFraction', arsFraction);<br />
setOutput('ArsR', ArsR * 1e6);<br />
<br />
// Set outputs<br />
setOutput('AsinTfactor', AsinTfactor);<br />
<br />
// Draw graph<br />
var dataNode = document.getElementById("accumulationFactorData");<br />
var graphNode = document.getElementById("accumulationFactorGraph");<br />
var data = {AsT:[], AsexT0:[], AsinT:[], AsinT2:[]};<br />
var bAsin, cAsin, Asin;<br />
// Some guesses<br />
var c2 = {}, x2;<br />
for(var a in c) c2[a] = c[a];<br />
c2.v5 *= 2;<br />
for(var AsexT0uM=0.1; AsexT0uM<=100; AsexT0uM*=1.1) {<br />
c.AsT = c.Vs*AsexT0uM*1e-6;<br />
c2.AsT = c.AsT;<br />
x = arsenicModelEquilibrium(c);<br />
x2 = arsenicModelEquilibrium(c2);<br />
data.AsT.push(c.AsT);<br />
data.AsexT0.push(c.AsT/c.Vs);<br />
data.AsinT.push(x.AsinT*c.Vc/c.AsT);<br />
data.AsinT2.push(x2.AsinT*c.Vc/c.AsT);<br />
}<br />
dataNode.data = data;<br />
if (graphNode.refresh) graphNode.refresh();<br />
}<br />
</script><br />
</html><br />
<br />
'''In conclusion:'''<br />
<br />
* Even at the accumulation levels of Koster <i>et al.</i> the amount of arsenic accumulated in <i>E. coli</i> is so little that it should not matter much for the buoyant density (which normally is about 1100kg/m<sup>3</sup>).<br />
* If you substitute constitutive promotors for Ars promotors, you can see that it is clearly advantageous to use constitutive promotors as just adding ars promoters does not increase the accumulation factor. A plasmid containing an ars promoter and (just) a gene coding for ArsR behind it might contain more arsenic, but there would also be more unbound arsenic, increasing the toxicity.<br />
* The model is not very sensitive to different values for K3d (with K3d=1mM the accumulation factor is 248.06 and with K3d=1nM it is 240.57).<br />
* The accumulation factor is greatly affected by the product of the half-life of ArsR and the production rate.<br />
<br />
<!-- ==Planning and requirements:==<br />
<br />
* '''Modelling'''<br />
** Speed<br />
** Metaliotheines concentration <br />
** How often does the ArsR sensitive operator/operon occur in our <i>E. coli</i>?<br />
* '''Lab'''<br />
** Measurements<br />
*** Transport Assays<br />
**** Protein expression levels determined by immunoblotting using anti-ArsA and anti-ArsD antibodies [[Team:Groningen/Literature#Lin2007-2|Lin 2007]]<br />
**** Inductively coupled mass spectrometry (ICP-MS) ([[Team:Groningen/Literature#Meng2004|Meng 2004]])<br />
*** Measure accumulation. By measuring before/after concentration metal with and without accumulation protein.<br />
*** Determine the dissociation constant of ArsR and As(III). (By measuring the ratio between bound and unbound ArsR?)<br />
**** It might be possible to do this with (tryptophan related) fluorescence (that is how it is done for ArsD in [[Team:Groningen/Literature#Chen1997|Chen 1997]]). In the paper ArsD is purified, but if that is not feasible for us, we might try to simply do it in living cells (and hope that ArsR both fluoresces enough and is produced enough to be measurable).<br />
*** Production rate of ArsR?<br />
** Biobrick Bba_K129004<br />
** Rest--><br />
<br />
==Copper==<br />
<br />
===MymT===<br />
<br />
MymT is a 5kDa-protein which binds Cu(I) but also to less extend Zn(II) from ''Mycobaterterium tuberculosis''. This MT was found to bind 4-6 Cu(I) ions per molecule. Induction of the expression of MymT is the strongest with Cd and Cu. But upon over-expression of MymT in ''E. coli'', the protein becomes insoluble ([[Team:Groningen/Literature#Gold2008|Gold 2008]]). This may be caused by the fact that it is a protein from a gram-positive bacteria expressed in a gram negative bacterium. Therefore specialized cultivation conditions are needed, the cells should be grown at a low temperature (16 &deg;C). The functionality of MymT can be measured by fluorescence spectroscopy, as also found for other copper binding metallothioneins. Copper bound to MT create Cu-thiolates which can be excited at 280nm and gives a Stokes shift towards 600 nm ([[Team:Groningen/Literature#Beltramini1981|Beltramini 1981]]). <br />
<br />
====Results:====<br />
PCR on ''mym''T from pGB68 unfortunately did not give any correct cDNA fragments, even though the primer quality was improved ([[Team:Groningen/Protocols|Protocol Biobrick primers]]). Therefore the sub-project was discontinued.<br />
<br />
==Zinc==<br />
Below toxic concentrations, zinc is essential for many biological processes. Examples are enzymatic hydroxylation, DNA and RNA synthesis, transcription and translation, signal transduction and apoptosis regulation ([[http://en.wikipedia.org/wiki/Zinc 1]] and [[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]). Methallothioneins can adjust the zinc absorption up to 14-40%, though a real excess of zinc can be toxic. A daily intake of 100–300 mg Zn/day can give rise to copper / iron deficiency and damage of nerve receptors ([[Team:Groningen/Literature#Fosmire1990|Fosmire 1990]]). Examples of metallothioneins sequestering zinc, are SmtA from the cyanobacterium ''Synechococcus'' PCC7942 ([[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]), ZiaR from ''Synechocystis'' PCC 6803 ([[Team:Groningen/Literature#Robinson2001|Robinson 2001]]), human metallothioneins like MT-1 and -2. The mammalian proteins were found to bind 7 Zn<sup>2+</sup> ions by the thiolate-group of there cysteins.<br />
<br />
===SmtA===<br />
SmtA is a MT from ''Synechococcus'' PCC 6803, it was found to bind 3-4Zn ions and is supposed to have a function in preventing zinc toxicity ([[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]), but it also binds copper and cadmium ([[Team:Groningen/Literature#Shi1992|Shi 1992]]). Upon binding of Zn, the glutathione transferase fusion-protein showed a 1:3 stoichiometry and SmtA a 1:4 stoichiometry ([[Team:Groningen/Literature#Robinson2001|Robinson 2001]]). SmtA binds the 4 Zn ions via cystein thiolate-bridges, forming a Zn<sub>4</sub>Cys<sub>11</sub> cluster whichs was also found in mammalian MT, though these proteins do not have a homologous DNA sequence ([[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]). ''SmtA'' is found on an operon with it's transcriptional regulator ''smtB''. SmtB releases from the promoter-operator region in front of this operon, when it binds Zn via its metal binding motif. SmtB and [[Team:Groningen/Project/Accumulation#Arsenic|ArsR]] (negative transcriptional regulator binding arsenic) have similar functionalities but differ in metal binding motifs ([[Team:Groningen/Literature#Robinson2001|Robinson 2001]]). That ''Synechococcus'' is a gram negative bacterium might increase the possibility of functional and stable overexpression in ''E. coli'' .<br />
<br />
===Results===<br />
PCR reactions to amplify SmtA from pET29a and SmtA-GST from pGEX-3x were successful, but unfortunately the DNA sequence used to design the SmtA primers was not correct so therefore wrong cDNA fragments were amplified. Because it was too late to order new primers, this sub-project was discontinued.<br />
<br />
<!--==Alternatives==<br />
{{todo|Inclusion bodies}} ([[Team:Groningen/Literature#Fowler1987|Fowler 1987]])<br><br />
{{todo|(Bacterio)Ferritins}}<br><br />
{{todo|Phytochelatins}}<br><br />
[http://www.wiley.com/legacy/products/subject/reference/messerschmidt_toc.html A list of opportunities]<br />
==Inhibitory characteristics?==--><br />
<br />
{{Team:Groningen/Project/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Parts/FreezerTeam:Groningen/Parts/Freezer2009-10-21T19:06:52Z<p>Jaspervdg: New page: {{Team:Groningen/Header}} ==Part List -80== {|cellpadding="10" cellspacing="1" border="10" style="font-size: small;" |'''Component''' |'''Description''' |'''Part or Accession #''' |'''Ba...</p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
==Part List -80==<br />
<br />
{|cellpadding="10" cellspacing="1" border="10" style="font-size: small;"<br />
|'''Component'''<br />
|'''Description'''<br />
|'''Part or Accession #'''<br />
|'''Base Pairs (bp)'''<br />
|'''Plasmid (backbone)'''<br />
|'''Resistance'''<br />
|'''Well'''<br />
|'''Quality control'''<br />
|-<br />
|GVP<br />
|Gas Vesicle Proteins<br />
|<partinfo>BBa_I750016</partinfo><br />
|6064<br />
|<partinfo>BBa_J61035</partinfo><br />
|Ampicillin/Gentamycin<br />
|plate 3, pos.1<br />
|?<br />
|-<br />
|GVP (2nd batch)<br />
|Gas Vesicle Proteins<br />
|<partinfo>BBa_I750016</partinfo><br />
|6064<br />
|<partinfo>BBa_J61035</partinfo><br />
|Ampicillin/Gentamycin<br />
|plate 3, pos.2<br />
|?<br />
|-<br />
|pHigh in low copy nr vector<br />
|High consitutive promoter<br />
|<partinfo>J23100</partinfo><br />
|35<br />
|<partinfo>pSB3K3</partinfo> <br />
|Kanamycin<br />
|Plate 3, pos. 4<br />
|PCR(?), restriction(+)<br />
|-<br />
|pMed in low copy nr vector<br />
|Medium consitutive promoter<br />
|<partinfo>J23106</partinfo><br />
|35<br />
|<partinfo>pSB3K3</partinfo> <br />
|Kanamycin<br />
|Plate 3, pos. 5<br />
|PCR(?), restriction(+)<br />
|-<br />
|pLow in low copy nr vector<br />
|Low consitutive promoter<br />
|<partinfo>J23109</partinfo><br />
|35<br />
|<partinfo>pSB3K3</partinfo> <br />
|Kanamycin<br />
|Plate 3, pos. 6<br />
|PCR(?), restriction(+)<br />
|-<br />
|pHigh in high copy nr vector<br />
|High consitutive promoter<br />
|<partinfo>J23100</partinfo><br />
|35<br />
|<partinfo>pSB1AC3</partinfo> <br />
|Ampicillin/Chloramphenicol<br />
|Plate 3, pos. 7<br />
|PCR(?), restriction(+)<br />
|-<br />
|pMed in high copy nr vector<br />
|Medium consitutive promoter<br />
|<partinfo>J23106</partinfo><br />
|35<br />
|<partinfo>pSB1AC3</partinfo> <br />
|Ampicillin/Chloramphenicol<br />
|Plate 3, pos. 8<br />
|PCR(?), restriction(+)<br />
|-<br />
|pLow in high copy nr vector<br />
|High consitutive promoter<br />
|<partinfo>J23109</partinfo><br />
|35<br />
|<partinfo>pSB1AC3</partinfo> <br />
|Ampicillin/Chloramphenicol<br />
|Plate 3, pos. 9<br />
|PCR(?), restriction(+)<br />
|-<br />
|Promotor (low expression)<br />
|Constitutive promotor<br />
|<partinfo>BBa_J23109</partinfo><br />
|35<br />
|<partinfo>BBa_J61002</partinfo><br />
|Ampicillin<br />
|plate 3, pos.10<br />
|No<br />
|-<br />
|Promotor (medium expression)<br />
|Constitutive promotor<br />
|<partinfo>BBa_J23106</partinfo><br />
|35<br />
|<partinfo>BBa_J61002</partinfo><br />
|Ampicillin<br />
|plate 3, pos.11<br />
|No<br />
|-<br />
|Promotor (high expression)<br />
|Constitutive promotor<br />
|<partinfo>BBa_J23100</partinfo><br />
|35<br />
|<partinfo>BBa_J61002</partinfo><br />
|Ampicillin<br />
|plate 3, pos.12<br />
|No<br />
|-<br />
|Inducible promoter<br />
|Lactose inducible promoter nr1<br />
|<partinfo>R0010</partinfo><br />
|200<br />
|<partinfo>pSB1A2</partinfo> <br />
|Ampicillin<br />
|Plate 3, pos. 14<br />
|PCR(?), restriction(+)<br />
|-<br />
|Inducible promoter<br />
|Lactose inducible promoter nr2<br />
|<partinfo>R0010</partinfo><br />
|200<br />
|<partinfo>pSB1A2</partinfo> <br />
|Ampicillin<br />
|Plate 3, pos. 15<br />
|PCR(?), restriction(+)<br />
|-<br />
|RBS<br />
|Ribosomal Binding Site<br />
|<partinfo>BBa_B0034</partinfo><br />
|12<br />
|<partinfo>pSB1A2</partinfo><br />
|Ampicillin<br />
|plate 3, pos.19<br />
|No<br />
|- <br />
|Terminator<br />
|Double terminator consisting of <partinfo>BBa_B0012</partinfo> and <partinfo>BBa_B0011</partinfo><br />
|<partinfo>BBa_B0014</partinfo><br />
|~90<br />
|<partinfo>pSB1AK3</partinfo><br />
|Ampicillin/Kanamycin<br />
|plate 3, pos.20<br />
|No<br />
|- <br />
|Const. Promoter + GVP<br />
|Low constitutive promoter with GVP cluster<br />
|<partinfo>BBa_J23109</partinfo> + <partinfo>BBa_I750016</partinfo><br />
|~6100<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/Chloramphenicol<br />
|plate 3, pos.21<br />
|<i>Eco</i>RI/<i>Pst</i>I + {{done|Sequenced Okay}}<br />
|- <br />
|Const. Promoter + GVP (no.2)<br />
|Low constitutive promoter with GVP cluster<br />
|<partinfo>BBa_J23109</partinfo> + <partinfo>BBa_I750016</partinfo><br />
|~6100<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/Chloramphenicol<br />
|plate 3, pos.22<br />
|<i>Eco</i>RI/<i>Pst</i>I + {{done|Sequenced Okay}}<br />
|- <br />
|Const. Promoter + GVP<br />
|Medium constitutive promoter with GVP cluster<br />
|<partinfo>BBa_J23106</partinfo> + <partinfo>BBa_I750016</partinfo><br />
|~6100<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/Chloramphenicol<br />
|plate 3, pos.23<br />
|<i>Eco</i>RI/<i>Pst</i>I + {{done|Sequenced Okay}}<br />
|- <br />
|Const. Promoter + GVP (no.2)<br />
|Medium constitutive promoter with GVP cluster<br />
|<partinfo>BBa_J23106</partinfo> + <partinfo>BBa_I750016</partinfo><br />
|~6100<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/Chloramphenicol<br />
|plate 3, pos.24<br />
|<i>Eco</i>RI/<i>Pst</i>I + {{done|Sequenced Okay}}<br />
|- <br />
|HmtA (1.1)<br />
|HmtA-His in pBAD(a)<br />
|None (to become <partinfo>BBa_K190018</partinfo>)<br />
|2004 <br />
|[http://ecoliwiki.net/colipedia/index.php/pBAD/myc-His_A pBAD]<br />
|Ampicillin<br />
|plate 3, pos.28<br />
|Restriction(+)<br />
|- <br />
|HmtA (2.1)<br />
|HmtA-His in pBAD(a)<br />
|None (to become <partinfo>BBa_K190018</partinfo>)<br />
|2004 <br />
|[http://ecoliwiki.net/colipedia/index.php/pBAD/myc-His_A pBAD]<br />
|Ampicillin<br />
|plate 3, pos.29<br />
|Restriction(+)<br />
|- <br />
|RBS MBPArsR<br />
| <partinfo>BBa_B0034</partinfo> + <partinfo>BBa_K190027</partinfo><br />
|None (to become <partinfo>BBa_K190018</partinfo>)<br />
|~1600 <br />
|<partinfo>pSB1A2</partinfo><br />
|Ampicillin<br />
|plate 3, pos.30,31,32<br />
|Restriction(+)PCR<br />
|-<br />
|pLac-fMT + Ars-RFP<br />
|pArs testing <br />
|<partinfo>BBa_K190032</partinfo> <partinfo>BBa_K190023</partinfo> <partinfo>BBa_J61002</partinfo> (without the backbone)<br />
|~1400<br />
|<partinfo>pSB1A2</partinfo><br />
|Ampicillin<br />
|plate 3, pos. 33,34,35<br />
|{{todo|Quality control}}<br />
|- <br />
|CueO- + GVP in J61035<br />
|CueO promoter without RBS in front of the GVP cluster<br />
|None<br />
|6149<br />
|<partinfo>BBa_J61035</partinfo> (without the part between <i>Eco</i>RI and <i>Xba</i>I)<br />
|Ampicillin<br />
|plate 3, pos.37<br />
|Restriction(+) + {{done|Sequenced Okay}}<br />
|- <br />
|ZntR- + GVP in J61035<br />
|ZntR promoter without RBS in front of the GVP cluster<br />
|None<br />
|~6150<br />
|<partinfo>BBa_J61035</partinfo> (without the part between <i>Eco</i>RI and <i>Xba</i>I)<br />
|Ampicillin<br />
|plate 3, pos.38<br />
|Restriction(+) + {{done|Sequenced (3 mutations)}}<br />
|- <br />
|ArsR- + GVP in J61035<br />
|ArsR promoter without RBS in front of the GVP cluster<br />
|None<br />
|~6150<br />
|<partinfo>BBa_J61035</partinfo> (without the part between <i>Eco</i>RI and <i>Xba</i>I)<br />
|Ampicillin<br />
|plate 3, pos.39<br />
|Restriction(+) + {{done|Sequenced Okay}}<br />
|- <br />
|ArsR- in J61002<br />
|pArsR (promoter without RBS)<br />
|<partinfo>BBa_K190015</partinfo><br />
|71<br />
|<partinfo>BBa_J61002</partinfo> (without the part between <i>Eco</i>RI and <i>Spe</i>I)<br />
|Ampicillin<br />
|plate 3, pos.40<br />
|<i>Eco</i>RI/<i>Spe</i>I(+), <i>Eco</i>RI/<i>Pst</i>I(+), {{done|Sequenced Okay}}<br />
|- <br />
|ZntR- in J61002<br />
|pZntR (promoter without RBS)<br />
|<partinfo>BBa_K190016</partinfo><br />
|65<br />
|<partinfo>BBa_J61002</partinfo> (without the part between <i>Eco</i>RI and <i>Spe</i>I)<br />
|Ampicillin<br />
|plate 3, pos.41<br />
|<i>Eco</i>RI/<i>Spe</i>I(+), <i>Eco</i>RI/<i>Pst</i>I(+), {{done|Sequenced (3 mutations)}}<br />
|- <br />
|CueO- in J61002<br />
|pCueO (promoter without RBS)<br />
|<partinfo>BBa_K190017</partinfo><br />
|43<br />
|<partinfo>BBa_J61002</partinfo> (without the part between <i>Eco</i>RI and <i>Spe</i>I)<br />
|Ampicillin<br />
|plate 3, pos.42<br />
|<i>Eco</i>RI/<i>Spe</i>I(+), <i>Eco</i>RI/<i>Pst</i>I(+), {{done|Sequenced Okay}}<br />
|- <br />
|ZntR+RBS in J61002<br />
|pZntR (promoter with own RBS)<br />
|<partinfo>BBa_K190022</partinfo><br />
|91<br />
|<partinfo>BBa_J61002</partinfo> (without the part between <i>Eco</i>RI and <i>Spe</i>I)<br />
|Ampicillin<br />
|plate 3, pos.43<br />
|<i>Eco</i>RI/<i>Spe</i>I(+), <i>Eco</i>RI/<i>Pst</i>I(+), {{done|Sequenced Okay}}<br />
|- <br />
|ArsR+RBS in J61002<br />
|pArsR (promoter with own RBS)<br />
|<partinfo>BBa_K190023</partinfo><br />
|81<br />
|<partinfo>BBa_J61002</partinfo> (without the part between <i>Eco</i>RI and <i>Spe</i>I)<br />
|Ampicillin<br />
|plate 3, pos.44<br />
|<i>Eco</i>RI/<i>Spe</i>I(+), <i>Eco</i>RI/<i>Pst</i>I(+), {{done|Sequenced Okay}}<br />
|- <br />
|CueO+RBS in J61002<br />
|pCueO (promoter with own RBS)<br />
|<partinfo>BBa_K190024</partinfo><br />
|71<br />
|<partinfo>BBa_J61002</partinfo> (without the part between EcoRI and SpeI)<br />
|Ampicillin<br />
|plate 3, pos.45<br />
|<i>Eco</i>RI/<i>Spe</i>I(+), <i>Eco</i>RI/<i>Pst</i>I(+), {{done|Sequenced Okay}}<br />
|-<br />
|SmtA-GST in pGEX-3x<br />
|SmtA-GST fusion <br />
|no biobrick primers available<br />
|1400<br />
|[http://www.ecoliwiki.net/colipedia/index.php/pGEX-3X pGEX-3x]<br />
|Ampicillin<br />
|plate 3, pos. 46<br />
|PCR, restriction<br />
|-<br />
|SmtA in pET29a<br />
|SmtA<br />
|<partinfo>BBa_K190021</partinfo><br />
|900<br />
|[http://www.merckbiosciences.co.uk/product/69871 pET29a]<br />
|Kanamycin<br />
|plate 3, pos. 47<br />
|PCR, restriction<br />
|-<br />
|MymT in pGB68<br />
|MymT<br />
|<partinfo>BBa_K190020</partinfo><br />
|215<br />
|[http://www.neb.com/nebecomm/products/productN6707.asp pTXB1] (NEB)<br />
|Ampicillin<br />
|plate 3, pos. 48<br />
|PCR, restriction<br />
|-<br />
|GlpF and fMT in pMAL-MT<br />
|GlpF and fMT on a synthetic operon in the vector<br />
|<partinfo>BBa_K190019</partinfo> and <partinfo>BBa_K190028</partinfo><br />
|fMT = 200, GlpF = 900?<br />
|[http://www.neb.com/nebecomm/products/productN8076.asp pMALc2x] (NEB)<br />
|Ampicillin<br />
|plate 3, pos. 49<br />
|PCR, restriction<br />
|-<br />
|MBP-ArsR<br />
|MBP-ArsR Fusion protein<br />
|<partinfo>BBa_K190027</partinfo><br />
|15180<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 53<br />
|[https://2009.igem.org/Team:Groningen/Notebook/18_August_2009#Metal_accumulation Restriction analysis] & [[Team:Groningen/Notebook/25_August_2009#Metal_Accumulation| PCR]]<br />
|-<br />
|pNL29<br />
|GVP Gene cluster<br />
|{{todo|}}<br />
|6000<br />
|[http://www.fermentas.com/techinfo/nucleicacids/mappbluescriptiiskks.htm pBluescriptIIKS]<br />
|{{todo| Ampicillin}}<br />
|plate 3, pos. 54<br />
|{{todo|Buoyancy phenotype}}<br />
|-<br />
|pLac-fMT<br />
|Metallothionein with inducible promotor<br />
|<partinfo>BBa_K190032</partinfo><br />
|430<br />
|<partinfo>pSB1A2</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 55<br />
|{{todo|Quality control}}<br />
|-<br />
|pLow-fMT #4<br />
|Metallothionein with low constitutive promotor<br />
|<partinfo>BBa_K190031</partinfo><br />
|265<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 56<br />
|{{todo|Quality control}}<br />
|-<br />
|pLow-fMT #3<br />
|Metallothionein with low constitutive promotor<br />
|<partinfo>BBa_K190031</partinfo><br />
|265 <br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 57<br />
|{{todo|Quality control}}<br />
|-<br />
|SmtA<br />
|Metallothionein<br />
|<partinfo>BBa_K190021</partinfo><br />
|678<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 58<br />
|{{todo|Quality control}}<br />
|-<br />
|fMT #6<br />
|Metallothionein for As<sup>3+</sup><br />
|<partinfo>BBa_K190019</partinfo><br />
|222<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 59<br />
|{{todo|Sequence 2 deletions between <i>Eco</i>RI and <i>Xba</i>I sites}}<br />
|-<br />
|fMT #4<br />
|Metallothionein for As<sup>3+</sup><br />
|<partinfo>BBa_K190019</partinfo><br />
| 222<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 60<br />
|{{done|Sequence Okay!}}<br />
|-<br />
|pZntR-GVP<br />
|Metal promoter<br />
|<partinfo>BBa_K190034</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB2K3</partinfo><br />
|Kanamycin<br />
|plate 3, pos. 69<br />
|{{todo|Quality control}}<br />
|-<br />
|pCueO-GVP<br />
|Metal promoter<br />
|<partinfo>BBa_K190035</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB2K3</partinfo><br />
|Kanamycin<br />
|plate 3, pos. 70<br />
|{{todo|Quality control}}<br />
|-<br />
|pLacI-GVP no.1<br />
|Inducible promoter<br />
|<partinfo>BBa_K190036</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB1A2</partinfo><br />
|Ampicillin<br />
|plate 3, pos. 71<br />
|{{todo|Quality control}}<br />
|-<br />
|pLacI-GVP no.2<br />
|Inducible promoter<br />
|<partinfo>BBa_K190036</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB1A2</partinfo><br />
|Ampicillin<br />
|plate 3, pos. 72<br />
|{{todo|Quality control}}<br />
|-<br />
|High consitutive promoter(with RFP)<br />
|Constitutive promoter<br />
|<partinfo>Bba_J23100</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 75<br />
|{{todo|Quality control}}<br />
|-<br />
|Medium consitutive promoter(with RFP)<br />
|Constitutive promoter<br />
|<partinfo>Bba_J23106</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 76<br />
|{{todo|Quality control}}<br />
|-<br />
|Low consitutive promoter(with RFP)<br />
|Constitutive promoter<br />
|<partinfo>Bba_J23109</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB1AC3</partinfo><br />
|Ampicillin/chloramphenicol<br />
|plate 3, pos. 77<br />
|{{todo|Quality control}}<br />
|-<br />
|High consitutive promoter(with RFP)<br />
|Constitutive promoter<br />
|<partinfo>Bba_J23100</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB3K3</partinfo><br />
|Kanamycin<br />
|plate 3, pos. 78<br />
|{{todo|Quality control}}<br />
|-<br />
|Medium consitutive promoter(with RFP)<br />
|Constitutive promoter<br />
|<partinfo>Bba_J23106</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB3K3</partinfo><br />
|Kanamycin<br />
|plate 3, pos. 79<br />
|{{todo|Quality control}}<br />
|-<br />
|Low consitutive promoter(with RFP)<br />
|Constitutive promoter<br />
|<partinfo>Bba_J23109</partinfo><br />
|{{todo|Base Pairs (bp)}}<br />
|<partinfo>pSB3K3</partinfo><br />
|Kanamycin<br />
|plate 3, pos. 80<br />
|{{todo|Quality control}}<br />
|-<br />
|Reference constitutive promoter)<br />
|Constitutive promoter<br />
|?<br />
|{{todo|Base Pairs (bp)}}<br />
|?<br />
|?<br />
|plate 3, pos. 81<br />
|{{todo|Quality control}}<br />
|-<br />
|ArsR-GvP<br />
|Ars promotor + GvP gas vesicle cluster<br />
|<br />
|?<br />
|?<br />
|Kanamycin<br />
|plate 3, pos. 64<br />
|?<br />
|}<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/PartsTeam:Groningen/Parts2009-10-21T19:03:39Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right">{{linkedImage|Next.JPG|Team:Groningen/Parts/Submitted_Parts}}</div><br />
<br />
*For a comprehensive list of all the parts we used, have a look at our [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2009&group=Groningen '''parts registry'''].<br />
*Here you can find an informative overview of our [[Team:Groningen/Modelling/Submitted Parts|'''submitted parts''']].<br />
*Experience we had with parts from the registry can be found under [[Team:Groningen/Modelling/Used Parts|'''used parts''']].<br />
<br />
<center style="font-size:x-large;margin:1cm;">[http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2009&group=Groningen Our sandbox]</center><br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Parts/Used_PartsTeam:Groningen/Parts/Used Parts2009-10-21T18:58:14Z<p>Jaspervdg: /* Used Parts */ Removed todo.</p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
<br />
<br />
==Used Parts==<br />
<!--{{todo}}Maybe some general information of parts used from the registry.--><br />
*To get to the partsregistry site of a particular part one can click on the '''name of the part'''.<br />
*To see what our main findings were (no details or derivations) regarding a particular part one can click on '''more information'''.<br />
<br />
===Miscellaneous===<br />
'''<partinfo>BBa_B0034</partinfo> RBS ((Elowitz 1999) -- defines RBS efficiency)''' <br />
{|<br />
|width='10%'|<br />
<partinfo>BBa_K190061 AddReview 5</partinfo><br />
<I> iGEM Groningen 2009 </I><br />
|width='60%' valign='top'|<br />
The ligation of part <partinfo>BBa_K190028</partinfo> behind the RBS was successful, confirmed by gel (correct vector size after digestion with EcoRI and PstI) and sequencing with VF2 primer. We used this part in combination with several biobricks for building our constructs e.g. <partinfo>BBa_K190061</partinfo>.<br />
|}<br />
<br />
'''<partinfo>BBa_B0014</partinfo> Double terminator (B0012-B0011)''' <br />
{|<br />
|width='10%'|<br />
<partinfo>BBa_B0014 AddReview 3</partinfo><br />
<I> iGEM Groningen 2009 </I><br />
|width='60%' valign='top'|<br />
The plasmid containing part <partinfo>BBa_B0014</partinfo> was successfully transformed into ''E. coli'' TOP10 cells (confirmed by single and double digestion). The original plan was to use the terminator behind one of our own designed parts <partinfo>BBa_K190027</partinfo>, and in front of pArsR-RFP. The MBP-ArsR fusion protein was thought to have a regulating effect on the arsenic promotor pArsR in the same way as ArsR regulates the promotor. The terminator separated the two parts on the plasmid. The construct was not used due to time constraints, and not sequenced.<br />
|}<br />
<br />
'''<partinfo>BBa_I750016</partinfo> GVP Gas Vesicle Proteins''' <br />
{|<br />
|width='10%'|<br />
<partinfo>BBa_I750016 AddReview 5</partinfo><br />
<I> iGEM Groningen 2009 </I><br />
|width='60%' valign='top'|<br />
Part <partinfo>BBa_I750016</partinfo> was one of our main focus points during our project. The part was originally submitted by Melbourne in 2007 with a very limited amount of information (short description and sequence mutations). On their site it was mentioned the cluster was difficult to use and ligation into a plasmid was hard, in contrast we found the cluster to be easily cut and ligated into different plasmids and behind several promotors. We used this part in combination with several biobricks for building our constructs e.g. <partinfo>BBa_K190033</partinfo> and <partinfo>BBa_K190036</partinfo>. Pictures of our cells with induced gas vesicle formation confirmed the production of vesicles in the expected shape and size. In addition, we characterized the part to improve the use in the future and added a lot of information on the registry.<br />
|}<br />
<br />
'''<partinfo>BBa_P1010</partinfo> ccdB cell death gene'''<br />
{|<br />
|width='10%'|<br />
<partinfo>BBa_P1010 AddReview 4</partinfo><br />
<I> iGEM Groningen 2009 </I><br />
|width='60%' valign='top'|<br />
P1010 is used when putting BioBrick parts into BioBrick plasmids. The part to be inserted and the plasmid are cut with BioBrick enzymes and mixed. The mixture will include both the original uncut or self ligated plasmid and the desired structure. However, because of CcdB, all of the cells containing the original plasmid die and the surviving colonies are the desired result. The ccdB cell death gene worked as expected killing our ''E. coli'' TOP10 cells, and keeping our ''E. coli'' DB3 cells alive. After noticing the inconsistent sequencing result for the pSB2K3 plasmid with ccdB cell death gene, we decided to choose a different pSB2K3 plasmid with random part to continue with our assemblies. This to minimize the chance of unwanted surprises in the end.<br />
|}<br />
<br />
===Promotors===<br />
'''<partinfo>J23100</partinfo> Constitutive promoter family member (high expression)''' <br> pHigh is a high consituative promotor. It consists of about 35 base pairs. It has been placed in the following vectors. <partinfo>pSB3K3</partinfo>, <partinfo>BBa_J61002</partinfo> and <partinfo>pSB1AC3</partinfo> <br> <br />
<br />
'''<partinfo>J23101</partinfo> Constitutive promoter family member (high expression, reference)''' <br> pHigh is a high consituative promotor. It consists of about 35 base pairs. It has been placed in the following vectors. <partinfo>pSB3K3</partinfo>, <partinfo>BBa_J61002</partinfo> and <partinfo>pSB1AC3</partinfo> <br> <br />
<br />
'''<partinfo>J23106</partinfo> Constitutive promoter family member (medium expression)''' <br> pMed is a medium consituative promotor. It consists of about 35 base pairs. It has been placed in the following vectors. <partinfo>pSB3K3</partinfo>, <partinfo>BBa_J61002</partinfo> and <partinfo>pSB1AC3</partinfo> <br> <br />
<br />
'''<partinfo>J23109</partinfo> Constitutive promoter family member (low expression)''' <br> pLow is a Low consituative promotor. It consists of about 35 base pairs. It has been placed in the following vectors. <partinfo>pSB3K3</partinfo>, <partinfo>BBa_J61002</partinfo> and <partinfo>pSB1AC3</partinfo><br> <br />
<br />
'''<partinfo>R0010</partinfo> Promoter (lacI regulated)''' <br> This part is an inverting regulator sensitive to LacI and CAP. It contains two protein binding sites. The first binds the CAP protein, which is generally present in E.coli and is asocciated with cell health and availability of glucose. The second binds LacI protein. <br> <br />
<br />
'''<partinfo>I0500</partinfo> pBad/araC''' <br> This part is <br> <br />
<br />
===Vectors===<br />
'''<partinfo>pSB1AC3</partinfo> High copy BioBrick assembly plasmid'''<br />
{|<br />
|width='10%'|<br />
<partinfo>BBa_K190028 AddReview 5</partinfo><br />
<I> iGEM Groningen 2009 </I><br />
|width='60%' valign='top'|<br />
pSB1AC3 is a high copy number plasmid carrying ampicillin and chloramphenicol resistance. Together with pSB1A2 the vector was used for most assemblies of our team, because the high copy number made it easy to work with and easy isolation. The transformations with pSB1AC3 (containing different biobricks of own design) into ''E. coli'' TOP10 cells, growth on both antibiotics, and gel analysis (undigested and digested with the EcoRI and PstI) worked as expected. The high (copy) number of plasmids per cell make it an easy to work with plasmid, ideal for cloning and assembly work.<br />
|}<br />
<br />
'''<partinfo>pSB1A2</partinfo> pSB1A2 (Replaced by pSB1A3 in registry) ''' <br> pSB1A2 is a high copy number plasmid carrying ampicillin resistance. Together with pSB1AC3 the vector was used for most assemblies of our team, because the high copy number made it easy to work with and easy isolation. <br><br />
<br />
'''<partinfo>pSB2K3</partinfo> A low copy number base vector''' <br> A low copy number base vector which as a resistance against Kanamycin <br><br />
<br />
'''<partinfo>pSB3K3</partinfo> A low copy number base vector''' <br> A low copy number base vector which as a resistance against Kanamycin <br><br />
<br />
'''<partinfo>BBa_J61002</partinfo> A normal base vector''' <br> A normal base vector which has a resistance against Ampicillin <br><br />
<br />
'''<partinfo>BBa_J61035</partinfo> Vector we get with GVP''' <br> It's the backbone of our GVP part is and it a resistance against Ampicillin/Gentamycin<br></div>Jaspervdghttp://2009.igem.org/Team:Groningen/Project/AccumulationTeam:Groningen/Project/Accumulation2009-10-21T18:49:48Z<p>Jaspervdg: /* Arsenic - ArsR */</p>
<hr />
<div>{{Team:Groningen/Project/Header|}}<br />
<div title="Arsie Says UP TO METAL SENSITIVE PROMOTORS" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Project/Promoters}}</div><br />
<br />
<div class="introduction"><br />
<br />
{|style="clear:both"<br />
|<html><style type="text/css"><br />
.intro { margin-left:0px; margin-top:10px; padding:10px; border-left:solid 5px #FFF6D5; border-right:solid 5px #FFF6D5; text-align:justify;background:#FFFFE5; }<br />
</style></html><br />
<div class="intro"><br />
=Accumulation=<br />
Once heavy metals have entered the cell, it is crucial to keep them there. As these metals are toxic to cell survival in critical amounts, evolution has provided us with biological detoxicification proteins such as [http://en.wikipedia.org/wiki/Metallothionein metallothioneins]. These proteins can aid us in our quest to accumulate a variety of heavy metals as they bind to a wide range of metals including cadmium, zinc, mercury, copper, arsenic, silver, coordinated in metal-thiolates. The metal chelating proteins are cloned in a synthetic operon with a metal specific transporter to make up the accumulation device. For arcummulation of arsenite fMT and ArsR used, which were characterized by our model. Enhanced arsenite uptake by ''E. coli'' fMT could not be determined by the arsenite uptake assay, where the internal arsenic concentration was measured by ICP-MS. <br />
</div><br />
<br><br><br><br />
</div><br />
|}<br />
<br />
==Metallothioneins==<br />
Metallothioneins are a class of low molecular-weight metal-binding proteins (<10kDa) rich in cysteines residues(~30%). The contain a conserved cys-x-cys or cys-x-his motif which coordinates metal binding, as can be seen in figure 1. They are capable of binding a variety of heavy metals (e.g. Zn, Cu, Cd, Hg, As) with high avidity (Kb), they are ''in vivo'' used as a defense against oxidative stress by chelating metals. This proteins do also have a function in storing, detoxify and distributing metals throughout the cell ([[Team:Groningen/Literature#Merrifield2004|Merrifield 2004]], [[Team:Groningen/Literature#Gold2008|Gold 2008]]). These proteins have readily been used to create cell based systems for purification of contaminated water ([[Team:Groningen/Literature#Chen1998|Chen 1998]], [[Team:Groningen/Literature#Brady1994|Brady 1994]]). In addition to their wide application possibilities, they also have the capacity to carry multiple metal ions at one time, in contrast to some other metalloproteins that carry them one-on-one ([[Team:Groningen/Literature#Chang1998|Chang 1998]]).<br />
Many forms of metallothioneins are known and their affinity for different metals has been investigated on several occasions, such as for cadmium ([[Team:Groningen/Literature#Deng2007|Deng 2007]]), arsenic ([[Team:Groningen/Literature#Ngu2006|Ngu 2006]], [[Team:Groningen/Literature#Kostal2004|Kostal 2004]], [[Team:Groningen/Literature#Singh2008|Singh 2008]]), mercury ([[Team:Groningen/Literature#Chen1998|Chen 1998]], [[Team:Groningen/Literature#Chen1998|Chen 1997-2]], [[Team:Groningen/Literature#Deng2008|Deng 2008]]), nickel ([[Team:Groningen/Literature#Deng2003|Deng 2003]]) or a combination of metals ([[Team:Groningen/Literature#Chang1998|Chang 1998]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]).<br />
Metal-protein complexes can be quantified using a fluorescent molecule ([[Team:Groningen/Literature#Cadosch2008 |Cadosch 2008]]) but Cu(I) binding to metallothioneins in metal thiolates, was shown to cause a concentration dependant increase in luminescence. These Cu(I) binding metallothioneins were shown to give rise to a Stokes shift of approximately 300nm upon excitation at 280nm ([[Team:Groningen/Literature#Beltramini1981|Beltramini 1981]], [[Team:Groningen/Literature#Gold2008|Gold 2008]]). <br />
<br />
<br />
<center>[[Image:800px-Zinc finger rendered.png|250px]] </center><br />
:Figure 1: Zinc finger protein, consisting of a α-helix and an anti-parallel β-sheet. The zinc atom (green) is bound by two histidines and two cysteins.<br />
<br />
==Cloning strategy==<br />
In order to have a functional accumulation device, the cDNA of a metallothionein (MT) will be amplified using [http://en.wikipedia.org/wiki/PCR PCR] and cloned into <partinfo>pSB1A2</partinfo>, also a corresponding metal-ion transporter was amplified by PCR and cloned behind the MT. Both will expressed by one promoter (constitutive or lactose inducible). In this way the bacterium will take up the metal-ion and consecutively the metal-ion will be sequestered by the MT. When this device is combined with the [[Team:Groningen/Project/Vesicle#Cloning_strategy|floating device]], the bacteria will start floating when a certain threshold of intracellular metal concentration is reached, because the negative regulator of the buoyancy device will be released and the gas vesicle cluster can be transcribed.<br />
<br />
[[Image:Accumulation device.PNG]]<br />
:Figure 2: Cloning strategy for the metal accumulation device. A promoter taken from <partinfo>J61002</partinfo> will be cloned in front of a metallothionein and a metal transporter in a <partinfo>pSB1A2</partinfo> vector. This device will be combined with the floating device.<br />
<br />
===Practical note===<br />
MTs are degraded intracellular inside lysozymes, especially when they are in the apo/non-bound state ([[Team:Groningen/Literature#Gold2008|Gold 2008]]), for bacteria the degradation rate is not known, but for <br />
mammalian MT this can be estimated around 0.8nmol apo-MT/mg protein/min ([[Team:Groningen/Literature#Klaassen1994|Klaassen 1994]]). This can be avoided by adding metal-salts (ZnCl, CuCl) to cells expressing the protein.<br />
<br />
==Metals==<br />
===Arsenic===<br />
For the accumulation of arsenic some MTs are possible, like rh-MT (human MT) ([[Team:Groningen/Literature#Ngu2006 |Ngu 2006]]) and fMT (the seaweed species ''Fucus vesiculosis'') both binding As(III). The oxidized version of arsenic (As (V)) can also be bound by the metallothioneins but with lower affinity ([[Team:Groningen/Literature#Singh2008 |Singh 2008]]), another way As(V) is proposed to be accumulated is by conversion of As(V) to As(III) by the arsenate reductase and subsequent bound to the metallothionein or ArsR. rh-MT is known to bind 6x As(III) per molecule, fMT binds 5x As(III). No extra quantitative information is known from literature.<br />
====ArsR====<br />
ArsR is a trans-acting repressor that senses environmental As(III)and regulates the chromosomal ars operon. The ArsR protein has a specific binding site for As(III) and discriminates effectively against other metals like: phosphate, cadmium, sulfate and cobalt. The affinity of ArsR for As(III) is very high 10<sup>-15</sup>M of AS(III) can induce the promotor. The specific binding site spans 33 nucleotides in the promotor region including the putative -35 promotor element. When ArsR was purified, its size corresponded to that of a homodimer, bound to promoter DNA. Because of the high affinity of ArsR for As(III) the protein could be used for arsenic remediation. Chen and co-workers overexpressed ArsR in <i>E. coli</i> JM109 cells and found that the specific AS(III) content was 13-fold higher than the control without ArsR expression. High level expression of ArsR appeared to be toxic as a 3-fold reduction in cell density was observed. It has been shown that fusion partners reduce the toxicity of overexpression. Originally, Chen and co-workers made a fusion between ArsR and ELP (elastin protein), which is build out of VPGVG repeats. Because making a ArsR ELP153 fusion is very time consuming, we choose to make a fusion between MBP (maltose binding protein) and ArsR ([[Team:Groningen/Literature#Chen1998|Chen 1998]]).<br />
<BR><br />
Also see the [https://2009.igem.org/Team:Groningen/Project/Promoters|Metal sensitive promoters]. <br />
As ordering rh-MT was not successful, we try to use fMT for accumulation of As(III) and use ArsR to regulate the expression of the GVP cluster behind the ArsR regulated promoter.<br />
<br />
=====Results=====<br />
<br />
The fusion protein MBP-ArsR was built by creating giving the reverse primer of the MBP and the Forward primer of the ArsR a mutual restriction site SacI. The linker region was designed in such a way that it contained a Tev cleavage site, containing a SacI restriction site and a string of alanine residues to facilitate folding. The fusion protein has been succesfully cloned into the psb1AC3 vector creating biobrick {{part|BBa_K190027}}, but further attempts to add a promotor and rbs failed. Due to time the MBP-ArsR fusion protein has not been equipped with a promotor and so overexpression could not be established.<br />
<br />
===fMT===<br />
The <i>Fucus</i> [[Team:Groningen/Glossary#Metallothionein|Metallothionein]] (fMT) was isolated from the [http://en.wikipedia.org/wiki/Seaweed macroalgae] [http://en.wikipedia.org/wiki/Fucus_vesiculosus <i>Fucus vesiculosus</i> ]([[Team:Groningen/Literature#Morris1999|Morris 1999]]). It consists of 67 amino acid residues and has 16 cysteine residues, a high cysteine content is a key feature of MT. Another characteristic is the lack of aromatic residues is also seen in fMT where it only has one, tryptophan. Two domains containing cysteine residues are presumed to be involved in the metal binding function. Unusual in fMT is the presence of a 14 amino acid linker region between the two putative metal-binding domains which contains no cysteine residues. Plant MTs show this feature with about 40 residues, where vertebrate MTs only have three residues ([[Team:Groningen/Literature#Morris1999|Morris 1999]]). Being a MT fMT binds a multitude of metal ions, 6 Cd<sup>2+</sup> ions or 5 As<sup>3+</sup> ions in a sequential order, facilitated by the elongated linker domain ([[Team:Groningen/Literature#Ngu2009|Ngu 2009]]). The organisms from which fMT was first isolated are known to have the ability to survive in highly metal polluted water and with it having been expressed in ''E. coli'' previously ([[Team:Groningen/Literature#Singh2008|Singh 2008]]) it was an ideal choice to use as an arsenic sequestering protein.<br />
<br />
<br />
====Results====<br />
Arsenite uptake [[Team:Groningen/Protocols|assays]] were done to determine the As(III) accumulation of ''E. coli'' WT and fMT / GlpF overexpression strains. The concentration was measured by [[Team:Groningen/Protocols|ICP-MS]]. <br />
<br />
The arsenic uptake in ''E. coli'' WT (figure 3) as measured during this project (by [http://www.rikilt.wur.nl/NL/ RIKILT], Wageningen University), was compared with the uptake of ''E. coli'' with ArsR overexpression (described by [[Team:Groningen/Literature#Kostal2004|Kostal 2004]], see figure 3). This shows that the arsenic uptake in ''E. coli'' WT behaves similar but has lower final As(III) uptake yield. The difference is about 10% in the standard mode, but a higher extracellular arsenic concentration seems to be needed to saturate the uptake of arsenic in ''E. coli'' WT compared to ''E. coli'' with ArsR overexpression. This can be seen by comparing the transition point to saturation in figure 3, which are respectively around 50µM As(III) and around 20µM. <br />
<br />
[[Image:As uptake in E coli ArsR overexp - Kostal 2004.PNG]]<br />
:Figure 3: Uptake of As(III) by ''E. coli'' WT (containing pSB1A2-pLac)<br />
<br />
There is a relatively large difference between the data generated by measuring the arsenic concentration with ICP-MS in the standard mode and measuring in the collusion cell technology mode (CCT mode). The difference between these two techniques is that in the standard mode it is possible that multi-atomic compounds lead to interference with the arsenic (mw = 75) peak, like argon-chloride (Ar = 40 + Cl = 35 (75%) or 37(25%)). Because 25% of this compound is found in the mw = 77 peak, a correction factor may be calculated to correct for this, the ICP-MS software (Thermo) automatically corrects for Ar-Cl interference. It uses the amount of Krypton and Selenium for this correction. In the CCT all multi-atomic compounds are supposed to be decomposed, therefore no interference will be found in this mode. But a disadvantage of this mode is that the resolution is 10x lower than the standard mode, leading to a smaller signal-to-noise ratio. Because of this, we decided to use the standard mode (corrected for interference) to determine the arsenic accumulation by ''E. coli''.<br />
<br />
A second arsenic measurement was performed (by [http://www.vwa.nl/portal/page?_pageid=119,1639634&_dad=portal&_schema=PORTAL Food and Consumer Product Safety Authority], Groningen) using ''E. coli'' WT and ''E. coli'' containing the [accumulation device] (<partinfo>BBa_K190038</partinfo>) and the different parts ([[Team:Groningen/Project/Transport#Arsenite uptake via GlpF|GlpF]] (<partinfo>BBa_K190028</partinfo>) and [[Team:Groningen/Project/Accumulation#Arsenic|fMT]] (<partinfo>BBa_K190019</partinfo>)). The data was measured in the standard mode and the calculated arsenic imported by the cells is shown in figure 4.<br />
<br />
[[Image:As_uptake_in_WT_fMT_GlpF_ArsR.PNG]]<br />
:Figure 4: Uptake of As(III) by ''E. coli'' WT, and the strains containing the different parts of the accumulation device. As a control the arsenic uptake of ''E. coli'' with ArsR overexpression (as described by [[Team:Groningen/Literature#Kostal2004|Kostal 2004]]) is also shown.<br />
<br />
The curves in this figure show that there is no difference between the arsenic uptake by ''E. coli'' WT and by ''E. coli'' plus (parts of) the accumulation device. As a second observation, it can be seen that the uptake of arsenic in measured here is higher than found before (figure 3). A ratio of 2-3x was found for the WT strains (pSB1A2 and pArsR-RFP). These two differences will be discussed below. fMT shows exceptionally low arsenite uptake, this may be caused by incidentally "burning" the already dried cells at ~100;deg&C.<br />
<br />
The raw data can be found at [https://2009.igem.org/Team:Groningen/Modelling/Downloads| downloads].<br />
<br />
====Discussion====<br />
Between the two data sets there are a few differences, first there seems to be no difference between arsenic uptake in WT and ''E. coli'' with the accumulation device (or parts of this). Secondly, the data of arsenic uptake by ''E. coli'' WT could was not reproducible and the last data set showed a arsenic uptake which was even higher for ''E. coli'' WT than the ''E. coli'' ArsR overexpression strain. <br />
<br />
*Why is there no difference between the ''E. coli'' WT and the ''E. coli'' with accumulation device?<br />
This can be caused by non-functional expression of one of the genes (fMT or GlpF) or both. For membrane proteins it is known that functional overexpression is harder than for cytoplasmic proteins ([[Team:Groningen/Literature#Lundstom2006|Lundstom 2006]]). This could be tested by doing As(III) uptake/binding experiments with purified proteins, but this requires protein purification which could be facilitated by the addition of a his-tag (not present yet). The function of the transporter can be tested by measuring the uptake in membrane vesicles and that of the accumulation protein can be tested by measuring metal binding for instance by isothermal titration calorimetry. Otherwise the proteins may not be produced at all, this should be tested by protein purification or sds-page. Another possibility is that these proteins cannot be produced by ‘’E. coli’’ at once, though functional expression was already proven by Singh ''et al.'' ([[Team:Groningen/Literature#Singh2008|Singh 2008]]).<br />
<br />
*Non reproducible concentrations of arsenic, imported by ''E. coli'' WT, which can be seen as there is a large difference (2-3x) in arsenic uptake determined from the first and the second measurement. All data from the second ICP-MS arsenic determination, were also unexpectedly higher than was found in literature ([[Team:Groningen/Literature#Kostal2004|Kostal 2004]], [[Team:Groningen/Literature#Singh2008|Singh 2008]]). This discrepancy may be caused by one of the following reasons.<br />
During the second arsenic uptake assay the time between the incubation and washing the cells was decreased to the minimum though during the first assay there was some time for the cells to export the As(III) via there exporter ArsB. This may have caused the lower uptake yield of arsenic in the first data set. Also there was a difference in cell concentration, in the second assay this was 2.5 times higher. It is presumably that with a higher cell concentration the uptake rate is slower but a saturating incubation time (>1hr) might cause that the equilibrium of arsenite concentration in/outside the cell is reached faster. After destruction of the samples of the first data set, the samples did not become a clear solution but a suspension containing white flakes. These were removed by centrifugation, but this seems to indicate incomplete destruction. This was not seen for the second samples, therefore an increased arsenite concentration may be measured as arsenite bound to the white flakes is not measured. <br />
It also might be, that during the second arsenite uptake assay the cells were washed less properly causing the concentration to become way higher than the first measurement. A more acidic buffer used for washing the cells is probably more efficient in removing metal ions than the TB74S buffer (pH 7.4), but as this protocol was the same as described by [[Team:Groningen/Literature#Kostal2004|Kostal 2004]], this should be a major problem. The expected increase in arsenic concentration should be linear with the external arsenite concentration, but this was not seen (figure 4), a clear saturation curve was seen. <br />
A plausible cause is that there was a mistake in the calculations, a correction factor which was forgotten to correct for. Another plausible cause is that the concentration is higher because the measured concentration was for some samples 5 times higher than the calibration range. It might be that linear extrapolation is not correct. This can cause the structural increased arsenic uptake. <br />
<br />
*Other considerations:<br />
-Metal buffer interactions, causing a lower free-As(III) concentration surrounding the cell suspension.<br />
-Arsenic oxidation in aerobic conditions to As(V), this equilibrium may change over hours, so if the stock solution is enriched with As(V) it may take hours before it is changed to As(III) again. <br />
- Binding of other metal ions to the metallothionein causing competition for arsenite binding to fMT. Possible metal ions can be: Copper(I) or other metal ions present in the undefined LB medium. A requiry is that the metal ion should bind stronger or as strong to the MT as arsenite, which binds less strongly to MT than Zn(II) for instance or Cu(I).<br />
<br />
====Conclusion====<br />
{{todo}}<br />
<br />
==Modelling==<br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
===Arsenic - ArsR===<br />
<br />
Below you can calculate how many grams of arsenic will be taken out of the water per cubic meter of cells. This extra weight raises the density of the cell and therefore lowers its capacity for buoyancy. Our preliminary results look very promising. Even under the assumption that the weight of the metal is added to the weight of the cells, without increasing their volume, we could add up to a hundred times the currently computed weight without having a large effect on the required fraction of gas vesicles (it will only go up from about 12.2% to 12.7%).<br />
<br />
At this moment we use four different variables:<br />
<br />
# Molecular weight of arsenic. Source: [http://en.wikipedia.org/wiki/Arsenic Arsenic page on Wikipedia]<br />
# Millimol arsenic per kg of cell dryweight (note that this is equivalent to nmol/mg). Source: [[Team:Groningen/Literature#Kostal2004|Kostal 2004]]<br />
# The proportion between the weight of a dry cell and a wet cell. Source: [http://redpoll.pharmacy.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi CCDB Database]<br />
# Cell density. Source: see our [[Team:Groningen/Project/Vesicle|gas vesicle page]].<br />
<br />
{|<br />
|style="vertical-align:top;"|<html><br />
<div style="background:#efe;border:1px solid #9c9;padding:1em;"><br />
<table style="border-collapse:collapse;background:none;"><tr><br />
<td style="border-right:1px solid #9c9;padding-right:1em;"><br />
aw<sub>As(III)</sub> = <input type="text" id="awAs" value="74.92"/> g/mol<br/><br />
<nobr>n<sub>As(III)</sub> / M<sub>cell(dry)</sub> = <input type="text" id="cAs" value="2"/> millimole/kg</nobr><br/> <!-- Reasonable estimate --><br />
M<sub>cell(dry)</sub> / M<sub>cell(wet)</sub> = <input type="text" id="Mcelldrywet" value="0.3"/><br/><br />
&rho;<sub>cell</sub> = <input type="text" id="rhocell" value="1100"/> kg/m<sup>3</sup><br/> <!-- Reasonable estimate --><br />
<br />
<button onClick="computeArsenicWeight()">Compute</button><br/><br />
</td><br />
<br />
<td style="padding-left:1em;"><br />
<div id="arsenicError" style="color:red"></div><br />
<nobr>As(III) intake per volume of cells</nobr><br/><br />
<nobr> = <span id="Aspercellvolume"></span> g/m<sup>3</sup></nobr><br/><br />
<nobr> = <span id="molAspercellvolume"></span> &micro;mol/liter</nobr><br/><br />
</td><br />
</tr></table><br />
</div><br />
<script type="text/javascript"><br />
<br />
addOnloadHook(computeArsenicWeight);<br />
<br />
function computeArsenicWeight() {<br />
// Intermediates (mostly useful for debugging)<br />
var arsenicErrorNode = document.getElementById("arsenicError");<br />
arsenicErrorNode.innerHTML = '';<br />
<br />
// Read inputs<br />
var awAs = getInput('awAs'); // g/mol<br />
var cAs = getInput('cAs') * 1e-3; // mmol/kg -> mol/kg<br />
var Mcelldrywet = getInput('Mcelldrywet'); // kg/kg<br />
var rhocell = getInput('rhocell'); // kg/m^3<br />
<br />
// Compute density(/-ies)<br />
try {<br />
var Aspercellvolume = awAs * cAs * Mcelldrywet * rhocell;<br />
var molAspercellvolume = cAs * Mcelldrywet * rhocell * 1e3;<br />
// 1e-3 to convert from /m^3 to /L and 1e6 to convert from mole to micromole<br />
} catch(err) {<br />
arsenicErrorNode.innerHTML = err.message;<br />
}<br />
<br />
// Set outputs<br />
setOutput('Aspercellvolume', Aspercellvolume);<br />
setOutput('molAspercellvolume', molAspercellvolume);<br />
}<br />
</script><br />
</html><br />
|style="vertical-align:top;"|<pre><br />
<br />
As per cell volume = awAs * nAs(III) /<br />
Mcell(dry) * Mcelldrywet * rhocell<br />
mol As per cell volume = nAs(III) / <br />
Mcell(dry) * Mcelldrywet * rhocell<br />
<br />
</pre><br />
|}<br />
<br />
[[Image:Arsenic_accumulation.png|frame]]<br />
<br />
At a lower level arsenic accumulation can be described using reactions between ArsR, As(III) and the ars promoter. As shown in the figure on the right, a number of different substances(/complexes) are involved. For our purposes it is especially important to determine what fraction of As(III) is unbound, if more As(III) is bound we can accumulate more.<br />
<br />
In addition to binding to As(III), ArsR can repress Ars, creating a negative feedback loop. In effect this regulates the production of ArsR based on the As(III) concentration ([[Team:Groningen/Literature#Chen1997|Chen 1997]]). In the <i>E. coli</i> top 10 there is only ars promoter present on the genome to produce ArsR (see [[Team:Groningen/BLAST|BLAST]] results). There are plasmids which produce both ArsR and ArsD, but these are not used in this project. We intend to introduce instead a constitutive promoter (pro), which produces just ArsR, in order to bind as much As(III) as possible.<br />
<br />
The calculator below tries to compute the ratio between bound and unbound arsenic, specifically As(III), in the cell.<br />
See our [[Team:Groningen/Modelling/Arsenic|Modelling]] page for detailed information on the constants/variables used and a derivation of the formulas. Note that the computations currently involve slightly more variables/constants than strictly necessary.<br />
<br />
<html><br />
<table style="background:#efe;border:1px solid #9c9;padding:1em;"><tr><td><br />
<table style="border-collapse:collapse;background:none;"><tr><br />
<td style="border-right:1px solid #9c9;padding-right:1em;"><br />
<dl><br />
<dt>Dissociation constants</dt><br />
<dd><br />
KR<sub>d</sub> (ArsR<sub>As</sub>) = <input type="text" id="K1d" value="6"/> &micro;M (??)<br/><br />
<nobr>KA<sub>d</sub> (ArsR<sub>ars</sub>) = <input type="text" id="K3d" value="0.33"/> &micro;M (</html>[[Team:Groningen/Literature#Chen1997|Chen1997]]<html>)</nobr><br/><br />
KM<sub>d</sub> (MBPArsR<sub>As</sub>) = <input type="text" id="KMd" value="6"/> &micro;M (???)<br/><br />
KF<sub>d</sub> (fMTArsR<sub>As</sub>) = <input type="text" id="KFd" value="6"/> &micro;M (???)<br/><br />
n<sub>f</sub> = <input type="text" id="nf" value="3"/> (???)<br/><br />
</dd><br />
<dt>Half-lifes</dt><br />
<dd><br />
&tau;R (ArsR) = <input type="text" id="tauR" value="0.1"/> min (???)<br/><br />
&tau;M (MBPArsR) = <input type="text" id="tauM" value="0.1"/> min (???)<br/><br />
&tau;F (fMT) = <input type="text" id="tauF" value="0.1"/> min (???)<br/><br />
</dd><br />
<dt>Production rates of the promoters</dt><br />
<dd><br />
<nobr>&beta;RN (ars1 &rarr; ArsR) = <input type="text" id="beta1" value="100"/> 1/second (???)</nobr><br/><br />
<nobr>&beta;R (proR &rarr; ArsR) = <input type="text" id="beta3" value="100"/> 1/second (???)</nobr><br/><br />
<nobr>&beta;M (proM &rarr; MBPArsR) = <input type="text" id="betaM" value="26.6"/> 1/second (???)</nobr><br/><br />
<nobr>&beta;F (proF &rarr; fMT) = <input type="text" id="betaF" value="200"/> 1/second (???)</nobr><br/><br />
</dd><br />
<!--As(III) = <input type="text" id="As3Concentration" value="10"/> &micro;M<br/>--><br />
<dt>Promoter concentrations<dt><br />
<dd><br />
ars1<sub>total</sub> = <input type="text" id="ars1TPerCell" value="1"/> per cell<br/><br />
<nobr>proR = <input type="text" id="proRPerCell" value="0"/> per cell (??)</nobr><br/><br />
<nobr>proM = <input type="text" id="proMPerCell" value="100"/> per cell (??)</nobr><br/><br />
<nobr>proF = <input type="text" id="proFPerCell" value="0"/> per cell (??)</nobr><br/><br />
V<sub>cell</sub> = <input type="text" id="Vcell" value="1"/> &micro;m<sup>3</sup> </html><br />
([http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi| CCBD])<html><br />
<br />
</dd><br />
</dl><br />
<br />
<button onClick="computeArsenicEquilibrium()">Compute</button><br/><br />
</td><br />
<br />
<td style="padding-left:1em;"><br />
<div id="arsenicEquilibriumError" style="color:red"></div><br />
<dl><br />
<dt>ArsR</dt><br />
<dd><br />
ars / ars<sub>total</sub> = <span id="arsFraction"></span><br/><br />
ArsR = <span id="ArsR"></span> &micro;M<br/><br />
<!--ArsR<sub>total</sub> = <span id="ArsRT"></span> &micro;M<br/>--><br />
</dd><br />
<dt>"Accumulation factor"</dt><br />
<dd><br />
<!--As(III)<sub>total</sub> = <span id="AsinT"></span> &micro;M<br/>--><br />
As(III)<sub>total</sub>/As(III) = <span id="AsinTfactor"></span><br/><br />
</dd><br />
</dl><br />
</html><br />
<span id="accumulationFactorData"></span><br />
{{graph|Team:Groningen/Graphs/AccumulationFactor|id=accumulationFactorGraph}}<br />
(For constants other than the ones on the left the [[Team:Groningen/Modelling/Arsenic.js|default values]] are used.)<br />
<html><br />
</td><br />
</tr></table><br />
</td></tr></table><br />
<script type="text/javascript"><br />
<br />
addOnloadHook(computeArsenicEquilibrium);<br />
<br />
function computeArsenicEquilibrium() {<br />
// Intermediates (mostly useful for debugging)<br />
var errorNode = document.getElementById("arsenicEquilibriumError");<br />
errorNode.innerHTML = '';<br />
<br />
// Read inputs<br />
var c = arsenicModelConstants();<br />
c.AsT = 0;<br />
c.K1d = getInput('K1d') * 1e-6; // micromolar -> molar<br />
c.K3d2 = Math.pow(getInput('K3d') * 1e-6,2); // micromolar -> molar<br />
c.KMd = getInput('KMd') * 1e-6; // micromolar -> molar<br />
c.KFd = getInput('KFd') * 1e-6; // micromolar -> molar<br />
c.nf = getInput('nf') * 1e-6; // micromolar -> molar<br />
c.tauR = getInput('tauR') * 60; // minutes -> seconds<br />
c.tauM = getInput('tauM') * 60; // minutes -> seconds<br />
c.tauF = getInput('tauF') * 60; // minutes -> seconds<br />
c.beta1 = getInput('beta1'); // 1/second<br />
c.beta3 = getInput('beta3'); // 1/second<br />
c.betaM = getInput('betaM'); // 1/second<br />
c.betaF = getInput('betaF'); // 1/second<br />
var avogadro = 6.02214179e23; // 1/mol<br />
var Vcell = getInput('Vcell') * 1e-15; // micrometer^3/cell -> liter/cell<br />
c.ars1T = getInput('ars1TPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
c.ars2T = 0;<br />
c.pro = getInput('proRPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
c.proM = getInput('proMPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
c.proF = getInput('proFPerCell') / (avogadro*Vcell); // 1/cell -> mol/liter<br />
<br />
// Compute density(/-ies)<br />
try {<br />
var x = arsenicModelEquilibrium(c);<br />
var ArsR = x._ArsR;<br />
var arsFraction = x._arsF;<br />
var AsinTfactor = 1 + ArsR/c.K1d;<br />
} catch(err) {<br />
errorNode.innerHTML = err.message;<br />
}<br />
<br />
// Set intermediates if they exist<br />
setOutput('arsFraction', arsFraction);<br />
setOutput('ArsR', ArsR * 1e6);<br />
<br />
// Set outputs<br />
setOutput('AsinTfactor', AsinTfactor);<br />
<br />
// Draw graph<br />
var dataNode = document.getElementById("accumulationFactorData");<br />
var graphNode = document.getElementById("accumulationFactorGraph");<br />
var data = {AsT:[], AsexT0:[], AsinT:[], AsinT2:[]};<br />
var bAsin, cAsin, Asin;<br />
// Some guesses<br />
var c2 = {}, x2;<br />
for(var a in c) c2[a] = c[a];<br />
c2.v5 *= 2;<br />
for(var AsexT0uM=0.1; AsexT0uM<=100; AsexT0uM*=1.1) {<br />
c.AsT = c.Vs*AsexT0uM*1e-6;<br />
c2.AsT = c.AsT;<br />
x = arsenicModelEquilibrium(c);<br />
x2 = arsenicModelEquilibrium(c2);<br />
data.AsT.push(c.AsT);<br />
data.AsexT0.push(c.AsT/c.Vs);<br />
data.AsinT.push(x.AsinT*c.Vc/c.AsT);<br />
data.AsinT2.push(x2.AsinT*c.Vc/c.AsT);<br />
}<br />
dataNode.data = data;<br />
if (graphNode.refresh) graphNode.refresh();<br />
}<br />
</script><br />
</html><br />
<br />
'''In conclusion:'''<br />
<br />
* Even at the accumulation levels of Koster <i>et al.</i> the amount of arsenic accumulated in <i>E. coli</i> is so little that it should not matter much for the buoyant density (which normally is about 1100kg/m<sup>3</sup>).<br />
* If you substitute constitutive promotors for Ars promotors, you can see that it is clearly advantageous to use constitutive promotors as just adding ars promoters does not increase the accumulation factor. A plasmid containing an ars promoter and (just) a gene coding for ArsR behind it might contain more arsenic, but there would also be more unbound arsenic, increasing the toxicity.<br />
* The model is not very sensitive to different values for K3d (with K3d=1mM the accumulation factor is 248.06 and with K3d=1nM it is 240.57).<br />
* The accumulation factor is greatly affected by the product of the half-life of ArsR and the production rate.<br />
<br />
<!-- ==Planning and requirements:==<br />
<br />
* '''Modelling'''<br />
** Speed<br />
** Metaliotheines concentration <br />
** How often does the ArsR sensitive operator/operon occur in our <i>E. coli</i>?<br />
* '''Lab'''<br />
** Measurements<br />
*** Transport Assays<br />
**** Protein expression levels determined by immunoblotting using anti-ArsA and anti-ArsD antibodies [[Team:Groningen/Literature#Lin2007-2|Lin 2007]]<br />
**** Inductively coupled mass spectrometry (ICP-MS) ([[Team:Groningen/Literature#Meng2004|Meng 2004]])<br />
*** Measure accumulation. By measuring before/after concentration metal with and without accumulation protein.<br />
*** Determine the dissociation constant of ArsR and As(III). (By measuring the ratio between bound and unbound ArsR?)<br />
**** It might be possible to do this with (tryptophan related) fluorescence (that is how it is done for ArsD in [[Team:Groningen/Literature#Chen1997|Chen 1997]]). In the paper ArsD is purified, but if that is not feasible for us, we might try to simply do it in living cells (and hope that ArsR both fluoresces enough and is produced enough to be measurable).<br />
*** Production rate of ArsR?<br />
** Biobrick Bba_K129004<br />
** Rest--><br />
<br />
==Copper==<br />
<br />
===MymT===<br />
<br />
MymT is a 5kDa-protein which binds Cu(I) but also to less extend Zn(II) from ''Mycobaterterium tuberculosis''. This MT was found to bind 4-6 Cu(I) ions per molecule. Induction of the expression of MymT is the strongest with Cd and Cu. But upon over-expression of MymT in ''E. coli'', the protein becomes insoluble ([[Team:Groningen/Literature#Gold2008|Gold 2008]]). This may be caused by the fact that it is a protein from a gram-positive bacteria expressed in a gram negative bacterium. Therefore specialized cultivation conditions are needed, the cells should be grown at a low temperature (16 &deg;C). The functionality of MymT can be measured by fluorescence spectroscopy, as also found for other copper binding metallothioneins. Copper bound to MT create Cu-thiolates which can be excited at 280nm and gives a Stokes shift towards 600 nm ([[Team:Groningen/Literature#Beltramini1981|Beltramini 1981]]). <br />
<br />
====Results:====<br />
PCR on ''mym''T from pGB68 unfortunately did not give any correct cDNA fragments, even though the primer quality was improved ([[Team:Groningen/Protocols|Protocol Biobrick primers]]). Therefore the sub-project was discontinued.<br />
<br />
==Zinc==<br />
Below toxic concentrations, zinc is essential for many biological processes. Examples are enzymatic hydroxylation, DNA and RNA synthesis, transcription and translation, signal transduction and apoptosis regulation ([[http://en.wikipedia.org/wiki/Zinc 1]] and [[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]). Methallothioneins can adjust the zinc absorption up to 14-40%, though a real excess of zinc can be toxic. A daily intake of 100–300 mg Zn/day can give rise to copper / iron deficiency and damage of nerve receptors ([[Team:Groningen/Literature#Fosmire1990|Fosmire 1990]]). Examples of metallothioneins sequestering zinc, are SmtA from the cyanobacterium ''Synechococcus'' PCC7942 ([[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]), ZiaR from ''Synechocystis'' PCC 6803 ([[Team:Groningen/Literature#Robinson2001|Robinson 2001]]), human metallothioneins like MT-1 and -2. The mammalian proteins were found to bind 7 Zn<sup>2+</sup> ions by the thiolate-group of there cysteins.<br />
<br />
===SmtA===<br />
SmtA is a MT from ''Synechococcus'' PCC 6803, it was found to bind 3-4Zn ions and is supposed to have a function in preventing zinc toxicity ([[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]), but it also binds copper and cadmium ([[Team:Groningen/Literature#Shi1992|Shi 1992]]). Upon binding of Zn, the glutathione transferase fusion-protein showed a 1:3 stoichiometry and SmtA a 1:4 stoichiometry ([[Team:Groningen/Literature#Robinson2001|Robinson 2001]]). SmtA binds the 4 Zn ions via cystein thiolate-bridges, forming a Zn<sub>4</sub>Cys<sub>11</sub> cluster whichs was also found in mammalian MT, though these proteins do not have a homologous DNA sequence ([[Team:Groningen/Literature#Blindauer2001|Blindauer 2001]]). ''SmtA'' is found on an operon with it's transcriptional regulator ''smtB''. SmtB releases from the promoter-operator region in front of this operon, when it binds Zn via its metal binding motif. SmtB and [[Team:Groningen/Project/Accumulation#Arsenic|ArsR]] (negative transcriptional regulator binding arsenic) have similar functionalities but differ in metal binding motifs ([[Team:Groningen/Literature#Robinson2001|Robinson 2001]]). That ''Synechococcus'' is a gram negative bacterium might increase the possibility of functional and stable overexpression in ''E. coli'' .<br />
<br />
===Results===<br />
PCR reactions to amplify SmtA from pET29a and SmtA-GST from pGEX-3x were successful, but unfortunately the DNA sequence used to design the SmtA primers was not correct so therefore wrong cDNA fragments were amplified. Because it was too late to order new primers, this sub-project was discontinued.<br />
<br />
<!--==Alternatives==<br />
{{todo|Inclusion bodies}} ([[Team:Groningen/Literature#Fowler1987|Fowler 1987]])<br><br />
{{todo|(Bacterio)Ferritins}}<br><br />
{{todo|Phytochelatins}}<br><br />
[http://www.wiley.com/legacy/products/subject/reference/messerschmidt_toc.html A list of opportunities]<br />
==Inhibitory characteristics?==--><br />
<br />
{{Team:Groningen/Project/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/ArsenicTeam:Groningen/Modelling/Arsenic2009-10-21T18:49:08Z<p>Jaspervdg: </p>
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<div>{{Team:Groningen/Modelling/Header}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Modelling/Characterization}}</div><br />
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[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
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==Detailed Model==<br />
Based on the [[#QuasiSteadyState|quasi-steady-state derivation]] below we have made the simplified version of our model shown below. The simplification is based on two key assumptions (which are also illustrated below, next to the table "Breakdown of core substances"):<br />
<br />
*Binding and unbinding of arsenic to/from the transporters occurs on a much smaller time scale than changes in the concentration of arsenic inside and outside the cell. And similarly, we assume that (un)binding of ArsR to/from the ars promoter is much faster than the production of ArsR (for example).<br />
*The concentration of transporters is insignificant compared to the concentration of arsenic inside and outside the cell.<br />
<br />
This leads to the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation for import, but also some more general equations for export using ArsB and accumulation with ArsR (for example, the Hill equation can be recognized in the activity of the ars promoter).<br />
<br />
The inexperienced viewer may find the following tables and formulas baffeling. I would reccommend that one would look at the raw model first to gain an understanding of the basic reactions involved then have a look at the steady-state and the quasi steady-state model. It is not manditory, but is probably the the best route to get a better understanding of the model as a whole. For the moddelers of other teams who do not study biology: it would be best if one first tries to understand [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] kinetics and then procedes to understand the model.<br />
<br />
[[Image:Arsenic_filtering.png|frame|A schematic representation of the processes involved in arsenic filtering (keep in mind that ArsR ''represses'' the expression of the genes behind ars). Note that MBPArsR and fMT are not shown for clarity.<!-- Also, ArsD is not shown here, as it is [[Team:Groningen/BLAST|not present in our E. coli]] and has a role analogous to ArsR.-->]]<br />
<br />
{|class="ourtable"<br />
|+ Reactions<br />
!colspan="2"|Reaction<br />
!Description<br />
!Rate<br />
|-<br />
|colspan="4"|''Transport''<br />
|-<br />
| ||As(III)<sub>ex</sub>T &rarr; As(III)<sub>in</sub>T||Import of arsenic.||(Vc/Vs) v5<sup>&dagger;</sup> As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T)<br />
|-<br />
| ||As(III)<sub>in</sub>T &rarr; As(III)<sub>ex</sub>T||Export of arsenic.|| k8 ArsB<sub>As</sub><br />
|-<br />
| ||style="white-space:nowrap;"|ars1T → ars1T + ArsBT||Production of ArsB.|| βB ars1<br />
|-<br />
| ||ArsBT &rarr; null||Degradation of ArsB|| (ln(2)/τB) ArsB<br />
|-<br />
|colspan="4"|''Accumulation''<br />
|-<br />
| ||ars1T → ars1T + ArsRT||From chromosomal operon.|| βRN ars1<br />
|-<br />
| ||proR → proR + ArsRT||Production of ArsR.|| βR pro<br />
|-<br />
| ||style="white-space:nowrap;"|proM → proM + MBPArsRT||Production of MBPArsR.|| βM pro<br />
|-<br />
| ||proF → proF + fMTT||Production of fMT.|| βF pro<br />
|-<br />
| ||ArsRT → null||Degradation of ArsR.|| (ln(2)/τR) ArsR<br />
|-<br />
| ||MBPArsRT → null||Degradation of MBPArsR.|| (ln(2)/τM) MBPArsR<br />
|-<br />
| ||fMTT → null||Degradation of fMT.|| (ln(2)/τF) fMT<br />
|-<br />
|colspan="4"|''Gas vesicles''<br />
|-<br />
| ||ars2T → ars2T + GV||Transcription + translation.|| βG ars2<br />
|-<br />
| ||GV → null||Degradation of gas vesicles.|| (ln(2)/τG) GV<br />
|}<br />
<br />
{|class="ourtable" style="clear:right;"<br />
|+ Core Substances<br />
!colspan="2"|Name<br />
!Description<br />
!Derivative to time<br />
|-<br />
|colspan="4"|''Extracellular''<br />
|-<br />
| ||As(III)<sub>ex</sub>T || As(III) in the solution. || (Vc/Vs) k8 ArsB<sub>As</sub> - (Vc/Vs) v5<sup>&dagger;</sup> As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T)<br />
|-<br />
|colspan="4"|''Membrane (all naturally occurring, but we plan to bring GlpF to overexpression)''<br />
|-<br />
| ||GlpFT || Importer of As(III) (concentration w.r.t. the exterior of the cell). || (not used directly in model, assumed to be constant)<br />
|-<br />
| ||ArsBT || Exporter of As(III) (concentration w.r.t. the interior of the cell). || βB ars1 - (ln(2)/τB) ArsB<br />
|-<br />
|colspan="4"|''Intracellular (ars2, pro and GV are introduced)''<br />
|-<br />
| ||As(III)<sub>in</sub>T || As(III) (bound and unbound) in the cell. || v5 As(III)<sub>ex</sub>T / (K5+As(III)<sub>ex</sub>T) - k8 ArsB<sub>As</sub><br />
|-class="estimate"<br />
| ||ars1T || ArsR repressed promoters (bound and unbound) naturally occurring in E. coli. || (concentration is constant = 1.6605nM, one per cell)<br />
|-class="estimate"<br />
| ||ars2T || ArsR repressed promoters in front of gas vesicle genes. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proR || Constitutive promoters in front of arsR. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proM || Constitutive promoters in front of mbp-arsR. || (concentration is constant = 0-166.05nM)<br />
|-class="estimate"<br />
| ||proF || Constitutive promoters in front of fMT. || (concentration is constant = 0-166.05nM)<br />
|-<br />
| ||ArsRT || ArsR in the cell. || βRN ars1 + βR proR - (ln(2)/τR) ArsR<br />
|-<br />
| ||MBPArsRT || MBPArsR in the cell. || βM proM - (ln(2)/τM) MBPArsR<br />
|-<br />
| ||fMTT || fMT in the cell. || βF proF - (ln(2)/τF) fMT<br />
|-<br />
| ||GV || Concentration of gas vesicles. || βG ars2 - (ln(2)/τG) GV<br />
|-style="border:none;"<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Directly from paper.<br />
|class="selfDerived" style="padding:0;"|Based on data from paper.<br />
|class="experimental" style="padding:0;"|Based on experiment.<br />
|class="estimate" style="padding:0;"|Rough estimate.<br />
|class="unknown" style="padding:0;"|Totally unknown.<br />
|}<br />
|}<br />
<div style="text-align:right;font-size:smaller;"><sup>&dagger;</sup> Note that the "constant" v5 depends on the concentration of GlpF transporters in the cell, and this can depend on whether we bring GlpF to overexpression or not. For simplicity the production/degradation of GlpF is not included explicitly in the model, instead we can vary the constant v5 relative to the value found for wild-type E. coli.</div><br />
<br />
{|<br />
|style="vertical-align:top;"|<br />
{|class="ourtable"<br />
|+ Breakdown of core substances<br />
!Core substance<br />
!Component<br />
!Relative abundance<br />
|-<br />
|rowspan="2"|ArsBT<br />
|style="padding-left:0;"|ArsB<br />
|K7<br />
|-<br />
|ArsB<sub>As</sub><br />
|As(III)in<br />
|-<br />
|rowspan="4"|As(III)inT<br />
|style="padding-left:0;"|As(III)in<br />
|1<br />
|-<br />
|ArsR<sub>As</sub><br />
|ArsR / KR<sub>d</sub><br />
|-<br />
|MBPArsR<sub>As</sub><br />
|MBPArsRT / (KM<sub>d</sub> + As(III)in)<br />
|-<br />
|fMT<sub>As</sub><br />
|n<sub>f</sub> fMTT As(III)<sub>in</sub><sup>n<sub>f</sub>-1</sup> / (KF<sub>d</sub><sup>n<sub>f</sub></sup> + As(III)<sub>in</sub><sup>n<sub>f</sub></sup>)<br />
|-<br />
|rowspan="2"|arsT<br />
|style="padding-left:0;"|ars<br />
|KA<sub>d</sub>²<br />
|-<br />
|ArsR<sub>ars</sub><br />
|ArsR²<br />
|-<br />
|rowspan="2"|ars<br />
|style="padding-left:0;"|ars1<br />
|ars1T<br />
|-<br />
|ars2<br />
|ars2T<br />
|-<br />
|rowspan="3"|ArsRT<br />
|style="padding-left:0;"|ArsR<br />
|1<br />
|-<br />
|ArsR<sub>As</sub><br />
|As(III)<sub>in</sub> / KR<sub>d</sub><br />
|-<br />
|ArsR<sub>ars</sub><br />
|2 ArsR ars / KA<sub>d</sub>²<br />
|-<br />
|rowspan="2"|MBPArsRT<br />
|style="padding-left:0;"|MBPArsR<br />
|KM<sub>d</sub><br />
|-<br />
|MBPArsR<sub>As</sub><br />
|As(III)<sub>in</sub><br />
|-<br />
|rowspan="2"|fMTT<br />
|style="padding-left:0;"|fMT<br />
|KF<sub>d</sub><sup>n<sub>f</sub></sup><br />
|-<br />
|fMT<sub>As</sub><br />
|As(III)<sub>in</sub><sup>n<sub>f</sub></sup><br />
|}<br />
|[[Image:Arsenic Model - Substances.png|frame|Circles correspond to core substances. We consider the reactions between the overlapping substances so fast that we model them by determining the ratios between the substances when the reactions between them are in equilibrium. Also, the complexes formed with <strike>ars,</strike> GlpF and ArsB (the small circles) are considered to have such a low concentration that they are of no importance to the concentrations of As(III)in/-ex and ArsR (the large circles).]]<br />
|}<br />
<br />
{|class="ourtable"<br />
|+ Constants<br />
!Name<br />
!Units<br />
!Value<br />
!Description<br />
|-class="unknown"<br />
|k8<br />
|1/s<br />
|<br />
|Reaction rate constant representing how fast ArsB can export arsenic.<br />
|-class="estimate"<br />
|KR<sub>d</sub><br />
|M<br />
|6&micro;M<br />
|Dissociation constant for ArsR and As(III). Assumed to be about an order of magnitude smaller than KD<sub>d</sub> = 60&micro;M, the corresponding constant for the similar protein ArsD from [[Team:Groningen/Literature#Chen1997|Chen1997]].<br />
|-class="estimate"<br />
|KM<sub>d</sub><br />
|M<br />
|6&micro;M<br />
|Dissociation constant for MBPArsR and As(III). We assume this to be roughly equal to KR<sub>d</sub>.<br />
|-class="unknown"<br />
|KF<sub>d</sub><br />
|M<br />
|<br />
|Dissociation constant for fMT and As(III).<br />
|-class="unknown"<br />
|n<sub>f</sub><br />
|<br />
|<br />
|Hill coefficient for the formation of the complex fMTAs. This is related to the number of arsenic ions that bind to fMT.<br />
|-class="fromPaper"<br />
|KA<sub>d</sub><br />
|M<br />
|0.33&micro;M<br />
|Dissociation constants for ArsR and ars.<br />
* KA<sub>d</sub>² = kA<sub>off</sub>/kA<sub>on</sub> = (0.33&micro;M)²? ([[Team:Groningen/Literature#Chen1997|Chen1997]], suspect as the relevant reference doesn't actually seem to give any value for this)<br />
|-class="selfDerived"<br />
|v5<br />
|mol/(s&middot;L)<br />
|3.1863&micro;mol/(s·L)<br />
|Maximum import rate per liter of cells (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]). Note that we have purposefully chosen to write the units as mol/(s&middot;L) instead of M/s, to emphasize the fact that the rate is per liter of ''cells''.<br />
* v5 = k6 GlpFT (Vs/Vc)<br />
|-class="selfDerived"<br />
|K5<br />
|M<br />
|27.718&micro;M<br />
|Concentration at which import reaches half its maximum import rate (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]).<br />
* K5 = (k5off+k6) / k5on<br />
|-class="unknown"<br />
|K7<br />
|M<br />
|<br />
|Concentration at which export reaches half its maximum export rate (see [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten equation]]).<br />
* K7 = (k7off+k8) / k7on<br />
|-class="unknown"<br />
|&tau;B, &tau;R, &tau;G, etc.<br />
|s<br />
|<br />
|Half-lifes (of ArsB, ArsR and GV, respectively). Degradation rate = ln(2)/&tau; {{infoBox|1=If you take just the degradation into account you will have the equation dC/dt = -k*C, which leads to C(t) = C(0) e<sup>-k t</sup>. So if k = ln(2)/&tau; we get C(t) = C(0) e<sup>-ln(2)/&tau; t</sup> = C(0) 2<sup>-t/&tau;</sup>. In other words &tau; is the time it takes for the concentration to half.}}<br />
|-class="unknown"<br />
|&beta;B, &beta;R, etc.<br />
|1/s<br />
|<br />
|Production rates.<br />
* &beta;RN = the production rate for ArsR behind the ars1 promoter<br />
* &beta;B = the production rate for ArsB behind the ars1 promoter<br />
* &beta;G = the production rate for GV behind the ars2 promoter<br />
* &beta;R = the production rate for ArsR behind a constitutive promoter<br />
* &beta;M = the production rate for MBPArsR behind a constitutive promoter<br />
* &beta;F = the production rate for fMT behind a constitutive promoter<br />
|-<br />
|Vs<br />
|L<br />
|<br />
|Volume of solution (excluding cells).<br />
|-<br />
|Vc<br />
|L<br />
|<br />
|Total volume of cells (in solution) (so Vs+Vc is the total volume).<br />
|-style="border:none;"<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Directly from paper.<br />
|class="selfDerived" style="padding:0;"|Based on data from paper.<br />
|class="experimental" style="padding:0;"|Based on experiment.<br />
|class="estimate" style="padding:0;"|Rough estimate.<br />
|class="unknown" style="padding:0;"|Totally unknown.<br />
|}<br />
|}<br />
<br />
<br />
==The raw model==<br />
<html><style type="text/css"></html><br />
.import { background: LightGreen; }<br />
.export { background: LightBlue; }<br />
.accumulation { background: LightPink; }<br />
.production { background: LightGoldenRodYellow; }<br />
<html></style></html><br />
<br />
The following table gives all the reactions that take place inside the cell. You can look at the schematic representation of the processes involved to get a good grasp as how every reaction works to the other. Note that proR, ProM and MBPArsR, ProF and Fmt are not displayed in the figure. This has been done for clarity. These reactions are simple constituative promotor reactions. Once you have an insight in the reactions involved you can have a look at the next table.<br />
<br />
[[Image:Arsenic_filtering.png|frame|A schematic representation of the processes involved in arsenic filtering (keep in mind that ArsR ''represses'' the expression of the genes behind ars). Note that MBPArsR and fMT are not shown for clarity.<!-- Also, ArsD is not shown here, as it is [[Team:Groningen/BLAST|not present in our E. coli]] and has a role analogous to ArsR.-->]]<br />
<br />
{|class="ourtable"<br />
|+ Reactions<br />
!colspan="2"|Reaction<br />
!Description<br />
|-<br />
|colspan="3"|''Transport''{{infoBox|In the reactions below you can see the import of arsenic by GlpF and the export of arsenic by ArsB. Only the degradation of ArsB is taken into acount because the ars operon also produces ArsB, as can be seen in the accumulation section. We assume a constant number of GlpF importers. }}(based on [[Team:Groningen/Literature#Rosen1996|Rosen1996]], [[Team:Groningen/Literature#Meng2004|Meng2004]] and [[Team:Groningen/Literature#Rosen2009|Rosen2009]])<br />
|-<br />
| ||<span class="import">As(III)<sub>ex</sub> + GlpF &harr; GlpF<sub>As</sub></span>||The binding and detachment of rsenic to GlpF on the outside of the cell.||<br />
|-<br />
| ||<span class="import">GlpF<sub>As</sub> &rarr; GlpF + As(III)</span>||The release of arsenic on the inside of the cell by GlpF|| <br />
|-<br />
| ||<span class="export">As(III)<sub>in</sub> + ArsB &harr; ArsB<sub>As</sub></span>||The binding and detachment of arsenic to the Exporter ArsB|| <br />
|-<br />
| ||<span class="export">ArsB<sub>As</sub> &rarr; ArsB + As(III)<sub>ex</sub></span>||The release of the bound arsenic by ArsB on the outside of the cell.|| <br />
|-<br />
| ||<span class="export">ArsB &rarr; null</span> ||The degradation of Ars B||<br />
|-<br />
|colspan="3"|''Accumulation''{{infoBox|In the reactions below you can see the production and degradation of all our accumulation proteins. Two things should be noticed: ArsR represses it's own production and that of the GVP clusters and the ars1 operon does not only produce ArsR but also the exporter ArsB}}(mostly based on [[Team:Groningen/Literature#Chen1997|Chen1997]])<br />
|-<br />
| ||As(III)<sub>in</sub> + ArsR &harr; ArsR<sub>As</sub>||The binding and detachment of arsenic to ArsR||<br />
|-<br />
| ||As(III)<sub>in</sub> + MBPArsR &harr; MBPArsR<sub>As</sub>||The binding and detachment of arsenic to MBPArsR || <br />
|-<br />
| ||n<sub>f</sub> As(III)<sub>in</sub> + fMT &harr; fMT<sub>As</sub>||The binding and detachment of arsenic to fMT || <br />
|-<br />
| ||ars1 + 2 ArsR &harr; ArsR<sub>ars1</sub>||the repression of the promotor of the ars1 operon by 2 arsR molecules||<br />
|-<br />
| ||<span class="production">ars2 + 2 ArsR &harr; ArsR<sub>ars2</sub></span>||the repression of the promotor of the ars1 operon by 2 arsR molecules|| <br />
|-<br />
| ||ars1 &rarr; ars1 + ArsR<span class="export"> + ArsB</span> ||The transcription and translation of the ars1 operon to produce ArsR and ArsB||<br />
|-<br />
| ||proR &rarr; proR + ArsR ||The transcription and translation of the proR operon to produce ArsR||<br />
|-<br />
| ||proM &rarr; proM + MBPArsR ||The transcription and translation of the proM operon to produce MBPArsR||<br />
|-<br />
| ||proF &rarr; proF + fMT ||The transcription and translation of the proF operon to produce fMT||<br />
|-<br />
| ||ArsR &rarr; null ||The degradation of ArsR||<br />
|-<br />
| ||MBPArsR &rarr; null ||The degradation of MBPArsR||<br />
|-<br />
| ||fMT &rarr; null ||The degradation of fMT||<br />
|-<br />
|colspan="3"|''Gas vesicles''{{infoBox|These two reactions give the production and degradation rate of the GVP clusters. Keep in mind that ars2 is repressed by the accumulation protein ArsR. This reaction can be found under accumulation part.}}<br />
|-<br />
| ||ars2 &rarr; ars2<span class="production"> + GV</span> ||The transcription and translation of the ars2 operon to produce GVP clusters wich will make the cell float||<br />
|-<br />
| ||<span class="production">GV &rarr; null</span> ||The degradation of GVP||<br />
|-<br />
|colspan="3"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="estimate" style="padding:0;"|GVP Production related.<br />
|}<br />
|}<br />
<br />
Here you can find the time derivatives for each substance we derived. The constants are explained in the next teble. After one has a full understanding of all the constants and derivatives and and reactions. One can begin the process of simplifying the model and thus one can have a look at the quasi steady-state model and the steady-state model. <br />
<br />
{|class="ourtable"<br />
|+ Core substances<br />
!colspan="2"|substance<br />
!Description<br />
!Derivative to time<br />
|-<br />
|colspan="4"|''Extracellular''<br />
|-<br />
| ||As(III)<sub>ex</sub>||As(III) in the solution||(d/dt) As(III)<sub>ex</sub> = <span class="import">- (d/dt) GlpF<sub>As</sub> - k6 GlpF<sub>As</sub></span><span class="export"> + (Vc/Vs) k8 ArsB<sub>As</sub></span><br />
|-<br />
|colspan="4"|''Membrane'' (all naturally occurring, but we plan to bring GlpF to overexpression)<br />
|-<br />
| ||GlpF||concentration w.r.t. the exterior of the cell||(d/dt) GlpF = <span class="import">- (d/dt) GlpF<sub>As</sub></span><br />
|-<br />
| ||GlpF<sub>As</sub>||concentration w.r.t. the exterior of the cell||(d/dt) GlpF<sub>As</sub> = <span class="import">k5<sub>on</sub> As(III)<sub>ex</sub> GlpF - (k5<sub>off</sub>+k6) GlpF<sub>As</sub></span><br />
|-<br />
| ||ArsB||concentration w.r.t. the interior of the cell||(d/dt) ArsB = <span class="export">- (d/dt) ArsB<sub>As</sub> + &beta;4 ars1 - ln(2)/&tau;B ArsB</span><br />
|-<br />
| ||ArsB<sub>As</sub> ||concentration w.r.t. the interior of the cell||(d/dt) ArsB<sub>As</sub> = <span class="export">k7<sub>on</sub> As(III)<sub>in</sub> ArsB - (k7<sub>off</sub>+k8) ArsB<sub>As</sub></span><br />
|-<br />
|colspan="4"|''Intracellular'' (ars2, pro and GV are introduced)<br />
|-<br />
| ||As(III)<sub>in</sub>||concentration of As(III) inside the cell||(d/dt) As(III)<sub>in</sub> = - (d/dt) ArsR<sub>As</sub> - (d/dt) MBPArsR<sub>As</sub> - n<sub>f</sub> (d/dt) fMT<sub>As</sub><span class="export"> - (d/dt) ArsB<sub>As</sub> - k8 ArsB<sub>As</sub></span><span class="import"> + (Vs/Vc) k6 GlpF<sub>As</sub></span><br />
|-<br />
| ||ars1 {{infoBox|ars1 stands for the promotor in front of the operon which contains the information for the production of the accumulation protein ArsR and the exporter ArsB. It is selfregulatory in the sence that it produces it's own repressor in the form of ArsR}} ||concentration of unbound promoters naturally occurring in <i>E. coli</i>||(d/dt) ars1 = - (d/dt) ArsR<sub>ars1</sub><br />
|-<br />
| ||ars2 {{infoBox|ars2 stands for the promotor in front of the operon which contains the information for the production of Gas Vesicles. Unlike ars 1 it is not selfregulatory, but the if everything goes correctly the production of gas vesicles will only start if there arsenic inside the cell}}||concentration of unbound promoters in front of gas vesicle genes||(d/dt) ars2 = <span class="production">- (d/dt) ArsR<sub>ars2</sub></span><br />
|-<br />
| ||proR ||concentration of constitutive promoters in front of arsR|| (d/dt)proR = 0 in our model<br />
|-<br />
| ||proM ||concentration of constitutive promoters in front of mbp-arsR|| (d/dt)proM = 0 in our model<br />
|-<br />
| ||proF ||concentration of constitutive promoters in front of fMT|| (d/dt)proF = 0 in our model<br />
|-<br />
| ||ArsR {{infoBox|ArsR binds to ars to repress production of the genes they regulate, and binds to As(III) to make it less of a problem for the cell.}}||concentration of the accumulation protein ArsR||(d/dt) ArsR = &beta;RN ars1 + &beta;R proR - (ln(2)/&tau;R) ArsR - (d/dt) ArsR<sub>As</sub> - 2 (d/dt) ArsR<sub>ars1</sub><span class="production"> - 2 (d/dt) ArsR<sub>ars2</sub></span> <br />
|-<br />
| ||ArsR<sub>As</sub> || the concentration of ArsR bound to As(III)||(d/dt) ArsR<sub>As</sub> = kR<sub>on</sub> ArsR As(III)<sub>in</sub> - kR<sub>off</sub> ArsR<sub>As</sub><br />
|-<br />
| ||ArsR<sub>ars1</sub> ||the concentration of ArsR bound to ars1||(d/dt) ArsR<sub>ars1</sub> = kA<sub>on</sub> ArsR&sup2; ars1 - kA<sub>off</sub> ArsR<sub>ars1</sub><br />
|-<br />
| ||ArsR<sub>ars2</sub> ||the concentration of ArsR bound to ars2||(d/dt) ArsR<sub>ars2</sub> = <span class="production">kA<sub>on</sub> ArsR&sup2; ars2 - kA<sub>off</sub> ArsR<sub>ars2</sub></span><br />
|-<br />
| ||MBPArsR {{infoBox|A fusion of maltose binding protein and ArsR. It is more stable than the normal ArsR variant, but it is no longer able to act as a repressor for the ars promotor.}}|| a fusion of maltose binding protein and ArsR||(d/dt) MBPArsR = &beta;M proM - (ln(2)/&tau;M) MBPArsR - (d/dt) MBPArsR<sub>As</sub><br />
|-<br />
| ||MBPArsR<sub>As</sub> ||bound to As(III)||(d/dt) MBPArsR<sub>As</sub> = kM<sub>on</sub> MBPArsR As(III)<sub>in</sub> - kM<sub>off</sub> MBPArsR<sub>As</sub><br />
|-<br />
| ||fMT {{infoBox|It is another binding protein. Unlike it's counterpart it capeble of containing up to five As(III) particles or one As(V) particle }} || Arsenic binding metallotein ||(d/dt) fMT = &beta;F proF - (ln(2)/&tau;F) fMT - (d/dt) fMT<sub>As</sub><br />
|-<br />
| ||fMT<sub>As</sub> ||bound to multiple As(III)||fMT<sub>As</sub> = kF<sub>on</sub> fMT As(III)<sub>in</sub><sup>n<sub>f</sub></sup> - kF<sub>off</sub> fMT<sub>As</sub><br />
|-<br />
| ||ArsR<sub>As</sub> ||bound to As(III)<br />
|-<br />
| ||GV ||concentration of gas vesicles||(d/dt) GV = <span class="production">&beta;G ars2 - ln(2)/&tau;G GV</span><br />
|-<br />
|colspan="4"|<br />
{|class="ourtable" style="width:100%"<br />
!colspan="5"|<br />
|- style="text-align:center;"<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="fromPaper" style="padding:0;"|Import related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="experimental" style="padding:0;"|Export related.<br />
|class="estimate" style="padding:0;"|GVP Production related.<br />
|}<br />
|}<br />
<br />
The variables above can be related to each other through the following "reactions" (color coding is continued below to show which parts of the differential equations refer to which groups of reactions):<br />
<br />
<br />
Using the following constants/definitions:<br />
{|class="ourtable"<br />
|-<br />
!Name<br />
!Units<br />
!Description<br />
|-<br />
|kRon, kMon, k5on, etc.<br />
|1/(M&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kAon<br />
|1/(M²&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kFon<br />
|1/(M<sup>n<sub>f</sub></sup>&middot;s)<br />
|Reaction rate constants for reactions to a complex.<br />
|-<br />
|kRoff, kMoff, kFoff, kAoff, k5off, etc.<br />
|1/s<br />
|Reaction rate constants for reactions from a complex.<br />
|-<br />
|k6, k8<br />
|1/s<br />
|Reaction rate constants representing how fast transporters transport their cargo to "the other side".<br />
|-<br />
|&tau;B, &tau;R, &tau;M, &tau;F, &tau;G<br />
|s<br />
|Half-lifes (of ArsB, ArsR, MBPArsR, fMT and GV, respectively). Degradation rate = ln(2)/&tau; {{infoBox|1=If you take just the degradation into account you will have the equation dC/dt = -k*C, which leads to C(t) = C(0) e<sup>-k t</sup>. So if k = ln(2)/&tau; we get C(t) = C(0) e<sup>-ln(2)/&tau; t</sup> = C(0) 2<sup>-t/&tau;</sup>. In other words &tau; is the time it takes for the concentration to half.}}<br />
|-<br />
|&beta;RN, &beta;R, etc.<br />
|1/s<br />
|Production rates.<br />
* &beta;RN = the production rate for ArsR behind the ars1 promoter<br />
* &beta;B = the production rate for ArsB behind the ars1 promoter<br />
* &beta;G = the production rate for GV behind the ars2 promoter<br />
* &beta;R = the production rate for ArsR behind a constitutive promoter<br />
* &beta;M = the production rate for MBPArsR behind a constitutive promoter<br />
* &beta;F = the production rate for fMT behind a constitutive promoter<br />
|-<br />
|Vs<br />
|L<br />
|Volume of solution (excluding cells).<br />
|-<br />
|Vc<br />
|L<br />
|Total volume of cells (in solution) (so Vs+Vc is the total volume).<br />
|}<br />
See [[Team:Groningen/Literature#Chen1997|Chen1997]] for the interplay between ArsR and ArsD (the latter has a role similar to ArsR, but we do not treat it, as it is [[Team:Groningen/BLAST|not present in our system]]).<br />
<br />
==Quasi steady state{{anchor|QuasiSteadyState}}==<br />
First of all, we assume the concentration of transporters is quite low compared to the concentration of the transported substances. After all, if this were not the case the transporters would act more like "storage" proteins than transporters (note that this can be even more rigorously justified if, for example, GlpFT<<K5). This leads to:<br />
<br />
<pre><br />
As(III)exT &asymp; As(III)ex<br />
As(III)inT &asymp; As(III)in + ArsRAs + MBPArsRAs + nf fMTAs<br />
</pre><br />
<br />
Also, we assume the binding and unbinding of molecules to the transporters occurs on a much finer time-scale than any actual changes to the concentrations inside and outside the cell. Similarly, within the cell we assume diffusion processes are very fast and binding/unbinding of substances is quite fast compared to the production of proteins. This leads us to assume that the following ratios between substances are constantly in equilibrium:<br />
<br />
{{frame|1=<br />
<div style="text-align:left;"><br />
We use the following when grouping the ars promoters:<br />
<pre><br />
arsT = ars + ArsRars<br />
ars1 / ars1T = ars2 / ars2T<br />
<br />
ars = ars1 + ars2<br />
ars = ars1 (1 + ars2T / ars1T)<br />
ars1 = ars / (1 + ars2T / ars1T)<br />
ars1 = ars ars1T / arsT<br />
<br />
ars2 = ars ars2T / arsT<br />
</pre><br />
</div><br />
}}<br />
<br />
<pre><br />
As(III)ex : GlpFAs &asymp; As(III)ex : 0<br />
GlpF : GlpFAs<br />
ArsB : ArsBAs<br />
As(III)in : ArsRAs : MBPArsRAs : nf fMTAs : ArsBAs &asymp; As(III)in : ArsRAs : MBPArsRAs : nf fMTAs : 0<br />
ArsR : ArsRAs : 2 ArsRars<br />
ars : ArsRars<br />
</pre><br />
<br />
To determine what the unknown ratios are we can set the following derivatives to zero (these are the derivatives of the complexes corresponding to the four overlapping regions in the diagram):<br />
<br />
<pre><br />
0 = (d/dt) GlpFAs = k5on As(III)ex GlpF - (k5off+k6) GlpFAs<br />
0 = (d/dt) ArsBAs = k7on As(III)in ArsB - (k7off+k8) ArsBAs<br />
0 = (d/dt) ArsRars = kAon ArsR² ars - kAoff ArsRars<br />
0 = (d/dt) ArsRAs = kRon ArsR As(III)in - kRoff ArsRAs<br />
0 = (d/dt) MBPArsRAs = kMon MBPArsR As(III)in - kMoff MBPArsRAs<br />
0 = (d/dt) fMTAs = kFon fMT As(III)in^nf - kFoff fMTAs<br />
</pre><br />
<br />
The first two derivates let us determine the ratios between bound and unbound transporters:<br />
<br />
<pre><br />
0 = (d/dt) GlpFAs = k5on As(III)ex GlpF - (k5off+k6) GlpFAs<br />
<br />
k5on As(III)ex GlpF = (k5off+k6) GlpFAs<br />
GlpF = (k5off+k6)/k5on GlpFAs / As(III)ex<br />
GlpF = K5 GlpFAs / As(III)ex<br />
<br />
GlpF : GlpFAs<br />
K5 GlpFAs / As(III)ex : GlpFAs<br />
K5 : As(III)ex<br />
<br />
0 = (d/dt) ArsBAs = k7on As(III)in ArsB - (k7off+k8) ArsBAs<br />
<br />
k7on As(III)in ArsB = (k7off+k8) ArsBAs<br />
ArsB = (k7off+k8)/k7on ArsBAs / As(III)in<br />
ArsB = K7 ArsBAs / As(III)in<br />
<br />
ArsB : ArsBAs<br />
K7 ArsBAs / As(III)in : ArsBAs<br />
K7 : As(III)in<br />
</pre><br />
<br />
The next two differential equations can be used to determine the relative abundances of ArsR and ArsRAs, and ars and ArsRars:<br />
<br />
<pre><br />
0 = (d/dt) ArsRAs = kRon ArsR As(III)in - kRoff ArsRAs<br />
<br />
kRon ArsR As(III)in = kRoff ArsRAs<br />
ArsRAs = kRon/kRoff ArsR As(III)in<br />
ArsRAs = ArsR As(III)in / KRd<br />
<br />
ArsR : ArsRAs<br />
ArsR : ArsR As(III)in / KRd<br />
KRd : As(III)in<br />
<br />
0 = (d/dt) ArsRars = kAon ArsR² ars - kAoff ArsRars<br />
<br />
kAon ArsR² ars = kAoff ArsRars<br />
ArsRars = kAon/kAoff ArsR² ars<br />
ArsRars = ArsR² ars / KAd²<br />
<br />
ArsR : 2 ArsRars<br />
ArsR : 2 ArsR² ars / KAd²<br />
KAd² : 2 ArsR ars<br />
<br />
ars : ArsRars<br />
ars : ArsR² ars / KAd²<br />
KAd² : ArsR²<br />
</pre><br />
<br />
For MBPArsR and fMT we find:<br />
<br />
<pre><br />
0 = (d/dt) MBPArsRAs = kMon MBPArsR As(III)in - kMoff MBPArsRAs<br />
<br />
MBPArsR : MBPArsRAs = KMd : As(III)in<br />
<br />
0 = (d/dt) fMTAs = kFon fMT As(III)in^nf - kFoff fMTAs<br />
<br />
fMT : fMTAs = KFd^nf : As(III)in^nf<br />
</pre><br />
<br />
And finally the relative abundances of arsenic:<br />
<br />
<pre><br />
ArsRAs = ArsR As(III)in / KRd<br />
<br />
As(III)in : ArsRAs : MBPArsRAs : n fMTAs<br />
As(III)in : ArsR As(III)in / KRd : MBPArsRT As(III)in / (KMd+As(III)in) : n fMTT As(III)in^nf / (KFd^nf+As(III)in^nf)<br />
1 : ArsR / KRd : MBPArsRT / (KMd+As(III)in) : n fMTT As(III)in^(nf-1) / (KFd^nf+As(III)in^nf)<br />
</pre><br />
<br />
Summarizing:<br />
<br />
<pre><br />
GlpF : GlpFAs = K5 : As(III)ex<br />
ArsB : ArsBAs = K7 : As(III)in<br />
As(III)in : ArsRAs : MBPArsRAs : n fMTAs &asymp; 1 : ArsR / KRd : MBPArsRT / (KMd+As(III)in) : n fMTT As(III)in^(nf-1) / (KFd^nf+As(III)in^nf)<br />
ars : ArsRars = KAd² : ArsR²<br />
ArsR : ArsRAs : 2 ArsRars &asymp; 1 : As(III)in / KRd : 2 ArsR ars / KAd²<br />
MBPArsR : MBPArsRAs = KMd : As(III)in<br />
fMT : fMTAs = KFd^nf : As(III)in^nf<br />
</pre><br />
<br />
Now we can look at the differential equations for the totals of ArsB (so ArsBT=ArsB+ArsBAs), ArsR, As(III)in and As(III)ex (GlpFT and arsT are assumed to be constant):<br />
<br />
<pre><br />
(d/dt) As(III)exT = (d/dt) As(III)ex + (d/dt) GlpFAs<br />
= - (d/dt) GlpFAs - k6 GlpFAs + (Vc/Vs) k8 ArsBAs + (d/dt) GlpFAs<br />
= (Vc/Vs) k8 ArsBAs - k6 GlpFAs<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 GlpFAs / GlpFT<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 As(III)ex / (K5+As(III)ex)<br />
= (Vc/Vs) k8 ArsBAs - (Vc/Vs) v5 As(III)exT / (K5+As(III)exT)<br />
(d/dt) ArsBT = (d/dt) ArsB + (d/dt) ArsBAs<br />
= - (d/dt) ArsBAs + βB ars1 - ln(2)/τB ArsB + (d/dt) ArsBAs<br />
= βB ars1 - ln(2)/τB ArsB<br />
(d/dt) As(III)inT = -(Vs/Vc) (d/dt) As(III)exT<br />
= v5 As(III)exT / (K5+As(III)exT) - k8 ArsBT As(III)in / (K7+As(III)in)<br />
(d/dt) ArsRT = (d/dt) ArsR + (d/dt) ArsRAs + 2 (d/dt) ArsRars<br />
= βRN ars1 + βR proR - (ln(2)/τR) ArsR - (d/dt) ArsRAs - 2 (d/dt) ArsRars + (d/dt) ArsRAs + 2 (d/dt) ArsRars<br />
= βRN ars1 + βR proR - (ln(2)/τR) ArsR<br />
(d/dt) MBPArsRT = (d/dt) MBPArsR + (d/dt) MBPArsRAs<br />
= βM proM - (ln(2)/τM) MBPArsR<br />
(d/dt) fMTT = (d/dt) fMT + (d/dt) fMTAs<br />
= βF proF - (ln(2)/τF) fMT<br />
</pre><br />
<br />
==Steady state==<br />
By looking at the steady state of the system we can say something about its long-term behaviour. This also makes it easier to analyze relations between variables. To derive the steady state solution we take the quasi steady state solution and simplify it further by setting additional derivatives to zero:<br />
<br />
<pre><br />
0 = (d/dt) ArsBT = βB ars1 - ln(2)/τB ArsB<br />
0 = (d/dt) As(III)inT = v5 As(III)exT / (K5+As(III)exT) - k8 ArsBAs<br />
0 = (d/dt) ArsRT = βRN ars1 + βR pro - (ln(2)/τR) ArsR<br />
0 = (d/dt) MBPArsRT = βM proM - (ln(2)/τM) MBPArsR<br />
0 = (d/dt) fMTT = βF proF - (ln(2)/τF) fMT<br />
0 = (d/dt) GV = βG ars2 - ln(2)/τG GV<br />
</pre><br />
<br />
This directly leads to:<br />
<br />
<pre><br />
0 = βB ars1 - ln(2)/τB ArsB<br />
ArsB = βB (τB/ln(2)) ars1<br />
ArsB = βB (τB/ln(2)) ars1T KAd²/(KAd²+ArsR²)<br />
<br />
0 = βM proM - (ln(2)/τM) MBPArsR<br />
MBPArsR = βM (τM/ln(2)) proM<br />
<br />
0 = βF proF - (ln(2)/τF) fMT<br />
fMT = βF (τF/ln(2)) proF<br />
<br />
0 = βG ars2 - ln(2)/τG GV<br />
GV = βG (τB/ln(2)) ars2<br />
GV = βG (τB/ln(2)) ars2T KAd²/(KAd²+ArsR²)<br />
</pre><br />
<br />
For the intra- and extracellular concentrations we can find the following equation, giving a maximum for As(III)in of <code>K7 v5/(k8 ArsB)</code> (as As(III)exT cannot be negative){{infoBox|Conveniently the function <code>x/(c-x)</code> is non-negative and non-decreasing for x&isin;[0,c&rang;.}}:<br />
<br />
<pre><br />
0 = v5 As(III)exT / (K5+As(III)exT) - k8 ArsBAs<br />
0 = v5 As(III)exT / (K5+As(III)exT) - k8 ArsB As(III)in / K7<br />
0 = v5 As(III)exT - k8 ArsB As(III)in / K7 (K5+As(III)exT)<br />
0 = v5 As(III)exT - k8 ArsB As(III)in As(III)exT / K7 - k8 ArsB As(III)in K5 / K7<br />
0 = As(III)exT (v5 - k8 ArsB As(III)in / K7) - k8 ArsB As(III)in K5 / K7<br />
As(III)exT = k8 ArsB As(III)in K5 / (v5 K7 - k8 ArsB As(III)in)<br />
As(III)exT = K5 As(III)in / (K7 v5/(k8 ArsB) - As(III)in)<br />
</pre><br />
<br />
As we can safely assume arsenic neither disappears into nothingness nor appears from nothingness, we can use this to derive (As(III)T is the total amount of arsenic):<br />
<br />
<pre><br />
As(III)inT = As(III)in (1 + ArsR/KRd + MBPArsR/KMd + fMT As(III)in^(nf-1)/KFd^nf)<br />
<br />
As(III)T = Vs As(III)exT + Vc As(III)inT<br />
0 = Vs As(III)exT + Vc As(III)inT - As(III)T<br />
0 = Vs K5 As(III)in / (K7 v5/(k8 ArsB) - As(III)in) + Vc As(III)in (1 + ArsR/KRd + MBPArsR/KMd + fMT As(III)in^(nf-1)/KFd^nf) - As(III)T<br />
</pre><br />
<br />
As the function on the right-hand side is non-decreasing for <code>As(III)in&isin;[0,K7 v5/(k8 ArsB)&rang;</code> it at most has one zero on this interval (and it has one, as it starts at a negative value and gets arbitrarily large as As(III)in approaches the end of its range). So this zero can safely be found using any number of numerical methods.<br />
<br />
Finally, for ArsR we can find the following third-order equation:<br />
<br />
<pre><br />
0 = βRN ars1 + βR pro - (ln(2)/τR) ArsR<br />
0 = βRN ars1T KAd²/(KAd²+ArsR²) + βR pro - (ln(2)/τR) ArsR<br />
0 = βRN ars1T KAd² + βR pro (KAd²+ArsR²) - (ln(2)/τR) ArsR (KAd²+ArsR²)<br />
0 = βRN ars1T KAd² + βR pro KAd² + βR pro ArsR² - (ln(2)/τR) ArsR KAd² - (ln(2)/τR) ArsR³<br />
0 = (βRN ars1T + βR pro) KAd² - (ln(2)/τR) KAd² ArsR + βR pro ArsR² - (ln(2)/τR) ArsR³<br />
0 = (βRN ars1T + βR pro) (τR/ln(2)) KAd² - KAd² ArsR + βR (τR/ln(2)) pro ArsR² - ArsR³<br />
</pre><br />
<br />
According to Mathematica's solution of <code>Reduce[eq && KAd > 0 && arsT >= 0 && pro >= 0 && &beta;1 > 0 && &beta;3 > 0 && &tau;R > 0, ArsR, Reals]</code> (where eq is the equation shown above) there is only one real solution (examining the discriminant of eq confirms this), so we can solve the equation safely using Newton's (or Halley's) method.<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-21T17:41:35Z<p>Jaspervdg: Emphasized explorability/interactiveness.</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
<br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line. For one thing, this makes it easier to '''explore''' the model, up to the point that even non-modellers are able to explore the model.]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible '''interactively''' available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*'''Analysis''' of results. Using data from uptake experiments, promoter measurements and TEM pictures we can [[Team:Groningen/Modelling/Characterization|estimate further constants]] and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/DownloadsTeam:Groningen/Modelling/Downloads2009-10-21T16:42:40Z<p>Jaspervdg: Added more "downloads".</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<br />
==Downloads of Modelling data/code==<br />
<br />
*[http://code.google.com/p/igemgroningen/source/browse/trunk/buoyant/Raw%20Data/ All our raw data from papers] is available in SVN in a [http://code.google.com/p/igemgroningen/ Google Code project].<br />
*[http://igemgroningen.googlecode.com/svn/trunk/buoyant/Models/Heavy%20Metal%20Scavenger.xml An SBML version of our model.] (Not a complete match, because our model apparently needs a slightly too complex DAE.)<br />
*[http://code.google.com/p/igemgroningen/source/browse/trunk/# A patch to Inkscape's measure.inx/.py to be able to measure in nanometers.]<br />
*[http://igemgroningen.googlecode.com/svn/trunk/buoyant/Models/ Miscellaneous other stuff regarding our model.] (Early versions, Mathematica notebooks for computing certain parameters and so on.)<br />
<br />
==Downloads of Biological raw data==<br />
<br />
*Promoter test of J61002-ArsR promoter, under induction of 100uM NaAsO2.<br />
For the raw data click [http://spreadsheets.google.com/ccc?key=0AiVK6TJREwindDlQOEJCdUpISTU4M2cweE5PT3p3MVE&hl=en here] (GoogleDocs spreadsheet)<br />
*Arsenite uptake assay, first data set<br />
For the raw data click [http://spreadsheets.google.com/ccc?key=0AiVK6TJREwindE9OSjFpZzdGU2 here] (GoogleDocs spreadsheet)<br>For the zip file click [https://2009.igem.org/Image:Berekeningen.zip here]<br />
*Arsenite uptake assay, second data set<br />
For the raw data click [http://spreadsheets.google.com/ccc?key=0AiVK6TJREwindFdsLURvM1RYeD here] (GoogleDocs spreadsheet)<br />
*[http://igemgroningen.googlecode.com/svn/trunk/buoyant/Raw%20Data/Promoters/Fluorescence+OD.ods Promoter tests], using various constitutive and metal sensitive promoters.<br />
*[http://code.google.com/p/igemgroningen/source/browse/trunk/buoyant/Photos/ Photos] of our gas vesicles in test tubes <br />
and TEM pictures of our gas vesicles.<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/FutureTeam:Groningen/Future2009-10-21T15:59:44Z<p>Jaspervdg: /* Modeling */</p>
<hr />
<div>{{Team:Groningen/Header}}<br />
<br />
==Labwork==<br />
A large amount of progress has been obtained in the research line of arsenic accumulation, however several other interesting metals (e.g. copper, zinc) had to be abandoned which might provide more interesting applications. For this to occur, the constructs that were abandoned along the way (e.g. SmtA, HmtA) should be finished and characterized. But also for the existing arsenic devices more characterizing can be performed, ''e''.''g''. more detailed characterization of the uptake capacity of the transporter (using higher metal concentrations in death assays). In this project fermentation was used to supply the culture with medium saturated with air in higher amount than can be attained in shake cultures. This was to ensure a higher amount of gas to be available to enter the gas vesicles, for a future project it might be of interest to sparge nitrogen into broth to obtain anaerobic conditions. Anaerobic condition will influence the oxidation state of arsenic, probably having an effect on the uptake efficiency. A nice addition to the gas vesicle cluster would be the removal of the 10 time repeat, which was attempted in our project without success.<br />
<br />
==Modelling==<br />
===JavaScript===<br />
To make it possible to have interactive graphs and calculators on our Wiki, based on our model, we have implemented our entire model in JavaScript. This included developing our own ODE solver (among other things). We feel that having our model accessible on the Wiki has many advantages and it would be very useful to develop a library to handle ODE (and perhaps stochastic) models using JavaScript. Such a library could support:<br />
<br />
*Graphs that work well in pretty much any browser, including a legend (and possibly 3D functionality). Linked graphs would be a plus.<br />
*Reading from various sources, like an HTML table, Google Docs, csv files, etc.<br />
*Integration of ODE models defined by a function that returns the gradient based on the current values.<br />
*Equilibrium computations. Preferably based on the same function used for integrating ODE models.<br />
*Fitting a model to experimental data.<br />
<br />
==="Dumbed-down" user interface===<br />
Normally a model is used only "internally" to, for example, predict results and/or analyse them. We have made our model a more integral part of our project by making (parts of) it available right next to our theoretical texts and results, but this could be taken much further. It would be interesting to make an interface to our model that is suited for someone without an extensive background in molecular biology and/or modelling, with easy-to-use sliders and clear visual representations.<br />
<br />
A "dumbed-down" user interface would likely not be aimed at doing any of the normal modelling tasks, but would be more of an educational tool, allowing an interactive exploration of a project. This could be immensely useful in giving people insight into an iGEM project like our own.<br />
<br />
===Parameters===<br />
Our determination of the import rate of arsenic is reasonably accurate, but many more parameters of which we are much less certain remain. On [[Team:Groningen/Modelling/Characterization|our characterization page]] several different ways to find these parameters are discussed.<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Notebook/19_October_2009Team:Groningen/Notebook/19 October 20092009-10-21T14:52:38Z<p>Jaspervdg: /* Dry */</p>
<hr />
<div>{{Team:Groningen/Notebook/Day/Header}}<br />
<br />
==Wet==<br />
<br />
===GVP Cluster===<br />
<br />
===Transporters===<br />
<br />
===Metal Accumulation===<br />
<br />
===Vectors===<br />
<br />
==Dry==<br />
After having run our fitter on the data (time and concentration for wild type and time for ars+RFP) from the first uptake experiment over the weekend we determined a reasonable fit for just the wild type data, but incorporating the data from ars+RFP proved harder (not necessarily the best possible, but the best we got, without very extreme parameters):<br />
<br />
{|<br />
!Parameter<br />
!Just wild type<br />
!Including ars+RFP<br />
|-<br />
|<br />
|v5/K5 fixed<br />
|v5 and K5 fixed<br />
|-<br />
|v5<br />
|0.000018661<br />
|0.000018661<br />
|-<br />
|K5<br />
|0.00016234<br />
|0.00016234<br />
|-<br />
|k8/K7<br />
|4.2451·10<sup>5</sup><br />
|4.6480·10<sup>5</sup><br />
|-<br />
|k8<br />
|19.539<br />
|8.8724<br />
|-<br />
|K7<br />
|0.000046027<br />
|0.000019089<br />
|-<br />
|tauBbetaB<br />
|33.303<br />
|42.287<br />
|-<br />
|tauB<br />
|1.9893<br />
|0.96071<br />
|-<br />
|betaB<br />
|16.741<br />
|44.016<br />
|-<br />
|tauR<br />
|585.62<br />
|147.57<br />
|-<br />
|betaRN<br />
|12.661<br />
|22.376<br />
|-<br />
|ars2T<br />
| <br />
|90.763<br />
|-<br />
|E<br />
|0.11534<br />
|0.20179<br />
|}<br />
<br />
{{Team:Groningen/Notebook/Day/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Notebook/19_October_2009Team:Groningen/Notebook/19 October 20092009-10-21T14:49:32Z<p>Jaspervdg: Logged our fitting results.</p>
<hr />
<div>{{Team:Groningen/Notebook/Day/Header}}<br />
<br />
==Wet==<br />
<br />
===GVP Cluster===<br />
<br />
===Transporters===<br />
<br />
===Metal Accumulation===<br />
<br />
===Vectors===<br />
<br />
==Dry==<br />
After having run our fitter on the data (time and concentration for wild type and time for ars+RFP) from the first uptake experiment over the weekend we determined a reasonable fit for just the wild type data, but incorporating the data from ars+RFP proved harder (not necessarily the best possible, but the best we got, without very extreme parameters):<br />
<br />
{|<br />
!Parameter<br />
!Just wild type<br />
!Including ars+RFP<br />
|-<br />
|v5<br />
|0.000018661<br />
|0.000018661<br />
|-<br />
|K5<br />
|0.00016234<br />
|0.00016234<br />
|-<br />
|k8/K7<br />
|4.2451·10<sup>5</sup><br />
|4.6480·10<sup>5</sup><br />
|-<br />
|k8<br />
|19.539<br />
|8.8724<br />
|-<br />
|K7<br />
|0.000046027<br />
|0.000019089<br />
|-<br />
|tauBbetaB<br />
|33.303<br />
|42.287<br />
|-<br />
|tauB<br />
|1.9893<br />
|0.96071<br />
|-<br />
|betaB<br />
|16.741<br />
|44.016<br />
|-<br />
|tauR<br />
|585.62<br />
|147.57<br />
|-<br />
|betaRN<br />
|12.661<br />
|22.376<br />
|-<br />
|ars2T<br />
| <br />
|90.763<br />
|-<br />
|E<br />
|0.11534<br />
|0.20179<br />
|}<br />
<br />
{{Team:Groningen/Notebook/Day/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ProjectTeam:Groningen/Project2009-10-21T13:53:19Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Project/Header}}<br />
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<h1>Heavy metal scavengers with a vertical gas drive</h1><br />
'''Introduction'''<br />
Human health and the environment are endangered by heavy metal pollution in water and sediment. To improve purification strategies a metal selective microbacterial cleaning system was designed. The system comprises uptake, sequestering and metal sensitive buoyancy. <br />
All subsystems are interchangeable, which makes it suitable for almost any metal cleaning assay. For this project the modular system was focused on arsenic accumulation, using ''Escherichia coli'' as a chassis organism. <br />
Arsenite and arsenate are imported by GlpF, a aquaglycerol porin from ''E. coli''. Intracellular As(III) and As(V) are sequestered by fMT or ArsR. These proteins were used as the accumulation modules. Since ''E. coli'' does not have a buoyancy system, the polycistronic gas vesicle protein gene cluster from ''Bacillus megaterium'', GVP, was used. The arsenic promoter from ''E. coli'', pArsR, is regulated by the negative transcriptional regulator ArsR. GVP, under regulation of pArsR, was used as the metal sensitive buoyancy module.<br />
<br><br><br><br />
</div><br />
|style="vertical-align:top;width:583px;"|<br />
{{imageMap|imap|/wiki/images/8/89/Arsenic_Filtering_System.png|610|410|<br />
{{imageMapLink|arsenic|35|0|149|77|/wiki/images/2/2d/Arsenic_Filtering_System_-_Arsenic.png}}<br />
{{imageMapLink|transport|51|55|137|120|/wiki/images/4/44/Arsenic_Filtering_System_-_Transport.png}}<br />
{{imageMapLink|accumulation|183|143|153|77|/wiki/images/8/84/Arsenic_Filtering_System_-_Accumulation.png}}<br />
{{imageMapLink|gas|401|86|137|106|/wiki/images/7/72/Arsenic_Filtering_System_-_Gas_Vesicles.png}}<br />
{{imageMapLink|promoter|114|295|168|63|/wiki/images/5/5c/Arsenic_Filtering_System_-_Promoter.png}}<br />
}}<div style="display:block;position:relative;float:right;"><br />
<div id="imap" style="position:absolute;right:0px;"><div style="position:absolute;bottom:31px;right:72px;">{{linkedImage|Next.JPG|Team:Groningen/Project/Transport}}</div><br />
<html><ul><br />
<li id="arsenic"></html>It all starts with [[Team:Groningen/Application|arsenic]] in solution.<html></li><br />
<li id="transport"></html>[[Team:Groningen/Project/Transport|Metal transport]]<html></li><br />
<li id="accumulation"></html>[[Team:Groningen/Project/Accumulation|Metal accumulation]]<html></li><br />
<li id="gas"></html>[[Team:Groningen/Project/Vesicle|Gas Vesicle]]<html></li><br />
<li id="promoter"></html>[[Team:Groningen/Project/Promoters|Metal sensitive promoters]]<html></li><br />
</ul></html><br />
</div></div><br />
|}<br />
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'''Results'''<br />
All modules were cloned according to the BioBrick<sup>TM</sup> Standard Assembly (RFC 10). The synthetic gene GlpF , was successfully cloned into a synthetic operon, with fMT. The GVP cluster, with a ten times repeat sequence, was successfully cloned downstream of the pArsR promoter. These two subsystems were transformed in ''E. coli'' to complete the system.<br />
The system and its subparts were tested using several assays. Accumulation was tested by an uptake assay, however, since no reproducible results were obtained, the functionality of the accumulation module could not be determined from these data. Arsenic uptake was examined using a metal sensitivity assay. The ''E. coli'' strain overexpressing GlpF showed a decreased final cell density upon induction with As(III), suggesting functional expression of the transporter. The metal sensitive promoter pArsR was tested using a fluorescence assay. This showed a 2.3 fold increased activity upon induction with 100 µM NaAsO2. <br />
Buoyancy was tested by a sedimentation assay. Enhanced buoyancy was shown for the buoyancy module and the complete system, though no difference of the buoyancy phenotype could be observed upon addition of the accumulation module. Cells cultivated in aerobic conditions showed improved buoyancy compared to cells cultivated in semi-aerobic conditions.<br />
An interactive computer model was made for the whole system, with which the modules were further characterized. With the model, import rates of As(III) at different initial extracellular arsenic concentrations could be determined. Also the influence of different parameters on the accumulation factor, the ratio between bound and unbound arsenic, was calculated. The model also allowed qualitative determination of the regulation of pArsR by various expression levels of ArsR. Furthermore, the volume fraction gas vesicles in the cells needed for buoyancy, for several sizes of the gas vesicles, was computed.<br />
<br />
'''Conclusion'''<br />
The metal selective microbacterial cleaning system for arsenic was shown to be buoyant and the buoyancy module and uptake module were shown to work individually. For a better determination of the system an accumulation assay need to be redone. It was shown here that the system has potential as a cleaning system for arsenic. <br />
As mentioned earlier this modular system can also be implemented in cleaning of other substances. Literature research showed possible modules for copper, zinc, mercury and even gold. So not only cleaning water and sludge but also mining rare metals could be functionalized using this system.<br />
<br><br><br><br />
</div><br />
<br />
<br />
<br />
==Periodic table==<br />
<br />
In the periodic table below you can see for which elements we have identified a transporter, an accumulating protein and/or promotor. {{todo}} Make list more complete and add links to parts.<br />
<br />
<div style="clear:right;"></div><br />
{{periodic_table<br />
|AsInfo=<br />
Transporter: GlpF<br/><br />
Accumulator: ArsR<br/><br />
|SbInfo=<br />
Transporter: GlpF<br/><br />
|CuInfo=<br />
Transporter: {{part|BBa_K190018|HmtA}}<br/><br />
Accumulator: SmtA<br/><br />
|ZnInfo=<br />
Transporter: {{part|BBa_K190018|HmtA}}<br/><br />
Accumulator: SmtA<br/><br />
|HgInfo=<br />
Transporter: MerT<br/><br />
Accumulator: SmtA<br/><br />
|CdInfo=<br />
Accumulator: SmtA<br/><br />
}}<br />
<br />
<br />
<br />
==Basic Cloning Strategy:==<br />
<br />
We clone the organisms using the following strategy:<br />
<br />
# Transform ''E. coli'' TOP10 (genotype DH 10B) with gvp (BBa_I750016), a metal ion transporter (HmtA and GlpF) and accumulation proteins.<br />
# PCR the restriction sites out and add BioBrick pre- and suffix --> Use [http://openwetware.org/wiki/The_BioBricks_Foundation:BBFRFC10 BBFRCF10].<br />
##Primers should be ordered for the different genes.<br />
## Add a RBS (BBa_B0034)in the primer for the BioBrick prefix.<br />
## Add a terminator (BBa_B0014) via cloning. <br />
## For gvp the RBS is included in the construct, and biobrick suffix is included in the construct. The prefix is missing because of the ''Eco''RI site in the middle of the plasmid!! This may give problems!!<br />
# PCR restriction sites out. '''!!Both PCR reactions for pre/suffix and restriction sites can possibly be done in 3 PCR reactions --> Ask Frans or J. Kok!!'''<br />
# Test expression / phenotype '''of separate proteins''' (if possible in the vectors they are supplied in). <br />
# Put both systems (gvp and metal import) on a high and low copy number (supplied by "vector group"). This is needed to prevent plasmid / expression incompatibility when both systems are used in one strain. <br />
## The metal transporter and accumulation protein should be cloned behind each other. If possible on a synthetic operon.<br />
## Clone the different systems for Cu, Zn, As, (Hg) in [http://www.partsregistry.org/Assembly:Rolling_assembly parallel]. <br />
# ''(If needed and not already supplied by "vector group")'' [http://www.partsregistry.org/Assembly:Rolling_assembly In parallel clone] metal sensitive promoters in front of a fluorescent protein (GFP) and in front of the gvp cluster.<br />
# ''(If needed and not already supplied by "vector group")'' [http://www.partsregistry.org/Assembly:Rolling_assembly In parallel clone] different promoters in front of the two systems.<br />
## Inducible like Para or Plac<br />
## Constitutive with expected high and low expression yield<br />
## Metal sentitive promoter (only for gvp system)<br />
# Then try to get both systems in one E. coli strain, test different possibilities with the high + low copy nr vectors<br />
<br />
==Teams with similar projects==<br />
<br />
:→ [https://2009.igem.org/Team:UQ-Australia UQ Australia]<br />
<br />
Water contamination is a key environmental issue for many countries around the world, both developed and developing. In Queensland, Australia we have a particular problem with Mercury (Hg2+) contamination of water supplies around the major mining town of Mt Isa. After searching through the iGEM projects from previous years, the arsenic detection system inspired us. As the UQ 09' team we wish to take this idea one step further and completely remove Mercury from water systems.<br />
<br />
To do this we will be utilizing a strain of ''Escherichia coli'', and the already established mercury uptake, reduction and efflux system and making a few modifications. One of our aims is to couple the detection of Mercury to the expression of a native bacterial protein, Antigen 43 (AG43). This protein, when expressed, causes the bacteria to stick to one another. As the bacteria aggregate in clumps, they will fall to the bottom of the sample. Our idea is for the bacteria to take up the mercury, activating Ag43 expression, resulting in aggregation and the Mercury-filled bacteria will fall to the bottom leaving clean water.<br />
<br />
There are a number of parts that we hope to add to the registry. The first is Ag43 as a protein coding sequence and the MerR promoter sequence. We will also add the completed mercury uptake and aggregation system as an operon.<br />
<br />
:→ [https://2009.igem.org/Team:Newcastle Newcastle]<br />
<br />
The aim of our project is to genetically engineer ''Bacillus subtilis'' to be able to detect and sense cadmium which has been taken up from the soil environment and sequester them into a metallothionein. This metallothionein will then become incorporated into a Bacillus spore; the resilience of which means that the cadmium ions can become isolated from the environment (and made bio-unavailable) for many years.<br />
<br />
This project involves a number of steps, each of which can be considered as sub projects:<br />
# Metal intake<br />
# Metal sensing<br />
# Tuning of ''Bacillus subtilis'' normal stochastic switch<br />
# Metal sequestration by metallothionein<br />
# Second stochastic switch<br />
# Synthesizing a Promoter Library for ''Bacillus subtilis''<br />
<br />
<br />
==For our team==<br />
{| class='ourtable'<br />
|+'''Missing / available information'''<br />
!Metal<br />
!Transporter<br />
!Inducible promoter<br />
!Regulator<br />
!Accumulation protein<br />
|-<br />
|Arsenic<br />
|GlpF (organism?) - ordered<br />
|style="color:orange;"|Promoter region of ?? gene, responding on ArsR<br />
|ArsR (''E. coli'')- ordered<br />
|ArsR <br />
|-<br />
|Copper<br />
|HmtA (''Pseudomonas'' sp.)- available<br />
|style="color:red;"|None found in ''E. coli''<br />
|style="color:red;"|Idem<br />
|style="color:red;"|??<br />
|-<br />
|Zinc<br />
|HmtA (''Pseudomonas'' sp.)- available<br />
|style="color:red;"|??<br />
|style="color:red;"|??<br />
|style="color:red;"|??<br />
|-<br />
|Mercury<br />
|MerT (''E. coli'' and other sp)- PCR?<br />
|style="color:orange;"|Should be available in ''E. coli'' - PCR?<br />
|style="color:red;"|Idem<br />
|style="color:red;"|Idem<br />
|}<br />
<br />
<br />
<br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-20T19:46:08Z<p>Jaspervdg: More explanation.</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<br />
We have four kinds of parts we would like to characterize (RPS stands for Relative Promoter Strength):<br />
<br />
{|class="ourtable"<br />
!style="width:25%"|Importers<br />
!style="width:25%"|Accumulators<br />
!style="width:25%"|Sensors<br />
!style="width:25%"|GVP cluster<br />
|-style="text-align:center"<br />
|RPS &rarr; &Delta;v<sub>max</sub><br />
|RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|metal(t) &rarr; RPS(t)<br />
|RPS &rarr; GV<br />
|-<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
|<br />
For both MBPArsR and fMT we assume the amount of bound As(III) for a given relative promoter strength S obeys (for MBPArsR n=1):<br />
<pre><br />
Asbound(As(III)in)<br />
= S Bmax As(III)in^n<br />
/ (K^n + As(III)in^n)<br />
</pre><br />
The constants B<sub>max</sub>, K and n can be determined from uptake experiments comparing E. coli with and without fMT expression. Of course this can be done in general by fitting our model to experimental data, if enough data is provided the fit will be tight enough to allow this. However, even without fitting the full model it should be possible to make a fair estimation from equilibrium measurements.{{infoBox|If the total cell volume is much smaller than the volume of the solution it is reasonable to assume a constant import rate. Also, regardless of whether they feature fMT or not, in equilibrium the amount of ArsR is the same, as is the amount of ArsB, leading to the same amount of unbound arsenic being present. This means that any difference in uptake of arsenic is completely due to arsenic being bound to fMT or MBPArsR. By measuring the amount of arsenic in equilibrium in wild-type cells as well as in cells expressing fMT/MBPArsR for several different (inital) concentrations of As(III), at one or more (known) levels of expression, it is possible to determine the constants Bmax, K and n.}}<br />
|<br />
The ars promoter is part of a feedback loop, so it is not a simple matter of defining the (instantaneous) promoter strength. Instead we suggest using the relevant equations from [[Team:Groningen/Modelling/Arsenic|our model]]. The necessary parameters can be determined by fitting uptake measurement data to our model. Specifically, if the RPS is measured without arsenic present and with enough arsenic present to keep the promoter fully active during the experiment we can determine <code>&beta;RN &tau;R</code> as follows (under the assumption that the RPS is linearly dependent on arsT/ars and using the fact that without any arsenic present the cells will be in equilibrium):<br />
<pre><br />
S(max) / S(0) = ars(max) / ars(0)<br />
S(max) / S(0) = arsT / ars(0)<br />
S(max) / S(0) = 1 + ArsR(0)²/KAd²<br />
ArsR(0) = KAd &radic;(S(max)/S(0) - 1)<br />
<br />
0 = &beta;RN ars1(0) - (ln(2)/&tau;R) ArsR(0)<br />
0 = &beta;RN ars1T S(0)/S(max)<br />
- (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN ars1T S(0)/S(max)<br />
= (ln(2)/&tau;R) KAd &radic;(S(max)/S(0) - 1)<br />
&beta;RN &tau;R = (ln(2)/ars1T) KAd<br />
(S(max)/S(0)) &radic;(S(max)/S(0) - 1)<br />
</pre><br />
|RPS &rarr; GV<br />
The amount of gas vesicles can be expressed in terms of buoyant density, as volume fraction, using the total mass of the vesicles, etc. No matter how it is expressed, we assume a simple linear dependency between the RPS and the amount of gas vesicles. By taking (T)EM pictures of slices the amount of gas vesicles formed under influence of different RPSes can be determined and a straightforward fit made.<br />
|}<br />
<br />
==Uptake measurements==<br />
To fit our model to experimental data from different uptake experiments and/or papers we have implemented an optimization procedure that allows for experiments with different genotypes and circumstances by letting constants be overridden per experiment. It aims to optimize the sum of the RMS errors for each experiment using Simulated Annealing. By clicking the button "Fit" the optimization is started and its progress can be followed by looking at the table of constants and the graphs shown below the table (which are updated in real-time as the best solution is improved).<br />
<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
To efficiently look at both time and concentration dependent processes we took samples as in the table on the right.<br />
Below we list all results, which have been used for fitting all necessary parameters.<br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
<!--|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|--><br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:Infinity,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promotors.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:Infinity,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promotors.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5','v5',*/'k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {//v5: function(v){return v.v5;},<br />
//K5: function(v){return v.v5/v.v5_K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
//cSol.v5 = orgC.v5;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
//c.v5 = orgC.v5;<br />
c.k8 = 10;<br />
c.k8_K7 = 2e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
for(var a in mutateFuncs) {<br />
setOutput(a+mode,mutateFuncs[a](c));<br />
}<br />
setOutput('E'+mode,E);<br />
if (dc!=undefined) {<br />
for(var a in dc) {<br />
setOutput(a+mode+'gradient',dc[a]);<br />
}<br />
}<br />
}<br />
<br />
function constructPlot(id) {<br />
var width = 100, height = 100;<br />
var t = document.getElementById(id);<br />
t.minx = Number.NaN;<br />
t.miny = Number.NaN;<br />
t.maxx = Number.NaN;<br />
t.maxy = Number.NaN;<br />
t.points = [];<br />
t.createCaption();<br />
t.style.width = width + 'px';<br />
t.style.width = height + 'px';<br />
t.style.border = 'solid 1px #000';<br />
t.style.borderCollapse = 'collapse';<br />
for(var r=0; r<height; r++) {<br />
var newRow = t.insertRow(0);<br />
for(var c=0; c<width; c++) {<br />
var newCell = newRow.insertCell(0);<br />
newCell.style.width = '1px';<br />
newCell.style.height = '1px';<br />
newCell.style.background = '#fff';<br />
newCell.style.padding = '0px';<br />
}<br />
}<br />
}<br />
<br />
function plotMin(t,x,y,v) {<br />
if (x<0) return;<br />
if (y<0) return;<br />
var regrid = false;<br />
t.points.push({'x':x,'y':y,'v':v});<br />
if (isNaN(t.minx) || x<t.minx) { t.minx = x/1.5; regrid = true; }<br />
if (isNaN(t.maxx) || x>t.maxx) { t.maxx = x*1.5; regrid = true; }<br />
if (isNaN(t.miny) || y<t.miny) { t.miny = y/1.5; regrid = true; }<br />
if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
//alert('regridding' + [x,y,t.minx,t.miny,t.maxx,t.maxy,regrid]);<br />
setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
for(var r=0; r<t.rows.length; r++) {<br />
var row = t.rows[r];<br />
for(var c=0; c<row.cells.length; c++) {<br />
var cell = row.cells[c];<br />
cell.background = '#fff';<br />
}<br />
}<br />
for(var i in t.points) plotMinWork(t,t.points[i].x,t.points[i].y,t.points[i].v);<br />
} else {<br />
plotMinWork(t,x,y,v);<br />
}<br />
}<br />
<br />
function plotMinWork(t,x,y,v) {<br />
var r = Math.floor((y-t.miny)/(t.maxy-t.miny)*t.rows.length);<br />
var c = Math.floor((x-t.minx)/(t.maxx-t.minx)*t.rows[0].cells.length);<br />
var cell = t.rows[r].cells[c];<br />
if (cell.value==undefined || v<cell.value) {<br />
cell.value = v;<br />
cell.style.background = 'rgb('+Math.max(0,100*v)+'%,'+Math.min(100,100*(1-v))+'%,0%)';<br />
}<br />
}<br />
<br />
function setCaption(t,cap) {<br />
if (!t) return;<br />
var caps = t.getElementsByTagName('caption');<br />
if (caps.length>0) {<br />
caps[0].innerHTML = cap;<br />
return;<br />
}<br />
if (t.caption) {<br />
t.caption = cap;<br />
return;<br />
}<br />
}<br />
</script><br />
</html><br />
{|<br />
|<br />
{|id="v5K5plot"<br />
|}<br />
|<br />
{|id="k8K7plot"<br />
|}<br />
|}<br />
<br />
<!-- Model graphs start here --><br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
{|<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/GlpF|id=Meng2004Graph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Singh2008|id=Singh2008Graph}}<br />
|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3B|id=Kostal2004fig3BGraph}}--><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2time|id=pSB1A2timeGraph}}<br />
<!--|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPtime|id=pArsRRFPtimeGraph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3A|id=Kostal2004fig3AGraph}}<br />
|- --><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2con|id=pSB1A2conGraph}}<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPcon|id=pArsRRFPconGraph}}--><br />
|}<br />
<!-- Don't forget to update the refreshGraphs function above! --></div>Jaspervdghttp://2009.igem.org/Team:Groningen/Modelling/CharacterizationTeam:Groningen/Modelling/Characterization2009-10-20T12:21:10Z<p>Jaspervdg: Working on characterization info.</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
<br />
We have four kinds of parts we would like to characterize (RPS stands for Relative Promoter Strength):<br />
<br />
{|class="ourtable"<br />
!style="width:25%"|Importers<br />
!style="width:25%"|Accumulators<br />
!style="width:25%"|Sensors<br />
!style="width:25%"|GVP cluster<br />
|-style="text-align:center"<br />
|RPS &rarr; &Delta;v<sub>max</sub><br />
|RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
|metal(t) &rarr; RPS(t)<br />
|RPS &rarr; GV<br />
|-<br />
|<br />
We can measure how much v5 (v<sub>max</sub> for As(III) import via GlpF) is in wild-type E.coli and when we over express GlpF at a certain promoter strength <code>S</code> (measured in RPUs). As v5 is a constant times the amount of (active) GlpF this leads to a simple equation for &Delta;v5, if we assume the amount of (active) GlpF produced by our construct is linearly dependent on the promoter strength (v5(0) and v5(1) would be measured):<br />
<br />
<pre><br />
v5(RPS) = v5wt + &Delta;v5*RPS<br />
<br />
v5(0) = v5wt + &Delta;v5*0<br />
v5(S) = v5wt + &Delta;v5*S<br />
<br />
&Delta;v5 = (v5(1) - v5(0))/S<br />
</pre><br />
|RPS &rarr; As<sub>bound</sub>(As(III)<sub>in</sub>)<br />
For both MBPArsR and fMT we assume the amount of bound As(III) behaves as {{todo}}<br />
|metal(t) &rarr; RPS(t)<br />
|RPS &rarr; GV<br />
|}<br />
<br />
<br />
==Uptake measurements==<br />
{|class="ourtable" style="float:right;"<br />
|+Sampling scheme<br />
!rowspan="2" colspan="2"|<br />
!colspan="5" style="padding-left:0px;"|Time (min)<br />
|-<br />
!0<br />
!10<br />
!20<br />
!40<br />
!60<br />
|-<br />
!rowspan="5" style="padding-left:0px;"|As(III)<sub>ex</sub>T(0)<br/>(&micro;M)<br />
!0<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!10<br />
|x<br />
|x<br />
|x<br />
|x<br />
|x<br />
|-<br />
!20<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!50<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|-<br />
!100<br />
|<br />
|<br />
|<br />
|<br />
|x<br />
|}<br />
To efficiently look at both time and concentration dependent processes we took samples as in the table on the right.<br />
Below we list all results, which have been used for fitting all necessary parameters.<br />
<br />
{{todo|TODO: List results. Take conversion from nmol/mg and mg/ml to &micro;M and Vc/Vs into account.}}<br />
<br />
{|<br />
!id="iter"|<br />
!best<br />
!cur<br />
!gradient<br />
!solved<br />
|-<br />
|v5/K5<br />
|id="v5_K5"|<br />
|id="v5_K5cur"|<br />
|id="v5_K5curgradient"|<br />
|id="v5_K5sol"|<br />
|-<br />
|v5<br />
|id="v5"|<br />
|id="v5cur"|<br />
|id="v5curgradient"|<br />
|id="v5sol"|<br />
|-<br />
|K5<br />
|id="K5"|<br />
|id="K5cur"|<br />
|id="K5curgradient"|<br />
|id="K5sol"|<br />
|-<br />
|k8/K7<br />
|id="k8_K7"|<br />
|id="k8_K7cur"|<br />
|id="k8_K7curgradient"|<br />
|id="k8_K7sol"|<br />
|-<br />
|k8<br />
|id="k8"|<br />
|id="k8cur"|<br />
|id="k8curgradient"|<br />
|id="k8sol"|<br />
|-<br />
|K7<br />
|id="K7"|<br />
|id="K7cur"|<br />
|id="K7curgradient"|<br />
|id="K7sol"|<br />
|-<br />
|tauBbetaB<br />
|id="tauBbeta4"|<br />
|id="tauBbeta4cur"|<br />
|id="tauBbeta4curgradient"|<br />
|id="tauBbeta4sol"|<br />
|-<br />
|tauB<br />
|id="tauB"|<br />
|id="tauBcur"|<br />
|id="tauBcurgradient"|<br />
|id="tauBsol"|<br />
|-<br />
|betaB<br />
|id="beta4"|<br />
|id="beta4cur"|<br />
|id="beta4curgradient"|<br />
|id="beta4sol"|<br />
|-<br />
|tauR<br />
|id="tauR"|<br />
|id="tauRcur"|<br />
|id="tauRcurgradient"|<br />
|id="tauRsol"|<br />
|-<br />
|betaRN<br />
|id="beta1"|<br />
|id="beta1cur"|<br />
|id="beta1curgradient"|<br />
|id="beta1sol"|<br />
|-<br />
|tauFbetaF<br />
|id="tauFbetaF"|<br />
|id="tauFbetaFcur"|<br />
|id="tauFbetaFcurgradient"|<br />
|id="tauFbetaFsol"|<br />
|-<br />
|tauF<br />
|id="tauF"|<br />
|id="tauFcur"|<br />
|id="tauFcurgradient"|<br />
|id="tauFsol"|<br />
|-<br />
|betaF<br />
|id="betaF"|<br />
|id="betaFcur"|<br />
|id="betaFcurgradient"|<br />
|id="betaFsol"|<br />
|-<br />
|tauKbetaK<br />
|id="tauKbetaK"|<br />
|id="tauKbetaKcur"|<br />
|id="tauKbetaKcurgradient"|<br />
|id="tauKbetaKsol"|<br />
|-<br />
|tauK<br />
|id="tauK"|<br />
|id="tauKcur"|<br />
|id="tauKcurgradient"|<br />
|id="tauKsol"|<br />
|-<br />
|betaK<br />
|id="betaK"|<br />
|id="betaKcur"|<br />
|id="betaKcurgradient"|<br />
|id="betaKsol"|<br />
|-<br />
|tauGbeta5<br />
|id="tauGbeta5"|<br />
|id="tauGbeta5cur"|<br />
|id="tauGbeta5curgradient"|<br />
|id="tauGbeta5sol"|<br />
|-<br />
|tauG<br />
|id="tauG"|<br />
|id="tauGcur"|<br />
|id="tauGcurgradient"|<br />
|id="tauGsol"|<br />
|-<br />
|beta5<br />
|id="beta5"|<br />
|id="beta5cur"|<br />
|id="beta5curgradient"|<br />
|id="beta5sol"|<br />
|-<br />
|ars2T<br />
|id="ars2T"|<br />
|id="ars2Tcur"|<br />
|id="ars2Tcurgradient"|<br />
|id="ars2Tsol"|<br />
|-<br />
|E<br />
|id="E"|<br />
|id="Ecur"|<br />
|<br />
|id="Esol"|<br />
|}<br />
<html><br />
<input type="button" value="Fit" onClick="fitConstants();"/><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript"><br />
var experiments = {/*Meng2004:<br />
{constants:{Vc:0.0073,Vs:(1.1-0.0073),beta4:0,pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[101.917808219178e-6,394.520547945205e-6,723.287671232877e-6,<br />
1111.23287671233e-6,1229.58904109589e-6],<br />
time:[60,600,1200,2400,3600]}},<br />
Singh2008: // We assume 5g/L wet cells were used... (at 1100kg/m^3)<br />
{constants:{Vc:(0.004545455),Vs:(1-(0.004545455)),pro:0,ars2T:0,<br />
proF:1.6605e-9},AsT:0.467154987e-6,<br />
data:{AsexT:[0.419211538e-6,0.391262322e-6,0.378368845e-6,<br />
0.361791516e-6,0.332907991e-6,0.320748614e-6],<br />
time:[1.127*60,4.993*60,9.986*60,20.159*60,30.181*60,60.035*60]}},<br />
Kostal2004fig3A: // fig 3A<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},time:Infinity,<br />
data:{AsinT:[28.71e-6,78.87e-6,144.21e-6,377.19e-6,490.38e-6,617.76e-6,649.11e-6],<br />
AsT:[0.4e-6,1e-6,2e-6,5e-6,20e-6,50e-6,100e-6]}},<br />
Kostal2004fig3B: //fig 3B<br />
{constants:{Vc:0.006666667,Vs:(1-0.006666667),pro:0,ars2T:0,proK:1.6605e-9},AsT:20e-6,<br />
data:{AsinT:[2.25e-4,3.47e-4,4.19e-4,3.93e-4,4.19e-4,4.82e-4,4.82e-4,4.95e-4],<br />
time:[582,1212,1890,2514,3144,3828,4260,6036]}},*/<br />
pSB1A2con: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.000808081,Vs:(1-0.000808081),pro:0,ars2T:0},time:3600,<br />
data:{AsinT:[207.0208222e-6,229.0443139e-6,493.3262146e-6,585.8248799e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pSB1A2time: // concentration mode this is our first icps measerment wild type<br />
{constants:{Vc:0.002320346,Vs:(1-0.002320346),pro:0,ars2T:0},AsT:10e-6,<br />
data:{AsinT:[66.07047517e-6,83.68926855e-6,114.522157e-6,132.1409503e-6,207.0208222e-6],<br />
time:[180,600,1200,2400,3600]}}/*,<br />
pArsRRFPcon: // here the cell only contains extra RFP behind the the extra ArsR promotors.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.001272727,Vs:(1-0.001272727),pro:0},time:Infinity,<br />
data:{AsinT:[136.5456487e-6,277.4959957e-6,290.7100908e-6,343.5664709e-6],<br />
AsT:[10e-6,20e-6,50e-6,100e-6]}},<br />
pArsRRFPtime: // here the cell only contains extra RFP behind the the extra ArsR promotors.<br />
// We incorporate this in our model by pretending RFP=GVP (1st icps)<br />
{constants:{Vc:0.003333333,Vs:(1-0.003333333),pro:0},AsT:10e-6,<br />
data:{AsinT:[52.85638014e-6,92.49866524e-6,88.0939669e-6,136.5456487e-6],<br />
time:[180,600,2400,3600]}}*/}; <br />
<br />
/*var varsToMutate = ['K5','v5','K7','k8','tauB','beta4','tauR','beta1','tauF','betaF',<br />
'tauK','betaK','tauG','beta5'];<br />
var mutateFuncs = {v5: function(v){return v.v5;},<br />
K5: function(v){return v.K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.K7;},<br />
tauB: function(v){return v.tauB;},<br />
tauR: function(v){return v.tauR;},<br />
beta4: function(v){return v.beta4;},<br />
beta1: function(v){return v.beta1;},<br />
tauF: function(v){return v.tauF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauG;},<br />
beta5: function(v){return v.beta5;}};*/<br />
<br />
var varsToMutate = [/*'v5_K5','v5',*/'k8_K7','k8','tauBbeta4','beta4',<br />
'tauRbeta1_tauBbeta4','beta1_beta4'/*,'tauFbetaF','betaF',<br />
'tauKbetaK','betaK','tauGbeta5','beta5','tauF','betaF','tauK','betaK','tauG','beta5','ars2T'*/];<br />
var mutateFuncs = {//v5: function(v){return v.v5;},<br />
//K5: function(v){return v.v5/v.v5_K5;},<br />
k8: function(v){return v.k8;},<br />
K7: function(v){return v.k8/v.k8_K7;},<br />
tauB: function(v){return v.tauBbeta4/v.beta4;},<br />
beta4: function(v){return v.beta4;},<br />
tauR: function(v){return v.tauRbeta1_tauBbeta4*v.tauBbeta4/(v.beta4*v.beta1_beta4);},<br />
beta1: function(v){return v.beta4*v.beta1_beta4;}/*,<br />
//tauF: function(v){return v.tauF;},<br />
//betaF: function(v){return v.betaF;},<br />
//tauK: function(v){return v.tauK;},<br />
//betaK: function(v){return v.betaK;},<br />
//tauG: function(v){return v.tauG;},<br />
//ars2T: function(v){return v.ars2T;},<br />
//beta5: function(v){return v.beta5;},<br />
tauF: function(v){return v.tauFbetaF/v.betaF;},<br />
betaF: function(v){return v.betaF;},<br />
tauK: function(v){return v.tauKbetaK/v.betaK;},<br />
betaK: function(v){return v.betaK;},<br />
tauG: function(v){return v.tauGbeta5/v.beta5;},<br />
beta5: function(v){return v.beta5;}*/};<br />
<br />
function computeCost(v,e) {<br />
// Compute constants<br />
var c = arsenicModelConstants();<br />
for(var a in mutateFuncs) c[a] = mutateFuncs[a](v);<br />
<br />
// Go through all experiments<br />
var cost = 0, weight = 0, x0, xt, times;<br />
for(var i in e) {<br />
// Set up constants for this experiment<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
for(var a in e[i].constants) nc[a] = e[i].constants[a];<br />
<br />
if (e[i].AsT!=undefined) { // Vary time, with fixed AsT<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].AsT);<br />
xt = simulate(x0,e[i].data.time,function(t,d){return arsenicModelGradient(nc,d);});<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
var curcost = 0, n = 0;<br />
for(var xn in e[i].data) {<br />
if (xn=='time') continue;<br />
var avgv = 0;<br />
for(var j in e[i].data[xn]) avgv += e[i].data[xn][j];<br />
avgv /= e[i].data[xn].length;<br />
for(var j in xt.timeKey) {<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt.timeKey[j]])/avgv,2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
<br />
// Set last solution<br />
e[i].solution = {'cost':Math.sqrt(curcost/n), 'xt':xt};<br />
} else if (e[i].time==Infinity) { // Vary AsT, with equilibrium<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
xt = arsenicModelEquilibrium(nc,e[i].data.AsT[j]);<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
} else if (!isNaN(e[i].time)) { // Vary AsT, with t = e[i].time<br />
var avgv = {};<br />
for(var xn in e[i].data) {<br />
avgv[xn] = 0;<br />
for(var j in e[i].data[xn]) avgv[xn] += e[i].data[xn][j];<br />
avgv[xn] /= e[i].data[xn].length;<br />
}<br />
e[i].solution = {'xt':{'AsT':[]}};<br />
var curcost = 0, n = 0;<br />
for(var j in e[i].data.AsT) {<br />
// Simulate<br />
x0 = arsenicModelInitialization(nc,e[i].data.AsT[j]);<br />
xt = simulate(x0,e[i].time,function(t,d){return arsenicModelGradient(nc,d);});<br />
e[i].solution.xt.AsT[j] = e[i].data.AsT[j];<br />
<br />
// Fill solution<br />
for(var xn in xt) {<br />
if (e[i].solution.xt[xn]==undefined) e[i].solution.xt[xn] = [];<br />
e[i].solution.xt[xn][j] = xt[xn][xt[xn].length-1];<br />
}<br />
<br />
// Sum of (squares of) errors, divided by the average value<br />
for(var xn in e[i].data) {<br />
if (xn=='AsT') continue;<br />
curcost += Math.pow((e[i].data[xn][j]-xt[xn][xt[xn].length-1])/avgv[xn],2);<br />
n++;<br />
}<br />
}<br />
cost += Math.sqrt(curcost/n); // Compute the square root of the average of the squares (RMS)<br />
weight++;<br />
e[i].solution.cost = Math.sqrt(curcost/n);<br />
}<br />
}<br />
return cost/weight; // Take the average of the RMS values for all graphs, making it "easier" to disregard certain experiments in favour of the rest.<br />
}<br />
<br />
function randomLogNormal(mu,sigma) {<br />
var N = Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random()<br />
- (Math.random()+Math.random()+Math.random()+Math.random()+Math.random()+Math.random());<br />
return Math.exp(mu+sigma*N);<br />
}<br />
<br />
function mutate(c,dc) {<br />
var vn = varsToMutate[Math.floor(Math.random()*varsToMutate.length)];<br />
var nc = {};<br />
for(var a in c) nc[a] = c[a];<br />
<br />
// Mutate<br />
/*var factor = 1+0.01*(1-Math.exp(-Math.random()));<br />
if (Math.random()<0.5+Math.atan(dc[vn])/Math.PI) {<br />
factor = 1 / factor;<br />
}*/<br />
var sigma = 0.1;<br />
var factor = randomLogNormal(0,sigma);<br />
nc[vn] *= factor;<br />
return nc;<br />
}<br />
<br />
function fitConstants() {<br />
// Construct plots<br />
//constructPlot('v5K5plot');<br />
constructPlot('k8K7plot');<br />
<br />
// Show mathematica solution<br />
var orgC = arsenicModelConstants();<br />
var cSol = {};<br />
for(var i in varsToMutate) cSol[varsToMutate[i]] = 1;<br />
//cSol.v5_K5 = orgC.v5/orgC.K5;<br />
//cSol.v5 = orgC.v5;<br />
cSol.k8 = 10;<br />
cSol.k8_K7 = 2e5;<br />
cSol.tauBbeta4 = 55;<br />
cSol.beta4 = 18;<br />
cSol.tauRbeta1_tauBbeta4 = 400;<br />
cSol.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66;<br />
showOutputs('sol',computeCost(cSol,experiments),cSol);<br />
<br />
// Initialize<br />
var c = {};<br />
for(var i in varsToMutate) c[varsToMutate[i]] = 1;<br />
//c.v5_K5 = orgC.v5/orgC.K5;<br />
//c.v5 = orgC.v5;<br />
c.k8 = 10;<br />
c.k8_K7 = 2e5;<br />
c.tauBbeta4 = 55;<br />
c.beta4 = 18;<br />
c.tauRbeta1_tauBbeta4 = 400;<br />
c.beta1_beta4 = 2;<br />
// cSol.tauBbeta4 = 180000;<br />
// cSol.tauB = 180;<br />
// cSol.beta4 = 1000;<br />
// cSol.tauR = 60;<br />
// cSol.beta1 = 1000;<br />
// cSol.tauFbetaF = 120000;<br />
// cSol.tauF = 60;<br />
// cSol.betaF = 2000;<br />
// cSol.tauKbetaK = 9240;<br />
// cSol.tauK = 60;<br />
// cSol.betaK = 154;<br />
// cSol.tauGbeta5 = 3960;<br />
// cSol.tauG = 60;<br />
// cSol.beta5 = 66; <br />
var dc = {};<br />
for(var a in c) dc[a] = 0;<br />
var E = computeCost(c,experiments);<br />
var cBest = c, EBest = E;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
<br />
// Show initial situation<br />
showOutputs('cur',E,c,dc);<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
<br />
// Set up iteration<br />
var numiter = 100000;<br />
var iter = 0;<br />
var timer = setInterval(function(){<br />
iter++;<br />
if (iter>numiter) {<br />
clearInterval(timer);<br />
return;<br />
}<br />
setOutput('iter',iter);<br />
<br />
// Mutate and compute new energy and gradient<br />
var cNew = mutate(c,dc);<br />
var ENew = computeCost(cNew,experiments);<br />
for(var a in cNew) {<br />
var dca = (ENew-E)/(cNew[a]-c[a]);<br />
if (!(isNaN(dca) || !isFinite(dca))) dc[a] = (dc[a]+2*dca)/3;<br />
}<br />
<br />
// If better than best, accept<br />
if (ENew < EBest) {<br />
cBest = cNew;<br />
EBest = ENew;<br />
for(var i in experiments) experiments[i].bestSolution = experiments[i].solution;<br />
showOutputs('',EBest,cBest);<br />
refreshGraphs();<br />
}<br />
<br />
// Compute (decaying) "temperature" and accept new solution as current if it's not "too" bad<br />
var T = 1 - (iter/numiter);<br />
if (ENew<E || Math.exp((E-ENew)/(T))>=Math.random()) {<br />
c = cNew;<br />
E = ENew;<br />
showOutputs('cur',E,c,dc);<br />
}<br />
},1);<br />
}<br />
<br />
function refreshGraphs() {<br />
//document.getElementById('Meng2004Graph').refresh();<br />
//document.getElementById('Singh2008Graph').refresh();<br />
//document.getElementById('Kostal2004fig3BGraph').refresh();<br />
document.getElementById('pSB1A2timeGraph').refresh();<br />
//document.getElementById('pArsRRFPtimeGraph').refresh();<br />
//document.getElementById('Kostal2004fig3AGraph').refresh();<br />
document.getElementById('pSB1A2conGraph').refresh();<br />
//document.getElementById('pArsRRFPconGraph').refresh();<br />
}<br />
<br />
function showOutputs(mode,E,c,dc) {<br />
//plotMin(v5K5plot,mutateFuncs.v5(c),mutateFuncs.K5(c),E);<br />
plotMin(k8K7plot,mutateFuncs.k8(c),mutateFuncs.K7(c),E);<br />
for(var a in c) {<br />
setOutput(a+mode,c[a]);<br />
}<br />
for(var a in mutateFuncs) {<br />
setOutput(a+mode,mutateFuncs[a](c));<br />
}<br />
setOutput('E'+mode,E);<br />
if (dc!=undefined) {<br />
for(var a in dc) {<br />
setOutput(a+mode+'gradient',dc[a]);<br />
}<br />
}<br />
}<br />
<br />
function constructPlot(id) {<br />
var width = 100, height = 100;<br />
var t = document.getElementById(id);<br />
t.minx = Number.NaN;<br />
t.miny = Number.NaN;<br />
t.maxx = Number.NaN;<br />
t.maxy = Number.NaN;<br />
t.points = [];<br />
t.createCaption();<br />
t.style.width = width + 'px';<br />
t.style.width = height + 'px';<br />
t.style.border = 'solid 1px #000';<br />
t.style.borderCollapse = 'collapse';<br />
for(var r=0; r<height; r++) {<br />
var newRow = t.insertRow(0);<br />
for(var c=0; c<width; c++) {<br />
var newCell = newRow.insertCell(0);<br />
newCell.style.width = '1px';<br />
newCell.style.height = '1px';<br />
newCell.style.background = '#fff';<br />
newCell.style.padding = '0px';<br />
}<br />
}<br />
}<br />
<br />
function plotMin(t,x,y,v) {<br />
if (x<0) return;<br />
if (y<0) return;<br />
var regrid = false;<br />
t.points.push({'x':x,'y':y,'v':v});<br />
if (isNaN(t.minx) || x<t.minx) { t.minx = x/1.5; regrid = true; }<br />
if (isNaN(t.maxx) || x>t.maxx) { t.maxx = x*1.5; regrid = true; }<br />
if (isNaN(t.miny) || y<t.miny) { t.miny = y/1.5; regrid = true; }<br />
if (isNaN(t.maxy) || y>t.maxy) { t.maxy = y*1.5; regrid = true; }<br />
if (regrid==true) {<br />
//alert('regridding' + [x,y,t.minx,t.miny,t.maxx,t.maxy,regrid]);<br />
setCaption(t,'x = ['+formatNumberToHTML(t.minx,3)+','+formatNumberToHTML(t.maxx,3)+']<br/>y = ['+formatNumberToHTML(t.miny,3)+','+formatNumberToHTML(t.maxy,3)+']');<br />
for(var r=0; r<t.rows.length; r++) {<br />
var row = t.rows[r];<br />
for(var c=0; c<row.cells.length; c++) {<br />
var cell = row.cells[c];<br />
cell.background = '#fff';<br />
}<br />
}<br />
for(var i in t.points) plotMinWork(t,t.points[i].x,t.points[i].y,t.points[i].v);<br />
} else {<br />
plotMinWork(t,x,y,v);<br />
}<br />
}<br />
<br />
function plotMinWork(t,x,y,v) {<br />
var r = Math.floor((y-t.miny)/(t.maxy-t.miny)*t.rows.length);<br />
var c = Math.floor((x-t.minx)/(t.maxx-t.minx)*t.rows[0].cells.length);<br />
var cell = t.rows[r].cells[c];<br />
if (cell.value==undefined || v<cell.value) {<br />
cell.value = v;<br />
cell.style.background = 'rgb('+Math.max(0,100*v)+'%,'+Math.min(100,100*(1-v))+'%,0%)';<br />
}<br />
}<br />
<br />
function setCaption(t,cap) {<br />
if (!t) return;<br />
var caps = t.getElementsByTagName('caption');<br />
if (caps.length>0) {<br />
caps[0].innerHTML = cap;<br />
return;<br />
}<br />
if (t.caption) {<br />
t.caption = cap;<br />
return;<br />
}<br />
}<br />
</script><br />
</html><br />
{|<br />
|<br />
{|id="v5K5plot"<br />
|}<br />
|<br />
{|id="k8K7plot"<br />
|}<br />
|}<br />
<br />
<!-- Model graphs start here --><br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
{{GraphHeader}}<br />
{|<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/GlpF|id=Meng2004Graph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Singh2008|id=Singh2008Graph}}<br />
|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3B|id=Kostal2004fig3BGraph}}--><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2time|id=pSB1A2timeGraph}}<br />
<!--|-<br />
|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPtime|id=pArsRRFPtimeGraph}}<br />
|{{graph|Team:Groningen/Graphs/Characterization/Kostal2004fig3A|id=Kostal2004fig3AGraph}}<br />
|- --><br />
|{{graph|Team:Groningen/Graphs/Characterization/pSB1A2con|id=pSB1A2conGraph}}<br />
<!--|{{graph|Team:Groningen/Graphs/Characterization/pArsRRFPcon|id=pArsRRFPconGraph}}--><br />
|}<br />
<!-- Don't forget to update the refreshGraphs function above! --></div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-20T11:05:30Z<p>Jaspervdg: Exit parts...</p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
<br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line.]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible interactively available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*{{todo}}'''Analysis''' of results. Once we have uptake experiments (and new promoter measurements?) we could try to analyze the results to estimate further constants and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-20T11:00:24Z<p>Jaspervdg: </p>
<hr />
<div>{{Team:Groningen/Modelling/Header}}<br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
<br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line.]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible interactively available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*{{todo}}'''Analysis''' of results. Once we have uptake experiments (and new promoter measurements?) we could try to analyze the results to estimate further constants and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Parts==<br />
<br />
{{todo}}Here we need to give some genereal information about our parts.<br />
<br />
*For a comprehensive list of all the parts we used, have a look at our [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2009&group=Groningen '''parts registry'''].<br />
*Here you can find an informative overview of our [[Team:Groningen/Modelling/Submitted Parts|'''submitted parts''']].<br />
*Experience we had with parts from the registry can be found under [[Team:Groningen/Modelling/Used Parts|'''used parts''']].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/ModellingTeam:Groningen/Modelling2009-10-20T10:17:19Z<p>Jaspervdg: /* Introduction */ Image showing artifacts in modelling.</p>
<hr />
<div>{{Team:Groningen/Header}}<br />
[[Category:Team:Groningen/Disciplines/Analysis_and_Design|Modelling]]<br />
[[Category:Team:Groningen/Roles/Modeller|Modelling]]<br />
<br />
<br />
==Introduction==<br />
[[Image:Modelling.png|frame|right|Normally the design and analysis is done/documented on the wiki, and even lab measurements/protocols are in the Notebook. This is in contrast to most of the artifacts related to modelling (SBML files, data sheets, etc.). To make our models more accessible and an integral part of our project we put the entire modelling workflow on-line.]]<br />
Modelling is an integral part of synthetic biology and most of our modelling results are therefore integrated with our theoretical information and lab results on our [[Team:Groningen/Project|project pages]]. In general we have tried to make as much of our model as possible interactively available on our wiki. Specifically, we have constructed several interactive calculators that can be used to explore our model, some including interactive [https://2009.igem.org/Template:Graph graphs] to show the results.<br />
<br />
In our project we use modelling for the following purposes:<br />
<br />
*'''Description''' of our system. By modelling the system the different relationships between components in our system are made explicit.<br />
*'''Gaining insight''' in our system. Having modelled our system we can see how different variables interact, giving essential insights into how our system functions.<br />
*'''Verification''' of our design. For example, we looked at the number of gas vesicles needed to let our cells float, to check whether it should be possible.<br />
*'''Making design choices'''. We have shown that constitutive expression of ArsR can indeed significantly increase accumulation levels, and we would be able to show the impact of this constitutively expressed ArsR regulating the ars promoter on the expression of the GVP cluster (see [[Team:Groningen/Project/Promoters#Modelling|our promoter modelling]]).<br />
*'''Designing tests'''. By looking at the behaviour of GlpF/ArsB (importer/exporter for As(III)) we determined what range of concentrations would be interesting to use in our uptake experiments.<br />
*{{todo}}'''Analysis''' of results. Once we have uptake experiments (and new promoter measurements?) we could try to analyze the results to estimate further constants and/or explain the results.<br />
<br />
Our initial ideas on how and what to model (including a survey of previously used software) can be found at [[Team:Groningen/Brainstorm/Modelling|Brainstorm/Modelling]].<br />
<br />
==Parts==<br />
<br />
{{todo}}Here we need to give some genereal information about our parts.<br />
<br />
*For a comprehensive list of all the parts we used, have a look at our [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2009&group=Groningen '''parts registry'''].<br />
*Here you can find an informative overview of our [[Team:Groningen/Modelling/Submitted Parts|'''submitted parts''']].<br />
*Experience we had with parts from the registry can be found under [[Team:Groningen/Modelling/Used Parts|'''used parts''']].<br />
<br />
==Models==<br />
Apart from our physical model of [[Team:Groningen/Project/Vesicle|gas vesicles]] we have the following reaction model involving import, export and accumulation of arsenic (showing the "reactions" in the model):<br />
<br />
<center>{{LinkedImage|Arsenic_filtering.png|Team:Groningen/Modelling/Arsenic}}<br/>(Click to go to our detailed [[Team:Groningen/Modelling/Arsenic|modelling page]].)</center><br />
<br />
<!--==Michaelis-Menten revisited==<br />
By simplifying the model it is possible to reduce the number of parameters of the model, often making it easier to find reasonable values for the parameters. One popular way of simplifying a model is by using the [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten]] equation, or something similar, like the Hill equation. This type of simplification uses some assumptions to reduce a recurring reaction motif to one reaction involving a more complicated rate equation.<br />
<br />
{{todo|Explain what we did instead.}}--><br />
<br />
<!--== Kinetic Laws ==<br />
{{todo}} Add references.<br />
<br />
{{todo}} Find out how to determine experimentally which is applicable (and if you know, what the parameters are).<br />
<br />
;Mass Action<br />
:Molecules randomly interact, the reaction rate is simply the product of the concentrations of the reactants (multiplied by a constant).<br />
;Michaelis-Menten<br />
:Applicable to situations where there is a maximum reaction rate (due to needing a catalyst/transporter/binding site of which there is only a limited amount for example) under the assumption that there is much more of the "main" reactant than of the catalyst/transporter. Has two constants, the maximum reaction ''rate'' and the concentration at which the reaction rate is half the maximum reaction rate.<br />
;Michaelis-Menten reversible<br />
:{{todo}}<br />
;Hill<br />
:Generalization of Michaelis-Menten. {{todo|More detail.}}<br />
<br />
For rate parameters it is best to have both the forward and reverse reaction rates, if you don't then a dissociation constant can be used (which is the ratio of the reverse and forward rates), in combination with a "standard" rate of 10<sup>8</sup>-10<sup>9</sup> (see appendix A of [[Team:Groningen/Literature#Alon2007|Alon2007]]), in the case of two reactants at least.<br />
<br />
See http://www.biomodels.net/ for a database of models.<br />
--><br />
{{Team:Groningen/Footer}}</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Project/PromotersTeam:Groningen/Project/Promoters2009-10-20T10:14:17Z<p>Jaspervdg: /* Modelling */ Titles above graphs.</p>
<hr />
<div>{{Team:Groningen/Project/Header|}}<br />
<br />
<br />
'''A promoter is a part of DNA involved in the regulation of gene transcription by RNA polymerase. In general RNA polymerase tends to bind weakly to a strand of DNA until a suitable promoter is encountered and the binding becomes strong. Promoters are used to express genes of interest in cells in either a constitutive or induced manner. The constitutive promoters are used when a constant expression of enzymes is desired, and the amount of activity can be regulated by choosing from a range of promoters varying from low to high expression. If, however, expression is desired at certain points in time, or growth stage, inducible promoters are the best choice for regulating gene expression. In our system, we want to induce GVP production when the concentration of desired metal in the cells reaches a certain level. By choosing metal sensitive promoters already present in ''E. coli'' cells, the cells contain the necessary components for controlling the promoters, and the promoter sequence has only to be placed in front of the genes of interest.'''<br />
<br />
==Background==<br />
<br />
Metal sensitive promoters are widely used by bacteria in defence stategies against high concentrations of metals, which would have a destructive result on the cell. The promoters activate transcription of metal binding proteins to encapsule the ions, or transporters to pump the metals outside of the cell. In order to find different promoters to induce genes in the presence of different heavy metals we used the following list of databases and sites:<br />
{|<br />
|<br />
# [http://www.genome.jp/kegg/kegg2.html KEGG]<br />
# [http://www.ncbi.nlm.nih.gov NCBI]<br />
# [http://regtransbase.lbl.gov Regtransbase]<br />
|}<br />
<br />
We take into consideration the following promoters:<br />
*Copper Induced Promoters<br />
*Zink Induced Promoters<br />
*Mercury Induced Promoters<br />
*Arsenic Induced Promoters<br />
<br />
==Arsenic Induced Promoters==<br />
<br />
Because of the similarity to phosphate, sometimes arsenate is mistaken for phosphate, which is how it is introduced into living organisms, including <i>E. coli</i>, by the phosphate uptake system. Other molecules such as As(III) can also be introduced into the cells by various membrane transporters. (needs a ref.)<br />
<br />
====<i>E. coli</i>====<br />
<br />
Promoter arsRp is associated with the dimer of ArsR for the arsenic induced transcription of genes involved in arsenic efflux (arsR, arsB and arsC, which is present on the genome of <i>Escherichia coli</i> str. K-12 substrain MG1655). The sequence shows the typical -10 and -35 region of the promoter and can be found through the following [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00239 link]. A second region, located at -41.5 from the transcription start site, is thought to bind dimeric ArsR. Upon binding of arsenic, the dimer dissociates and allows the RNA polymerase space to attach itself, and can also be found in the same [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU00239 link].<br />
<br />
*ArsR belongs to the ArsR/SmtB family of transcriptional regulators that respond to a variety of metals. ArsR has a helix-turn-helix motif for DNA binding, a metal-binding site, and a dimerization domain. In ArsR the inducer-binding site contains three cysteine residues that bind arsenite and antimonite specifically and with high affinity. Dimerization of ArsR is required for DNA binding and its ability to act as a transcriptional repressor. The dimer recognizes and binds to a 12-2-12 inverted repeat, but the binding of arsenic or antimonite to ArsR causes a conformational change in it, leading to dissociation from DNA and hence derepression (KEGG).<br />
<br />
*ArsR negatively controls the expression of the genes involved in arsenical and antimonite metals resistance, whose expression is induced in the presence of these metals. The protein is autoregulated, because arsR is the first gene in the arsRBC operon that it regulates. Overexpression of ArsR in <i>Escherichia coli</i> has been used for removal of arsenite from contaminated water (KEGG).<br />
<br />
(ArsR)<sub>2</sub>-DNA &rarr; ArsR-Ar + ArsR-Ar + DNA &rarr; Activation of transription<br />
<br />
The presence of all genes and promoters on the chromosome of <i>E. coli</i> makes the use of the arsRp for induction of the GVP cluster relatively straith forward. The promoter sequence of arsRp, with the upstream binding box for ArsR dimer, can either be synthesized completely with the required restriction sites, or acquired using PCR and carefully designed primers. It might even be an option to alter the -10/-35 promoter region for higher or lower transcription of the genes.<br />
<br />
====Results====<br />
The functionality of pArsR was tested by using a test construct, composed of pArsR and RFP (Figure 1).<br />
<br />
[[Image:Promoter measurement device.png]]<br />
:Figure 1: The promoter testing device in J61002, where RFP expression is under control of the promoter which is placed in front of it. <br />
The fluorescence (and OD600) was measured as described in [[https://2009.igem.org/Team:Groningen/Protocols| protocols]]. Upon induction of the ArsR promoter the expression of RFP increased with 2.26RPU (calculated according to formula 9 as described by [[Team:Groningen/Literature#Kelly2009|Kelly 2009]]). The increase in fluorescence over time is shown in figure 2 and the fluorescence change due to a change in the internal as(III) concentration in figure 3. <br />
<br />
[[Image:Fluorescence over time.PNG]]<br />
:Figure 2:<br />
<br />
[[Image:RFP over As conc.PNG]]<br />
:Figure 3:<br />
<br />
===Modelling===<br />
{{GraphHeader}}<br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
<br />
The three graphs below illustrate the promoter response after induction with arsenic (directly in the cell, with the equivalent of 1&micro;M in the solution) with and without constitutive expression of ArsR (the first two graphs) and with slower production and degradation of ArsR (the two left graphs). Also, each graph has a line showing the formation of a product behind the ars promoter that does not degrade (and has production rate 1), subtracting the production that would have occurred without induction to show the effect of adding arsenic. Some conclusions:<br />
<br />
* Constitutive expression of ArsR greatly reduces (and slows) the promoter response.<br />
* On the other hand, if we divide the production and degradation rates of ArsR by ten the promoter response is ten times slower, producing ten times as much product.<br />
* In the bottom-right graph the induction is done gradually (the amount of arsenic increases linearly during the first five minutes), showing the high-pass behaviour of the promoter and that this can negatively impact product formation.<br />
<br />
<html><br />
<script type="text/javascript"><br />
addOnloadHook(computePromoterActivation);<br />
<br />
function computePromoterActivation() {<br />
// Set up constants<br />
var maxt = 600;<br />
var c = arsenicModelConstants();<br />
var cNP = {}, cS = {}, cG = {};<br />
c.v5 = 0;<br />
c.k8 = 0;<br />
c.pro = 0;<br />
c.ars2T = 0;<br />
for(var a in c) {<br />
cNP[a] = c[a];<br />
cS[a] = c[a];<br />
cG[a] = c[a];<br />
}<br />
<br />
var Vcell = 1 * 1e-15; // micrometer^3/cell -> liter/cell<br />
var avogadro = 6.02214179e23; // 1/mol<br />
c.pro = 2/(avogadro*Vcell); // 1/cell -> mol/L<br />
cS.tauR *= 10;<br />
cS.beta1 /= 10;<br />
cS.beta3 /= 10;<br />
cG.ars2T = 100*cG.ars1T;<br />
<br />
// Initialize<br />
var x0 = arsenicModelInitialization(c,0);<br />
var xNP0 = arsenicModelInitialization(cNP,0);<br />
var xS0 = arsenicModelInitialization(cS,0);<br />
var x20 = arsenicModelInitialization(c,0);<br />
var xG0 = arsenicModelInitialization(cG,0);<br />
var AsT = 1e-6*c.Vs;<br />
x0.AsinT = AsT/c.Vc;<br />
xNP0.AsinT = AsT/c.Vc;<br />
xS0.AsinT = AsT/c.Vc;<br />
x20.AsinT = 0;<br />
xG0.AsinT = AsT/c.Vc;<br />
<br />
// Simulate<br />
var x = simulate(x0,maxt,function(t,d){return arsenicModelGradient(c,d);});<br />
var xNP = simulate(xNP0,maxt,function(t,d){return arsenicModelGradient(cNP,d);});<br />
var xS = simulate(xS0,maxt*10,function(t,d){return arsenicModelGradient(cS,d);});<br />
var xG = simulate(xG0,maxt,function(t,d){return arsenicModelGradient(cG,d);});<br />
var x2 = simulate(x0,maxt,function(t,d){<br />
var Dx = arsenicModelGradient(c,d);<br />
if (t<maxt/2) Dx.AsinT += (AsT/c.Vc)*2/maxt;<br />
return Dx;<br />
});<br />
<br />
// Output<br />
function convertToSeries(c,x0,x) {<br />
var bAsin, cAsin, ArsR, ars, arsP, arsE;<br />
var arsInt = 0;<br />
var series = [[],[]];<br />
var preTime = -x.time[x._arsF.length-1]/(60*20);<br />
arsE = x0._arsF;<br />
series[0].push({x:preTime,y:100*arsE});<br />
series[0].push({x:0,y:100*arsE});<br />
series[1].push({x:preTime,y:0});<br />
for(var i=0; i<x._arsF.length; i++) {<br />
ars = x._arsF[i];<br />
if (i>0) arsInt += (x.time[i]-x.time[i-1])*(ars+arsP)/2;<br />
series[0].push({x:x.time[i]/60,y:100*ars});<br />
series[1].push({x:x.time[i]/60,y:(arsInt-x.time[i]*arsE)});<br />
arsP = ars;<br />
}<br />
return series;<br />
}<br />
document.getElementById("promoterActivationData").data = {<br />
ars:convertToSeries(c,x0,x),<br />
arsNP:convertToSeries(cNP,xNP0,xNP),<br />
arsS:convertToSeries(cS,xS0,xS),<br />
arsG:convertToSeries(cG,xG0,xG),<br />
ars2:convertToSeries(c,x20,x2)};<br />
var graphNodes = [document.getElementById("promoterActivationGraph"),<br />
document.getElementById("promoterActivationGraphNP"),<br />
document.getElementById("promoterActivationGraphS"),<br />
document.getElementById("promoterActivationGraphG"),<br />
document.getElementById("promoterActivationGraph2")];<br />
for(var i in graphNodes) if (graphNodes[i]) graphNodes[i].refresh();<br />
}<br />
</script><br />
</html><br />
<span id="promoterActivationData"></span><br />
{|<br />
!Wild-type<br />
!+ ArsR overexpression<br />
!+ extra ars promoters<br />
|-<br />
|{{graph|Team:Groningen/Graphs/PromoterActivationNP|promoterActivitationGraphNP}}<br />
|{{graph|Team:Groningen/Graphs/PromoterActivation|promoterActivitationGraph}}<br />
|{{graph|Team:Groningen/Graphs/PromoterActivationG|promoterActivitationGraphG}}<br />
|-<br />
!Slower response<br />
!Gradual induction<br />
|-<br />
|{{graph|Team:Groningen/Graphs/PromoterActivationSlow|promoterActivitationGraphS}}<br />
|{{graph|Team:Groningen/Graphs/PromoterActivation2|promoterActivitationGraph2}}<br />
|}<br />
<br />
===Other organisms===<br />
''Bacillus subtilis''<br />
<br />
In <i>B. subtilis</i>, an ArsR family repressor (ArsR<sub>BS</sub>) responds to As(III) and Sb(III) and regulates the ars operon encoding itself (ArsR), and arsenate reductase (ArsC), an arsenite efflux pump (ArsB) and a protein of unknown function (YqcK). The order in which ArsR<sub>BS</sub> recognises metals is as follows: As(III)>As(V)>Cd(II)~Ag(I).<br />
<br />
A second protein, AseR, negatively regulates itself and AseA, an As(III) efflux pump which contributes to arsenite resistance in cells lacking a functional ars operon. The order in which AseR recognises metals is as follows: As(III)>As(V).<br />
<br />
==Copper Induced Promoters==<br />
<br />
Copper is an essential element that becomes highly cytotoxic when concentrations exceed the capacity of cells to sequester the ion. The toxicity of copper is largely due to its tendency to alternate between its cuprous, Cu(I), and cupric, Cu(II), oxidation states, differentiating copper from other trace metals, such as zinc or nickel. Under aerobic conditions, this redox cycling leads to the generation of highly reactive hydroxyl radicals that readily and efficiently damage biomolecules, such as DNA, proteins, and lipids.(needs a ref.). Most organisms have specialized mechanisms to deal with dangerous levels of heavy metals, like the production of efflux pumps. These genes are regulated by promoters, which are inducible by the respective metals.<br />
<br />
====<i>E. coli </i>====<br />
<br />
"The intracellular level of copper in ''E. coli'' is controlled by the export of excess copper, but the entire systems of copper uptake and intracellular copper delivery are not fully understood. Two regulatory systems, the<br />
CueR and CusR systems, have been identified to be involved in transcription regulation of the genes for copper<br />
homeostasis (Rensing et al., 2000; Rensing and Grass, 2003). CueR, a MerR-family transcription factor, stimulates<br />
copper-induced transcription of both copA encoding Cu(I)-translocating P-type ATPase pump (exporter), that is the central component for maintenance of the copper homeostasis, and cueO encoding a periplasmic multicopper<br />
oxidase for detoxification (Outten et al., 2000; Petersen and Moller, 2000)." (from Yamamoto K., 2005)<br />
<br />
Promoter cusCp is associated with the two component system CusR and CusS for the copper induced transcription of genes involved in copper efflux (cusC, cusF, cusB and cusA, which is present on the genome of <i>Escherichia coli </i> str. K-12 substrain MG1655). The sequence shows the typical -10 and -35 region of the promoter and can be found through the following [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU0-1821 link]. A second region, located at -53.5 from the transcription start site, is thought to bind CusR. Upon binding of CusR, the RNA polymerase is able to recognize the site and attach itself, and can also be found in the same [http://biocyc.org/ECOLI/NEW-IMAGE?type=OPERON&object=TU0-1821 link].<br />
<br />
*CusS, a sensory histidine kinase in a two-component regulatory system with CusR, is able to recognize copper ions, phosphorilate, and form a complex with CusR. It's a 480 amino acid long protein of which the sequence (aa and nt) can be found [http://www.genome.jp/dbget-bin/www_bget?eco+b0570 here] along with other information.<br />
<br />
*CusR, "Cu-sensing regulator", regulates genes related to the copper and silver efflux systems under '''anaerobic growth''' and under '''extreme copper stress''' in aerobic growth . It's a 227 amino acid long protein of which the sequence (aa and nt) can be found [http://www.genome.jp/dbget-bin/www_bget?eco+b0571 here] along with other information. <br />
<br />
Cu &rarr; CusS &rarr; +P &rarr; CusR &rarr; Activation of transription<br />
<br />
The problem so far is the site of detection of copper. The CusS protein senses the external copper concentrations and not the internal. For our project it would be nice to have an internal sensor for the induction of the floatation genes, so it will float after uptake. In addition to CusR, three other systems involved in copper resistence are present (CueR, CpxR and YedW). Both CpxR and YedW have the same problem of sensing external copper instead of internal copper, CueR is thought to respond to intracellular concentrations of copper. The choice for CusR over CueR would be based on the frequency of binding sites of both on the genome of <i>E. coli</i> (1 vs. 197 times), which gives CusR more chance of binding to our promoter. However, the idea behind our project is to induce GVP transtriction at a high intracellular concentration, and results in the CueR related promoter.<br />
<br />
===Parts Registry===<br />
<br />
Promoter from the copper-sensitive CusR/CusS two component signal system in <i>E. coli</i> (the <i>CusR/CusS</i> genes are not in parts registry, and are for external Cu concentration as mentioned before).<br />
<br />
'''Abs''': This nucleotide sequence is believed to be able to bind with phosphorylated CusR transcription factor in <i>E. coli</i>. CusR protein is phosphorylated by CusS transmembrane protein in a case of high extracellular concentration of copper ions. After phosphorylation CusR interacts with described DNA sequence and activates the transcription of <i>cusA</i>, Promoter from the copper-sensitive CusR/CusS two component signal system in <i>E. coli</i> (the <i>cusR/cusS</i> genes are not in parts registry, and are for external Cu concentration as mentioned before).<i>CusB</i>, <i>cusC</i> and Promoter from the copper-sensitive CusR/CusS two component signal system in <i>E. coli</i> (the <i>cusR/cusS</i> genes are not in parts registry, and are for external Cu concentration as mentioned before). <i>CusF</i> genes coding the proteins of copper metabolic system were used by Saint-Petersburg Team of 2007 for constructing a copper biosensor system.<br />
*{{part|BBa_I760005}}<br />
*Cu-sensitive promoter <br />
*Part-only sequence (16 bp):<br />
::atgacaaaattgtcat<br />
<br />
====Other organisms====<br />
<br />
''Mycobacterium tuberculosis'' <br><br />
'''Abs.''': Cu(I) binding to the CsoR–DNA complex induces a conformational change in the dimer that decreases its affinity for the DNA [[Team:Groningen/Literature#Liu2006|Liu 2006]].<br />
<br />
''Pseudomonas syringae'' <br><br />
'''Abs.''': The copper resistance (cop) operon promoter (Pcop) of <i>Pseudomonas syringae</i> is copper-inducible, and requires the regulatory genes <i>copR</i> and <i>copS</i>. Primer extension analysis identified the transcriptional initiation site of Pcop 59 bp 5' to the translational start site of <i>copA</i> [[Team:Groningen/Literature#Mills1994|Mills 1994]].<br />
<br />
''Sulfolobus solfataricus'' <br><br />
'''Abs.''': That CopT binds to the copMA promoter at multiple sites, both upstream and downstream of the predicted TATA-BRE site. Copper was found to specifically modulate the affinity of DNA binding by CopT. This study describes a copper-responsive operon in archaea, a new family of archaeal DNA-binding proteins, and supports the idea that this domain plays a prominent role in the archaeal copper response. A model is proposed for copper-responsive transcriptional regulation of the <i>copMA</i> gene cluster [[Team:Groningen/Literature#Ettema2006|Ettema 2006]].<br />
<br />
''Lactococcus lactis'' <br><br />
'''Abs.''': Two regulatory genes (<i>lcoR</i> and <i>lcoS</i>) were identified from a plasmid-borne lactococcal copper resistance determinant and characterized by transcriptional fusion to the promoterless chloramphenicol acetyltransferase gene (<i>cat</i>). The transcription start site involved in copper induction was mapped by primer extension [[Team:Groningen/Literature#Khunajakr1999|Khunajakr 1999]].<br />
<br />
==Zink Induced Promoters==<br />
<br />
====Other organisms====<br />
''Bacillus subtilis''<br />
<br />
'''Abs.''': The ''Bacillus subtilis'' cation efflux pump czcD, which mediates resistance against Zn2+, Co2+, Ni2+ and Cu2+, is regulated by an ArsR-type repressor (CzrABS) as well [[Team:Groningen/Literature#Moore2005|Moore 2005]].<br />
<br />
''Streptococcus pneumoniae''<br />
<br />
'''Abs.''': Activation of the czcD promoter by SczA is shown to proceed by Zn2+-dependent binding of SczA to a conserved DNA motif. In the absence of Zn2+, SczA binds to a second site in the czcD promoter, thereby fully blocking czcD expression. A metalloregulatory protein belonging to the TetR family<br />
Kloosterman T.G., et al. (O.P. Kuipers), The novel transcriptional regulator SczA mediates protection against Zn2+ stress by activation of the Zn2+-resistance gene czcD in Streptococcus pneumoniae, Molecular Microbiology, 2007, 65(4), 1049–1063. Retrieved from "https://2009.igem.org/Team:Groningen/Project/Promoters" <br />
<br />
<br />
''Staphylococcus aureus''<br />
<br />
'''Abs.''': In ''Staphylococcus aureus'' CzrA, a member of the ArsR/SmtB family of DNA binding proteins, functions as a repressor of the czr operon, that consists of czrA and the gene encoding the CzcD homologue CzrB (Xiong and Jayaswal, 1998; Kuroda et al., 1999; Singh et al., 1999). CzrA-mediated repression is alleviated in the presence of Zn2+ and Co2+ (Xiong and Jayaswal, 1998; Kuroda et al., 1999; Singh et al., 1999).<br />
<br />
<br />
<br />
<div title="Arsie Says UP TO GAS VESICLES" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Project/Vesicle|}}</div><br />
{{Team:Groningen/Project/Footer}}</div>Jaspervdghttp://2009.igem.org/File:Modelling.pngFile:Modelling.png2009-10-20T10:07:26Z<p>Jaspervdg: </p>
<hr />
<div>Artifacts most relevant to [[Team:Groningen|our]] modelling.</div>Jaspervdghttp://2009.igem.org/File:Modelling.pngFile:Modelling.png2009-10-20T10:06:18Z<p>Jaspervdg: uploaded a new version of "Image:Modelling.png": Reversed an arrow.</p>
<hr />
<div>Artifacts most relevant to modelling.</div>Jaspervdghttp://2009.igem.org/File:Modelling.pngFile:Modelling.png2009-10-20T10:00:30Z<p>Jaspervdg: Artifacts most relevant to modelling.</p>
<hr />
<div>Artifacts most relevant to modelling.</div>Jaspervdghttp://2009.igem.org/Team:Groningen/Project/TransportTeam:Groningen/Project/Transport2009-10-19T07:52:22Z<p>Jaspervdg: /* Modelling uptake GlpF */</p>
<hr />
<div>{{Team:Groningen/Project/Header|}}<br />
<div title="Arsie Says UP TO ACCUMULATION" style="float:right" >{{linkedImage|Next.JPG|Team:Groningen/Project/Accumulation}}</div><br />
<br />
==Introduction==<br />
We are trying to find suitable systems capable of isolating heavy metals from the environment. There are several different mechanisms to achieve such a thing. We examined 3 kinds:<br />
*Metal transporters, that transport the metal from the environment (<i>i.e.</i> wastewater) to the cytoplasm<br />
**Uncoupled<br />
**Coupled with 'helper' compounds<br />
*Metal binding proteins in the periplasm<br />
<br />
We will investigate severals systems, to find which are suitable for the final design.<br />
The following systems are under consideration:<br />
<br />
*Arsenite uptake via GlpF<br />
*Copper/zinc uptake via HmtA<br />
*Heavy metal uptake coupled to citrate via ''ef''CitH ''bs''CitM<br />
*Periplasmic accumulation of heavy metals via Mer Operon.<br />
<br />
==Arsenite uptake via GlpF==<br />
<!--[[Image:GlpF.jpeg|200px|thumb|right|73As(III) and 125Sb(III) uptake into cells of E. coli is facilitated by the aquaglyceroporin channel GlpF.]]--><br />
<br />
===GlpF===<br />
<br />
GlpF is an aquaglycerol porin of E.coli which facilitates not only glycerol import, but also arsenic (As) and antimone (Sb) import [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000]]), [[Team:Groningen/Literature#Meng, YL, et al.2004|(Meng, YL, et al.2004]]), [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007]]), [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009)]] . It has homologues in other organisms; Fps1p has shown to facilitate arsenic import in yeast and AQP9 is the mammalian homologue [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007]]), [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009)]] .<br />
The GlpF aquaglycerol porin is a membrane protein with a symmetric arrangement of four independent GlpF channels. One monomer of this tetramer GlpF porin consists of six transmembrane and two half membrane-spanning α-helices that form a right-handed helical bundle around the channel. The channel has a diameter of ~15Å at the periplasmid end, which constricts towards a diameter of ~3.8Å at the beginning of a 28 Å long selective channel that ends at the cytoplasmic end [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000)]].<br />
The GlpF is a stereospecific channel that is thought to be more selective on molecular size than on chemical structure [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000]], [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]] . It does allow transport of a variance of polyhydric alcohols, glycerol being one of them, and arsenic and antimone [[Team:Groningen/Literature#Fu, DX, et al.2000|(Fu, DX, et al.2000]]), [[Team:Groningen/Literature#Meng, YL, et al.2004|(Meng, YL, et al.2004]]), [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007)]], [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009]]), [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]]. Carbon sugars and ions are shown to be unable to be transported by GlpF [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]]. At physiological pH arsenic and antimone are not present in their ionic state but rather as As(OH)3 and Sb(OH)3 [[Team:Groningen/Literature#Rosen, BR, et al.2009|(Rosen, BR, et al.2009)]]. These elements show a charge distribution similar to glycerol and a smaller but comparable volume. The structural similarities are thought to be the reason for the possibility of these elements to be transported in the cell by GlpF [[Team:Groningen/Literature#Porquet, A, et al.2007|(Porquet, A, et al.2007)]].<br />
If GlpF behaves as a nonsaturable transporter, a transport rate of 1umol of glycerol is transported per minute per mgr of cell protein [[Team:Groningen/Literature#Heller, KB, et al.1980|(Heller, KB, et al.1980)]]. The transport rate of GlpF for arsenic is estimated to be……<br />
<br />
===Modelling uptake GlpF===<br />
<html><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Model.js?action=raw"></script><br />
<script type="text/javascript" src="/Team:Groningen/Modelling/Arsenic.js?action=raw"></script><br />
</html><br />
<html><style type="text/css"></html><br />
{{InfoBox/Style.css}}<br />
.infoIcon { display: inline; }<br />
<html></style></html><br />
The import of As(III) via GlpF is modelled as a simple import reaction with [[Team:Groningen/Glossary#MichaelisMenten|Michaelis-Menten kinetics]], in part because this makes it easy to specify, but also because we only have very high level data. The following allows a comparison with the data acquired from figure 1B from [[Team:Groningen/Literature#Meng2004|Meng 2004]].<br />
<html><br />
<div style="background:#efe;border:1px solid #9c9;padding:1em;"><br />
<table style="border-collapse:collapse;background:none;"><tr><br />
<td style="border-right:1px solid #9c9;padding-right:1em;"><br />
<dl><br />
<dt>Initial values</dt><br />
<dd><br />
As(III)<sub>ex</sub> = <input type="text" id="As3exInitial" value="9.15164271986822"/> &micro;M<br/><br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(10&micro;M &middot; 1mL / 1.092mL)<br />
</dd><br />
<dt>Volumes</dt><br />
<dd><br />
V<sub>total</sub> = <input type="text" id="Vtotal" value="1.1"/> mL<br/><br />
V<sub>cells</sub> = <input type="text" id="Vcells" value="0.0073"/> mL<br/><br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(0.1ml &middot; 80mg/mL / 1100mg/mL) </html>{{infoBox|E. coli has a density of approximately 1100mg/mL, see [[Team:Groningen/Project/Vesicle|our gas vesicle page]] for more information.}}<html><br />
</dd><br />
<dt>Kinetic Constants</dt><br />
<dd><br />
<nobr>v5 = <input type="text" id="v5" value="3.1862846729357852"/> &micro;mol/(s&middot;L)</nobr><br/><br />
K5 = <input type="text" id="K5" value="27.71808199428998"/> &micro;M<br/><br />
</dd><br />
</dl><br />
<br />
<button onClick="computeGlpFTransport()">Compute</button><br/><br />
</td><br />
<br />
<td style="padding-left:1em;"><br />
<div id="glpFTransportError" style="color:red"></div><br />
</html>{{graph|Team:Groningen/Graphs/GlpFTransport|id=glpFTransportGraph}}<html><br />
</td><br />
</tr></table><br />
</div><br />
<script type="text/javascript"><br />
<br />
//The graph already initializes itself (and we don't do any other computations).<br />
//addOnloadHook(computeGlpFTransport);<br />
<br />
function computeGlpFTransport() {<br />
document.getElementById('glpFTransportGraph').refresh();<br />
}<br />
</script><br />
</html><br />
<br />
To determine the constants v5 and K5 we performed the following steps:<br />
<br />
# '''Read the wild-type line in figure 1B''' of [[Team:Groningen/Literature#Meng2004|Meng 2004]] by pasting it in a drawing program and aligning/scaling the axes and then manually determining the coordinates of each data point.<br />
# '''Converted to units of concentration''' using the data in Meng 2004 and [http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi the CCDB] (assuming that the cells are resting/non-growing), see our [http://spreadsheets.google.com/pub?key=t4gilzCbEaCFAvpEVWUE_zQ Google Docs spreadsheet]. Here we disregarded the fact that the measurements were made by taking out 0.1mL samples, as this does not change the concentrations. Specifically (note that uptake is in nmol/mg):<br />
#* uptake<sub>total</sub> (nmol) = uptake &middot; 8mg &middot; 0.3 {{infoBox|The ratio between dry and wet weight is 0.3 (see the [http://gchelpdesk.ualberta.ca/CCDB/cgi-bin/STAT_NEW.cgi CCDB]).}}<br />
#* As(III)<sub>ex</sub> (&micro;M=nmol/mL) = (10nmol/mL &middot; 1mL - uptake<sub>total</sub>) / (1.1-0.0073)mL {{infoBox|1=The experiment started with 1mL of a 10&micro;M=10nmol/mL solution of As(III). After adding the cells the total volume of the solution was 1.1mL, and 0.0073mL is an estimate of the total volume of cells in the solution, see below.}}<br />
# '''Fit the Michaelis-Menten equation''' to find the constants v5 and K5 in Mathematica (see [http://igemgroningen.googlecode.com/svn/trunk/buoyant/Models/Meng2004%20Figure%201B.nb the Mathematica notebook in SVN]) using the method from [[Team:Groningen/Literature#Goudar1999|Goudar 1999]] (a least squares fit of a closed-form solution of the differential equation).<br />
<br />
{{GraphHeader}}<br />
<br />
<br><br />
<br />
===Missing information/To Do===<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*<del>Q:Eliminate BioBrick restriction sites</del><br />
*<del>Q: What does the ars operon of our <i>E. coli</i> look like? Do we have both ArsA and ArsB? (And what about ArsR and ArsD?)</del> A: We only have ArsRBC, see [[Team:Groningen/BLAST|our BLAST results]].<br />
<br />
<br><br />
<br />
===Additional sources===<br />
<br><br />
* [[Team:Groningen/Literature#Meng2004|Meng 2004]] (As(III) and Sb(III) Uptake by GlpF and Efflux by ArsB in Escherichia coli)<br />
* [[Team:Groningen/Literature#Rosen2009|Rosen 2009]] (Transport pathways for arsenic and selenium: A minireview)<br />
*[[Team:Groningen/Literature#Porquet, A, et al.2007|Porquet, A, et al.2007]] (structural similarity between As(OH)3 and glycerol)<br />
* [[Team:Groningen/Literature#Fu, DX, et al.2000|Fu, DX, et al.2000]] (Structure of the GlpF channel)<br />
*[[Team:Groningen/Literature#Heller, KB, et al.1980|Heller, KB, et al.1980]] (Glycerol transport properties of GlpF)<br />
<br />
==Copper/zinc uptake via HmtA==<br />
<br />
HmtA, heavy metal transporter A from <i>Pseudomonas aeruginosa</i> Q9I147 is a P-type ATPase importer. It mediates the uptake of copper (Cu) and zinc (Zn) and is functionally expressed in E.coli ([http://www.ncbi.nlm.nih.gov/pubmed/19264958 Lewinson 2009]). We want to use this membrane protein to accumulate copper and zinc into the cells we believe this active transport is efficient enough to clear the medium from these compounds.<br />
NCBI database informations on HmtA: gi|81857196|sp|Q9I147|Q9I147_PSEAE Probable cation-transporting P-type ATPase.<br />
<br />
===Restriction sites===<br />
<br />
There are several restriction sites to be modified from the papers bBAD construct.<br />
We will create these mutations via PCR.<br />
<br />
{| border="1"<br />
!Enzyme<br />
!Number of Sites<br />
|-<br />
|EcoRI<br />
|1<br />
|-<br />
|XbaI<br />
|0<br />
|-<br />
|NotI<br />
|0<br />
|-<br />
|SpeI<br />
|0<br />
|-<br />
|PstI<br />
|2<br />
|}<br />
<br />
<br />
===Missing information/To Do===<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*Eliminate BioBrick restriction sites<br />
<br />
==Heavy metal uptake coupled to citrate via ''ef''CitH ''bs''CitM==<br />
<br />
Citrate uptake coupled to heavy metals enables forcefeeding of the toxic compounds into the cell when citrate is the only carbon source available. This could be a very efficient strategy to accumulate vast ammounts of heavy metals.<br />
The current candidates are CitM from ''Bacilus subtilis'' and CitH form ''Enterococcus faecalis''. <br />
<br />
'''Missing information/To Do'''<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*Eliminate BioBrick restriction sites<br />
<br />
<br />
===Additional sources===<br />
<br />
More information on this topic can be found in:<br />
<br />
Bastiaan Krom. Citrate transporters of <i>Bacilus subtilis</i> PhD thesis. [[http://dissertations.ub.rug.nl/faculties/science/2002/b.p.krom/ Dissertation Groningen]]<br />
<br />
Jessica B. Warner. Regulation and expression of the metal citrate transporter CitM PhD thesis. [[http://dissertations.ub.rug.nl/faculties/science/2002/j.b.warner/ Dissertation Groningen]]<br />
<br />
==Periplasmic accumulation of heavy metals via Mer Operon==<br />
Periplasmic accumulation of heavy metals via Mer proteins enables the harvesting of heavy metals from the medium by binding the cytosolic and periplasmic metals to metallothionein and transporting the metal-protein complex into the periplasm.<br />
The MerR family consists of different proteins for one specific metal (<i>i.e.</i><br />
PbrR (lead), CueR (copper), ZntR (zinc), MerR (mercury), ArsR (arsenic), CadR (cadmium)).<br />
<br />
As the cells die after uptake of Mg (and induction of the Mer transporter), this system is not very well usable for our project. The dead cells will not produce the gas vesicles (it may be used however by having the gas vesicles consitutively expressed), thereby bouyancy may be a problem ([[Team:Groningen/Literature#Pennella2005|Pennella 2005]], [[Team:Groningen/Literature#Kao2008|Kao 2008]]).<br />
<br />
===Missing information/To Do===<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*Eliminate BioBrick restriction sites<br />
<br />
==Planning and requirements==<br />
<br />
* '''Modelling:'''<br />
** Import speed<br />
** Amount <br />
** Max<br />
* '''Lab:'''<br />
** HmtA<br />
*** Zn/Cu alone<br />
*** B-type ATPase (could be use if there is a ATP shortage?)<br />
** CitM (probably not used)<br />
*** Divalent ions<br />
*** Citrate around<br />
*** Citrate can bind metals that are already bound.<br />
** Measurements (both for the "normal" cell and the cell with overexpression of the transporter)<br />
*** Transporter, on/off mechanism, up to what concentration (in the cell) does it still have metal uptake.<br />
*** Measure concentration of metal. difference between begin and end concentrations of metal outside the cell.<br />
*** How fast does it transport metal in/out the cell.<br />
**** Set up tests with (initial) extracellular concentrations of about <sup>1</sup>/<sub>3</sub>K (25% of V<sub>max</sub>), K (50% of V<sub>max</sub>), 3K (75% of V<sub>max</sub>) and 10mM (99.7% of V<sub>max</sub>, corresponding to extremely polluted water), and a control with no arsenic. Obviously, more tests is better. In general a desired fraction of V<sub>max</sub> at the initial concentration can be attained by using an initial concentration of x/(1-x) times K.<br />
**** Determine "final" (steady-state) concentration of As(III) in the solution and in the cells. (Concentration over time is even better!)<br />
**** This means that the total volume of the cells (and the solution) has to be determined. Possibly through looking at the dry weight (without arsenic!).<br />
**** By manipulating the equation for the derivative of As(III) in equilibrium, As(III) can be expressed as a function of As(III)<sub>ex</sub> (given the V and K constants). We can try to fill in the computed V and K constants for GlpF and then use a least squares fit to estimate the V and K constants for ArsB.<br />
**** '''NOTE:''' Interestingly [[Team:Groningen/Literature#Kostal2004|Kostal 2004]] already did an experiment like this with cells that overexpressed ArsR. We're looking at analysing these results under the assumption that overexpressing ArsR only gives a constant factor more accumulation (for 1-100&microM As(III)), but it would be very nice to do this ourselves for unmodified cells to determine whether this is indeed true (and to determine the factor).<br />
<br />
==Export of arsenicum via Ars operon==<br />
<br />
GlpF is the importer of arsenicum. After arsenicum enters the cell, in response the Ars operon produces ArsR. At the same time, ArsB is also produced by Ars operon. This happens because the Ars operon contains three open reading frames: the first is ArsR, second ArsB and the last one is ArsC. ArsB is the exporter of arsenicum. The ars operon is located on the chromosomal DNA of E. coli.<br />
For more information see: [http://biocyc.org/ECOLI/NEW-IMAGE?type=GENE-IN-CHROM-BROWSER&object=EG12235 biocyc].<br />
<br />
[[Image:ArsRBC_operon.PNG|600px]]<br />
<br />
<br />
===Missing information/To do===<br />
*Expression assesment<br />
**Stability<br />
**Level<br />
*Functional assesment<br />
**Uptake speed<br />
**Affinity<br />
**Electrolyte potential generating force<br />
*Eliminate BioBrick restriction sites<br />
<br />
<br />
<br />
<br />
{{Team:Groningen/Project/Footer}}</div>Jaspervdg