http://2009.igem.org/wiki/index.php?title=Special:Contributions/Bigben&feed=atom&limit=50&target=Bigben&year=&month=2009.igem.org - User contributions [en]2024-03-29T10:51:05ZFrom 2009.igem.orgMediaWiki 1.16.5http://2009.igem.org/Team:USTC_Software/TeammemberTeam:USTC Software/Teammember2010-04-03T06:39:40Z<p>Bigben: </p>
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<font size = "5">'''About USTC_Software'''</font><br />
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A bunch of energetic young guys bumping into each other in pursuit of the truth of life, and this is basically the essential reason why we are here now.<br />
<br />
This year, we are much more populated than before. This not only gets solid proof from the increasing coverage of participants' number, but also can be demonstrsted by the big variance among participants' backgrounds. The 2009 iGEM team of USTC, well, if we just count the dry team, consists of two graduate students and four undergraduates. Our major varies from electrnic engineering to condensed matter physics, from geophysics to computational biology. By such a colorful combination, anything exciting could be possible relying on our brotherhood. We feel so lucky to get acquaintance with each other and really enjoy all the funny days we are together. We will enjoy the days in MIT, just join us! <br />
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[[Image:USTC_Software_member.jpg|center|550px|thumb|USTC_Software]]<br />
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<font size = "5">'''Who we are'''</font><br />
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|[[Image:wpan.jpg|[https://2009.igem.org/User:bigben Wei Pan]|center|250px|thumb]]<br />
|Hi, I'm Wei Pan (Big Ben), as a leader of our team. Currently, I'm a second year master student majored in [http://sist.ustc.edu.cn/ Biomedical Engineering] and a RA in [http://www.picb.ac.cn/PSB/ PICB]. I got my bachelor's degree in Automation, [http://scit.hit.edu.cn/hjgao/home.htm Harbin Institute of Technology]. Fascinated by biology, I try to apply control theory to Systems and Synthetic biology. <br />
|- <br />
|Hi, I am an undergraduate student of School for the Gifted Young at University and Science and Technology of China. I'm in my senior year. My major is condensed matter physics, and I also have a wide interest in Systems and Synthetic Biology and Computer Science. <br />
<br />
|[[Image:ywcui.jpg|[https://2009.igem.org/User:Ywcui Yuwei Cui]|center|250px|thumb]]<br />
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|[[Image:xmyao.jpg|[https://2009.igem.org/User:soimort Xiaomo Yao]|center|250px|thumb]]<br />
|Xiaomo, or Soimort Yao is a fantastic guy who is the youngest among us. He joint us when he just accomplished his first tryout in ACM as a freshman. He smoothly finishes all the GUI design part of the ABCD Suite with QT toolkit. He majors in Geophysics.<br />
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|Jiahao is a sophomore student (this semester a junior) coming from School of Information Science and Technology Sciences. He's not only the designer of ABCD's I/O connection with SBML, but also a mild tempered Bejinger who can do Taekwondo.<br />
|[[Image:jhli.jpg|[https://2009.igem.org/User:Jiahao Jiahao Li]|center|250px|thumb]]<br />
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|- <br />
|[[Image:Heyu.jpg|[https://igem.org/User:Heyu3 Yu He]|center|250px|thumb]]<br />
|Yu is a CMP majored senior student who finds interdecipline research of this sort really fits well with his appetite. And he always says that 'from teammates I do learn and gain happiness'. More Info about him is avaliable [http://home.ustc.edu.cn/~heyu3 here].<br />
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|I am the instructor of our team.It is my third time to take part in iGEM.It is excited to work together with our team members.My major is computational biology. Click [https://2007.igem.org/USTC/DingBo here] to know more about me <br />
|[[Image:dbche.jpg|[https://2009.igem.org/User:dbche Bo Ding]|center|250px|thumb]]<br />
|}<br />
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<font size = "5">'''We have FUN!'''</font><br />
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iGEM is fun! And even when the 'wetness' is drained, fun remains the same for 'dryness'. We and the USTC wet team work together to help find inspirations and fun. Here follows snapshots of those happy moments.<br />
<br />
<gallery widths="225px" perrow="2"><br />
Image:ustc-team-1.jpg<br />
Image:ustc-team-2.jpg<br />
Image:ustc-team-31.jpg<br />
Image:ustc-team-5.jpg<br />
Image:ustc-team-6.jpg<br />
Image:ustc-team-71.jpg<br />
</gallery><br />
<br />
<br />
<br />
*The recruitment<br />
<br />
*Yuan Xiao Festival<br />
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*Spring Outing<br />
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*Duan Wu Festival<br />
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*On Mid-Autumn Day<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/HomeTeam:USTC Software/Home2009-10-22T03:26:52Z<p>Bigben: </p>
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<font size = "5">'''Quick Start'''</font><br />
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<!---[[Image:USTCSW_QuickStart.png|center|500x500px]]---><br />
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<ul id="imap"><br />
<li id="wow"></html>[[Team:USTC_Software/Project]]<html></li><br />
<li id="why"></html>[[Team:USTC_Software/Why]]<html></li><br />
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<li id="how"></html>[[Team:USTC_Software/hoWDesign]]<html></li><br />
<li id="who"></html>[[Team:USTC_Software/Teammember]]<html></li><br />
<li id="when"></html>[[Team:USTC_Software/When]]<html></li><br />
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circle 695 728 209 [[https://2009.igem.org/Team:USTC_Software/Project/#QuickTutorial|Quick Tutorial]]<br />
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<!---[[Image:USTC_Software_logo.jpg|center|300px|thumb|Automatic Biological Circuits Design]]---><br />
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<br />
<font size = "4">'''Project Scope'''</font><br />
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<br />
<font size = "3">'''the ABCs of Automatic Biological Circuit Design'''</font><br />
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{|-<br />
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One ultimate goal of synthetic biology is to program complex biological networks that could achieve desired phenotype and produce significant metabolites in purpose of real world application, by fabricating standard components from an engineering-driven perspective. This project explores the application of theoretical approaches to automatically design synthetic complex biological networks with desired functions defined as dynamical behavior and input-output property. <br />
<br />
We propose a novel design scheme highlighted in the notion of trade-off that synthetic networks could be obtained by a compromise between performance and robustness. Moreover, series of eligible strategies, which consist of various topologies and possible standard components such as BioBricks, provide multiple choices to facilitate the wet experiment procedure. Description of all feasible solutions takes advantage of SBML and SBGN standard to guarantee extensibility and compatibility. <br />
|}<br />
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<!------><br />
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<br />
<font size = "3">'''The Campus'''</font><br />
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{|-<br />
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University of Science and Technology of China, or as we abbreviate it for USTC, locates in Hefei, east of China. It's typical subtropic continent climate here, as midsummer could be sizzling while you'll have plenty of snow to expect in winter. Like the higher education in China itself, founded in Sept 20, 1958, USTC is a young campus packed with vigorous and young faces. There are two major parts, the east campus where physical, chemical sciences and SGY locates, and the west campus where we are here endeavoring together for iGEM. Going against the prevailing trend of expanding enrollment, USTC is subject to our pride to be one of the very '''''few''''' USTCers for all these years.<br />
<br />
[[Image:USTC_Software.jpg|right|350px|thumb|Members of USTC_Software, in front of main building of School of Life Sciences]]<br />
<br />
The main building of School of Life Sciences is among the most advanced and eye-catching buildings on campus. Another reason for young guys' eyes to be caught here is due to the breakdown of USTC's characteristic guy-to-girl ratio here :-). Usually young men here will willingly (or unwillingly, anyways it never matters) leave the front row for ladies in a classroom with a typical capacity of 200 people. However here, inside the life sciences building, Goddess bless it, the ratio almost rises to 2-1! No wonder the Biology Department is always the among majors hardest to get enrolled in.<br />
|}<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/HomeTeam:USTC Software/Home2009-10-22T03:18:01Z<p>Bigben: </p>
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<div>__NOTOC__<br />
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<font size = "5">'''Quick Start'''</font><br />
|}<br />
<br /><br />
<!---[[Image:USTCSW_QuickStart.png|center|500x500px]]---><br />
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<div id="placeholder" style="width: 500px; height: 500px; margin-left: auto; margin-right: auto;"><br />
{{imageMap|imap|/wiki/images/3/38/USTCSW_QuickStart1.png|510|510|<br />
{{imageMapLink|wow|180|196|338|358|}}<br />
{{imageMapLink|why|182|5|315|125|}}<br />
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{{imageMapLink|who|58|366|194|490|}}<br />
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}}<html><center><br />
<ul id="imap"><br />
<li id="wow"></html>[[Team:USTC_Software/Project]]<html></li><br />
<li id="why"></html>[[Team:USTC_Software/Why]]<html></li><br />
<li id="what"></html>[[Team:USTC_Software/WhatOverview]]<html></li><br />
<li id="how"></html>[[Team:USTC_Software/hoWDesign]]<html></li><br />
<li id="who"></html>[[Team:USTC_Software/Teammember]]<html></li><br />
<li id="when"></html>[[Team:USTC_Software/When]]<html></li><br />
<!---<li id="wow"></html>[[Team:USTC_Software/Project]]<html></li>---><br />
</ul><br />
</center></html><br />
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<!---<br />
<imagemap><br />
Image:USTCSW_QuickStart.png|<br />
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circle 695 728 209 [[https://2009.igem.org/Team:USTC_Software/Project/#QuickTutorial|Quick Tutorial]]<br />
poly 483 123 482 321 841 322 846 118 698 118 700 91 811 87 824 49 764 1 669 28 627 70 631 110 482 122 482 122 [[https://2009.igem.org/Team:USTC_Software/Why|Why]]<br />
circle 179 528 160 [[https://2009.igem.org/Team:USTC_Software/When|When]]<br />
poly 284 948 536 1136 430 1291 168 1114 160 1089 250 956 [[https://2009.igem.org/Team:USTC_Software/Who|Who]]<br />
poly 887 1134 1085 890 1263 1024 1055 1277 1011 1261 902 1168 [[https://2009.igem.org/Team:USTC_Software/hoW|hoW]]<br />
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desc none<br />
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---><br />
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<!---[[Image:USTC_Software_logo.jpg|center|300px|thumb|Automatic Biological Circuits Design]]---><br />
<br />
<br />
<font size = "4">'''Project Scope'''</font><br />
----<br />
<br />
<font size = "3">'''the ABCs of Automatic Biological Circuit Design'''</font><br />
----<br />
{|-<br />
|align = "justify" bgcolor = "#F3F3F3"|<br />
One ultimate goal of synthetic biology is to program complex biological networks that could achieve desired phenotype and produce significant metabolites in purpose of real world application, by fabricating standard components from an engineering-driven perspective. This project explores the application of theoretical approaches to automatically design synthetic complex biological networks with desired functions defined as dynamical behavior and input-output property. <br />
<br />
We propose a novel design scheme highlighted in the notion of trade-off that synthetic networks could be obtained by a compromise between performance and robustness. Moreover, series of eligible strategies, which consist of various topologies and possible standard components such as BioBricks, provide multiple choices to facilitate the wet experiment procedure. Description of all feasible solutions takes advantage of SBML and SBGN standard to guarantee extensibility and compatibility. <br />
|}<br />
<br />
<!------><br />
<br />
<br />
<font size = "3">'''The Campus'''</font><br />
----<br />
{|-<br />
|align = "justify" bgcolor = "#F3F3F3"|<br />
University of Science and Technology of China, or as we abbreviate it for USTC, locates in Hefei, east of China. It's typical subtropic continent climate here, as midsummer could be sizzling while you'll have plenty of snow to expect in winter. Like the higher education in China itself, founded in Sept 20, 1958, USTC is a young campus packed with vigorous and young faces. There are two major parts, the east campus where physical, chemical sciences and SGY locates, and the west campus where we are here endeavoring together for iGEM. Going against the prevailing trend of expanding enrollment, USTC is subject to our pride to be one of the very '''''few''''' USTCers for all these years.<br />
<br />
[[Image:USTC_Software.jpg|right|350px|thumb|Members of USTC_Software, in front of main building of School of Life Sciences]]<br />
<br />
The main building of School of Life Sciences is among the most advanced and eye-catching buildings on campus. Another reason for young guys' eyes to be caught here is due to the breakdown of USTC's characteristic guy-to-girl ratio here :-). Usually young men here will willingly (or unwillingly, anyways it never matters) leave the front row for ladies in a classroom with a typical capacity of 200 people. However here, inside the life sciences building, Goddess bless it, the ratio almost rises to 2-1! No wonder the Biology Department is always the among majors hardest to get enrolled in.<br />
|}<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDownloadTeam:USTC Software/WhatDownload2009-10-22T03:05:14Z<p>Bigben: /* The software is available on sourceforge.net */</p>
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=The software is available on sourceforge.net=<br />
<br />
[https://sourceforge.net/projects/ustcabcd/ <font size = "4"> Click here to download</font> ]</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDownloadTeam:USTC Software/WhatDownload2009-10-22T02:59:41Z<p>Bigben: </p>
<hr />
<div>{{USTCSW_Heading}}<br />
<br />
=The software is available on sourceforge.net=<br />
<br />
[https://sourceforge.net/projects/ustcabcd/ Click here to download]</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDownloadTeam:USTC Software/WhatDownload2009-10-22T02:57:43Z<p>Bigben: </p>
<hr />
<div>The software is available on sourceforge.net<br />
<br />
[https://sourceforge.net/projects/ustcabcd/ Click here to download]</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDownloadTeam:USTC Software/WhatDownload2009-10-22T02:57:07Z<p>Bigben: </p>
<hr />
<div>The software is available on sourceforge.net[https://sourceforge.net/projects/ustcabcd/ Download ABCD]</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatPlatformTeam:USTC Software/WhatPlatform2009-10-22T02:54:51Z<p>Bigben: Team:USTC Software/WhatPlatform moved to Team:USTC Software/WhatCooperation</p>
<hr />
<div>#REDIRECT [[Team:USTC Software/WhatCooperation]]</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T02:54:51Z<p>Bigben: Team:USTC Software/WhatPlatform moved to Team:USTC Software/WhatCooperation</p>
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==Introduction==<br />
We help [https://2009.igem.org/Team:USTC_Software USTC Wet Team] ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE==<br />
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<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
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==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
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<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
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<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
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<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
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<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
==Identification Results==<br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
===Parameters===<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
===Simulation Comparison with Raw Data===<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
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<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDemoTeam:USTC Software/WhatDemo2009-10-22T02:53:57Z<p>Bigben: /* Mathematical Formulation */</p>
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'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MM <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
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<br />
=Example 1. A Synthetic Oscillator=<br />
<br />
==Introduction==<br />
<br />
The [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659856&query_hl=2 synthetic oscillatory network] designed by [http://www.elowitz.caltech.edu/ Michael Elowitz] is pioneering work. In the first place, based on his model, we want to illustrate how to tune the parameters to get pre-defined wave amplitude and wave frequency. In the second place, besides this three node repressive model, is it possible to propose a alternative topology that could also achieve tunable oscillation. In [http://gardnerlab.bu.edu/ Tim Gardner]'s PhD dissertation, such a different topology is proposed. We search feasible parameter that could achieve oscillation. <br />
<br />
==Mathematical Formulation==<br />
<br />
The activities of a gene are regulated by other genes through the<br />
interactions between them, i.e., the transcription and translation<br />
factors. Here, we assume that this system follows Hill kinetic law.<br />
<br />
<math>\begin{align}<br />
\frac{dm_{i}}{dt} &=-a_{i}m_{i}+\sum\limits_{j}b_{ij}\frac{p_{j}^{H_{ij}}}{K_{ij}+p_{j}^{H_{ij}}}+l_{i}, \\<br />
\frac{dp_{i}}{dt} &=-c_{i}p_{i}+d_{i}m_{i}, (i=1,2,...,n)<br />
\end{align}\,\!</math><br />
<br />
where <math>m_{i}(t), p_{i}(t)\in {\mathbb{R}}</math> are concentrations of mRNA and protein of the <math>i</math>th node at time <math>t</math>, respectively, <math>a_{i}</math> and<br />
<math>c_{i}</math> are the degradation rates of the mRNA and<br />
protein, <math>d_{i}</math> is the translation rate. Term (1)<br />
describes the transcription process and term (2) describes the<br />
translation process.<br />
Negative and positive signs of <math>b_{ij}</math> indicates the<br />
mutual interaction relationship that could be attributed to negative<br />
or positive feedback. The values describe the strength of promoters<br />
which is tunable by inserting different promoters in gene circuits.<br />
<math>H_{ij}</math> is Hill coefficient describing cooperativity.<br />
<math>K_{ij}</math> is the apparent dissociation constant derived<br />
from the law of mass action (equilibrium constant for dissociation).<br />
We can write <math>K_{ij}=\left( \hat{K}_{ij}\right) ^{n}</math><br />
where <math>\hat{K}</math> is ligand concentration producing half<br />
occupation (ligand concentration occupying half of the binding<br />
sites), that is also the microscopic dissociation constant.<br />
<br />
==A Tunable Oscillator==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &=-am_{1}+b\frac{p_{3}^{H_{13}}}{K+p_{3}^{H_{1}}}, \\<br />
\frac{dm_{2}}{dt} &=-am_{2}+b\frac{p_{1}^{H_{21}}}{K+p_{1}^{H_{2}}}, \\<br />
\frac{dm_{3}}{dt} &=-am_{3}+b\frac{p_{2}^{H_{32}}}{K+p_{2}^{H_{32}}}, \\<br />
\frac{dp_{1}}{dt} &=-cp_{1}+dm_{1}, \\<br />
\frac{dp_{2}}{dt} &=-cp_{2}+dm_{2}, \\<br />
\frac{dp_{3}}{dt} &=-cp_{3}+dm_{3},\text{ }<br />
\end{align}\,\!</math><br />
<br />
where <math>a, b,</math> <math>c,</math><br />
<math>d,</math> <math>H_{1},</math> <math>H_{2},</math><br />
<math>H_{3},</math> <math>K</math> are tunable parameters that could<br />
change wave amplitude and frequency. For simplicity, we assume that<br />
<math>H_{13}=H_{21}=H_{32}=2,</math> meaning that the system<br />
contains only positively cooperative reaction that once one ligand<br />
molecule is bound to the enzyme, its affinity for other ligand<br />
molecules increases.<br />
<br />
[[Image:Osc1_Amp_Tun.png|center|550px|thumb|Tunable Amplitude: <br />
The Black curve shows the original amplitude of the oscillator. <br />
The Red curve shows the desired amplitude of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
[[Image:Osc1_Freq_Tun.png|center|550px|thumb|Tunable Frequency: <br />
The Black curve shows the original frequency of the oscillator. <br />
The Red curve shows the desired frequency of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
==An Alternative Topology That Leads to Oscillation==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &= -a_{1}x_{1}+\frac{b_{1}}{K_{1}+p_{2}^{H_{12}}}, \\<br />
\frac{dm_{2}}{dt} &= -a_{2}x_{2}+\frac{b_{2}p_{3}^{H_{23}}}{%<br />
K_{2}+p_{1}^{H_{21}}+p_{3}^{H_{23}}}, \\<br />
\frac{dm_{3}}{dt} &= -a_{3}x_{3}+\frac{b_{3}}{K_{3}+p_{2}^{H_{32}}} \\<br />
\frac{dp_{1}}{dt} &= -c_{1}p_{1}+d_{1}m_{1}, \\<br />
\frac{dp_{2}}{dt} &= -c_{2}p_{2}+d_{2}m_{2}, \\<br />
\frac{dp_{3}}{dt} &= -c_{3}p_{3}+d_{3}m_{3},<br />
\end{align}\,\!</math><br />
<br />
[[Image:Osc2.png|center|550px|thumb|An Alternative Topology the leads to Oscillation]]<br />
<br />
=Example 2: Perfect Adaptation=<br />
<br />
==Introduction==<br />
<br />
In this example, we try to seek different network topologies that can achieve adaptation-the ability to reset themselves after responding to a stimulus.. Actually, most of the scripts are cited from a newly published paper on [http://www.cell.com/ Cell]: [http://www.ncbi.nlm.nih.gov/pubmed/19703401 Defining Network Topologies that Can Achieve Biochemical Adaptation]. It 's quite by accident that issues discussed in this paper share some similarities with our project. To test our ABCD is powerful or not, the only thing we need to do is to search the two topologies found in this paper. By running nearly two days, we prove the solution. <br />
<br />
==Mathematical Formulation==<br />
<br />
We assume that each node (labeled as <math>A</math>, <math>B</math>, <math>C</math>) has a fixed concentration<br />
(normalized to <math>1</math>) but has two forms: active and<br />
inactive (here <math>A</math> represents the concentration of active state, and <br />
<math>1-A</math> is the concentration of the<br />
inactive state). The enzymatic regulation converts its target node<br />
between the two forms. For example, a positive regulation of node<br />
<math>B</math> by node <math>A</math> as denoted by a link<br />
<br />
<math>A\longrightarrow B</math> <br />
<br />
would mean that the active <math>A</math> convertsBfrom its inactive to its active form and<br />
would be modeled by the rate <br />
<br />
<math>R(B_{inactive}\longrightarrow<br />
B_{active})=k_{AB}A(1-B)/\left[ (1-B)+K_{AB}\right] </math>, <br />
<br />
where <math>A</math> is the normalized concentration of the active form of<br />
node <math>A</math> and <math>1-B</math> the normalized<br />
concentrations of the inactive form of node B. Likewise,<br />
<math>A-|B</math> implies that the active A catalyzes the reverse<br />
transition of node B from its active to its inactive form, with a<br />
rate <br />
<br />
<math>R(B_{active}\longrightarrow B_{inactive})=k_{AB}^{^{\prime }}/(B+K_{AB}^{^{\prime }}).</math> <br />
<br />
When there are multiple regulations of the same sign on a node, the<br />
effect is additive. For example, if node C is positively regulated<br />
by node A and node B, <br />
<br />
<math> R(C_{inactive}\longrightarrow C_{active})= k_{AC}A(1-C)/\left[ (1-C)+K_{AC}\right]</math> + <math>k_{BC}B(1-C)/\left[ (1-C)+K_{BC}\right] </math> . <br />
<br />
We assume that the interconversion between active and inactive forms of<br />
a node is reversible. Thus if a node <math>i</math> has only<br />
positive incoming links, it is assumed that there is a background<br />
(constitutive) deactivating enzyme Fi of a constant concentration<br />
(set to be <math>0.5</math>) to catalyze the reverse reaction.<br />
Similarly, a background activating enzyme <math>E_{i}=0.5</math> is<br />
added for the nodes that have only negative incoming links. The rate<br />
equation for a node (e.g., node <math>B</math>) takes the form:<br />
<br />
<math>\begin{align} \frac{dB}{dt}=\sum\limits_{i}X_{i}\cdot<br />
k_{X_{i}B}\frac{(1-B)}{ (1-B)+K_{X_{i}B}}-\sum\limits_{i}Y_{i}\cdot<br />
k_{X_{i}B}\frac{B}{B+K_{Y_{i}B}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>Xi=A,B,C,E_{A},E_{B},</math> or <math>E_{c}</math> are<br />
the activating enzymes (positive regulators) of <math>B</math> and<br />
<math>Yi=A,B,C,F_{A},F_{B},</math> or <math>F_{C}</math> are the<br />
deactivating enzymes (negative regulators) of <math>B</math>. In the<br />
equation for node A, an input term is added to the righthand-side of<br />
the equation: <br />
<br />
<math> Ik_{IA}(1-A)/((1-A)+K_{IA})</math>. <br />
<br />
The number of parameters in a network is <math> n_{p}=2n_{I}+2</math>, where<br />
<math>n_{I}</math> is the number of links in the network (including<br />
links from the basal enzymes if present).<br />
<br />
<br />
Then we hope the output of interested node tracks the target dynamics by a sudden stimulus and search the feasible topologies that achieve adaptation in the scope of all possible topologies. Two possible topologies are listed below:<br />
<br />
[[ Image:Adaptation.png|center|550px|thumb|Two topologies that can achieve adaptation: Negative Feedback Loop with a Buffer Node (NFBLB) and Incoherent Feedforward Loop with a Proportioner Node (IFFLP) (Figure reproduced from [http://www.ncbi.nlm.nih.gov/pubmed/19703401 ''Defining Network Topologies that Can Achieve Biochemical Adaptation''])]]<br />
<br />
==Feedback loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&C\cdot k_{CB}\frac{(1-B)}{(1-B)+K_{CB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>F_{A}</math> and <math>F_{B}</math> represent the<br />
concentrations of basal enzymes that carry out the reverse reactions<br />
on nodes <math>A</math> and <math>B</math>, respectively (they<br />
oppose the active network links that activate <math>A</math> and<br />
<math>B</math>). In this circuit, node <math>A</math> simply<br />
functions as a passive relay of the input to node <math>C</math>;<br />
the circuit would work in the same way if the input were directly<br />
acting on node <math>C</math> (just replacing <math>A</math> with<br />
<math>I</math> in the third equation of Equation 1). Analyzing the<br />
parameter sets that enabled this topology to adapt indicates that<br />
the two constants <math>K_{CB}</math> and <math>K_{F_{B}B}^{^{\prime<br />
}}</math> (Michaelis-Menten constants for activation of<br />
<math>B</math> by <math>C</math> and inhibition of <math>B </math><br />
by the basal enzyme) tend to be small, suggesting that the two<br />
enzymes acting on node <math>B</math> must approach saturation to<br />
achieve adaptation. Indeed, it can be shown that in the case of<br />
saturation this topology can achieve perfect adaptation.<br />
<br />
<math>\begin{align}<br />
\begin{tabular}{l}<br />
</math>figure\text{ 1}\text{: desired input}</math> \\<br />
</math>figure\text{ 2}\text{: different inputs}</math> \\<br />
</math>figure\text{ 3: }</math>topology<br />
\end{tabular}<br />
\\ \end{align}\,\!</math><br />
<br />
[[ Image:Adapt2.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptationSim1.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
Global Sensitivity Analysis<br />
We carry out global sensitivity analysis for this model, the result shows that<br />
the sensitivity coefficient of stimilus is very small which also prove the <br />
reliability of sensitivity analysis at the same time.<br />
The following figure shows global sensitivity coefficients<br />
of 12 parameters in this system:<br />
[[Image:Global_sensitivity.png|center|550px|thumb|global sensitivity coefficients<br />
of 12 parameters in this system]]<br />
Besides the external stimulus "input", we also check other two paramters. k_CB has the<br />
greatest global senstivity value, we change its value by -5% and +5%, then simulate the<br />
system again, the following figure shows change on species 3:<br />
[[Image:SensKCB.png|center|550px|thumb|pertubation on species 3 after change of k_CB]]<br />
<br />
==Feedforward loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AB}\frac{(1-B)}{(1-B)+K_{AB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
The adaptation mechanism is mathematically captured in the<br />
<br />
equation for node <math>C</math>: if the steady-state concentration<br />
of the negative regulator B is proportional to that of the positive<br />
regulator <math>A</math>, the equation determining the steady-state<br />
value of <math>C</math>, <math>dC/dt=0</math>, would be independent<br />
of <math>A</math> and hence of the input <math>I</math>. In this<br />
case, the equation for node <math>B</math> generates the condition<br />
under which the steady-state value <math> B^*</math> would be<br />
proportional to <math>A^*</math>: the first term in<br />
<math>dB/dt</math> equation should depend on <math>A</math> only and<br />
the second term on <math>B</math> only. The condition can be<br />
satisfied if the first term is in the saturated region region<br />
<br />
<math>((1-B)\gg K_{AB})</math> <br />
<br />
and the second in the linear region<br />
<br />
<math>B\ll K_{F_{B}B}^{^{\prime }}</math>, <br />
<br />
leading to<br />
<br />
<math>\begin{align} B^{\ast }=A^{\ast }\cdot<br />
k_{AB}K_{F_{B}B}^{^{\prime }}/(F_{B}k_{F_{B}B}^{^{\prime }})<br />
\\ \end{align}\,\!</math><br />
<br />
This relationship, established by the equation for node<br />
<math>B</math>, shows that the steady-state concentration of active<br />
<math>B</math> is proportional to the steady-state concentration of<br />
active <math>A</math>. Thus <math>B</math> will negatively regulate<br />
<math>C</math> in proportion to the degree of pathway input. This<br />
effect of <math>B</math> acting as a proportioner node of<br />
<math>A</math> can be graphically gleaned from the plot of the<br />
<math>B</math> and <math>C</math> nullclines (Figure feedforward).<br />
In this case, maintaining a constant <math>C^{\ast }</math> requires<br />
the B nullcline to move the same distance as the <math>C</math><br />
nullcline in response to an input change. Here again, the<br />
sensitivity of the circuit (the magnitude of the transient response)<br />
depends on the ratio of the speeds of the two signal transduction<br />
branches: <br />
<br />
<math> A\longrightarrow C</math> <br />
<br />
and<br />
<br />
<math>A\longrightarrow B-|C</math>, <br />
<br />
which can be independently tunedfrom the adaptation precision.<br />
<br />
<br />
<br />
[[ Image:AdaptFeedforward1.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptFeedforward2.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
=Example 3. Bistable Toggle Switch=<br />
<br />
==Introduction==<br />
<br />
A good example of engineering in Synthetic Biology include the pioneering work of [http://gardnerlab.bu.edu/ Tim Gardner] and [http://www.bu.edu/abl/ James Collins] on an [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659857&query_hl=5 engineered genetic toggle switch]. Here, we want to show how to tune parameters to guarantee bistability.<br />
<br />
==Mathematical Formulation==<br />
<br />
<br />
<math>\begin{align}<br />
\dot{u}(t) &=\frac{\alpha _{1}}{1+v^{\theta }(t)}-\beta _{1}u(t),<br />
(.....................................equation1)<br />
\\<br />
\dot{v}(t) &=\frac{\alpha _{2}X^{\eta }}{X^{\eta }+1+u^{\gamma }(t)}-\beta<br />
_{2}v(t),(..............................................equation2)<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>X</math> is input, <math>u</math> is the concentration<br />
of repressor 1, <math>v</math> is the concentration of repressor 2,<br />
<math>\alpha _{1}</math> is the effective rate of synthesis of<br />
repressor 1, <math>\alpha _{2}</math> is the effective rate of<br />
synthesis of repressor 2, <math>\theta </math> is the cooperativity<br />
of repression of promoter 2 and <math>\gamma </math> is the<br />
cooperativity of repression of promoter 1. The above model is<br />
derived from a biochemical rate equation formulation of gene<br />
expression. The final form of the toggle equations preserves the two<br />
most fundamental aspects of the network: cooperative repression of<br />
constitutively transcribed promoters (the first term in each<br />
equation), and degradation/dilution of the repressors (the second<br />
term in each equation).<br />
<br />
The parameters <math>\alpha _{1}</math> and <math>\alpha _{2}</math><br />
are lumped parameters that describe the net effect of RNA polymerase<br />
binding, open-complex formation, transcript elongation, transcript<br />
termination, repressor binding, ribosome binding and polypeptide<br />
elongation. The cooperativity described by <math>\theta </math> and<br />
<math>\gamma </math> can arise from the multimerization of the<br />
repressor proteins and the cooperative binding of repressor<br />
multimers to multiple operator sites in the promoter. An additional<br />
modification to equation (1) is needed to describe induction of the<br />
repressors.<br />
<br />
<math>\alpha _{1},\alpha _{2},\gamma ,\theta ,\eta ,\beta _{1},\beta<br />
_{2}</math> should be indentified to guarantee bistability. We<br />
assume that <math>\gamma =\theta =\eta =2</math> as parameter<br />
restriction. Thus, there are four parameters to be indentified.<br />
[[Image:Toggle_Switch_Species1.png|center|550px|thumb|Identification Result<br />
for the first species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
[[Image:Toggle_Switch_Species2.png|center|550px|thumb|Identification Result<br />
for the second species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDemoTeam:USTC Software/WhatDemo2009-10-22T02:44:42Z<p>Bigben: /* Feedforward loop */</p>
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<br />
=Example 1. A Synthetic Oscillator=<br />
<br />
==Introduction==<br />
<br />
The [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659856&query_hl=2 synthetic oscillatory network] designed by [http://www.elowitz.caltech.edu/ Michael Elowitz] is pioneering work. In the first place, based on his model, we want to illustrate how to tune the parameters to get pre-defined wave amplitude and wave frequency. In the second place, besides this three node repressive model, is it possible to propose a alternative topology that could also achieve tunable oscillation. In [http://gardnerlab.bu.edu/ Tim Gardner]'s PhD dissertation, such a different topology is proposed. We search feasible parameter that could achieve oscillation. <br />
<br />
==Mathematical Formulation==<br />
<br />
The activities of a gene are regulated by other genes through the<br />
interactions between them, i.e., the transcription and translation<br />
factors. Here, we assume that this system follows Hill kinetic law.<br />
<br />
<math>\begin{align}<br />
\frac{dm_{i}}{dt} &=-a_{i}m_{i}+\sum\limits_{j}b_{ij}\frac{p_{j}^{H_{ij}}}{K_{ij}+p_{j}^{H_{ij}}}+l_{i}, \\<br />
\frac{dp_{i}}{dt} &=-c_{i}p_{i}+d_{i}m_{i}, (i=1,2,...,n)<br />
\end{align}\,\!</math><br />
<br />
where <math>m_{i}(t), p_{i}(t)\in {\mathbb{R}}</math> are concentrations of mRNA and protein of the <math>i</math>th node at time <math>t</math>, respectively, <math>a_{i}</math> and<br />
<math>c_{i}</math> are the degradation rates of the mRNA and<br />
protein, <math>d_{i}</math> is the translation rate. Term (1)<br />
describes the transcription process and term (2) describes the<br />
translation process.<br />
Negative and positive signs of <math>b_{ij}</math> indicates the<br />
mutual interaction relationship that could be attributed to negative<br />
or positive feedback. The values describe the strength of promoters<br />
which is tunable by inserting different promoters in gene circuits.<br />
<math>H_{ij}</math> is Hill coefficient describing cooperativity.<br />
<math>K_{ij}</math> is the apparent dissociation constant derived<br />
from the law of mass action (equilibrium constant for dissociation).<br />
We can write <math>K_{ij}=\left( \hat{K}_{ij}\right) ^{n}</math><br />
where <math>\hat{K}</math> is ligand concentration producing half<br />
occupation (ligand concentration occupying half of the binding<br />
sites), that is also the microscopic dissociation constant.<br />
<br />
==A Tunable Oscillator==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &=-am_{1}+b\frac{p_{3}^{H_{13}}}{K+p_{3}^{H_{1}}}, \\<br />
\frac{dm_{2}}{dt} &=-am_{2}+b\frac{p_{1}^{H_{21}}}{K+p_{1}^{H_{2}}}, \\<br />
\frac{dm_{3}}{dt} &=-am_{3}+b\frac{p_{2}^{H_{32}}}{K+p_{2}^{H_{32}}}, \\<br />
\frac{dp_{1}}{dt} &=-cp_{1}+dm_{1}, \\<br />
\frac{dp_{2}}{dt} &=-cp_{2}+dm_{2}, \\<br />
\frac{dp_{3}}{dt} &=-cp_{3}+dm_{3},\text{ }<br />
\end{align}\,\!</math><br />
<br />
where <math>a, b,</math> <math>c,</math><br />
<math>d,</math> <math>H_{1},</math> <math>H_{2},</math><br />
<math>H_{3},</math> <math>K</math> are tunable parameters that could<br />
change wave amplitude and frequency. For simplicity, we assume that<br />
<math>H_{13}=H_{21}=H_{32}=2,</math> meaning that the system<br />
contains only positively cooperative reaction that once one ligand<br />
molecule is bound to the enzyme, its affinity for other ligand<br />
molecules increases.<br />
<br />
[[Image:Osc1_Amp_Tun.png|center|550px|thumb|Tunable Amplitude: <br />
The Black curve shows the original amplitude of the oscillator. <br />
The Red curve shows the desired amplitude of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
[[Image:Osc1_Freq_Tun.png|center|550px|thumb|Tunable Frequency: <br />
The Black curve shows the original frequency of the oscillator. <br />
The Red curve shows the desired frequency of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
==An Alternative Topology That Leads to Oscillation==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &= -a_{1}x_{1}+\frac{b_{1}}{K_{1}+p_{2}^{H_{12}}}, \\<br />
\frac{dm_{2}}{dt} &= -a_{2}x_{2}+\frac{b_{2}p_{3}^{H_{23}}}{%<br />
K_{2}+p_{1}^{H_{21}}+p_{3}^{H_{23}}}, \\<br />
\frac{dm_{3}}{dt} &= -a_{3}x_{3}+\frac{b_{3}}{K_{3}+p_{2}^{H_{32}}} \\<br />
\frac{dp_{1}}{dt} &= -c_{1}p_{1}+d_{1}m_{1}, \\<br />
\frac{dp_{2}}{dt} &= -c_{2}p_{2}+d_{2}m_{2}, \\<br />
\frac{dp_{3}}{dt} &= -c_{3}p_{3}+d_{3}m_{3},<br />
\end{align}\,\!</math><br />
<br />
[[Image:Osc2.png|center|550px|thumb|An Alternative Topology the leads to Oscillation]]<br />
<br />
=Example 2: Perfect Adaptation=<br />
<br />
==Introduction==<br />
<br />
In this example, we try to seek different network topologies that can achieve adaptation-the ability to reset themselves after responding to a stimulus.. Actually, most of the scripts are cited from a newly published paper on [http://www.cell.com/ Cell]: [http://www.ncbi.nlm.nih.gov/pubmed/19703401 Defining Network Topologies that Can Achieve Biochemical Adaptation]. It 's quite by accident that issues discussed in this paper share some similarities with our project. To test our ABCD is powerful or not, the only thing we need to do is to search the two topologies found in this paper. By running nearly two days, we prove the solution. <br />
<br />
==Mathematical Formulation==<br />
<br />
We assume that each node (labeled as <math>A</math>, <math>B</math>, <math>C</math>) has a fixed concentration<br />
(normalized to <math>1</math>) but has two forms: active and<br />
inactive (here <math>A</math> represents the concentration of active state, and <br />
<math>1-A</math> is the concentration of the<br />
inactive state). The enzymatic regulation converts its target node<br />
between the two forms. For example, a positive regulation of node<br />
<math>B</math> by node <math>A</math> as denoted by a link<br />
<br />
<math>A\longrightarrow B</math> <br />
<br />
would mean that the active <math>A</math> convertsBfrom its inactive to its active form and<br />
would be modeled by the rate <br />
<br />
<math>R(B_{inactive}\longrightarrow<br />
B_{active})=k_{AB}A(1-B)/\left[ (1-B)+K_{AB}\right] </math>, <br />
<br />
where <math>A</math> is the normalized concentration of the active form of<br />
node <math>A</math> and <math>1-B</math> the normalized<br />
concentrations of the inactive form of node B. Likewise,<br />
<math>A-|B</math> implies that the active A catalyzes the reverse<br />
transition of node B from its active to its inactive form, with a<br />
rate <br />
<br />
<math>R(B_{active}\longrightarrow B_{inactive})=k_{AB}^{^{\prime }}/(B+K_{AB}^{^{\prime }}).</math> <br />
<br />
When there are multiple regulations of the same sign on a node, the<br />
effect is additive. For example, if node C is positively regulated<br />
by node A and node B, <br />
<br />
<math> R(C_{inactive}\longrightarrow C_{active})= k_{AC}A(1-C)/\left[ (1-C)+K_{AC}\right]</math> + <math>k_{BC}B(1-C)/\left[ (1-C)+K_{BC}\right] </math> . <br />
<br />
We assume that the interconversion between active and inactive forms of<br />
a node is reversible. Thus if a node <math>i</math> has only<br />
positive incoming links, it is assumed that there is a background<br />
(constitutive) deactivating enzyme Fi of a constant concentration<br />
(set to be <math>0.5</math>) to catalyze the reverse reaction.<br />
Similarly, a background activating enzyme <math>E_{i}=0.5</math> is<br />
added for the nodes that have only negative incoming links. The rate<br />
equation for a node (e.g., node <math>B</math>) takes the form:<br />
<br />
<math>\begin{align} \frac{dB}{dt}=\sum\limits_{i}X_{i}\cdot<br />
k_{X_{i}B}\frac{(1-B)}{ (1-B)+K_{X_{i}B}}-\sum\limits_{i}Y_{i}\cdot<br />
k_{X_{i}B}\frac{B}{B+K_{Y_{i}B}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>Xi=A,B,C,E_{A},E_{B},</math> or <math>E_{c}</math> are<br />
the activating enzymes (positive regulators) of <math>B</math> and<br />
<math>Yi=A,B,C,F_{A},F_{B},</math> or <math>F_{C}</math> are the<br />
deactivating enzymes (negative regulators) of <math>B</math>. In the<br />
equation for node A, an input term is added to the righthand-side of<br />
the equation: <br />
<br />
<math> Ik_{IA}(1-A)/((1-A)+K_{IA})</math>. <br />
<br />
The number of parameters in a network is <math> n_{p}=2n_{I}+2</math>, where<br />
<math>n_{I}</math> is the number of links in the network (including<br />
links from the basal enzymes if present).<br />
<br />
<br />
Then we hope the output of interested node tracks the target dynamics by a sudden stimulus and search the feasible topologies that achieve adaptation in the scope of all possible topologies. Two possible topologies are listed below:<br />
<br />
[[ Image:Adaptation.png|center|550px|thumb|Two topologies that can achieve adaptation: Negative Feedback Loop with a Buffer Node (NFBLB) and Incoherent Feedforward Loop with a Proportioner Node (IFFLP) (Figure reproduced from [http://www.ncbi.nlm.nih.gov/pubmed/19703401 ''Defining Network Topologies that Can Achieve Biochemical Adaptation''])]]<br />
<br />
==Feedback loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&C\cdot k_{CB}\frac{(1-B)}{(1-B)+K_{CB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>F_{A}</math> and <math>F_{B}</math> represent the<br />
concentrations of basal enzymes that carry out the reverse reactions<br />
on nodes <math>A</math> and <math>B</math>, respectively (they<br />
oppose the active network links that activate <math>A</math> and<br />
<math>B</math>). In this circuit, node <math>A</math> simply<br />
functions as a passive relay of the input to node <math>C</math>;<br />
the circuit would work in the same way if the input were directly<br />
acting on node <math>C</math> (just replacing <math>A</math> with<br />
<math>I</math> in the third equation of Equation 1). Analyzing the<br />
parameter sets that enabled this topology to adapt indicates that<br />
the two constants <math>K_{CB}</math> and <math>K_{F_{B}B}^{^{\prime<br />
}}</math> (Michaelis-Menten constants for activation of<br />
<math>B</math> by <math>C</math> and inhibition of <math>B </math><br />
by the basal enzyme) tend to be small, suggesting that the two<br />
enzymes acting on node <math>B</math> must approach saturation to<br />
achieve adaptation. Indeed, it can be shown that in the case of<br />
saturation this topology can achieve perfect adaptation.<br />
<br />
<math>\begin{align}<br />
\begin{tabular}{l}<br />
</math>figure\text{ 1}\text{: desired input}</math> \\<br />
</math>figure\text{ 2}\text{: different inputs}</math> \\<br />
</math>figure\text{ 3: }</math>topology<br />
\end{tabular}<br />
\\ \end{align}\,\!</math><br />
<br />
[[ Image:Adapt2.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptationSim1.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
Global Sensitivity Analysis<br />
We carry out global sensitivity analysis for this model, the result shows that<br />
the sensitivity coefficient of stimilus is very small which also prove the <br />
reliability of sensitivity analysis at the same time.<br />
The following figure shows global sensitivity coefficients<br />
of 12 parameters in this system:<br />
[[Image:Global_sensitivity.png|center|550px|thumb|global sensitivity coefficients<br />
of 12 parameters in this system]]<br />
Besides the external stimulus "input", we also check other two paramters. k_CB has the<br />
greatest global senstivity value, we change its value by -5% and +5%, then simulate the<br />
system again, the following figure shows change on species 3:<br />
[[Image:SensKCB.png|center|550px|thumb|pertubation on species 3 after change of k_CB]]<br />
<br />
==Feedforward loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AB}\frac{(1-B)}{(1-B)+K_{AB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
The adaptation mechanism is mathematically captured in the<br />
<br />
equation for node <math>C</math>: if the steady-state concentration<br />
of the negative regulator B is proportional to that of the positive<br />
regulator <math>A</math>, the equation determining the steady-state<br />
value of <math>C</math>, <math>dC/dt=0</math>, would be independent<br />
of <math>A</math> and hence of the input <math>I</math>. In this<br />
case, the equation for node <math>B</math> generates the condition<br />
under which the steady-state value <math> B^*</math> would be<br />
proportional to <math>A^*</math>: the first term in<br />
<math>dB/dt</math> equation should depend on <math>A</math> only and<br />
the second term on <math>B</math> only. The condition can be<br />
satisfied if the first term is in the saturated region region<br />
<br />
<math>((1-B)\gg K_{AB})</math> <br />
<br />
and the second in the linear region<br />
<br />
<math>B\ll K_{F_{B}B}^{^{\prime }}</math>, <br />
<br />
leading to<br />
<br />
<math>\begin{align} B^{\ast }=A^{\ast }\cdot<br />
k_{AB}K_{F_{B}B}^{^{\prime }}/(F_{B}k_{F_{B}B}^{^{\prime }})<br />
\\ \end{align}\,\!</math><br />
<br />
This relationship, established by the equation for node<br />
<math>B</math>, shows that the steady-state concentration of active<br />
<math>B</math> is proportional to the steady-state concentration of<br />
active <math>A</math>. Thus <math>B</math> will negatively regulate<br />
<math>C</math> in proportion to the degree of pathway input. This<br />
effect of <math>B</math> acting as a proportioner node of<br />
<math>A</math> can be graphically gleaned from the plot of the<br />
<math>B</math> and <math>C</math> nullclines (Figure feedforward).<br />
In this case, maintaining a constant <math>C^{\ast }</math> requires<br />
the B nullcline to move the same distance as the <math>C</math><br />
nullcline in response to an input change. Here again, the<br />
sensitivity of the circuit (the magnitude of the transient response)<br />
depends on the ratio of the speeds of the two signal transduction<br />
branches: <br />
<br />
<math> A\longrightarrow C</math> <br />
<br />
and<br />
<br />
<math>A\longrightarrow B-|C</math>, <br />
<br />
which can be independently tunedfrom the adaptation precision.<br />
<br />
<br />
<br />
[[ Image:AdaptFeedforward1.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptFeedforward2.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
=Example 3. Bistable Toggle Switch=<br />
<br />
==Introduction==<br />
<br />
A good example of engineering in Synthetic Biology include the pioneering work of [http://gardnerlab.bu.edu/ Tim Gardner] and [http://www.bu.edu/abl/ James Collins] on an [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659857&query_hl=5 engineered genetic toggle switch]. Here, we want to show how to tune parameters to guarantee bistability.<br />
<br />
==Mathematical Formulation==<br />
<br />
<br />
<math>\begin{align}<br />
\dot{u}(t) &=\frac{\alpha _{1}}{1+v^{\theta }(t)}-\beta _{1}u(t),<br />
(.....................................equation1)<br />
\\<br />
\dot{v}(t) &=\frac{\alpha _{2}X^{\eta }}{X^{\eta }+1+u^{\gamma }(t)}-\beta<br />
_{2}v(t),(..............................................equation2)<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>X</math> is input, <math>u</math> is the concentration<br />
of repressor 1, <math>v</math> is the concentration of repressor 2,<br />
<math>\alpha _{1}</math> is the effective rate of synthesis of<br />
repressor 1, <math>\alpha _{2}</math> is the effective rate of<br />
synthesis of repressor 2, <math>\theta </math> is the cooperativity<br />
of repression of promoter 2 and <math>\gamma </math> is the<br />
cooperativity of repression of promoter 1. The above model is<br />
derived from a biochemical rate equation formulation of gene<br />
expression. The final form of the toggle equations preserves the two<br />
most fundamental aspects of the network: cooperative repression of<br />
constitutively transcribed promoters (the first term in each<br />
equation), and degradation/dilution of the repressors (the second<br />
term in each equation).<br />
<br />
The parameters <math>\alpha _{1}</math> and <math>\alpha _{2}</math><br />
are lumped parameters that describe the net effect of RNA polymerase<br />
binding, open-complex formation, transcript elongation, transcript<br />
termination, repressor binding, ribosome binding and polypeptide<br />
elongation. The cooperativity described by <math>\theta </math> and<br />
<math>\gamma </math> can arise from the multimerization of the<br />
repressor proteins and the cooperative binding of repressor<br />
multimers to multiple operator sites in the promoter. An additional<br />
modification to equation (1) is needed to describe induction of the<br />
repressors.<br />
<br />
<math>\alpha _{1},\alpha _{2},\gamma ,\theta ,\eta ,\beta _{1},\beta<br />
_{2}</math> should be indentified to guarantee bistability. We<br />
assume that <math>\gamma =\theta =\eta =2</math> as parameter<br />
restriction. Thus, there are four parameters to be indentified.<br />
[[Image:Toggle_Switch_Species1.png|center|550px|thumb|Identification Result<br />
for the first species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
[[Image:Toggle_Switch_Species2.png|center|550px|thumb|Identification Result<br />
for the second species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
Parameters:<br />
<math>\alpha _{1}</math> 26.3082 14<br />
<math>\beta _{1}</math> 1.79953 1<br />
<math>\alpha _{2}</math> 4.35684 5<br />
<math>\beta _{2}</math> 0.610341 1<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/HomeTeam:USTC Software/Home2009-10-22T02:26:29Z<p>Bigben: </p>
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<div>__NOTOC__<br />
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<font size = "5">'''Quick Start'''</font><br />
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<br /><br />
<!---[[Image:USTCSW_QuickStart.png|center|500x500px]]---><br />
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<div id="placeholder" style="width: 500px; height: 500px; margin-left: auto; margin-right: auto;"><br />
{{imageMap|imap|/wiki/images/3/38/USTCSW_QuickStart1.png|510|510|<br />
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<ul id="imap"><br />
<li id="wow"></html>[[Team:USTC_Software/Project]]<html></li><br />
<li id="why"></html>[[Team:USTC_Software/Why]]<html></li><br />
<li id="what"></html>[[Team:USTC_Software/WhatOverview]]<html></li><br />
<li id="how"></html>[[Team:USTC_Software/hoWDesign]]<html></li><br />
<li id="who"></html>[[Team:USTC_Software/Teammember]]<html></li><br />
<li id="when"></html>[[Team:USTC_Software/When]]<html></li><br />
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</center></html><br />
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<br />
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circle 695 728 209 [[https://2009.igem.org/Team:USTC_Software/Project/#QuickTutorial|Quick Tutorial]]<br />
poly 483 123 482 321 841 322 846 118 698 118 700 91 811 87 824 49 764 1 669 28 627 70 631 110 482 122 482 122 [[https://2009.igem.org/Team:USTC_Software/Why|Why]]<br />
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<!---[[Image:USTC_Software_logo.jpg|center|300px|thumb|Automatic Biological Circuits Design]]---><br />
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<br />
<font size = "4">'''Project Scope'''</font><br />
----<br />
<br />
<font size = "3">'''the ABCs of Automatic Biological Circuit Design'''</font><br />
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One ultimate goal of synthetic biology is to program complex biological networks that could achieve desired phenotype and produce significant metabolites in purpose of real world application, by fabricating standard components from an engineering-driven perspective. This project explores the application of theoretical approaches to automatically design synthetic complex biological networks with desired functions defined as dynamical behavior and input-output property. <br />
<br />
We propose a novel design scheme highlighted in the notion of trade-off that synthetic networks could be obtained by a compromise between performance and robustness. Moreover, series of eligible strategies, which consist of various topologies and possible standard components such as BioBricks, provide multiple choices to facilitate the wet experiment procedure. Description of all feasible solutions takes advantage of SBML and SBGN standard to guarantee extensibility and compatibility. <br />
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<font size = "3">'''The Campus'''</font><br />
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University of Science and Technology of China, or as we abbreviate it for USTC, locates in Hefei, east of China. It's typical subtropic continent climate here, as midsummer could be sizzling while you'll have plenty of snow to expect in winter. Like the higher education in China itself, founded in Sept 20, 1958, USTC is a young campus packed with vigorous and young faces. There are two major parts, the east campus where physical, chemical sciences and SGY locates, and the west campus where we are here endeavoring together for iGEM. Going against the prevailing trend of expanding enrollment, USTC is subject to our pride to be one of the very '''''few''''' USTCers for all these years.<br />
<br />
[[Image:USTC_Software.jpg|right|350px|thumb|Members of USTC_Software, in front of main building of School of Life Sciences]]<br />
<br />
The main building of School of Life Sciences is among the most advanced and eye-catching buildings on campus. Another reason for young guys' eyes to be caught here is due to the breakdown of USTC's characteristic guy-to-girl ratio here :-). Usually young men here will willingly (or unwillingly, anyways it never matters) leave the front row for ladies in a classroom with a typical capacity of 200 people. However here, inside the life sciences building, Goddess bless it, the ratio almost rises to 2-1! No wonder the Biology Department is always the among majors hardest to get enrolled in.<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:39:15Z<p>Bigben: /* Introduction */</p>
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==Introduction==<br />
We help [https://2009.igem.org/Team:USTC_Software USTC Wet Team] ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
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<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
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<br />
==Identification Results==<br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
===Parameters===<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
===Simulation Comparison with Raw Data===<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:33:36Z<p>Bigben: /* Identification Results */</p>
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==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
==Identification Results==<br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
===Parameters===<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
===Simulation Comparison with Raw Data===<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:29:52Z<p>Bigben: /* A Simplified Model */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
<br /><br />
|align = "justify"|<br />
<br />
==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
==Identification Results==<br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:27:39Z<p>Bigben: /* Reactions and ODE' */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
<br /><br />
|align = "justify"|<br />
<br />
==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:26:48Z<p>Bigben: </p>
<hr />
<div>{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
<br /><br />
|align = "justify"|<br />
<br />
==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE'==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:25:48Z<p>Bigben: </p>
<hr />
<div>{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|align = "justify"|<br />
<br />
==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE'==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.<br />
<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:22:19Z<p>Bigben: </p>
<hr />
<div>==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration. With the permission from both teams, we share the source code of this description page together<br />
<br />
<br />
==pConX<sub>2</sub>+LuxR+pLux/Tet+GFP==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
==Reactions and ODE'==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
==A Simplified Model==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
With the help of [https://2009.igem.org/Team:USTC USTC Wet Team], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
'''k3=0.8; rAHL=0.001; C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)''' <br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:17:22Z<p>Bigben: </p>
<hr />
<div>==Introduction==<br />
We help USTC Wet Team ''identify the kinetic parameters'' in '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' device.<br />
The completion of this model are a result of collaboration.<br />
<br />
<br />
== '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' ==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
== '''Reactions and ODE''' ==<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
== '''A Simplified Model''' ==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
With the help of [https://2009.igem.org/Team:USTC_Software USTC_Software], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
k3=0.8; rAHL=0.001;<br />
C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatCooperationTeam:USTC Software/WhatCooperation2009-10-22T01:11:14Z<p>Bigben: New page: [https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg ] == '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' == '''Parts:''' <partinfo>K176026</partinfo> <partinfo>K176...</p>
<hr />
<div>[https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg ]<br />
<br />
<br />
<br />
<br />
== '''pConX<sub>2</sub>+LuxR+pLux/Tet+GFP''' ==<br />
<br />
'''Parts:''' <br />
<partinfo>K176026</partinfo> <partinfo>K176026 DeepComponents</partinfo><br />
<partinfo>K176126</partinfo> <partinfo>K176128</partinfo> <partinfo>K176130</partinfo> <br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/43/Model-2-2.jpg/800px-Model-2-2.jpg"><br />
</html><br />
<br />
== '''Simplified Model-2''' ==<br />
We employed an ODE model. We defined the input to be AHL<sub>out</sub> the and the output to be the synthesis rate of mature GFP. In this system,we assumed the concentration of the LuxR was constant.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/79/S-m-2-1.jpg/500px-S-m-2-1.jpg"><br />
</html><br />
<br />
To simplify the model, the (Recation S2-4), (Recation S2-5) and (Recation S2-6) were considered to be able to get balance in a very short time.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/7/73/Sm2-1-1-3.jpg/900px-Sm2-1-1-3.jpg"><br />
</html><br />
<br />
<br />
From above equations, we can the change of PoPS respond to the AHL<sub>in</sub>.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/3/33/Sm2-2.jpg/600px-Sm2-2.jpg"><br />
</html><br />
<br />
<br />
For this system, the value of parameter d, 0.00847, could be estimated based on the measurement of the OD. For instance, when the concentration of AHL<sub>out</sub> was zero, the value of d was 0.00368 per minute. The values of 4.8E-3 per sec for rmG, 1.8E-3 per sec for a and 0.4 per sec for pG were got from the experiment conducted by Barry Canton and Anna Labno in 2004, click [http://partsregistry.org/Part:BBa_F2620:Experience/Endy/Data_analysis here] to the details.<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/4/4f/SM2-3.jpg/450px-SM2-3.jpg"><br />
</html><br />
<br />
With the help of [https://2009.igem.org/Team:USTC_Software USTC_Software], we succeeded to estimate the values of k<sub>3</sub>, r<sub>AHLin</sub>, C<sub>1</sub>, C<sub>2</sub>, C<sub>3</sub> and C<sub>4</sub>. The simulation results as follows.<br />
<br />
k3=0.8; rAHL=0.001;<br />
C1=1.5*10^(-10); C2=1*10^(10); C3=8*10^(-7); C4=5.8*10^(11)<br />
<br />
<html><br />
<img src="https://static.igem.org/mediawiki/2009/thumb/5/55/Sm2-4.jpg/800px-Sm2-4.jpg"><br />
</html><br />
<br />
In this picture, the dots were the measuring poingts in our system and the curves were the corresponding simulations to a particular concentration of AHL<sub>out</sub>.</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDemoTeam:USTC Software/WhatDemo2009-10-21T19:52:41Z<p>Bigben: /* Mathematical Formulation */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
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{|-<br />
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'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MM <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
<br />
=Example 1. A Synthetic Oscillator=<br />
<br />
==Introduction==<br />
<br />
The [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659856&query_hl=2 synthetic oscillatory network] designed by [http://www.elowitz.caltech.edu/ Michael Elowitz] is pioneering work. In the first place, based on his model, we want to illustrate how to tune the parameters to get pre-defined wave amplitude and wave frequency. In the second place, besides this three node repressive model, is it possible to propose a alternative topology that could also achieve tunable oscillation. In [http://gardnerlab.bu.edu/ Tim Gardner]'s PhD dissertation, such a different topology is proposed. We search feasible parameter that could achieve oscillation. <br />
<br />
==Mathematical Formulation==<br />
<br />
The activities of a gene are regulated by other genes through the<br />
interactions between them, i.e., the transcription and translation<br />
factors. Here, we assume that this system follows Hill kinetic law.<br />
<br />
<math>\begin{align}<br />
\frac{dm_{i}}{dt} &=-a_{i}m_{i}+\sum\limits_{j}b_{ij}\frac{p_{j}^{H_{ij}}}{K_{ij}+p_{j}^{H_{ij}}}+l_{i}, \\<br />
\frac{dp_{i}}{dt} &=-c_{i}p_{i}+d_{i}m_{i}, (i=1,2,...,n)<br />
\end{align}\,\!</math><br />
<br />
where <math>m_{i}(t), p_{i}(t)\in {\mathbb{R}}</math> are concentrations of mRNA and protein of the <math>i</math>th node at time <math>t</math>, respectively, <math>a_{i}</math> and<br />
<math>c_{i}</math> are the degradation rates of the mRNA and<br />
protein, <math>d_{i}</math> is the translation rate. Term (1)<br />
describes the transcription process and term (2) describes the<br />
translation process.<br />
Negative and positive signs of <math>b_{ij}</math> indicates the<br />
mutual interaction relationship that could be attributed to negative<br />
or positive feedback. The values describe the strength of promoters<br />
which is tunable by inserting different promoters in gene circuits.<br />
<math>H_{ij}</math> is Hill coefficient describing cooperativity.<br />
<math>K_{ij}</math> is the apparent dissociation constant derived<br />
from the law of mass action (equilibrium constant for dissociation).<br />
We can write <math>K_{ij}=\left( \hat{K}_{ij}\right) ^{n}</math><br />
where <math>\hat{K}</math> is ligand concentration producing half<br />
occupation (ligand concentration occupying half of the binding<br />
sites), that is also the microscopic dissociation constant.<br />
<br />
==A Tunable Oscillator==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &=-am_{1}+b\frac{p_{3}^{H_{13}}}{K+p_{3}^{H_{1}}}, \\<br />
\frac{dm_{2}}{dt} &=-am_{2}+b\frac{p_{1}^{H_{21}}}{K+p_{1}^{H_{2}}}, \\<br />
\frac{dm_{3}}{dt} &=-am_{3}+b\frac{p_{2}^{H_{32}}}{K+p_{2}^{H_{32}}}, \\<br />
\frac{dp_{1}}{dt} &=-cp_{1}+dm_{1}, \\<br />
\frac{dp_{2}}{dt} &=-cp_{2}+dm_{2}, \\<br />
\frac{dp_{3}}{dt} &=-cp_{3}+dm_{3},\text{ }<br />
\end{align}\,\!</math><br />
<br />
where <math>a, b,</math> <math>c,</math><br />
<math>d,</math> <math>H_{1},</math> <math>H_{2},</math><br />
<math>H_{3},</math> <math>K</math> are tunable parameters that could<br />
change wave amplitude and frequency. For simplicity, we assume that<br />
<math>H_{13}=H_{21}=H_{32}=2,</math> meaning that the system<br />
contains only positively cooperative reaction that once one ligand<br />
molecule is bound to the enzyme, its affinity for other ligand<br />
molecules increases.<br />
<br />
[[Image:Osc1_Amp_Tun.png|center|550px|thumb|Tunable Amplitude: <br />
The Black curve shows the original amplitude of the oscillator. <br />
The Red curve shows the desired amplitude of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
[[Image:Osc1_Freq_Tun.png|center|550px|thumb|Tunable Frequency: <br />
The Black curve shows the original frequency of the oscillator. <br />
The Red curve shows the desired frequency of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
==An Alternative Topology That Leads to Oscillation==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &= -a_{1}x_{1}+\frac{b_{1}}{K_{1}+p_{2}^{H_{12}}}, \\<br />
\frac{dm_{2}}{dt} &= -a_{2}x_{2}+\frac{b_{2}p_{3}^{H_{23}}}{%<br />
K_{2}+p_{1}^{H_{21}}+p_{3}^{H_{23}}}, \\<br />
\frac{dm_{3}}{dt} &= -a_{3}x_{3}+\frac{b_{3}}{K_{3}+p_{2}^{H_{32}}} \\<br />
\frac{dp_{1}}{dt} &= -c_{1}p_{1}+d_{1}m_{1}, \\<br />
\frac{dp_{2}}{dt} &= -c_{2}p_{2}+d_{2}m_{2}, \\<br />
\frac{dp_{3}}{dt} &= -c_{3}p_{3}+d_{3}m_{3},<br />
\end{align}\,\!</math><br />
<br />
[[Image:Osc2.png|center|550px|thumb|An Alternative Topology the leads to Oscillation]]<br />
<br />
=Example 2: Perfect Adaptation=<br />
<br />
==Introduction==<br />
<br />
In this example, we try to seek different network topologies that can achieve adaptation-the ability to reset themselves after responding to a stimulus.. Actually, most of the scripts are cited from a newly published paper on [http://www.cell.com/ Cell]: [http://www.ncbi.nlm.nih.gov/pubmed/19703401 Defining Network Topologies that Can Achieve Biochemical Adaptation]. It 's quite by accident that issues discussed in this paper share some similarities with our project. To test our ABCD is powerful or not, the only thing we need to do is to search the two topologies found in this paper. By running nearly two days, we prove the solution. <br />
<br />
==Mathematical Formulation==<br />
<br />
We assume that each node (labeled as <math>A</math>, <math>B</math>, <math>C</math>) has a fixed concentration<br />
(normalized to <math>1</math>) but has two forms: active and<br />
inactive (here <math>A</math> represents the concentration of active state, and <br />
<math>1-A</math> is the concentration of the<br />
inactive state). The enzymatic regulation converts its target node<br />
between the two forms. For example, a positive regulation of node<br />
<math>B</math> by node <math>A</math> as denoted by a link<br />
<br />
<math>A\longrightarrow B</math> <br />
<br />
would mean that the active <math>A</math> convertsBfrom its inactive to its active form and<br />
would be modeled by the rate <br />
<br />
<math>R(B_{inactive}\longrightarrow<br />
B_{active})=k_{AB}A(1-B)/\left[ (1-B)+K_{AB}\right] </math>, <br />
<br />
where <math>A</math> is the normalized concentration of the active form of<br />
node <math>A</math> and <math>1-B</math> the normalized<br />
concentrations of the inactive form of node B. Likewise,<br />
<math>A-|B</math> implies that the active A catalyzes the reverse<br />
transition of node B from its active to its inactive form, with a<br />
rate <br />
<br />
<math>R(B_{active}\longrightarrow B_{inactive})=k_{AB}^{^{\prime }}/(B+K_{AB}^{^{\prime }}).</math> <br />
<br />
When there are multiple regulations of the same sign on a node, the<br />
effect is additive. For example, if node C is positively regulated<br />
by node A and node B, <br />
<br />
<math> R(C_{inactive}\longrightarrow C_{active})= k_{AC}A(1-C)/\left[ (1-C)+K_{AC}\right]</math> + <math>k_{BC}B(1-C)/\left[ (1-C)+K_{BC}\right] </math> . <br />
<br />
We assume that the interconversion between active and inactive forms of<br />
a node is reversible. Thus if a node <math>i</math> has only<br />
positive incoming links, it is assumed that there is a background<br />
(constitutive) deactivating enzyme Fi of a constant concentration<br />
(set to be <math>0.5</math>) to catalyze the reverse reaction.<br />
Similarly, a background activating enzyme <math>E_{i}=0.5</math> is<br />
added for the nodes that have only negative incoming links. The rate<br />
equation for a node (e.g., node <math>B</math>) takes the form:<br />
<br />
<math>\begin{align} \frac{dB}{dt}=\sum\limits_{i}X_{i}\cdot<br />
k_{X_{i}B}\frac{(1-B)}{ (1-B)+K_{X_{i}B}}-\sum\limits_{i}Y_{i}\cdot<br />
k_{X_{i}B}\frac{B}{B+K_{Y_{i}B}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>Xi=A,B,C,E_{A},E_{B},</math> or <math>E_{c}</math> are<br />
the activating enzymes (positive regulators) of <math>B</math> and<br />
<math>Yi=A,B,C,F_{A},F_{B},</math> or <math>F_{C}</math> are the<br />
deactivating enzymes (negative regulators) of <math>B</math>. In the<br />
equation for node A, an input term is added to the righthand-side of<br />
the equation: <br />
<br />
<math> Ik_{IA}(1-A)/((1-A)+K_{IA})</math>. <br />
<br />
The number of parameters in a network is <math> n_{p}=2n_{I}+2</math>, where<br />
<math>n_{I}</math> is the number of links in the network (including<br />
links from the basal enzymes if present).<br />
<br />
<br />
Then we hope the output of interested node tracks the target dynamics by a sudden stimulus and search the feasible topologies that achieve adaptation in the scope of all possible topologies. Two possible topologies are listed below:<br />
<br />
[[ Image:Adaptation.png|center|550px|thumb|Two topologies that can achieve adaptation: Negative Feedback Loop with a Buffer Node (NFBLB) and Incoherent Feedforward Loop with a Proportioner Node (IFFLP) (Figure reproduced from [http://www.ncbi.nlm.nih.gov/pubmed/19703401 ''Defining Network Topologies that Can Achieve Biochemical Adaptation''])]]<br />
<br />
==Feedback loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&C\cdot k_{CB}\frac{(1-B)}{(1-B)+K_{CB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>F_{A}</math> and <math>F_{B}</math> represent the<br />
concentrations of basal enzymes that carry out the reverse reactions<br />
on nodes <math>A</math> and <math>B</math>, respectively (they<br />
oppose the active network links that activate <math>A</math> and<br />
<math>B</math>). In this circuit, node <math>A</math> simply<br />
functions as a passive relay of the input to node <math>C</math>;<br />
the circuit would work in the same way if the input were directly<br />
acting on node <math>C</math> (just replacing <math>A</math> with<br />
<math>I</math> in the third equation of Equation 1). Analyzing the<br />
parameter sets that enabled this topology to adapt indicates that<br />
the two constants <math>K_{CB}</math> and <math>K_{F_{B}B}^{^{\prime<br />
}}</math> (Michaelis-Menten constants for activation of<br />
<math>B</math> by <math>C</math> and inhibition of <math>B </math><br />
by the basal enzyme) tend to be small, suggesting that the two<br />
enzymes acting on node <math>B</math> must approach saturation to<br />
achieve adaptation. Indeed, it can be shown that in the case of<br />
saturation this topology can achieve perfect adaptation.<br />
<br />
<math>\begin{align}<br />
\begin{tabular}{l}<br />
</math>figure\text{ 1}\text{: desired input}</math> \\<br />
</math>figure\text{ 2}\text{: different inputs}</math> \\<br />
</math>figure\text{ 3: }</math>topology<br />
\end{tabular}<br />
\\ \end{align}\,\!</math><br />
<br />
[[ Image:Adapt2.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptationSim1.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
Global Sensitivity Analysis<br />
We carry out global sensitivity analysis for this model, the result shows that<br />
the sensitivity coefficient of stimilus is very small which also prove the <br />
reliability of sensitivity analysis at the same time.<br />
The following figure shows global sensitivity coefficients<br />
of 12 parameters in this system:<br />
[[Image:Global_sensitivity.png|center|550px|thumb|global sensitivity coefficients<br />
of 12 parameters in this system]]<br />
Besides the external stimulus "input", we also check other two paramters. k_CB has the<br />
greatest global senstivity value, we change its value by -5% and +5%, then simulate the<br />
system again, the following figure shows change on species 3:<br />
[[Image:SensKCB.png|center|550px|thumb|pertubation on species 3 after change of k_CB]]<br />
<br />
==Feedforward loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AB}\frac{(1-B)}{(1-B)+K_{AB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
The adaptation mechanism is mathematically captured in the<br />
<br />
equation for node <math>C</math>: if the steady-state concentration<br />
of the negative regulator B is proportional to that of the positive<br />
regulator <math>A</math>, the equation determining the steady-state<br />
value of <math>C</math>, <math>dC/dt=0</math>, would be independent<br />
of <math>A</math> and hence of the input <math>I</math>. In this<br />
case, the equation for node <math>B</math> generates the condition<br />
under which the steady-state value <math> B^*</math> would be<br />
proportional to <math>A^*</math>: the first term in<br />
<math>dB/dt</math> equation should depend on <math>A</math> only and<br />
the second term on <math>B</math> only. The condition can be<br />
satisfied if the first term is in the saturated region region<br />
<br />
<math>((1-B)\gg K_{AB})</math> <br />
<br />
and the second in the linear region<br />
<br />
<math>B\ll K_{F_{B}B}^{^{\prime }}</math>, <br />
<br />
leading to<br />
<br />
<math>\begin{align} B^{\ast }=A^{\ast }\cdot<br />
k_{AB}K_{F_{B}B}^{^{\prime }}/(F_{B}k_{F_{B}B}^{^{\prime }})<br />
\\ \end{align}\,\!</math><br />
<br />
This relationship, established by the equation for node<br />
<math>B</math>, shows that the steady-state concentration of active<br />
<math>B</math> is proportional to the steady-state concentration of<br />
active <math>A</math>. Thus <math>B</math> will negatively regulate<br />
<math>C</math> in proportion to the degree of pathway input. This<br />
effect of <math>B</math> acting as a proportioner node of<br />
<math>A</math> can be graphically gleaned from the plot of the<br />
<math>B</math> and <math>C</math> nullclines (Figure feedforward).<br />
In this case, maintaining a constant <math>C^{\ast }</math> requires<br />
the B nullcline to move the same distance as the <math>C</math><br />
nullcline in response to an input change. Here again, the<br />
sensitivity of the circuit (the magnitude of the transient response)<br />
depends on the ratio of the speeds of the two signal transduction<br />
branches: <br />
<br />
<math> A\longrightarrow C</math> <br />
<br />
and<br />
<br />
<math>A\longrightarrow B-|C</math>, <br />
<br />
which can be independently tunedfrom the adaptation precision.<br />
<br />
[[第3张PP:拓扑图]]<br />
<br />
[[ Image:AdaptFeedforward1.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptFeedforward2.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
=Example 3. Bistable Toggle Switch=<br />
<br />
==Introduction==<br />
<br />
A good example of engineering in Synthetic Biology include the pioneering work of [http://gardnerlab.bu.edu/ Tim Gardner] and [http://www.bu.edu/abl/ James Collins] on an [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659857&query_hl=5 engineered genetic toggle switch]. Here, we want to show how to tune parameters to guarantee bistability.<br />
<br />
==Mathematical Formulation==<br />
<br />
<br />
<math>\begin{align}<br />
\dot{u}(t) &=\frac{\alpha _{1}}{1+v^{\theta }(t)}-\beta _{1}u(t),<br />
(.....................................equation1)<br />
\\<br />
\dot{v}(t) &=\frac{\alpha _{2}X^{\eta }}{X^{\eta }+1+u^{\gamma }(t)}-\beta<br />
_{2}v(t),(..............................................equation2)<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>X</math> is input, <math>u</math> is the concentration<br />
of repressor 1, <math>v</math> is the concentration of repressor 2,<br />
<math>\alpha _{1}</math> is the effective rate of synthesis of<br />
repressor 1, <math>\alpha _{2}</math> is the effective rate of<br />
synthesis of repressor 2, <math>\theta </math> is the cooperativity<br />
of repression of promoter 2 and <math>\gamma </math> is the<br />
cooperativity of repression of promoter 1. The above model is<br />
derived from a biochemical rate equation formulation of gene<br />
expression. The final form of the toggle equations preserves the two<br />
most fundamental aspects of the network: cooperative repression of<br />
constitutively transcribed promoters (the first term in each<br />
equation), and degradation/dilution of the repressors (the second<br />
term in each equation).<br />
<br />
The parameters <math>\alpha _{1}</math> and <math>\alpha _{2}</math><br />
are lumped parameters that describe the net effect of RNA polymerase<br />
binding, open-complex formation, transcript elongation, transcript<br />
termination, repressor binding, ribosome binding and polypeptide<br />
elongation. The cooperativity described by <math>\theta </math> and<br />
<math>\gamma </math> can arise from the multimerization of the<br />
repressor proteins and the cooperative binding of repressor<br />
multimers to multiple operator sites in the promoter. An additional<br />
modification to equation (1) is needed to describe induction of the<br />
repressors.<br />
<br />
<math>\alpha _{1},\alpha _{2},\gamma ,\theta ,\eta ,\beta _{1},\beta<br />
_{2}</math> should be indentified to guarantee bistability. We<br />
assume that <math>\gamma =\theta =\eta =2</math> as parameter<br />
restriction. Thus, there are four parameters to be indentified.<br />
[[Image:Toggle_Switch_Species1.png|center|550px|thumb|Identification Result<br />
for the first species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
[[Image:Toggle_Switch_Species2.png|center|550px|thumb|Identification Result<br />
for the second species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
Parameters:<br />
<math>\alpha _{1}</math> 26.3082 14<br />
<math>\beta _{1}</math> 1.79953 1<br />
<math>\alpha _{2}</math> 4.35684 5<br />
<math>\beta _{2}</math> 0.610341 1<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDemoTeam:USTC Software/WhatDemo2009-10-21T19:50:24Z<p>Bigben: /* Mathematical Formulation */</p>
<hr />
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'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MM <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
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<br />
=Example 1. A Synthetic Oscillator=<br />
<br />
==Introduction==<br />
<br />
The [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659856&query_hl=2 synthetic oscillatory network] designed by [http://www.elowitz.caltech.edu/ Michael Elowitz] is pioneering work. In the first place, based on his model, we want to illustrate how to tune the parameters to get pre-defined wave amplitude and wave frequency. In the second place, besides this three node repressive model, is it possible to propose a alternative topology that could also achieve tunable oscillation. In [http://gardnerlab.bu.edu/ Tim Gardner]'s PhD dissertation, such a different topology is proposed. We search feasible parameter that could achieve oscillation. <br />
<br />
==Mathematical Formulation==<br />
<br />
The activities of a gene are regulated by other genes through the<br />
interactions between them, i.e., the transcription and translation<br />
factors. Here, we assume that this system follows Hill kinetic law.<br />
<br />
<math>\begin{align}<br />
\frac{dm_{i}}{dt} &=-a_{i}m_{i}+\sum\limits_{j}b_{ij}\frac{p_{j}^{H_{ij}}}{K_{ij}+p_{j}^{H_{ij}}}+l_{i}, \\<br />
\frac{dp_{i}}{dt} &=-c_{i}p_{i}+d_{i}m_{i}, (i=1,2,...,n)<br />
\end{align}\,\!</math><br />
<br />
where <math>m_{i}(t), p_{i}(t)\in {\mathbb{R}}</math> are concentrations of mRNA and protein of the <math>i</math>th node at time <math>t</math>, respectively, <math>a_{i}</math> and<br />
<math>c_{i}</math> are the degradation rates of the mRNA and<br />
protein, <math>d_{i}</math> is the translation rate. Term (1)<br />
describes the transcription process and term (2) describes the<br />
translation process.<br />
Negative and positive signs of <math>b_{ij}</math> indicates the<br />
mutual interaction relationship that could be attributed to negative<br />
or positive feedback. The values describe the strength of promoters<br />
which is tunable by inserting different promoters in gene circuits.<br />
<math>H_{ij}</math> is Hill coefficient describing cooperativity.<br />
<math>K_{ij}</math> is the apparent dissociation constant derived<br />
from the law of mass action (equilibrium constant for dissociation).<br />
We can write <math>K_{ij}=\left( \hat{K}_{ij}\right) ^{n}</math><br />
where <math>\hat{K}</math> is ligand concentration producing half<br />
occupation (ligand concentration occupying half of the binding<br />
sites), that is also the microscopic dissociation constant.<br />
<br />
==A Tunable Oscillator==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &=-am_{1}+b\frac{p_{3}^{H_{13}}}{K+p_{3}^{H_{1}}}, \\<br />
\frac{dm_{2}}{dt} &=-am_{2}+b\frac{p_{1}^{H_{21}}}{K+p_{1}^{H_{2}}}, \\<br />
\frac{dm_{3}}{dt} &=-am_{3}+b\frac{p_{2}^{H_{32}}}{K+p_{2}^{H_{32}}}, \\<br />
\frac{dp_{1}}{dt} &=-cp_{1}+dm_{1}, \\<br />
\frac{dp_{2}}{dt} &=-cp_{2}+dm_{2}, \\<br />
\frac{dp_{3}}{dt} &=-cp_{3}+dm_{3},\text{ }<br />
\end{align}\,\!</math><br />
<br />
where <math>a, b,</math> <math>c,</math><br />
<math>d,</math> <math>H_{1},</math> <math>H_{2},</math><br />
<math>H_{3},</math> <math>K</math> are tunable parameters that could<br />
change wave amplitude and frequency. For simplicity, we assume that<br />
<math>H_{13}=H_{21}=H_{32}=2,</math> meaning that the system<br />
contains only positively cooperative reaction that once one ligand<br />
molecule is bound to the enzyme, its affinity for other ligand<br />
molecules increases.<br />
<br />
[[Image:Osc1_Amp_Tun.png|center|550px|thumb|Tunable Amplitude: <br />
The Black curve shows the original amplitude of the oscillator. <br />
The Red curve shows the desired amplitude of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
[[Image:Osc1_Freq_Tun.png|center|550px|thumb|Tunable Frequency: <br />
The Black curve shows the original frequency of the oscillator. <br />
The Red curve shows the desired frequency of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
==An Alternative Topology That Leads to Oscillation==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &= -a_{1}x_{1}+\frac{b_{1}}{K_{1}+p_{2}^{H_{12}}}, \\<br />
\frac{dm_{2}}{dt} &= -a_{2}x_{2}+\frac{b_{2}p_{3}^{H_{23}}}{%<br />
K_{2}+p_{1}^{H_{21}}+p_{3}^{H_{23}}}, \\<br />
\frac{dm_{3}}{dt} &= -a_{3}x_{3}+\frac{b_{3}}{K_{3}+p_{2}^{H_{32}}} \\<br />
\frac{dp_{1}}{dt} &= -c_{1}p_{1}+d_{1}m_{1}, \\<br />
\frac{dp_{2}}{dt} &= -c_{2}p_{2}+d_{2}m_{2}, \\<br />
\frac{dp_{3}}{dt} &= -c_{3}p_{3}+d_{3}m_{3},<br />
\end{align}\,\!</math><br />
<br />
[[Image:Osc2.png|center|550px|thumb|An Alternative Topology the leads to Oscillation]]<br />
<br />
=Example 2: Perfect Adaptation=<br />
<br />
==Introduction==<br />
<br />
In this example, we try to seek different network topologies that can achieve adaptation-the ability to reset themselves after responding to a stimulus.. Actually, most of the scripts are cited from a newly published paper on [http://www.cell.com/ Cell]: [http://www.ncbi.nlm.nih.gov/pubmed/19703401 Defining Network Topologies that Can Achieve Biochemical Adaptation]. It 's quite by accident that issues discussed in this paper share some similarities with our project. To test our ABCD is powerful or not, the only thing we need to do is to search the two topologies found in this paper. By running nearly two days, we prove the solution. <br />
<br />
==Mathematical Formulation==<br />
<br />
We assume that each node (labeled as <math>A</math>, <math>B</math>, <math>C</math>) has a fixed concentration<br />
(normalized to <math>1</math>) but has two forms: active and<br />
inactive (here <math>A</math> represents the concentration of active state, and <br />
<math>1-A</math> is the concentration of the<br />
inactive state). The enzymatic regulation converts its target node<br />
between the two forms. For example, a positive regulation of node<br />
<math>B</math> by node <math>A</math> as denoted by a link<br />
<br />
<math>A\longrightarrow B</math> <br />
<br />
would mean that the active <math>A</math> convertsBfrom its inactive to its active form and<br />
would be modeled by the rate <br />
<br />
<math>R(B_{inactive}\longrightarrow<br />
B_{active})=k_{AB}A(1-B)/\left[ (1-B)+K_{AB}\right] </math>, <br />
<br />
where <math>A</math> is the normalized concentration of the active form of<br />
node <math>A</math> and <math>1-B</math> the normalized<br />
concentrations of the inactive form of node B. Likewise,<br />
<math>A-|B</math> implies that the active A catalyzes the reverse<br />
transition of node B from its active to its inactive form, with a<br />
rate <br />
<br />
<math>R(B_{active}\longrightarrow B_{inactive})=k_{AB}^{^{\prime }}/(B+K_{AB}^{^{\prime }}).</math> <br />
<br />
When there are multiple regulations of the same sign on a node, the<br />
effect is additive. For example, if node C is positively regulated<br />
by node A and node B, <br />
<br />
<math> R(C_{inactive}\longrightarrow C_{active})= k_{AC}A(1-C)/\left[ (1-C)+K_{AC}\right]</math> + <math>k_{BC}B(1-C)/\left[ (1-C)+K_{BC}\right] </math> . <br />
<br />
We assume that the interconversion between active and inactive forms of<br />
a node is reversible. Thus if a node <math>i</math> has only<br />
positive incoming links, it is assumed that there is a background<br />
(constitutive) deactivating enzyme Fi of a constant concentration<br />
(set to be <math>0.5</math>) to catalyze the reverse reaction.<br />
Similarly, a background activating enzyme <math>E_{i}=0.5</math> is<br />
added for the nodes that have only negative incoming links. The rate<br />
equation for a node (e.g., node <math>B</math>) takes the form:<br />
<br />
<math>\begin{align} \frac{dB}{dt}=\sum\limits_{i}X_{i}\cdot<br />
k_{X_{i}B}\frac{(1-B)}{ (1-B)+K_{X_{i}B}}-\sum\limits_{i}Y_{i}\cdot<br />
k_{X_{i}B}\frac{B}{B+K_{Y_{i}B}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>Xi=A,B,C,E_{A},E_{B},</math> or <math>E_{c}</math> are<br />
the activating enzymes (positive regulators) of <math>B</math> and<br />
<math>Yi=A,B,C,F_{A},F_{B},</math> or <math>F_{C}</math> are the<br />
deactivating enzymes (negative regulators) of <math>B</math>. In the<br />
equation for node A, an input term is added to the righthand-side of<br />
the equation: <br />
<br />
<math> Ik_{IA}(1-A)/((1-A)+K_{IA})</math>. <br />
<br />
The number of parameters in a network is <math> n_{p}=2n_{I}+2</math>, where<br />
<math>n_{I}</math> is the number of links in the network (including<br />
links from the basal enzymes if present).<br />
<br />
<br />
Then we hope the output of interested node tracks the target dynamics by a sudden stimulus and search the feasible topologies that achieve adaptation in the scope of all possible topologies. Two possible topologies are listed below:<br />
<br />
[[ Image:Adaptation.png|center|550px|thumb|Two topologies that can achieve adaptation: Negative Feedback Loop with a Buffer Node (NFBLB) and Incoherent Feedforward Loop with a Proportioner Node (IFFLP) (Figure reproduced from [http://www.ncbi.nlm.nih.gov/pubmed/19703401 ''Defining Network Topologies that Can Achieve Biochemical Adaptation'']) ]]<br />
<br />
==Feedback loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&C\cdot k_{CB}\frac{(1-B)}{(1-B)+K_{CB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>F_{A}</math> and <math>F_{B}</math> represent the<br />
concentrations of basal enzymes that carry out the reverse reactions<br />
on nodes <math>A</math> and <math>B</math>, respectively (they<br />
oppose the active network links that activate <math>A</math> and<br />
<math>B</math>). In this circuit, node <math>A</math> simply<br />
functions as a passive relay of the input to node <math>C</math>;<br />
the circuit would work in the same way if the input were directly<br />
acting on node <math>C</math> (just replacing <math>A</math> with<br />
<math>I</math> in the third equation of Equation 1). Analyzing the<br />
parameter sets that enabled this topology to adapt indicates that<br />
the two constants <math>K_{CB}</math> and <math>K_{F_{B}B}^{^{\prime<br />
}}</math> (Michaelis-Menten constants for activation of<br />
<math>B</math> by <math>C</math> and inhibition of <math>B </math><br />
by the basal enzyme) tend to be small, suggesting that the two<br />
enzymes acting on node <math>B</math> must approach saturation to<br />
achieve adaptation. Indeed, it can be shown that in the case of<br />
saturation this topology can achieve perfect adaptation.<br />
<br />
<math>\begin{align}<br />
\begin{tabular}{l}<br />
</math>figure\text{ 1}\text{: desired input}</math> \\<br />
</math>figure\text{ 2}\text{: different inputs}</math> \\<br />
</math>figure\text{ 3: }</math>topology<br />
\end{tabular}<br />
\\ \end{align}\,\!</math><br />
<br />
[[ Image:Adapt2.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptationSim1.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
Global Sensitivity Analysis<br />
We carry out global sensitivity analysis for this model, the result shows that<br />
the sensitivity coefficient of stimilus is very small which also prove the <br />
reliability of sensitivity analysis at the same time.<br />
The following figure shows global sensitivity coefficients<br />
of 12 parameters in this system:<br />
[[Image:Global_sensitivity.png|center|550px|thumb|global sensitivity coefficients<br />
of 12 parameters in this system]]<br />
Besides the external stimulus "input", we also check other two paramters. k_CB has the<br />
greatest global senstivity value, we change its value by -5% and +5%, then simulate the<br />
system again, the following figure shows change on species 3:<br />
[[Image:SensKCB.png|center|550px|thumb|pertubation on species 3 after change of k_CB]]<br />
<br />
==Feedforward loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AB}\frac{(1-B)}{(1-B)+K_{AB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
The adaptation mechanism is mathematically captured in the<br />
<br />
equation for node <math>C</math>: if the steady-state concentration<br />
of the negative regulator B is proportional to that of the positive<br />
regulator <math>A</math>, the equation determining the steady-state<br />
value of <math>C</math>, <math>dC/dt=0</math>, would be independent<br />
of <math>A</math> and hence of the input <math>I</math>. In this<br />
case, the equation for node <math>B</math> generates the condition<br />
under which the steady-state value <math> B^*</math> would be<br />
proportional to <math>A^*</math>: the first term in<br />
<math>dB/dt</math> equation should depend on <math>A</math> only and<br />
the second term on <math>B</math> only. The condition can be<br />
satisfied if the first term is in the saturated region region<br />
<br />
<math>((1-B)\gg K_{AB})</math> <br />
<br />
and the second in the linear region<br />
<br />
<math>B\ll K_{F_{B}B}^{^{\prime }}</math>, <br />
<br />
leading to<br />
<br />
<math>\begin{align} B^{\ast }=A^{\ast }\cdot<br />
k_{AB}K_{F_{B}B}^{^{\prime }}/(F_{B}k_{F_{B}B}^{^{\prime }})<br />
\\ \end{align}\,\!</math><br />
<br />
This relationship, established by the equation for node<br />
<math>B</math>, shows that the steady-state concentration of active<br />
<math>B</math> is proportional to the steady-state concentration of<br />
active <math>A</math>. Thus <math>B</math> will negatively regulate<br />
<math>C</math> in proportion to the degree of pathway input. This<br />
effect of <math>B</math> acting as a proportioner node of<br />
<math>A</math> can be graphically gleaned from the plot of the<br />
<math>B</math> and <math>C</math> nullclines (Figure feedforward).<br />
In this case, maintaining a constant <math>C^{\ast }</math> requires<br />
the B nullcline to move the same distance as the <math>C</math><br />
nullcline in response to an input change. Here again, the<br />
sensitivity of the circuit (the magnitude of the transient response)<br />
depends on the ratio of the speeds of the two signal transduction<br />
branches: <br />
<br />
<math> A\longrightarrow C</math> <br />
<br />
and<br />
<br />
<math>A\longrightarrow B-|C</math>, <br />
<br />
which can be independently tunedfrom the adaptation precision.<br />
<br />
[[第3张PP:拓扑图]]<br />
<br />
[[ Image:AdaptFeedforward1.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptFeedforward2.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
=Example 3. Bistable Toggle Switch=<br />
<br />
==Introduction==<br />
<br />
A good example of engineering in Synthetic Biology include the pioneering work of [http://gardnerlab.bu.edu/ Tim Gardner] and [http://www.bu.edu/abl/ James Collins] on an [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659857&query_hl=5 engineered genetic toggle switch]. Here, we want to show how to tune parameters to guarantee bistability.<br />
<br />
==Mathematical Formulation==<br />
<br />
<br />
<math>\begin{align}<br />
\dot{u}(t) &=\frac{\alpha _{1}}{1+v^{\theta }(t)}-\beta _{1}u(t),<br />
(.....................................equation1)<br />
\\<br />
\dot{v}(t) &=\frac{\alpha _{2}X^{\eta }}{X^{\eta }+1+u^{\gamma }(t)}-\beta<br />
_{2}v(t),(..............................................equation2)<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>X</math> is input, <math>u</math> is the concentration<br />
of repressor 1, <math>v</math> is the concentration of repressor 2,<br />
<math>\alpha _{1}</math> is the effective rate of synthesis of<br />
repressor 1, <math>\alpha _{2}</math> is the effective rate of<br />
synthesis of repressor 2, <math>\theta </math> is the cooperativity<br />
of repression of promoter 2 and <math>\gamma </math> is the<br />
cooperativity of repression of promoter 1. The above model is<br />
derived from a biochemical rate equation formulation of gene<br />
expression. The final form of the toggle equations preserves the two<br />
most fundamental aspects of the network: cooperative repression of<br />
constitutively transcribed promoters (the first term in each<br />
equation), and degradation/dilution of the repressors (the second<br />
term in each equation).<br />
<br />
The parameters <math>\alpha _{1}</math> and <math>\alpha _{2}</math><br />
are lumped parameters that describe the net effect of RNA polymerase<br />
binding, open-complex formation, transcript elongation, transcript<br />
termination, repressor binding, ribosome binding and polypeptide<br />
elongation. The cooperativity described by <math>\theta </math> and<br />
<math>\gamma </math> can arise from the multimerization of the<br />
repressor proteins and the cooperative binding of repressor<br />
multimers to multiple operator sites in the promoter. An additional<br />
modification to equation (1) is needed to describe induction of the<br />
repressors.<br />
<br />
<math>\alpha _{1},\alpha _{2},\gamma ,\theta ,\eta ,\beta _{1},\beta<br />
_{2}</math> should be indentified to guarantee bistability. We<br />
assume that <math>\gamma =\theta =\eta =2</math> as parameter<br />
restriction. Thus, there are four parameters to be indentified.<br />
[[Image:Toggle_Switch_Species1.png|center|550px|thumb|Identification Result<br />
for the first species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
[[Image:Toggle_Switch_Species2.png|center|550px|thumb|Identification Result<br />
for the second species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
Parameters:<br />
<math>\alpha _{1}</math> 26.3082 14<br />
<math>\beta _{1}</math> 1.79953 1<br />
<math>\alpha _{2}</math> 4.35684 5<br />
<math>\beta _{2}</math> 0.610341 1<br />
|valign = "top"|<br />
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|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDemoTeam:USTC Software/WhatDemo2009-10-21T19:38:21Z<p>Bigben: /* Other Topology */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
|align = "justify"|<br />
{|-<br />
|align = "justify" border = "1" bordercolor = "black" bgcolor = "red"|<br />
'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MM <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
<br />
=Example 1. A Synthetic Oscillator=<br />
<br />
==Introduction==<br />
<br />
The [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659856&query_hl=2 synthetic oscillatory network] designed by [http://www.elowitz.caltech.edu/ Michael Elowitz] is pioneering work. In the first place, based on his model, we want to illustrate how to tune the parameters to get pre-defined wave amplitude and wave frequency. In the second place, besides this three node repressive model, is it possible to propose a alternative topology that could also achieve tunable oscillation. In [http://gardnerlab.bu.edu/ Tim Gardner]'s PhD dissertation, such a different topology is proposed. We search feasible parameter that could achieve oscillation. <br />
<br />
==Mathematical Formulation==<br />
<br />
The activities of a gene are regulated by other genes through the<br />
interactions between them, i.e., the transcription and translation<br />
factors. Here, we assume that this system follows Hill kinetic law.<br />
<br />
<math>\begin{align}<br />
\frac{dm_{i}}{dt} &=-a_{i}m_{i}+\sum\limits_{j}b_{ij}\frac{p_{j}^{H_{ij}}}{K_{ij}+p_{j}^{H_{ij}}}+l_{i}, \\<br />
\frac{dp_{i}}{dt} &=-c_{i}p_{i}+d_{i}m_{i}, (i=1,2,...,n)<br />
\end{align}\,\!</math><br />
<br />
where <math>m_{i}(t), p_{i}(t)\in {\mathbb{R}}</math> are concentrations of mRNA and protein of the <math>i</math>th node at time <math>t</math>, respectively, <math>a_{i}</math> and<br />
<math>c_{i}</math> are the degradation rates of the mRNA and<br />
protein, <math>d_{i}</math> is the translation rate. Term (1)<br />
describes the transcription process and term (2) describes the<br />
translation process.<br />
Negative and positive signs of <math>b_{ij}</math> indicates the<br />
mutual interaction relationship that could be attributed to negative<br />
or positive feedback. The values describe the strength of promoters<br />
which is tunable by inserting different promoters in gene circuits.<br />
<math>H_{ij}</math> is Hill coefficient describing cooperativity.<br />
<math>K_{ij}</math> is the apparent dissociation constant derived<br />
from the law of mass action (equilibrium constant for dissociation).<br />
We can write <math>K_{ij}=\left( \hat{K}_{ij}\right) ^{n}</math><br />
where <math>\hat{K}</math> is ligand concentration producing half<br />
occupation (ligand concentration occupying half of the binding<br />
sites), that is also the microscopic dissociation constant.<br />
<br />
==A Tunable Oscillator==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &=-am_{1}+b\frac{p_{3}^{H_{13}}}{K+p_{3}^{H_{1}}}, \\<br />
\frac{dm_{2}}{dt} &=-am_{2}+b\frac{p_{1}^{H_{21}}}{K+p_{1}^{H_{2}}}, \\<br />
\frac{dm_{3}}{dt} &=-am_{3}+b\frac{p_{2}^{H_{32}}}{K+p_{2}^{H_{32}}}, \\<br />
\frac{dp_{1}}{dt} &=-cp_{1}+dm_{1}, \\<br />
\frac{dp_{2}}{dt} &=-cp_{2}+dm_{2}, \\<br />
\frac{dp_{3}}{dt} &=-cp_{3}+dm_{3},\text{ }<br />
\end{align}\,\!</math><br />
<br />
where <math>a, b,</math> <math>c,</math><br />
<math>d,</math> <math>H_{1},</math> <math>H_{2},</math><br />
<math>H_{3},</math> <math>K</math> are tunable parameters that could<br />
change wave amplitude and frequency. For simplicity, we assume that<br />
<math>H_{13}=H_{21}=H_{32}=2,</math> meaning that the system<br />
contains only positively cooperative reaction that once one ligand<br />
molecule is bound to the enzyme, its affinity for other ligand<br />
molecules increases.<br />
<br />
[[Image:Osc1_Amp_Tun.png|center|550px|thumb|Tunable Amplitude: <br />
The Black curve shows the original amplitude of the oscillator. <br />
The Red curve shows the desired amplitude of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
[[Image:Osc1_Freq_Tun.png|center|550px|thumb|Tunable Frequency: <br />
The Black curve shows the original frequency of the oscillator. <br />
The Red curve shows the desired frequency of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
==An Alternative Topology That Leads to Oscillation==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &= -a_{1}x_{1}+\frac{b_{1}}{K_{1}+p_{2}^{H_{12}}}, \\<br />
\frac{dm_{2}}{dt} &= -a_{2}x_{2}+\frac{b_{2}p_{3}^{H_{23}}}{%<br />
K_{2}+p_{1}^{H_{21}}+p_{3}^{H_{23}}}, \\<br />
\frac{dm_{3}}{dt} &= -a_{3}x_{3}+\frac{b_{3}}{K_{3}+p_{2}^{H_{32}}} \\<br />
\frac{dp_{1}}{dt} &= -c_{1}p_{1}+d_{1}m_{1}, \\<br />
\frac{dp_{2}}{dt} &= -c_{2}p_{2}+d_{2}m_{2}, \\<br />
\frac{dp_{3}}{dt} &= -c_{3}p_{3}+d_{3}m_{3},<br />
\end{align}\,\!</math><br />
<br />
[[Image:Osc2.png|center|550px|thumb|An Alternative Topology the leads to Oscillation]]<br />
<br />
=Example 2: Perfect Adaptation=<br />
<br />
==Introduction==<br />
<br />
In this example, we try to seek different network topologies that can achieve adaptation-the ability to reset themselves after responding to a stimulus.. Actually, most of the scripts are cited from a newly published paper on [http://www.cell.com/ Cell]: [http://www.ncbi.nlm.nih.gov/pubmed/19703401 Defining Network Topologies that Can Achieve Biochemical Adaptation]. It 's quite by accident that issues discussed in this paper share some similarities with our project. To test our ABCD is powerful or not, the only thing we need to do is to search the two topologies found in this paper. By running nearly two days, we prove the solution. <br />
<br />
==Mathematical Formulation==<br />
<br />
We assume that each node (labeled as <math>A</math>, <math>B</math>, <math>C</math>) has a fixed concentration<br />
(normalized to <math>1</math>) but has two forms: active and<br />
inactive (here <math>A</math> represents the concentration of active state, and <br />
<math>1-A</math> is the concentration of the<br />
inactive state). The enzymatic regulation converts its target node<br />
between the two forms. For example, a positive regulation of node<br />
<math>B</math> by node <math>A</math> as denoted by a link<br />
<br />
<math>A\longrightarrow B</math> <br />
<br />
would mean that the active <math>A</math> convertsBfrom its inactive to its active form and<br />
would be modeled by the rate <br />
<br />
<math>R(B_{inactive}\longrightarrow<br />
B_{active})=k_{AB}A(1-B)/\left[ (1-B)+K_{AB}\right] </math>, <br />
<br />
where <math>A</math> is the normalized concentration of the active form of<br />
node <math>A</math> and <math>1-B</math> the normalized<br />
concentrations of the inactive form of node B. Likewise,<br />
<math>A-|B</math> implies that the active A catalyzes the reverse<br />
transition of node B from its active to its inactive form, with a<br />
rate <br />
<br />
<math>R(B_{active}\longrightarrow B_{inactive})=k_{AB}^{^{\prime }}/(B+K_{AB}^{^{\prime }}).</math> <br />
<br />
When there are multiple regulations of the same sign on a node, the<br />
effect is additive. For example, if node C is positively regulated<br />
by node A and node B, <br />
<br />
<math> R(C_{inactive}\longrightarrow C_{active})= k_{AC}A(1-C)/\left[ (1-C)+K_{AC}\right]</math> + <math>k_{BC}B(1-C)/\left[ (1-C)+K_{BC}\right] </math> . <br />
<br />
We assume that the interconversion between active and inactive forms of<br />
a node is reversible. Thus if a node <math>i</math> has only<br />
positive incoming links, it is assumed that there is a background<br />
(constitutive) deactivating enzyme Fi of a constant concentration<br />
(set to be <math>0.5</math>) to catalyze the reverse reaction.<br />
Similarly, a background activating enzyme <math>E_{i}=0.5</math> is<br />
added for the nodes that have only negative incoming links. The rate<br />
equation for a node (e.g., node <math>B</math>) takes the form:<br />
<br />
<math>\begin{align} \frac{dB}{dt}=\sum\limits_{i}X_{i}\cdot<br />
k_{X_{i}B}\frac{(1-B)}{ (1-B)+K_{X_{i}B}}-\sum\limits_{i}Y_{i}\cdot<br />
k_{X_{i}B}\frac{B}{B+K_{Y_{i}B}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>Xi=A,B,C,E_{A},E_{B},</math> or <math>E_{c}</math> are<br />
the activating enzymes (positive regulators) of <math>B</math> and<br />
<math>Yi=A,B,C,F_{A},F_{B},</math> or <math>F_{C}</math> are the<br />
deactivating enzymes (negative regulators) of <math>B</math>. In the<br />
equation for node A, an input term is added to the righthand-side of<br />
the equation: <br />
<br />
<math> Ik_{IA}(1-A)/((1-A)+K_{IA})</math>. <br />
<br />
The number of parameters in a network is <math> n_{p}=2n_{I}+2</math>, where<br />
<math>n_{I}</math> is the number of links in the network (including<br />
links from the basal enzymes if present).<br />
<br />
<br />
Then we hope the output of interested node tracks the target dynamics by a sudden stimulus and search the feasible topologies that achieve adaptation in the scope of all possible topologies. <br />
<br />
<br />
==Feedback loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&C\cdot k_{CB}\frac{(1-B)}{(1-B)+K_{CB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>F_{A}</math> and <math>F_{B}</math> represent the<br />
concentrations of basal enzymes that carry out the reverse reactions<br />
on nodes <math>A</math> and <math>B</math>, respectively (they<br />
oppose the active network links that activate <math>A</math> and<br />
<math>B</math>). In this circuit, node <math>A</math> simply<br />
functions as a passive relay of the input to node <math>C</math>;<br />
the circuit would work in the same way if the input were directly<br />
acting on node <math>C</math> (just replacing <math>A</math> with<br />
<math>I</math> in the third equation of Equation 1). Analyzing the<br />
parameter sets that enabled this topology to adapt indicates that<br />
the two constants <math>K_{CB}</math> and <math>K_{F_{B}B}^{^{\prime<br />
}}</math> (Michaelis-Menten constants for activation of<br />
<math>B</math> by <math>C</math> and inhibition of <math>B </math><br />
by the basal enzyme) tend to be small, suggesting that the two<br />
enzymes acting on node <math>B</math> must approach saturation to<br />
achieve adaptation. Indeed, it can be shown that in the case of<br />
saturation this topology can achieve perfect adaptation.<br />
<br />
<math>\begin{align}<br />
\begin{tabular}{l}<br />
</math>figure\text{ 1}\text{: desired input}</math> \\<br />
</math>figure\text{ 2}\text{: different inputs}</math> \\<br />
</math>figure\text{ 3: }</math>topology<br />
\end{tabular}<br />
\\ \end{align}\,\!</math><br />
<br />
[[ Image:Adapt2.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptationSim1.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
Global Sensitivity Analysis<br />
We carry out global sensitivity analysis for this model, the result shows that<br />
the sensitivity coefficient of stimilus is very small which also prove the <br />
reliability of sensitivity analysis at the same time.<br />
The following figure shows global sensitivity coefficients<br />
of 12 parameters in this system:<br />
[[Image:Global_sensitivity.png|center|550px|thumb|global sensitivity coefficients<br />
of 12 parameters in this system]]<br />
Besides the external stimulus "input", we also check other two paramters. k_CB has the<br />
greatest global senstivity value, we change its value by -5% and +5%, then simulate the<br />
system again, the following figure shows change on species 3:<br />
[[Image:SensKCB.png|center|550px|thumb|pertubation on species 3 after change of k_CB]]<br />
<br />
==Feedforward loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AB}\frac{(1-B)}{(1-B)+K_{AB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
The adaptation mechanism is mathematically captured in the<br />
<br />
equation for node <math>C</math>: if the steady-state concentration<br />
of the negative regulator B is proportional to that of the positive<br />
regulator <math>A</math>, the equation determining the steady-state<br />
value of <math>C</math>, <math>dC/dt=0</math>, would be independent<br />
of <math>A</math> and hence of the input <math>I</math>. In this<br />
case, the equation for node <math>B</math> generates the condition<br />
under which the steady-state value <math> B^*</math> would be<br />
proportional to <math>A^*</math>: the first term in<br />
<math>dB/dt</math> equation should depend on <math>A</math> only and<br />
the second term on <math>B</math> only. The condition can be<br />
satisfied if the first term is in the saturated region region<br />
<br />
<math>((1-B)\gg K_{AB})</math> <br />
<br />
and the second in the linear region<br />
<br />
<math>B\ll K_{F_{B}B}^{^{\prime }}</math>, <br />
<br />
leading to<br />
<br />
<math>\begin{align} B^{\ast }=A^{\ast }\cdot<br />
k_{AB}K_{F_{B}B}^{^{\prime }}/(F_{B}k_{F_{B}B}^{^{\prime }})<br />
\\ \end{align}\,\!</math><br />
<br />
This relationship, established by the equation for node<br />
<math>B</math>, shows that the steady-state concentration of active<br />
<math>B</math> is proportional to the steady-state concentration of<br />
active <math>A</math>. Thus <math>B</math> will negatively regulate<br />
<math>C</math> in proportion to the degree of pathway input. This<br />
effect of <math>B</math> acting as a proportioner node of<br />
<math>A</math> can be graphically gleaned from the plot of the<br />
<math>B</math> and <math>C</math> nullclines (Figure feedforward).<br />
In this case, maintaining a constant <math>C^{\ast }</math> requires<br />
the B nullcline to move the same distance as the <math>C</math><br />
nullcline in response to an input change. Here again, the<br />
sensitivity of the circuit (the magnitude of the transient response)<br />
depends on the ratio of the speeds of the two signal transduction<br />
branches: <br />
<br />
<math> A\longrightarrow C</math> <br />
<br />
and<br />
<br />
<math>A\longrightarrow B-|C</math>, <br />
<br />
which can be independently tunedfrom the adaptation precision.<br />
<br />
[[第3张PP:拓扑图]]<br />
<br />
[[第4张PP:来个冲击然后还adaptation]]<br />
[[ Image:AdaptFeedforward1.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptFeedforward2.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
<br />
=Example 3. Bistable Toggle Switch=<br />
<br />
==Introduction==<br />
<br />
A good example of engineering in Synthetic Biology include the pioneering work of [http://gardnerlab.bu.edu/ Tim Gardner] and [http://www.bu.edu/abl/ James Collins] on an [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659857&query_hl=5 engineered genetic toggle switch]. Here, we want to show how to tune parameters to guarantee bistability.<br />
<br />
==Mathematical Formulation==<br />
<br />
<br />
<math>\begin{align}<br />
\dot{u}(t) &=\frac{\alpha _{1}}{1+v^{\theta }(t)}-\beta _{1}u(t),<br />
(.....................................equation1)<br />
\\<br />
\dot{v}(t) &=\frac{\alpha _{2}X^{\eta }}{X^{\eta }+1+u^{\gamma }(t)}-\beta<br />
_{2}v(t),(..............................................equation2)<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>X</math> is input, <math>u</math> is the concentration<br />
of repressor 1, <math>v</math> is the concentration of repressor 2,<br />
<math>\alpha _{1}</math> is the effective rate of synthesis of<br />
repressor 1, <math>\alpha _{2}</math> is the effective rate of<br />
synthesis of repressor 2, <math>\theta </math> is the cooperativity<br />
of repression of promoter 2 and <math>\gamma </math> is the<br />
cooperativity of repression of promoter 1. The above model is<br />
derived from a biochemical rate equation formulation of gene<br />
expression. The final form of the toggle equations preserves the two<br />
most fundamental aspects of the network: cooperative repression of<br />
constitutively transcribed promoters (the first term in each<br />
equation), and degradation/dilution of the repressors (the second<br />
term in each equation).<br />
<br />
The parameters <math>\alpha _{1}</math> and <math>\alpha _{2}</math><br />
are lumped parameters that describe the net effect of RNA polymerase<br />
binding, open-complex formation, transcript elongation, transcript<br />
termination, repressor binding, ribosome binding and polypeptide<br />
elongation. The cooperativity described by <math>\theta </math> and<br />
<math>\gamma </math> can arise from the multimerization of the<br />
repressor proteins and the cooperative binding of repressor<br />
multimers to multiple operator sites in the promoter. An additional<br />
modification to equation (1) is needed to describe induction of the<br />
repressors.<br />
<br />
<math>\alpha _{1},\alpha _{2},\gamma ,\theta ,\eta ,\beta _{1},\beta<br />
_{2}</math> should be indentified to guarantee bistability. We<br />
assume that <math>\gamma =\theta =\eta =2</math> as parameter<br />
restriction. Thus, there are four parameters to be indentified.<br />
[[Image:Toggle_Switch_Species1.png|center|550px|thumb|Identification Result<br />
for the first species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
[[Image:Toggle_Switch_Species2.png|center|550px|thumb|Identification Result<br />
for the second species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
Parameters:<br />
<math>\alpha _{1}</math> 26.3082 14<br />
<math>\beta _{1}</math> 1.79953 1<br />
<math>\alpha _{2}</math> 4.35684 5<br />
<math>\beta _{2}</math> 0.610341 1<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/File:Adaptation.pngFile:Adaptation.png2009-10-21T19:37:21Z<p>Bigben: Topology of Adaptation</p>
<hr />
<div>Topology of Adaptation</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T19:19:36Z<p>Bigben: /* Work Flow */</p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|align = "justify"|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process.<br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillation behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific organisms. It is only an imagination that we have a long way to go. Then the first goal is to make a network work stably. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or conditions can be the input simultaneously. And the output is a list of networks that have similar phenotypes approximating to the requirement, along with the kinetic parameters and robustness evaluation.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: (1) the optimization of parameters in a fixed mathematic model, (2) the selection of interaction forms in a fixed topology, (3) the comparison and screening of different topologies. And during the optimization of the parameters, there are two ''score functions'' considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive to uncertainties. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, a list of the best selected networks will output as the final solutions.<br />
<br />
==Platform==<br />
<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization Algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model. In past several years, PSO has been successfully applied in optimizing the parameters for nonlinear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that it is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. Parallelization of the optimization process will be implemented in our next version.<br />
<br />
===Genetic Algorithm===<br />
<br />
Genetic Algorithm (GA) is employed to search the best topologies and the best interaction forms. It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition. It is suitable for our problems; because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot to do to achieve the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T19:16:31Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|align = "justify"|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process.<br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillation behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific organisms. It is only an imagination that we have a long way to go. Then the first goal is to make a network work stably. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or conditions can be the input simultaneously. And the output is a list of networks that have similar phenotypes approximating to the requirement, along with the kinetic parameters and robustness evaluation.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: (1) the optimization of parameters in a fixed mathematic model, (2) the selection of interaction forms in a fixed topology, (3) the comparison and screening of different topologies. And during the optimization of the parameters, there are two '''score functions''' considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive to uncertainties. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, a list of the best selected networks will output as the final solutions.<br />
<br />
==Platform==<br />
<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization Algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model. In past several years, PSO has been successfully applied in optimizing the parameters for nonlinear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that it is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. Parallelization of the optimization process will be implemented in our next version.<br />
<br />
===Genetic Algorithm===<br />
<br />
Genetic Algorithm (GA) is employed to search the best topologies and the best interaction forms. It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition. It is suitable for our problems; because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot to do to achieve the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T19:07:32Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|align = "justify"|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process.<br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillation behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific organisms. It is only an imagination that we have a long way to go. Then the first goal is to make a network work stably. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or conditions can be the input simultaneously. And the output is a list of networks that have similar phenotypes approximating to the requirement, along with the kinetic parameters and robustness evaluation.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: (1) the optimization of parameters in a fixed mathematic model, (2) the selection of interaction forms in a fixed topology, (3) the comparison and screening of different topologies. And during the optimization of the parameters, there are two '''score functions''' considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive to uncertainties. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, a list of the best selected networks will output as the final solutions.<br />
<br />
==Platform==<br />
<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization Algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
===Genetic Algorithm===<br />
<br />
Genetic Algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWRestrictionTeam:USTC Software/hoWRestriction2009-10-21T17:43:20Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
|valign = "top" align = "justify" border = "0" width = "600px" bordercolor = "#F3F3F3"|<br />
<br />
==Restrictions - Input File List==<br />
<br />
{| border = "0" align = "center" width = "400px"<br />
|-<br />
|width = "50" align = "center"|<br />
No <br />
|width = "100" align = "center"|<br />
Item<br />
|width = "250" align = "center"|<br />
Instructions<br />
|-<br />
|1. <br />
|Node<br />
|[[Image:Node.png|center|200px|thumb]]<br />
|-<br />
|2. <br />
|Target Time Course<br />
|[[Image:TargetTimeCourse.png|center|200px|thumb]]<br />
|-<br />
|3. <br />
|Input Data<br />
|[[Image:InputData.png|center|200px|thumb]]<br />
|-<br />
|4. <br />
|Initial Values<br />
|[[Image:InitialValues.png|center|200px|thumb]]<br />
|-<br />
|5. <br />
|Initial Parameters<br />
|[[Image:InitialParameters.png|center|200px|thumb]]<br />
|-<br />
|6. <br />
|Network Restriction<br />
|[[Image:NetworkRestriction.png|center|200px|thumb]]<br />
|-<br />
|7. <br />
|Parameter Restriction<br />
|[[Image:ParameterRestriction.png|center|200px|thumb]]<br />
|-<br />
|8.<br />
|align = "left"|<br />
Parameter Relation Restriction<br />
|[[Image:ParameterRelationRestriction.png|center|200px|thumb]]<br />
|-<br />
|9.<br />
|Parameter Range<br />
|[[Image:ParameterRange.png|center|200px|thumb]]<br />
|-<br />
|10.<br />
|Candidate Function List<br />
|[[Image:CandidateFunctionList.png|center|200px|thumb]] <br />
|-<br />
|11.<br />
|Algorithm Parameters<br />
|[[Image:AlgorithmParameters.png|center|200px|thumb]]<br />
|}<br />
<br />
<br />
# '''Node:''' Lets you specify the numbers of species you need to construct a network<br />
# '''Target Time Course:''' Target time course represent the desired behavior of a system if you choose the function of "identification". While in the case of "simulation" or "sensitivity analysis", the target file determine the time course used in the simulation process<br />
# '''Input Data:''' Lets you input desired dynamics of one or more species as time course. Note that you must assign which species an input is act on in the first line of this file. If an input is act on more than one species(exist in more than one ODE), you should repeat it for each species it acts on.<br />
# '''Initial Values:''' Lets you specify the initial value of species, this file must exist unless you choose to import your model with SBML file.<br />
# '''Initial Parameters:''' Lets you specify the initial value of a parameter. There are six columns in this file: (1) flag (2) object (3)activator (4)function (5)para_index (6)value. Every line in this file represent only ONE parameter, the first five columns is used to locate a term in the ODEs and to locate a parameter in a term while the last column gives the value of a parameter. If you want to carry out simulation or sensitivity analysis, each paramter must be initialized in this file.<br />
## Flag indicate the number of species involved in a term if it is a positive value and "-1" represent degradation term, "-2" represent constant term.<br />
## Object indicate which species this term affect, or which ODE this term in. <br />
## Activator indicate index of species involved in a term, the number of activators must in accordance with flag tag.<br />
## Function indicate the type of reaction of this term.<br />
## Para_index_value indicate the index of parameter in current reaction, since more than one parameters may exist in a reaction.<br />
## The last column indicate the value of a parameter.<br />
#'''Network Restriction:''' If you want to carry out topological identification, this file lets you cut unnecessary edges between species and restrict special rate term form of ceritain species. For other cases, this file also plays the role to input a certain topological structure. Compared to Initial Parameters File, there are two less columns in this file. The first three columns "flag", "object", "activator" are used to specify an edge in the network while the last column "func_list" determine type of the edge. <br />
# '''Parameter Restriction:''' Lets you specify a parameter value that holds at all times during the identification. The organization of this file is absolutely the same with Initial Parameters File. This file is not needed unless you want to do identification.<br />
# '''Parameter Relation Restriction:''' Lets you specify mathematical constraints on one or more parameters, species, or compartments that must hold during a simulation<br />
# '''Parameter Range:''' Lets you specify the feasible range of parameters regardless of "7. PARAM_RESTRI". The organization of this file is similar to Initial Parameter File, while the last two columns "min" and "max" are minimum and maximum value of a parameter, instead of a certain value.<br />
# '''Candidate Function List:''' All possible types of functions following different kinetic laws (see Table.1). User define functions are added to the end of this file.<br />
# '''Algorithm Parameters:''' Lets you specify parameter values in genetic algorithm. "population","mutation_ratio","recombine_ratio","max_cycle" are set in this file.<br />
<br />
<br/><br />
{|width = "60pt"|<br />
[[Image:Candidate_Kinetic_Law.png|center|500px|thumb|Candidate Kinetic Law Table]]<br />
|align = "left"|<br />
|}<br />
<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhenTeam:USTC Software/When2009-10-21T17:26:44Z<p>Bigben: /* Desired Dynamics Input */</p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
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{{USTCSW_SideBarL}}<br />
|valign = "top" align = "justify" border = "0" width = "600px" bordercolor = "#F3F3F3"|<br />
<br />
=Future Plan=<br />
<br />
==Desired Dynamics Input==<br />
<br />
'''Q1:''' <br />
:How can we characterize the property of our desired dynamics instead of importing time course? I mean I don't care much on the exact behavior the system perform but some key characters of the dynamics?<br />
<br />
'''A1:''' <br />
:It should be referred to the selection of the evaluation function. One possible solution is to convert the time dependent function from time domain to frequency domain. [http://en.wikipedia.org/wiki/Fourier_transform Fourier transform] should be introduced for its advantage of simplifying many of complicated periodic functions. <br />
<br />
:For other common conventions and notations, see [http://en.wikipedia.org/wiki/Fourier_transform#Other_conventions Other conventions] and [http://en.wikipedia.org/wiki/Fourier_transform#Other_notations Other notations] below. The [http://en.wikipedia.org/wiki/Fourier_transform#Fourier_transform_on_Euclidean_space Fourier transform on Euclidean space] is treated separately, in which the variable ''x'' often represents position and ''ξ'' momentum.<br />
<br />
[[Image:Fourier.png|center|500px|thumb|Instead of comparing with target function in real space consists of substance concentration and time axis, one potential alternative for avoiding dilemmas like unmatched phase in oscillation is to move the score function into frequency space after Fourier Transformation.]]<br />
<br />
'''Q2:''' <br />
:The desired time course for different node are largely different in order of magnitude? Also, some results of my experiment cannot be expressed as absolute values but relative ones. How to keep the dimension of different species?<br />
<br />
'''A2:''' <br />
:The data may vary significantly in dimension. And it is unfortunately true for most real-case reactions' dynamics/thermodynamics constant. Therefore we consider it to be a worthwhile trial to move all calculations to logarithmatic space to overcome the strong order-dependence of initial values of inputs. Related changes are systematical, from the substitution of variables and functions to the transformation of first order deriatives.<br />
<br />
[[Image:Regime.png|center|400x500px|thumb|Though we are familiar with working at linear space, here it is more convenient and effective to move all sampling and initialization in logarithmatic space, where the step of calculation can easily jump among different orders.]]<br />
<br />
==Restriction Input==<br />
<br />
'''Q1:''' <br />
:The input box and steps for users is a little complicated and even have some small requirements for the users to be capable of transform rate equations to differential equations. It has confused me a little.<br />
<br />
'''A1:''' <br />
:In fact this is one of the most serious headache we are suffering for now. On one hand, we have to make the input sound and standard; on the other hand we still feel it an urgent call from our users to cut off unnecessary inputs. So far, this input box is perhaps the simplest one after discussing a lot with our USTC wet team. By proposing many possible solutions, they chose this one. After the publishing of current version, we hope feedback from users can help improve the next version.<br />
<br />
==Mathematical model==<br />
<br />
'''Q1:''' <br />
:The general mathematical model seems to cope with two nodes coupling together at most. How about more than two nodes?<br />
<br />
'''A1:''' <br />
:In current version, we allow more than two nodes reaction function as user-defined form which requires the users to input themselves. Actually, it is easy to add more than two nodes form reaction functions in the model. But the condition of computation time and RAM space will drastically be exacerbated as long as the interaction is related to more than three units. For the next version, we will change our data structure to accommodate more types but more efficient. <br />
<br />
:Meanwhile, we do believe the 'two-body' approximation to be a moderately acceptable choice. With reference to the classical way physists dealing with Hamiltonian of multi-electron system, we expect the same approximation for interaction among substances - that is, all multi-substances' interaction could always be boiled down to two-body interactions.<br />
<br />
:One possible mathematical approach is to adopt Tylor Series expansion to shorten each term describing interactions. The physical nature of this mathematical method is nothing but exactly how two-body interactions are interwined to form multi-body interactions.<br />
<br/><br />
[[Image:tylorinmultibody.png|center|300px|thumb|If three substance x, y and z have an interaction form of 1/(x+y+z), when concentration have significant differences, tylor expansion might work to introduce a perturbation in to this system, avoiding complex calcultions.]]<br />
<br />
==Algorithm==<br />
<br />
'''Q1:''' <br />
:Can this software run faster and faster?<br />
<br />
'''A1''': <br />
:Firstly, in our software, we choose and modify these best optimization algorithms carefully by comparing with possible optimization algorithm. How to improve the efficiency of optimization algorithm is an open problem in computer science and mathematics. Collaboration with experts in this field is needed.<br />
<br />
:Secondly, the speed is quite dependent on the performance of computer. We test these programs separately on Linux system in our high performance workstation. The result is fairly better than the test on our personal computer.<br />
<br />
:Thirdly, to improve the algorithm performance, parallel computing is a better choice. For this reason, the algorithms we adopt are parallel in nature and extension to parallel algorithm is possible. In the future, we will rewrite our software this form via MPI. <br />
<br />
'''Q2:''' <br />
:Can this software run more and more precisely?<br />
<br />
'''A2:''' <br />
:The imprecision is largely caused by Local minimum and initial value dependence. Similar as above, these are also open problems. For we adopt Monte Carlo sampling in our algorithm, the results may vary time to time due to the randomness nature. It also remains a problem for us to solve in the future. We will make effort to modify existing algorithms or even create new one.<br />
<br />
==Output==<br />
<br />
'''Q1:''' <br />
:Is it better to export a graph following SBGN standard?<br />
<br />
'''A1:''' <br />
:Currently, we are working on it. The basic drag-drop function has been accomplished in our software of current version. In the near future, we will complete this function.<br />
<br />
[[Image:Drag1.png|left|250px|thumb|It is much convenient for users to locate and combine substances/biobricks with this easy-drag interface.]][[Image:Drag2.png|right|250px|thumb|Output of time course plot.]]<br />
<br/><br />
<br/><br />
<br/><br />
'''Q2:''' <br />
:Can you export the robustness analysis along with the SBML model in one sheet?<br />
<br />
'''A2:''' <br />
:It is not easy to implement such information in a single SBML file. In current version, we can realize a robustness analysis by importing a SBML file which two sheets will be generated. In next version, we will try to incorporate such information to a general form. With such change, there is also a need to modify libSBML as a result.<br />
<br />
==Database==<br />
<br />
'''Q1:''' <br />
:Does the database contain too little biobricks?<br />
<br />
'''A1:''' <br />
:Since the concept of standard components that contain enough information is relatively new in synthetic biology. The acquisition to the information is rather difficult for us because we have to learn each bricks in detail. In the current version, we construct one that is suitable for our illustrative examples as well as our USTC wet team’s new submitted biobricks. A relatively “full” database needs collaborations of different teams who should submit information of the same format. Otherwise, we propose a developing [https://2009.igem.org/Team:USTC_Software/Standard standard] for such a design.<br />
<br />
'''Q2:''' <br />
:Is the search algorithm fast enough for the database?<br />
<br />
'''A2:''' <br />
:For lager database, searching algorithm is quite important. It is also an open problem in computer science. To our extent, we seek collaborations inside or outside our campus.<br />
<br />
'''Q3:''' <br />
:How do you manage these data efficiently?<br />
<br />
'''A3:''' <br />
:To manage a large database, manage software is needed. Luckily, Berkeley tools team are focusing on this problem. We are expecting cooperation with them.<br />
<br />
'''Q4:''' <br />
:Is it too difficult to obtain the kinetic parameters and reaction type?<br />
<br />
'''A4:''' <br />
:Firstly, in the next version, we will make a web server that makes our database open access. Then users can freely update the database by submitting the data in a general form.<br />
Secondly, we can also apply a text mining technique to get detailed information for published papers.<br />
<br />
==Link to SBW==<br />
<br />
'''Q1:''' <br />
:Why not incorporate SBW in this software to make it more powerful?<br />
<br />
'''A1:''' <br />
:As SBML has become a standard description format for modeling a biological system. Considering the output of our design obeys this standard, a combination with SBW tools such as cell designer should be incorporated in our software for analysis and simulation purpose. We have left a button “SBW” and have written the interface template in our software.<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWRestrictionTeam:USTC Software/hoWRestriction2009-10-21T17:25:29Z<p>Bigben: /* Restrictions - Input File List */</p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
|valign = "top" align = "justify" border = "0" width = "600px" bordercolor = "#F3F3F3"|<br />
<br />
==Restrictions - Input File List==<br />
<br />
{| border = "1" align = "center" width = "200px"<br />
|-<br />
|No <br />
|Item<br />
|-<br />
|1. <br />
|Node<br />
|-<br />
|2. <br />
|Target Time Course<br />
|-<br />
|3. <br />
|Input Data<br />
|-<br />
|4. <br />
|Initial Values<br />
|-<br />
|5. <br />
|Initial Parameters<br />
|-<br />
|6. <br />
|Network Restriction<br />
|-<br />
|7. <br />
|Parameter Restriction<br />
|-<br />
|8.<br />
|align = "left"|<br />
Parameter Relation Restriction<br />
|-<br />
|9.<br />
|Parameter Range<br />
|-<br />
|10.<br />
|Candidate Function List <br />
|-<br />
|11.<br />
|Algorithm Parameters<br />
|}<br />
<br />
<br />
'''1. Node:''' Lets you specify the numbers of species you need to construct a network<br />
<br />
'''2. Target Time Course:''' Target time course represent the desired behavior of a system if you choose the function of "identification". While in the case of "simulation" or "sensitivity analysis", the target file determine the time course used in the simulation process<br />
<br />
'''3. Input Data:''' Lets you input desired dynamics of one or more species as time course. Note that you must assign which species an input is act on in the first line of this file. If an input is act on more than one species(exist in more than one ODE), you should repeat it for each species it acts on.<br />
<br />
'''4. Initial Values:''' Lets you specify the initial value of species, this file must exist unless you choose to import your model with SBML file.<br />
<br />
'''5. Initial Parameters:''' Lets you specify the initial value of a parameter. There are six columns in this file: (1) flag (2) object (3)activator (4)function (5)para_index (6)value<br />
<br />
*(1). Flag indicate the number of species involved in a term if it is a positive value and "-1" represent degradation term, "-2" represent constant term.<br />
<br />
*(2). Object indicate which species this term affect, or which ODE this term in. <br />
<br />
*(3). Activator indicate index of species involved in a term, the number of activators must in accordance with flag tag.<br />
<br />
*(4). Function indicate the type of reaction of this term.<br />
<br />
*(5). Para_index_value indicate the index of parameter in current reaction, since more than one parameters may exist in a reaction.<br />
<br />
*(6). The last column indicate the value of a parameter.<br />
<br />
Every line in this file represent only ONE parameter, the first five columns is used to locate a term in the ODEs and to locate a parameter in a term while the last column gives the value of a parameter. If you want to carry out simulation or sensitivity analysis, each paramter must be initialized in this file.<br />
<br />
'''6. Network Restriction:''' If you want to carry out topological identification, this file lets you cut unnecessary edges between species and restrict special rate term form of ceritain species. For other cases, this file also plays the role to input a certain topological structure. Compared to Initial Parameters File, there are two less columns in this file. The first three columns "flag", "object", "activator" are used to specify an edge in the network while the last column "func_list" determine type of the edge. <br />
<br />
'''7. Parameter Restriction:''' Lets you specify a parameter value that holds at all times during the identification. The organization of this file is absolutely the same with Initial Parameters File. This file is not needed unless you want to do identification.<br />
<br />
'''8. Parameter Relation Restriction:''' Lets you specify mathematical constraints on one or more parameters, species, or compartments that must hold during a simulation<br />
<br />
'''9. Parameter Range:''' Lets you specify the feasible range of parameters regardless of "7. PARAM_RESTRI". The organization of this file is similar to Initial Parameter File, while the last two columns "min" and "max" are minimum and maximum value of a parameter, instead of a certain value.<br />
<br />
'''10. Candidate Function List:''' All possible types of functions following different kinetic laws (see Table.1)<br />
user define functions are added to the end of this file.<br />
<br />
{|width = "60pt"|<br />
[[Image:Candidate_Kinetic_Law.png|center|500px|thumb|Candidate Kinetic Law Table]]<br />
|align = "left"|<br />
|}<br />
<br />
'''12. Algorithm Parameters:''' Lets you specify parameter values in genetic algorithm. "population","mutation_ratio","recombine_ratio","max_cycle" are set in this file.<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWDesignTeam:USTC Software/hoWDesign2009-10-21T17:05:52Z<p>Bigben: </p>
<hr />
<div>{{USTCSW_Heading}}<br />
<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
align = "justify"<br />
<br />
==Design Level==<br />
<br />
You should choose what level you focus on. Generally, there are four levels: parts level, device level, system level and abstract level respectively. The former three levels should be designated before design for a certain database should be selected to link. They are aimed at real application by using practical materials. The last level is rather general and mathematical. It doesn’t link to certain database while providing topology information only.<br />
<br />
===Parts Level:=== <br />
<br />
Since, the function of parts can only display when they are in device with other kinds of parts. Thus, this level is to serve the device level that details about parts could be retrieved while designing a device. Details about kinetic laws and kinetic parameters these parts play in biochemical reactions are needed. <br />
<br />
===Device Level:=== <br />
<br />
Devices are composed by basic parts and fabricated in a special manner. The function may vary be inserting different parts of same kind like promoter to the same place in device. This way is actually means to change the kinetic parameters in order to change the response of the device. Both static and dynamic transfer functions are needed to describe each device in order to be inserted or replaced in the software for simulation and design purpose. <br />
<br />
===System Level:===<br />
<br />
Systems are usually composed by devices while details of parts are not emphasized. The system level is an extension of device level, but focusing on much complicated ones even the entire cell, organism and ecosystem. <br />
<br />
===Abstract (mathematical) Level:===<br />
<br />
Topology is crucial for a network even if the kinetic laws are not that clear. Here, we do not care what concrete parts we use but rather mathematical and graphic form. It is universally significant and instructive for design process. <br />
<br />
==Design Type (Sub Level)==<br />
<br />
After you choose what design level you focus, there are four types of sublevels to select. We define these sublevels because the users are unnecessary to run the every design step that we give prior for an entire design process but some certain functions. Given these information, users could quickly start their design without wasting additional running time. Though our software runs relevant functions according to your input, it will be helpful and clear for the users to know what sublevels fit their need to complete their design efficiently. <br />
{| border = "1" align = "center"<br />
|-<br />
|ID <br />
|Interaction <br />
|Kinetic Law<br />
|-<br />
| 1 <br />
| Y <br />
| Y<br />
|-<br />
| 2 <br />
| Y <br />
| N<br />
|-<br />
| 3 <br />
| N <br />
| Y<br />
|-<br />
| 4 <br />
| N <br />
| N<br />
|}<br />
<br />
===Sub Level 1:===<br />
<br />
The mutual interactions and kinetic laws are absolutely clear that only kinetic parameters are unknown or partly known. Based on the restrictions the user inputs, our software give a series of possible solutions to choose. In this sublevel, only parameter identification algorithm is recalled. Construction of E-parts of out wet team is on this sublevel. <br />
<br />
===Sub Level 2:===<br />
<br />
The mutual interactions are already known but kinetic laws are not that clear. Usually, the structure is clear to the users but kinetic laws are changeable for design. On the other hand, kinetic laws largely determine the dynamics. The [https://2009.igem.org/Team:USTC_Software/WhatDemo#Example_1._Synthetic_Oscillator Oscillator] and [https://2009.igem.org/Team:USTC_Software/WhatDemo#Example_3._Bistable_Toggle_Switch Bistable Toggle Switch] example is on this sub level.<br />
<br />
===Sub Level 3:===<br />
<br />
The reaction types are already known but mutual interactions are not that clear. Sometimes kinetic laws are easy to identify based on some basic ones like MassAction, Michaelis-Menten, or Hill Kinetics, etc. The [https://2009.igem.org/Team:USTC_Software/WhatDemo#Example_2:_Perfect_Adaptation Adaptation] example is on this sublevel. <br />
<br />
===Sub Level 4:===<br />
<br />
Nothing is known about the design. Urr….. Just wait, we will give some solutions anyway. What you need to do is just to wait.<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWMMDTeam:USTC Software/hoWMMD2009-10-21T17:02:26Z<p>Bigben: /* Candidate Kinetic Laws */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
|align = "justify"|<br />
{|-<br />
|align = "justify" border = "1" bordercolor = "black" bgcolor = "red"|<br />
'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MMD <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
==Mathematical Formulation==<br />
<br />
High dimensional model representation(HDMR) is a general set of<br />
quantitative model assessment and analysis tools for capturing high<br />
dimensional IO system behavior. As the impact of the multiple input<br />
variables on the output can be independent and cooperative, it is<br />
natural to express the model output ()fx as a finite hierarchical<br />
correlated function expansion in terms of the input variables:<br />
<br />
<math><br />
f(x) = f_{0}+\sum_{i=1}^{n}f_{i}(x_{i})+\sum_{1\leq<br />
i<j\leq n} f_{ij}(x_{i}, x_{j})+ <br />
</math><br />
<br /><br />
::<math>\sum_{1\leq i<j<k\leq<br />
n}f_{ijk}(x_{i},x_{j},x_{k})+...+<br />
</math><br />
<br /><br />
::<math><br />
\sum_{1\leq i_{1}<...<i_{l}\leq<br />
n}f_{i_{1}i_{2}...i_{l}}(x_{i1},x_{i2},...,x_{il})+...+f_{12...n}(x_{1},x_{2},...,x_{n})<br />
</math><br />
<br />
<br />
where the zeroth-order component function <math>f_{0}</math> is a<br />
constant representing<br />
the mean response to <math>f(x)</math>, and the first order component function <math><br />
f_{i}(x_{i})</math> gives the independent contribution to<br />
<math>f(x)</math> by the ith input variable acting alone, the second<br />
order component function <math>f_{ij}(x_{i},x_{j})</math> gives the<br />
pair correlated contribution to <math>f(x)</math> by the input<br />
variables <math>x_{i}</math> and <math>x_{j}</math>, etc. The last<br />
term contains any residual <math>n</math>th order correlated<br />
contribution of all input variables.<br />
<br />
The basic conjecture underlying HDMR is that the component functions<br />
arising in typical real problems are likely to exhibit only low<br />
order l cooperativity among the input variables such that the<br />
significant terms in the HDMR expansion are expected to satisfy the<br />
relation: l<<n< for n>>1. An HDMR<br />
expansion to second order<br />
<br />
<math>\begin{align}<br />
f(x)=f_{0}+\sum\limits_{i=1}^{n}f_{i}(x_{i})+\sum\limits_{1\leq<br />
i<j\leq n}f_{ij}(x_{i},x_{j}), \\ \end{align}\,\!</math><br />
<br />
often provides a satisfactory description of <math>f(x)</math> for<br />
many high dimensional systems when the input variables are properly<br />
chosen. This is also the formula we use to achieve HDMR expansion.<br />
Similarly, reactants of two at most are usually involed in<br />
biochemical reactions. Thus, we can simplify the differential<br />
equations to the following form:<br />
<br />
<math>\begin{align}<br />
\frac{dx_{k}}{dt} &=&\sum\limits_{i=1}^{n}f_{i}(x_{i},{\mathbf{p}}<br />
_{i})+\sum\limits_{1\leq i<j\leq n}f_{ij}(x_{i},x_{j},{\mathbf{p}}<br />
_{ij})-kx_{i}+C_{k}\\ \end{align}\,\!</math><br />
<br />
<math>\begin{align}s.t.\text{ algebra equations} <br />
\\ \end{align}\,\!</math><br />
<br />
for <math>k=1,\ldots ,n.</math> The left side term of the equation<br />
above represents the changing rate of variable <math>x_{k}.</math>We<br />
assume that each term on the right side represents one step<br />
biochemical reaction which is equivalent to the rate term defined in<br />
SBML. It means that changing rate of one variavle is determined by<br />
different rate terms. <math>C_{k}</math> is a constant number.<br />
<math>f_{i}(\cdot )</math> and <math>f_{ij}(\cdot )</math> have<br />
similar definitions and represent<br />
reaction rates that vary according to kinetic laws. <math>{\mathbf{p}}_{i}</math> and <math>{<br />
\mathbf{p}}_{ij}</math> contain the parameter values of the kinetic<br />
law. It should mention that the last term<math>-kx_{i}</math><br />
represents the degradation of <math>x_{i},</math> which seems to<br />
belong to <math>f_{i}(x_{i})</math> that may render degradation<br />
term undermined, we should add such a term for its ubiqutious<br />
existence in biological systems.<br />
<br />
It is illustrative to consider the network generation task using a<br />
compact mathematical framework. Especially for metabolic networks,<br />
the structural and kinetic information can be well summarized using<br />
a time variant<br />
concentration vector <math>\mathbf{x}</math>, a time invariant stoichimetric matrix <math>S</math><br />
, and a time variant reaction rate vector <math>\mathbf{v}</math>.<br />
Vector <math>v</math> contains concentrations for all the<br />
<math>k</math> species <math>(x_{k},k=1,...,n)</math>. The<br />
<math>n\times m</math> matrix <math>S</math> represents the network<br />
structure by storing stoichiometric coefficients of all n reactions<br />
in its columns. The element <math>S(i,j)>0</math> if reaction<br />
<math>j</math> produces species <math>i</math>,<br />
<math>S(i,j)<0</math> if reaction <math>j</math> consumes species<br />
<math>i</math>, and otherwise <math>S(i,j)=0</math>. The reaction<br />
rate vector <math>\mathbf{v}</math> describes reaction rates<br />
<math>v_{j}</math>, <math>j=1,...,n</math>. Reaction rates vary<br />
according to kinetic laws which are linear or nonlinear algebraic<br />
functions.<br />
<br />
Typically, kinetic laws determine the rates based on the amounts of<br />
species participating to reactions as well as various reaction<br />
specific parameters. Altogether, an ODE model can be formulated as<br />
<br />
<math>\begin{align} \frac{d\mathbf{x}}{dt}=S\mathbf{v}<br />
\\ \end{align}\,\!</math><br />
<br />
The reaction rates <math>v_{j}</math>, <math>j=1,...,m</math> are determined by kinetic laws<br />
<math>f_{j} </math> as<br />
<br />
<math>\begin{align} v_{j}=f_{j}({\mathbf{x}}_{j},{\mathbf{p}}_{j}),<br />
\\ \end{align}\,\!</math><br />
<br />
in which <math>{\mathbf{x}}_{j}</math> includes concentrations of<br />
species taking part in the reaction <math>j</math>, and<br />
<math>{\mathbf{p}}_{j}</math> contains the parameter values of the<br />
kinetic law.<br />
<br />
==Candidate Kinetic Laws==<br />
<br />
Inspired by Matlab SimBiology (The MathWorks™), we list possible kinetic laws that are mostly encountered in biochemical reactions. These candidate kinetic laws are utilized in design sub level [https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_1: 1],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_2: 2],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_3: 3] and will be shuffled in [https://2009.igem.org/Team:USTC_Software/hoWAlgorithm Genetic Algorithm]. <br />
<br />
{|width = "60pt"|<br />
[[Image:Candidate_Kinetic_Law.png|center|550px|thumb|Candidate Kinetic Law Table]]<br />
|align = "left"|<br />
|}<br />
<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWMMDTeam:USTC Software/hoWMMD2009-10-21T17:01:41Z<p>Bigben: /* Candidate Kinetic Laws */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
|align = "justify"|<br />
{|-<br />
|align = "justify" border = "1" bordercolor = "black" bgcolor = "red"|<br />
'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MMD <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
==Mathematical Formulation==<br />
<br />
High dimensional model representation(HDMR) is a general set of<br />
quantitative model assessment and analysis tools for capturing high<br />
dimensional IO system behavior. As the impact of the multiple input<br />
variables on the output can be independent and cooperative, it is<br />
natural to express the model output ()fx as a finite hierarchical<br />
correlated function expansion in terms of the input variables:<br />
<br />
<math><br />
f(x) = f_{0}+\sum_{i=1}^{n}f_{i}(x_{i})+\sum_{1\leq<br />
i<j\leq n} f_{ij}(x_{i}, x_{j})+ <br />
</math><br />
<br /><br />
::<math>\sum_{1\leq i<j<k\leq<br />
n}f_{ijk}(x_{i},x_{j},x_{k})+...+<br />
</math><br />
<br /><br />
::<math><br />
\sum_{1\leq i_{1}<...<i_{l}\leq<br />
n}f_{i_{1}i_{2}...i_{l}}(x_{i1},x_{i2},...,x_{il})+...+f_{12...n}(x_{1},x_{2},...,x_{n})<br />
</math><br />
<br />
<br />
where the zeroth-order component function <math>f_{0}</math> is a<br />
constant representing<br />
the mean response to <math>f(x)</math>, and the first order component function <math><br />
f_{i}(x_{i})</math> gives the independent contribution to<br />
<math>f(x)</math> by the ith input variable acting alone, the second<br />
order component function <math>f_{ij}(x_{i},x_{j})</math> gives the<br />
pair correlated contribution to <math>f(x)</math> by the input<br />
variables <math>x_{i}</math> and <math>x_{j}</math>, etc. The last<br />
term contains any residual <math>n</math>th order correlated<br />
contribution of all input variables.<br />
<br />
The basic conjecture underlying HDMR is that the component functions<br />
arising in typical real problems are likely to exhibit only low<br />
order l cooperativity among the input variables such that the<br />
significant terms in the HDMR expansion are expected to satisfy the<br />
relation: l<<n< for n>>1. An HDMR<br />
expansion to second order<br />
<br />
<math>\begin{align}<br />
f(x)=f_{0}+\sum\limits_{i=1}^{n}f_{i}(x_{i})+\sum\limits_{1\leq<br />
i<j\leq n}f_{ij}(x_{i},x_{j}), \\ \end{align}\,\!</math><br />
<br />
often provides a satisfactory description of <math>f(x)</math> for<br />
many high dimensional systems when the input variables are properly<br />
chosen. This is also the formula we use to achieve HDMR expansion.<br />
Similarly, reactants of two at most are usually involed in<br />
biochemical reactions. Thus, we can simplify the differential<br />
equations to the following form:<br />
<br />
<math>\begin{align}<br />
\frac{dx_{k}}{dt} &=&\sum\limits_{i=1}^{n}f_{i}(x_{i},{\mathbf{p}}<br />
_{i})+\sum\limits_{1\leq i<j\leq n}f_{ij}(x_{i},x_{j},{\mathbf{p}}<br />
_{ij})-kx_{i}+C_{k}\\ \end{align}\,\!</math><br />
<br />
<math>\begin{align}s.t.\text{ algebra equations} <br />
\\ \end{align}\,\!</math><br />
<br />
for <math>k=1,\ldots ,n.</math> The left side term of the equation<br />
above represents the changing rate of variable <math>x_{k}.</math>We<br />
assume that each term on the right side represents one step<br />
biochemical reaction which is equivalent to the rate term defined in<br />
SBML. It means that changing rate of one variavle is determined by<br />
different rate terms. <math>C_{k}</math> is a constant number.<br />
<math>f_{i}(\cdot )</math> and <math>f_{ij}(\cdot )</math> have<br />
similar definitions and represent<br />
reaction rates that vary according to kinetic laws. <math>{\mathbf{p}}_{i}</math> and <math>{<br />
\mathbf{p}}_{ij}</math> contain the parameter values of the kinetic<br />
law. It should mention that the last term<math>-kx_{i}</math><br />
represents the degradation of <math>x_{i},</math> which seems to<br />
belong to <math>f_{i}(x_{i})</math> that may render degradation<br />
term undermined, we should add such a term for its ubiqutious<br />
existence in biological systems.<br />
<br />
It is illustrative to consider the network generation task using a<br />
compact mathematical framework. Especially for metabolic networks,<br />
the structural and kinetic information can be well summarized using<br />
a time variant<br />
concentration vector <math>\mathbf{x}</math>, a time invariant stoichimetric matrix <math>S</math><br />
, and a time variant reaction rate vector <math>\mathbf{v}</math>.<br />
Vector <math>v</math> contains concentrations for all the<br />
<math>k</math> species <math>(x_{k},k=1,...,n)</math>. The<br />
<math>n\times m</math> matrix <math>S</math> represents the network<br />
structure by storing stoichiometric coefficients of all n reactions<br />
in its columns. The element <math>S(i,j)>0</math> if reaction<br />
<math>j</math> produces species <math>i</math>,<br />
<math>S(i,j)<0</math> if reaction <math>j</math> consumes species<br />
<math>i</math>, and otherwise <math>S(i,j)=0</math>. The reaction<br />
rate vector <math>\mathbf{v}</math> describes reaction rates<br />
<math>v_{j}</math>, <math>j=1,...,n</math>. Reaction rates vary<br />
according to kinetic laws which are linear or nonlinear algebraic<br />
functions.<br />
<br />
Typically, kinetic laws determine the rates based on the amounts of<br />
species participating to reactions as well as various reaction<br />
specific parameters. Altogether, an ODE model can be formulated as<br />
<br />
<math>\begin{align} \frac{d\mathbf{x}}{dt}=S\mathbf{v}<br />
\\ \end{align}\,\!</math><br />
<br />
The reaction rates <math>v_{j}</math>, <math>j=1,...,m</math> are determined by kinetic laws<br />
<math>f_{j} </math> as<br />
<br />
<math>\begin{align} v_{j}=f_{j}({\mathbf{x}}_{j},{\mathbf{p}}_{j}),<br />
\\ \end{align}\,\!</math><br />
<br />
in which <math>{\mathbf{x}}_{j}</math> includes concentrations of<br />
species taking part in the reaction <math>j</math>, and<br />
<math>{\mathbf{p}}_{j}</math> contains the parameter values of the<br />
kinetic law.<br />
<br />
==Candidate Kinetic Laws==<br />
<br />
Inspired by Matlab SimBiology (The MathWorks™), we list possible kinetic laws that are mostly encountered in biochemical reactions. These candidate kinetic laws are utilized in design sub level [https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_1: 1],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_2: 2],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_3: 3] and will be shuffled in [https://2009.igem.org/Team:USTC_Software/hoWAlgorithm GA]. <br />
<br />
{|width = "60pt"|<br />
[[Image:Candidate_Kinetic_Law.png|center|550px|thumb|Candidate Kinetic Law Table]]<br />
|align = "left"|<br />
|}<br />
<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWMMDTeam:USTC Software/hoWMMD2009-10-21T17:01:16Z<p>Bigben: /* Mathematical Formulation */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
|align = "justify"|<br />
{|-<br />
|align = "justify" border = "1" bordercolor = "black" bgcolor = "red"|<br />
'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MMD <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
==Mathematical Formulation==<br />
<br />
High dimensional model representation(HDMR) is a general set of<br />
quantitative model assessment and analysis tools for capturing high<br />
dimensional IO system behavior. As the impact of the multiple input<br />
variables on the output can be independent and cooperative, it is<br />
natural to express the model output ()fx as a finite hierarchical<br />
correlated function expansion in terms of the input variables:<br />
<br />
<math><br />
f(x) = f_{0}+\sum_{i=1}^{n}f_{i}(x_{i})+\sum_{1\leq<br />
i<j\leq n} f_{ij}(x_{i}, x_{j})+ <br />
</math><br />
<br /><br />
::<math>\sum_{1\leq i<j<k\leq<br />
n}f_{ijk}(x_{i},x_{j},x_{k})+...+<br />
</math><br />
<br /><br />
::<math><br />
\sum_{1\leq i_{1}<...<i_{l}\leq<br />
n}f_{i_{1}i_{2}...i_{l}}(x_{i1},x_{i2},...,x_{il})+...+f_{12...n}(x_{1},x_{2},...,x_{n})<br />
</math><br />
<br />
<br />
where the zeroth-order component function <math>f_{0}</math> is a<br />
constant representing<br />
the mean response to <math>f(x)</math>, and the first order component function <math><br />
f_{i}(x_{i})</math> gives the independent contribution to<br />
<math>f(x)</math> by the ith input variable acting alone, the second<br />
order component function <math>f_{ij}(x_{i},x_{j})</math> gives the<br />
pair correlated contribution to <math>f(x)</math> by the input<br />
variables <math>x_{i}</math> and <math>x_{j}</math>, etc. The last<br />
term contains any residual <math>n</math>th order correlated<br />
contribution of all input variables.<br />
<br />
The basic conjecture underlying HDMR is that the component functions<br />
arising in typical real problems are likely to exhibit only low<br />
order l cooperativity among the input variables such that the<br />
significant terms in the HDMR expansion are expected to satisfy the<br />
relation: l<<n< for n>>1. An HDMR<br />
expansion to second order<br />
<br />
<math>\begin{align}<br />
f(x)=f_{0}+\sum\limits_{i=1}^{n}f_{i}(x_{i})+\sum\limits_{1\leq<br />
i<j\leq n}f_{ij}(x_{i},x_{j}), \\ \end{align}\,\!</math><br />
<br />
often provides a satisfactory description of <math>f(x)</math> for<br />
many high dimensional systems when the input variables are properly<br />
chosen. This is also the formula we use to achieve HDMR expansion.<br />
Similarly, reactants of two at most are usually involed in<br />
biochemical reactions. Thus, we can simplify the differential<br />
equations to the following form:<br />
<br />
<math>\begin{align}<br />
\frac{dx_{k}}{dt} &=&\sum\limits_{i=1}^{n}f_{i}(x_{i},{\mathbf{p}}<br />
_{i})+\sum\limits_{1\leq i<j\leq n}f_{ij}(x_{i},x_{j},{\mathbf{p}}<br />
_{ij})-kx_{i}+C_{k}\\ \end{align}\,\!</math><br />
<br />
<math>\begin{align}s.t.\text{ algebra equations} <br />
\\ \end{align}\,\!</math><br />
<br />
for <math>k=1,\ldots ,n.</math> The left side term of the equation<br />
above represents the changing rate of variable <math>x_{k}.</math>We<br />
assume that each term on the right side represents one step<br />
biochemical reaction which is equivalent to the rate term defined in<br />
SBML. It means that changing rate of one variavle is determined by<br />
different rate terms. <math>C_{k}</math> is a constant number.<br />
<math>f_{i}(\cdot )</math> and <math>f_{ij}(\cdot )</math> have<br />
similar definitions and represent<br />
reaction rates that vary according to kinetic laws. <math>{\mathbf{p}}_{i}</math> and <math>{<br />
\mathbf{p}}_{ij}</math> contain the parameter values of the kinetic<br />
law. It should mention that the last term<math>-kx_{i}</math><br />
represents the degradation of <math>x_{i},</math> which seems to<br />
belong to <math>f_{i}(x_{i})</math> that may render degradation<br />
term undermined, we should add such a term for its ubiqutious<br />
existence in biological systems.<br />
<br />
It is illustrative to consider the network generation task using a<br />
compact mathematical framework. Especially for metabolic networks,<br />
the structural and kinetic information can be well summarized using<br />
a time variant<br />
concentration vector <math>\mathbf{x}</math>, a time invariant stoichimetric matrix <math>S</math><br />
, and a time variant reaction rate vector <math>\mathbf{v}</math>.<br />
Vector <math>v</math> contains concentrations for all the<br />
<math>k</math> species <math>(x_{k},k=1,...,n)</math>. The<br />
<math>n\times m</math> matrix <math>S</math> represents the network<br />
structure by storing stoichiometric coefficients of all n reactions<br />
in its columns. The element <math>S(i,j)>0</math> if reaction<br />
<math>j</math> produces species <math>i</math>,<br />
<math>S(i,j)<0</math> if reaction <math>j</math> consumes species<br />
<math>i</math>, and otherwise <math>S(i,j)=0</math>. The reaction<br />
rate vector <math>\mathbf{v}</math> describes reaction rates<br />
<math>v_{j}</math>, <math>j=1,...,n</math>. Reaction rates vary<br />
according to kinetic laws which are linear or nonlinear algebraic<br />
functions.<br />
<br />
Typically, kinetic laws determine the rates based on the amounts of<br />
species participating to reactions as well as various reaction<br />
specific parameters. Altogether, an ODE model can be formulated as<br />
<br />
<math>\begin{align} \frac{d\mathbf{x}}{dt}=S\mathbf{v}<br />
\\ \end{align}\,\!</math><br />
<br />
The reaction rates <math>v_{j}</math>, <math>j=1,...,m</math> are determined by kinetic laws<br />
<math>f_{j} </math> as<br />
<br />
<math>\begin{align} v_{j}=f_{j}({\mathbf{x}}_{j},{\mathbf{p}}_{j}),<br />
\\ \end{align}\,\!</math><br />
<br />
in which <math>{\mathbf{x}}_{j}</math> includes concentrations of<br />
species taking part in the reaction <math>j</math>, and<br />
<math>{\mathbf{p}}_{j}</math> contains the parameter values of the<br />
kinetic law.<br />
<br />
==Candidate Kinetic Laws==<br />
<br />
Inspired by Matlab SimBiology (The MathWorks™), we list possible kinetic laws that are mostly encountered in biochemical reactions. These candidate kinetic laws are utilized in design sub level [https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_1: 1],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_2: 2],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_3: 3] and will be shuffled in [https://2009.igem.org/Team:USTC_Software/hoWAlgorithm GA]. <br />
<br />
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{|width = "60pt"|<br />
[[Image:Candidate_Kinetic_Law.png|center|550px|thumb|Candidate Kinetic Law Table]]<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWMMDTeam:USTC Software/hoWMMD2009-10-21T17:00:14Z<p>Bigben: </p>
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<div>{{USTCSW_Heading}}<br />
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{|-<br />
|align = "justify" border = "1" bordercolor = "black" bgcolor = "red"|<br />
'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MMD <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
==Mathematical Formulation==<br />
<br />
High dimensional model representation(HDMR) is a general set of<br />
quantitative model assessment and analysis tools for capturing high<br />
dimensional IO system behavior. As the impact of the multiple input<br />
variables on the output can be independent and cooperative, it is<br />
natural to express the model output ()fx as a finite hierarchical<br />
correlated function expansion in terms of the input variables:<br />
<br />
<math>\begin{align}<br />
f(x)& =f_{0}+\sum_{i=1}^{n}f_{i}(x_{i})+\sum_{1\leq<br />
i<j\leq n} f_{ij}(x_{i}, x_{j})+ \sum_{1\leq i<j<k\leq<br />
n}f_{ijk}(x_{i},x_{j},x_{k})+...+\sum_{1\leq i_{1}<...<i_{l}\leq<br />
n}f_{i_{1}i_{2}...i_{l}}(x_{i1},x_{i2},...,x_{il})<br />
+...+f_{12...n}(x_{1},x_{2},...,x_{n})\\ \end{align}\,\!</math><br />
<br />
<br />
where the zeroth-order component function <math>f_{0}</math> is a<br />
constant representing<br />
the mean response to <math>f(x)</math>, and the first order component function <math>%<br />
f_{i}(x_{i})</math> gives the independent contribution to<br />
<math>f(x)</math> by the ith input variable acting alone, the second<br />
order component function <math>f_{ij}(x_{i},x_{j})</math> gives the<br />
pair correlated contribution to <math>f(x)</math> by the input<br />
variables <math>x_{i}</math> and <math>x_{j}</math>, etc. The last<br />
term contains any residual <math>n</math>th order correlated<br />
contribution of all input variables.<br />
<br />
The basic conjecture underlying HDMR is that the component functions<br />
arising in typical real problems are likely to exhibit only low<br />
order l cooperativity among the input variables such that the<br />
significant terms in the HDMR expansion are expected to satisfy the<br />
relation: <math>l\ll n</math> for <math>n\gg 1 </math>. An HDMR<br />
expansion to second order<br />
<br />
<math>\begin{align}<br />
f(x)=f_{0}+\sum\limits_{i=1}^{n}f_{i}(x_{i})+\sum\limits_{1\leq<br />
i<j\leq n}f_{ij}(x_{i},x_{j}), \\ \end{align}\,\!</math><br />
<br />
often provides a satisfactory description of <math>f(x)</math> for<br />
many high dimensional systems when the input variables are properly<br />
chosen. This is also the formula we use to achieve HDMR expansion.<br />
Similarly, reactants of two at most are usually involed in<br />
biochemical reactions. Thus, we can simplify the differential<br />
equations to the following form:<br />
<br />
<math>\begin{align}<br />
\frac{dx_{k}}{dt} &=&\sum\limits_{i=1}^{n}f_{i}(x_{i},{\mathbf{p}}<br />
_{i})+\sum\limits_{1\leq i<j\leq n}f_{ij}(x_{i},x_{j},{\mathbf{p}}<br />
_{ij})-kx_{i}+C_{k}\\ \end{align}\,\!</math><br />
<br />
<math>\begin{align}s.t.\text{ algebra equations} <br />
\\ \end{align}\,\!</math><br />
<br />
for <math>k=1,\ldots ,n.</math> The left side term of the equation<br />
above represents the changing rate of variable <math>x_{k}.</math>We<br />
assume that each term on the right side represents one step<br />
biochemical reaction which is equivalent to the rate term defined in<br />
SBML. It means that changing rate of one variavle is determined by<br />
different rate terms. <math>C_{k}</math> is a constant number.<br />
<math>f_{i}(\cdot )</math> and <math>f_{ij}(\cdot )</math> have<br />
similar definitions and represent<br />
reaction rates that vary according to kinetic laws. <math>{\mathbf{p}}_{i}</math> and <math>{%<br />
\mathbf{p}}_{ij}</math> contain the parameter values of the kinetic<br />
law. It should mention that the last term\ <math>-kx_{i}</math>\<br />
represents the degradation of <math>x_{i},</math>\ which seems to<br />
belong to <math>f_{i}(x_{i})</math> that\ may render degradation<br />
term undermined, we should add such a term for its ubiqutious<br />
existence in biological systems.<br />
<br />
It is illustrative to consider the network generation task using a<br />
compact mathematical framework. Especially for metabolic networks,<br />
the structural and kinetic information can be well summarized using<br />
a time variant<br />
concentration vector <math>\mathbf{x}</math>, a time invariant stoichimetric matrix <math>S</math>%<br />
, and a time variant reaction rate vector <math>\mathbf{v}</math>.<br />
Vector <math>v</math> contains concentrations for all the<br />
<math>k</math> species <math>(x_{k},k=1,...,n)</math>. The<br />
<math>n\times m</math> matrix <math>S</math> represents the network<br />
structure by storing stoichiometric coefficients of all n reactions<br />
in its columns. The element <math>S(i,j)>0</math> if reaction<br />
<math>j</math> produces species <math>i</math>,<br />
<math>S(i,j)<0</math> if reaction <math>j</math> consumes species<br />
<math>i</math>, and otherwise <math>S(i,j)=0</math>. The reaction<br />
rate vector <math>\mathbf{v}</math> describes reaction rates<br />
<math>v_{j}</math>, <math>j=1,...,n</math>. Reaction rates vary<br />
according to kinetic laws which are linear or nonlinear algebraic<br />
functions.<br />
<br />
Typically, kinetic laws determine the rates based on the amounts of<br />
species participating to reactions as well as various reaction<br />
specific parameters. Altogether, an ODE model can be formulated as<br />
<br />
<math>\begin{align} \frac{d\mathbf{x}}{dt}=S\mathbf{v}<br />
\\ \end{align}\,\!</math><br />
<br />
The reaction rates <math>v_{j}</math>, <math>j=1,...,m</math> are determined by kinetic laws<br />
<math>f_{j} </math> as%<br />
<br />
<math>\begin{align} v_{j}=f_{j}({\mathbf{x}}_{j},{\mathbf{p}}_{j}),<br />
\\ \end{align}\,\!</math><br />
<br />
in which <math>{\mathbf{x}}_{j}</math> includes concentrations of<br />
species taking part in the reaction <math>j</math>, and<br />
<math>{\mathbf{p}}_{j}</math> contains the parameter values of the<br />
kinetic law.<br />
<br />
==Candidate Kinetic Laws==<br />
<br />
Inspired by Matlab SimBiology (The MathWorks™), we list possible kinetic laws that are mostly encountered in biochemical reactions. These candidate kinetic laws are utilized in design sub level [https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_1: 1],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_2: 2],[https://2009.igem.org/Team:USTC_Software/hoWDesign#Sub_Level_3: 3] and will be shuffled in [https://2009.igem.org/Team:USTC_Software/hoWAlgorithm GA]. <br />
<br />
<br/><br />
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[[Image:Candidate_Kinetic_Law.png|center|550px|thumb|Candidate Kinetic Law Table]]<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatDemoTeam:USTC Software/WhatDemo2009-10-21T16:58:00Z<p>Bigben: </p>
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<div>{{USTCSW_Heading}}<br />
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{|-<br />
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{{USTCSW_SideBarL}}<br />
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{|-<br />
|align = "justify" border = "1" bordercolor = "black" bgcolor = "red"|<br />
'''Due to the incapaility of 2009.igem.org to interpret formula in Latex form to elligible expressions, we have to relink this page [https://igem.org/User:Heyu3/MM <font size = "4">HERE</font>]. This has been authorized by the organizers of iGEM. If you don't mind the formula part, you may still work with this page.'''<br />
<br /><br />
|}<br />
<br />
=Example 1. A Synthetic Oscillator=<br />
<br />
==Introduction==<br />
<br />
The [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659856&query_hl=2 synthetic oscillatory network] designed by [http://www.elowitz.caltech.edu/ Michael Elowitz] is pioneering work. In the first place, based on his model, we want to illustrate how to tune the parameters to get pre-defined wave amplitude and wave frequency. In the second place, besides this three node repressive model, is it possible to propose a alternative topology that could also achieve tunable oscillation. In [http://gardnerlab.bu.edu/ Tim Gardner]'s PhD dissertation, such a different topology is proposed. We search feasible parameter that could achieve oscillation. <br />
<br />
==Mathematical Formulation==<br />
<br />
The activities of a gene are regulated by other genes through the<br />
interactions between them, i.e., the transcription and translation<br />
factors. Here, we assume that this system follows Hill kinetic law.<br />
<br />
<math>\begin{align}<br />
\frac{dm_{i}}{dt} &=-a_{i}m_{i}+\sum\limits_{j}b_{ij}\frac{p_{j}^{H_{ij}}}{K_{ij}+p_{j}^{H_{ij}}}+l_{i}, \\<br />
\frac{dp_{i}}{dt} &=-c_{i}p_{i}+d_{i}m_{i}, (i=1,2,...,n)<br />
\end{align}\,\!</math><br />
<br />
where <math>m_{i}(t), p_{i}(t)\in {\mathbb{R}}</math> are concentrations of mRNA and protein of the <math>i</math>th node at time <math>t</math>, respectively, <math>a_{i}</math> and<br />
<math>c_{i}</math> are the degradation rates of the mRNA and<br />
protein, <math>d_{i}</math> is the translation rate. Term (1)<br />
describes the transcription process and term (2) describes the<br />
translation process.<br />
Negative and positive signs of <math>b_{ij}</math> indicates the<br />
mutual interaction relationship that could be attributed to negative<br />
or positive feedback. The values describe the strength of promoters<br />
which is tunable by inserting different promoters in gene circuits.<br />
<math>H_{ij}</math> is Hill coefficient describing cooperativity.<br />
<math>K_{ij}</math> is the apparent dissociation constant derived<br />
from the law of mass action (equilibrium constant for dissociation).<br />
We can write <math>K_{ij}=\left( \hat{K}_{ij}\right) ^{n}</math><br />
where <math>\hat{K}</math> is ligand concentration producing half<br />
occupation (ligand concentration occupying half of the binding<br />
sites), that is also the microscopic dissociation constant.<br />
<br />
==A Tunable Oscillator==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &=-am_{1}+b\frac{p_{3}^{H_{13}}}{K+p_{3}^{H_{1}}}, \\<br />
\frac{dm_{2}}{dt} &=-am_{2}+b\frac{p_{1}^{H_{21}}}{K+p_{1}^{H_{2}}}, \\<br />
\frac{dm_{3}}{dt} &=-am_{3}+b\frac{p_{2}^{H_{32}}}{K+p_{2}^{H_{32}}}, \\<br />
\frac{dp_{1}}{dt} &=-cp_{1}+dm_{1}, \\<br />
\frac{dp_{2}}{dt} &=-cp_{2}+dm_{2}, \\<br />
\frac{dp_{3}}{dt} &=-cp_{3}+dm_{3},\text{ }<br />
\end{align}\,\!</math><br />
<br />
where <math>a, b,</math> <math>c,</math><br />
<math>d,</math> <math>H_{1},</math> <math>H_{2},</math><br />
<math>H_{3},</math> <math>K</math> are tunable parameters that could<br />
change wave amplitude and frequency. For simplicity, we assume that<br />
<math>H_{13}=H_{21}=H_{32}=2,</math> meaning that the system<br />
contains only positively cooperative reaction that once one ligand<br />
molecule is bound to the enzyme, its affinity for other ligand<br />
molecules increases.<br />
<br />
[[Image:Osc1_Amp_Tun.png|center|550px|thumb|Tunable Amplitude: <br />
The Black curve shows the original amplitude of the oscillator. <br />
The Red curve shows the desired amplitude of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
[[Image:Osc1_Freq_Tun.png|center|550px|thumb|Tunable Frequency: <br />
The Black curve shows the original frequency of the oscillator. <br />
The Red curve shows the desired frequency of the oscillator, <br />
The blue curve is the identification result]]<br />
<br />
==An Alternative Topology That Leads to Oscillation==<br />
<br />
The original three repressors model is described as follows:%<br />
<br />
<math>\begin{align}<br />
\frac{dm_{1}}{dt} &= -a_{1}x_{1}+\frac{b_{1}}{K_{1}+p_{2}^{H_{12}}}, \\<br />
\frac{dm_{2}}{dt} &= -a_{2}x_{2}+\frac{b_{2}p_{3}^{H_{23}}}{%<br />
K_{2}+p_{1}^{H_{21}}+p_{3}^{H_{23}}}, \\<br />
\frac{dm_{3}}{dt} &= -a_{3}x_{3}+\frac{b_{3}}{K_{3}+p_{2}^{H_{32}}} \\<br />
\frac{dp_{1}}{dt} &= -c_{1}p_{1}+d_{1}m_{1}, \\<br />
\frac{dp_{2}}{dt} &= -c_{2}p_{2}+d_{2}m_{2}, \\<br />
\frac{dp_{3}}{dt} &= -c_{3}p_{3}+d_{3}m_{3},<br />
\end{align}\,\!</math><br />
<br />
[[Image:Osc2.png|center|550px|thumb|An Alternative Topology the leads to Oscillation]]<br />
<br />
=Example 2: Perfect Adaptation=<br />
<br />
==Introduction==<br />
<br />
In this example, we try to seek different network topologies that can achieve adaptation-the ability to reset themselves after responding to a stimulus.. Actually, most of the scripts are cited from a newly published paper on [http://www.cell.com/ Cell]: [http://www.ncbi.nlm.nih.gov/pubmed/19703401 Defining Network Topologies that Can Achieve Biochemical Adaptation]. It 's quite by accident that issues discussed in this paper share some similarities with our project. To test our ABCD is powerful or not, the only thing we need to do is to search the two topologies found in this paper. By running nearly two days, we prove the solution. <br />
<br />
==Mathematical Formulation==<br />
<br />
We assume that each node (labeled as <math>A</math>, <math>B</math>, <math>C</math>) has a fixed concentration<br />
(normalized to <math>1</math>) but has two forms: active and<br />
inactive (here <math>A</math> represents the concentration of active state, and <br />
<math>1-A</math> is the concentration of the<br />
inactive state). The enzymatic regulation converts its target node<br />
between the two forms. For example, a positive regulation of node<br />
<math>B</math> by node <math>A</math> as denoted by a link<br />
<br />
<math>A\longrightarrow B</math> <br />
<br />
would mean that the active <math>A</math> convertsBfrom its inactive to its active form and<br />
would be modeled by the rate <br />
<br />
<math>R(B_{inactive}\longrightarrow<br />
B_{active})=k_{AB}A(1-B)/\left[ (1-B)+K_{AB}\right] </math>, <br />
<br />
where <math>A</math> is the normalized concentration of the active form of<br />
node <math>A</math> and <math>1-B</math> the normalized<br />
concentrations of the inactive form of node B. Likewise,<br />
<math>A-|B</math> implies that the active A catalyzes the reverse<br />
transition of node B from its active to its inactive form, with a<br />
rate <br />
<br />
<math>R(B_{active}\longrightarrow B_{inactive})=k_{AB}^{^{\prime }}/(B+K_{AB}^{^{\prime }}).</math> <br />
<br />
When there are multiple regulations of the same sign on a node, the<br />
effect is additive. For example, if node C is positively regulated<br />
by node A and node B, <br />
<br />
<math> R(C_{inactive}\longrightarrow C_{active})= k_{AC}A(1-C)/\left[ (1-C)+K_{AC}\right]</math> + <math>k_{BC}B(1-C)/\left[ (1-C)+K_{BC}\right] </math> . <br />
<br />
We assume that the interconversion between active and inactive forms of<br />
a node is reversible. Thus if a node <math>i</math> has only<br />
positive incoming links, it is assumed that there is a background<br />
(constitutive) deactivating enzyme Fi of a constant concentration<br />
(set to be <math>0.5</math>) to catalyze the reverse reaction.<br />
Similarly, a background activating enzyme <math>E_{i}=0.5</math> is<br />
added for the nodes that have only negative incoming links. The rate<br />
equation for a node (e.g., node <math>B</math>) takes the form:<br />
<br />
<math>\begin{align} \frac{dB}{dt}=\sum\limits_{i}X_{i}\cdot<br />
k_{X_{i}B}\frac{(1-B)}{ (1-B)+K_{X_{i}B}}-\sum\limits_{i}Y_{i}\cdot<br />
k_{X_{i}B}\frac{B}{B+K_{Y_{i}B}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>Xi=A,B,C,E_{A},E_{B},</math> or <math>E_{c}</math> are<br />
the activating enzymes (positive regulators) of <math>B</math> and<br />
<math>Yi=A,B,C,F_{A},F_{B},</math> or <math>F_{C}</math> are the<br />
deactivating enzymes (negative regulators) of <math>B</math>. In the<br />
equation for node A, an input term is added to the righthand-side of<br />
the equation: <br />
<br />
<math> Ik_{IA}(1-A)/((1-A)+K_{IA})</math>. <br />
<br />
The number of parameters in a network is <math> n_{p}=2n_{I}+2</math>, where<br />
<math>n_{I}</math> is the number of links in the network (including<br />
links from the basal enzymes if present).<br />
<br />
<br />
Then we hope the output of interested node tracks the target dynamics by a sudden stimulus and search the feasible topologies that achieve adaptation in the scope of all possible topologies. <br />
<br />
<br />
==Feedback loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&C\cdot k_{CB}\frac{(1-B)}{(1-B)+K_{CB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>F_{A}</math> and <math>F_{B}</math> represent the<br />
concentrations of basal enzymes that carry out the reverse reactions<br />
on nodes <math>A</math> and <math>B</math>, respectively (they<br />
oppose the active network links that activate <math>A</math> and<br />
<math>B</math>). In this circuit, node <math>A</math> simply<br />
functions as a passive relay of the input to node <math>C</math>;<br />
the circuit would work in the same way if the input were directly<br />
acting on node <math>C</math> (just replacing <math>A</math> with<br />
<math>I</math> in the third equation of Equation 1). Analyzing the<br />
parameter sets that enabled this topology to adapt indicates that<br />
the two constants <math>K_{CB}</math> and <math>K_{F_{B}B}^{^{\prime<br />
}}</math> (Michaelis-Menten constants for activation of<br />
<math>B</math> by <math>C</math> and inhibition of <math>B </math><br />
by the basal enzyme) tend to be small, suggesting that the two<br />
enzymes acting on node <math>B</math> must approach saturation to<br />
achieve adaptation. Indeed, it can be shown that in the case of<br />
saturation this topology can achieve perfect adaptation.<br />
<br />
<math>\begin{align}<br />
\begin{tabular}{l}<br />
</math>figure\text{ 1}\text{: desired input}</math> \\<br />
</math>figure\text{ 2}\text{: different inputs}</math> \\<br />
</math>figure\text{ 3: }</math>topology<br />
\end{tabular}<br />
\\ \end{align}\,\!</math><br />
<br />
[[ Image:Adapt2.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptationSim1.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
<br />
==Feedforward loop==<br />
<br />
The kinetic equations are as follows:<br />
<br />
<math>\begin{align} \frac{dA}{dt} &=&I\cdot<br />
k_{IA}\frac{(1-A)}{(1-A)+K_{IA}}-F_{A}\cdot<br />
k_{F_{A}A}^{^{\prime }}\frac{A}{A+K_{F_{A}A}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AB}\frac{(1-B)}{(1-B)+K_{AB}}-F_{B}\cdot<br />
k_{F_{B}B}^{^{\prime }}\frac{B}{B+K_{F_{B}B}^{^{\prime }}}, \\<br />
\frac{dB}{dt} &=&A\cdot k_{AC}\frac{(1-C)}{(1-C)+K_{AC}}-B\cdot<br />
k_{BC}^{^{\prime }}\frac{C}{C+K_{BC}^{^{\prime }}},<br />
\\ \end{align}\,\!</math><br />
<br />
The adaptation mechanism is mathematically captured in the<br />
<br />
equation for node <math>C</math>: if the steady-state concentration<br />
of the negative regulator B is proportional to that of the positive<br />
regulator <math>A</math>, the equation determining the steady-state<br />
value of <math>C</math>, <math>dC/dt=0</math>, would be independent<br />
of <math>A</math> and hence of the input <math>I</math>. In this<br />
case, the equation for node <math>B</math> generates the condition<br />
under which the steady-state value <math> B^*</math> would be<br />
proportional to <math>A^*</math>: the first term in<br />
<math>dB/dt</math> equation should depend on <math>A</math> only and<br />
the second term on <math>B</math> only. The condition can be<br />
satisfied if the first term is in the saturated region region<br />
<br />
<math>((1-B)\gg K_{AB})</math> <br />
<br />
and the second in the linear region<br />
<br />
<math>B\ll K_{F_{B}B}^{^{\prime }}</math>, <br />
<br />
leading to<br />
<br />
<math>\begin{align} B^{\ast }=A^{\ast }\cdot<br />
k_{AB}K_{F_{B}B}^{^{\prime }}/(F_{B}k_{F_{B}B}^{^{\prime }})<br />
\\ \end{align}\,\!</math><br />
<br />
This relationship, established by the equation for node<br />
<math>B</math>, shows that the steady-state concentration of active<br />
<math>B</math> is proportional to the steady-state concentration of<br />
active <math>A</math>. Thus <math>B</math> will negatively regulate<br />
<math>C</math> in proportion to the degree of pathway input. This<br />
effect of <math>B</math> acting as a proportioner node of<br />
<math>A</math> can be graphically gleaned from the plot of the<br />
<math>B</math> and <math>C</math> nullclines (Figure feedforward).<br />
In this case, maintaining a constant <math>C^{\ast }</math> requires<br />
the B nullcline to move the same distance as the <math>C</math><br />
nullcline in response to an input change. Here again, the<br />
sensitivity of the circuit (the magnitude of the transient response)<br />
depends on the ratio of the speeds of the two signal transduction<br />
branches: <br />
<br />
<math> A\longrightarrow C</math> <br />
<br />
and<br />
<br />
<math>A\longrightarrow B-|C</math>, <br />
<br />
which can be independently tunedfrom the adaptation precision.<br />
<br />
[[第3张PP:拓扑图]]<br />
<br />
[[第4张PP:来个冲击然后还adaptation]]<br />
[[ Image:AdaptFeedforward1.png|center|550px|thumb|Simulation Result under stimulus 1]]<br />
<br />
[[Image:AdaptFeedforward2.png|center|550px|thumb|Simulation Result under stimulus 2]]<br />
==Other Topology==<br />
<br />
[[第5张PP:拓扑图]]<br />
<br />
[[第6张PP:来个冲击然后不adaptation]]<br />
<br />
[[第7张PP:拓扑图]]<br />
<br />
[[第8张PP:来个冲击然后不adaptation]]<br />
<br />
[[第9张PP:拓扑图]]<br />
<br />
[[第10张PP:来个冲击然后不adaptation]]<br />
<br />
=Example 3. Bistable Toggle Switch=<br />
<br />
==Introduction==<br />
<br />
A good example of engineering in Synthetic Biology include the pioneering work of [http://gardnerlab.bu.edu/ Tim Gardner] and [http://www.bu.edu/abl/ James Collins] on an [http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&list_uids=10659857&query_hl=5 engineered genetic toggle switch]. Here, we want to show how to tune parameters to guarantee bistability.<br />
<br />
==Mathematical Formulation==<br />
<br />
<br />
<math>\begin{align}<br />
\dot{u}(t) &=\frac{\alpha _{1}}{1+v^{\theta }(t)}-\beta _{1}u(t),<br />
(.....................................equation1)<br />
\\<br />
\dot{v}(t) &=\frac{\alpha _{2}X^{\eta }}{X^{\eta }+1+u^{\gamma }(t)}-\beta<br />
_{2}v(t),(..............................................equation2)<br />
\\ \end{align}\,\!</math><br />
<br />
where <math>X</math> is input, <math>u</math> is the concentration<br />
of repressor 1, <math>v</math> is the concentration of repressor 2,<br />
<math>\alpha _{1}</math> is the effective rate of synthesis of<br />
repressor 1, <math>\alpha _{2}</math> is the effective rate of<br />
synthesis of repressor 2, <math>\theta </math> is the cooperativity<br />
of repression of promoter 2 and <math>\gamma </math> is the<br />
cooperativity of repression of promoter 1. The above model is<br />
derived from a biochemical rate equation formulation of gene<br />
expression. The final form of the toggle equations preserves the two<br />
most fundamental aspects of the network: cooperative repression of<br />
constitutively transcribed promoters (the first term in each<br />
equation), and degradation/dilution of the repressors (the second<br />
term in each equation).<br />
<br />
The parameters <math>\alpha _{1}</math> and <math>\alpha _{2}</math><br />
are lumped parameters that describe the net effect of RNA polymerase<br />
binding, open-complex formation, transcript elongation, transcript<br />
termination, repressor binding, ribosome binding and polypeptide<br />
elongation. The cooperativity described by <math>\theta </math> and<br />
<math>\gamma </math> can arise from the multimerization of the<br />
repressor proteins and the cooperative binding of repressor<br />
multimers to multiple operator sites in the promoter. An additional<br />
modification to equation (1) is needed to describe induction of the<br />
repressors.<br />
<br />
<math>\alpha _{1},\alpha _{2},\gamma ,\theta ,\eta ,\beta _{1},\beta<br />
_{2}</math> should be indentified to guarantee bistability. We<br />
assume that <math>\gamma =\theta =\eta =2</math> as parameter<br />
restriction. Thus, there are four parameters to be indentified.<br />
[[Image:Toggle_Switch_Species1.png|center|550px|thumb|Identification Result<br />
for the first species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
[[Image:Toggle_Switch_Species2.png|center|550px|thumb|Identification Result<br />
for the second species, the black curve is the desired behavior while the<br />
red curve is the identification result]]<br />
Parameters:<br />
<math>\alpha _{1}</math> 26.3082 14<br />
<math>\beta _{1}</math> 1.79953 1<br />
<math>\alpha _{2}</math> 4.35684 5<br />
<math>\beta _{2}</math> 0.610341 1<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:57:10Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|align = "justify"|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process.<br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization Algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/hoWDesignTeam:USTC Software/hoWDesign2009-10-21T16:50:04Z<p>Bigben: /* Sub Level 2: */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
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{|-<br />
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{{USTCSW_SideBarL}}<br />
<br />
|<br />
<br />
==Design Level==<br />
<br />
You should choose what level you focus on. Generally, there are four levels: parts level, device level, system level and abstract level respectively. The former three levels should be designated before design for a certain database should be selected to link. They are aimed at real application by using practical materials. The last level is rather general and mathematical. It doesn’t link to certain database while providing topology information only.<br />
<br />
===Parts Level:=== <br />
<br />
Since, the function of parts can only display when they are in device with other kinds of parts. Thus, this level is to serve the device level that details about parts could be retrieved while designing a device. Details about kinetic laws and kinetic parameters these parts play in biochemical reactions are needed. <br />
<br />
===Device Level:=== <br />
<br />
Devices are composed by basic parts and fabricated in a special manner. The function may vary be inserting different parts of same kind like promoter to the same place in device. This way is actually means to change the kinetic parameters in order to change the response of the device. Both static and dynamic transfer functions are needed to describe each device in order to be inserted or replaced in the software for simulation and design purpose. <br />
<br />
===System Level:===<br />
<br />
Systems are usually composed by devices while details of parts are not emphasized. The system level is an extension of device level, but focusing on much complicated ones even the entire cell, organism and ecosystem. <br />
<br />
===Abstract (mathematical) Level:===<br />
<br />
Topology is crucial for a network even if the kinetic laws are not that clear. Here, we do not care what concrete parts we use but rather mathematical and graphic form. It is universally significant and instructive for design process. <br />
<br />
==Design Type (Sub Level)==<br />
<br />
After you choose what design level you focus, there are four types of sublevels to select. We define these sublevels because the users are unnecessary to run the every design step that we give prior for an entire design process but some certain functions. Given these information, users could quickly start their design without wasting additional running time. Though our software runs relevant functions according to your input, it will be helpful and clear for the users to know what sublevels fit their need to complete their design efficiently. <br />
{| border = "1" align = "center"<br />
|-<br />
|ID <br />
|Interaction <br />
|Kinetic Law<br />
|-<br />
| 1 <br />
| Y <br />
| Y<br />
|-<br />
| 2 <br />
| Y <br />
| N<br />
|-<br />
| 3 <br />
| N <br />
| Y<br />
|-<br />
| 4 <br />
| N <br />
| N<br />
|}<br />
<br />
===Sub Level 1:===<br />
<br />
The mutual interactions and kinetic laws are absolutely clear that only kinetic parameters are unknown or partly known. Based on the restrictions the user inputs, our software give a series of possible solutions to choose. In this sublevel, only parameter identification algorithm is recalled. Construction of E-parts of out wet team is on this sublevel. <br />
<br />
===Sub Level 2:===<br />
<br />
The mutual interactions are already known but kinetic laws are not that clear. Usually, the structure is clear to the users but kinetic laws are changeable for design. On the other hand, kinetic laws largely determine the dynamics. The [https://2009.igem.org/Team:USTC_Software/WhatDemo#Example_1._Synthetic_Oscillator Oscillator] and [https://2009.igem.org/Team:USTC_Software/WhatDemo#Example_3._Bistable_Toggle_Switch Bistable Toggle Switch] example is on this sub level.<br />
<br />
===Sub Level 3:===<br />
<br />
The reaction types are already known but mutual interactions are not that clear. Sometimes kinetic laws are easy to identify based on some basic ones like MassAction, Michaelis-Menten, or Hill Kinetics, etc. The [https://2009.igem.org/Team:USTC_Software/WhatDemo#Example_2:_Perfect_Adaptation Adaptation] example is on this sublevel. <br />
<br />
===Sub Level 4:===<br />
<br />
Nothing is known about the design. Urr….. Just wait, we will give some solutions anyway. What you need to do is just to wait.<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
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|}<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhyTeam:USTC Software/Why2009-10-21T16:39:53Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
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{{USTCSW_SideBarL}}<br />
|valign = "top" align = "justify" border = "0" width = "600px"|<br />
{|-<br />
<br /><br />
<font size = "5">Why ABCD?</font><br />
----<br />
|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
These computational tools (detailed listed in figure below, Figure reproduced from [http://www.nature.com/nrm/journal/v10/n6/abs/nrm2698.html ''The second wave of synthetic biology: from modules to systems'']) are designed to facilitate the scientists in wet lab in purpose of saving time and cost. On the other hand, standardization components provide a powerful tool for engineering biological systems in lab even in future industrial factories. In other words, all the current efforts are put to assist the scientists and could never replace the intelligence of human beings who are the leading roles in designing experiments and mathematical models. <br />
<br />
Is it possible to move further to the steps of intelligence? Is it possible to generate the design protocol and list feasible biobricks? Is it possible to make design of biological networks a funny game even for laymen who know little about synthetic biology? Even not that further, is it possible to suggest different topologies of network that can achieve desired functions? Is it possible to tune an existing network to perform new functions? Is it possible to make a biological network more robust against uncertainties? <br />
<br />
Another unavoidable challenge is to fill the gap between dry design and wet experiment. Is it possible to guarantee our design solution biologically significant? Is it possible to propose several “strong” examples to illustrate availability and efficiency of our idea?<br />
<br />
Here, we try our best to challenge these seemingly impossibilities and make them possible. We hope our software could be cradle where amazing happens. We don't mean we are on the summit of pyramid of computational synthetic biology and it’s of little significance to say whose work is more important or not. Instead, a vast of collaborations are needed among computational scientists, biologists and engineers. As we described in our flowcharts, ABCs of ABCD, relevant tools are strongly needed to cope with difficulties we meet separately.<br />
<br />
[[Image:Computational_Software.png|center|480px|thumb|Computational_Software (Figure reproduced from [http://www.nature.com/nrm/journal/v10/n6/abs/nrm2698.html ''The second wave of synthetic biology: from modules to systems''])]]<br />
|}<br />
<br />
|valign = "top"|<br />
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|}<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:35:28Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process.<br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization Algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:28:04Z<p>Bigben: /* Particle Swarm Optimization algorithm */</p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
'''One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process. ''' <br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization Algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:27:38Z<p>Bigben: /* Work Flow */</p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
'''One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process. ''' <br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:25:58Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|<br />
=Project Overview=<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
'''One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process. ''' <br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The flow chart is shown in Figure1. The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:22:16Z<p>Bigben: /* Project Overview */</p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
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<br /><br />
|<br />
{|-<br />
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<br /><br />
<font size = "5">Project Overview</font><br />
----<br />
<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
'''One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process. ''' <br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The flow chart is shown in Figure1. The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhyTeam:USTC Software/Why2009-10-21T16:21:09Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
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{|-<br />
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<br /><br />
<font size = "5">Why ABCD?</font><br />
----<br />
|-<br />
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These computational tools (detailed listed in figure below, Figure reproduced from [http://www.nature.com/nrm/journal/v10/n6/abs/nrm2698.html ''The second wave of synthetic biology: from modules to systems'']) are designed to facilitate the scientists in wet lab in purpose of saving time and cost. On the other hand, standardization components provide a powerful tool for engineering biological systems in lab even in future industrial factories. In other words, all the current efforts are put to assist the scientists and could never replace the intelligence of human beings who are the leading roles in designing experiments and mathematical models. <br />
<br />
Is it possible to move further to the steps of intelligence? Is it possible to generate the design protocol and list feasible biobricks? Is it possible to make design of biological networks a funny game even for laymen who know little about synthetic biology? Even not that further, is it possible to suggest different topologies of network that can achieve desired functions? Is it possible to tune an existing network to perform new functions? Is it possible to make a biological network more robust against uncertainties? <br />
<br />
Another unavoidable challenge is to fill the gap between dry design and wet experiment. Is it possible to guarantee our design solution biologically significant? Is it possible to propose several “strong” examples to illustrate availability and efficiency of our idea?<br />
<br />
Here, we try our best to challenge these seemingly impossibilities and make them possible. We hope our software could be cradle where amazing happens. We don't mean we are on the summit of pyramid of computational synthetic biology and it’s of little significance to say whose work is more important or not. Instead, a vast of collaborations are needed among computational scientists, biologists and engineers. As we described in our flowcharts, ABCs of ABCD, relevant tools are strongly needed to cope with difficulties we meet separately.<br />
<br />
[[Image:Computational_Software.png|center|480px|thumb|Computational_Software (Figure reproduced from [http://www.nature.com/nrm/journal/v10/n6/abs/nrm2698.html ''The second wave of synthetic biology: from modules to systems''])]]<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhatOverviewTeam:USTC Software/WhatOverview2009-10-21T16:17:17Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
{|-<br />
|valign = "top"|<br />
{{USTCSW_SideBarL}}<br />
<br /><br />
|<br />
=Project Overview=<br />
<br />
{|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
'''One goal of synthetic biology is to understand the exciting biological phenomenon by reconstructing the systems that have the similar behavior to the native. The design of networks are always challenging to the biologists as the desired phenotype is the only hint for the design. And after the design is finished in mind, there is still a gap in realizing it in experiments.The choices of reactors, the stability of the system are still important in the wet experiments. Here we are trying to escape the biologists from the design nightmare, employing the computer instead of the human brain to do the design process. ''' <br />
|-<br />
|<br />
==Goal== <br />
<br />
The ultimate goal of our program is to assist the experimentalists to design the plasmid that works as the requirement. For example, if an oscillating behavior is the requirement as the input of the software, then the output in our imagination is a DNA sequence which works as an oscillator in E.coli or other specific biology. It is only an imagination that we have a long way to go. So, as the first goal, the output we are trying to do for the software is a network which can stably work as the requirement. Generally, the desired phenotype is the input of the software, and, optionally, the restrictions extracted from the other experiments or from the condition can be the input at the same time. And the output is a list of networks that have the similar phenotypes to the requirement, with the information of the value of parameters and the sensitivities.<br />
<br />
==Work Flow==<br />
<br />
The flow chart is shown in Figure1. The three-layer optimization is expected during the whole design process: the optimization of parameters in a fixed mathematic model, the selection of interaction forms in a fixed topology and the comparison and screening of different topologies. And during the optimization of the parameters, there are two score functions considered. One is the RMSD(root mean square deviation) between the phenotype of the designed network and the requirement, and the other is the sensitivity of each parameter. As the cell system is noisy, the networks are hard to realize in experiments if some parameters are too sensitive. So the parameters' sensitivities are working as a filter to get rid of the networks that works not stably enough. After the three-layer's optimization and comparison, the list of the best networks are output as the final results.<br />
<br />
==Platform==<br />
A user-friendly network-design platform is realized in our software with C# for the experimentalists. The interface is shown in Figure2.Users can input the requirement curves with uploading a data file. And the picture files for curves are also supported by our software. And the network can be designed by manually drawing the species and the interactions. The phenotypes of the designed networks will be shown with graphs that users can directly see the performances of the results and the deviation between the results and the requirement.<br />
<br />
==Algorithm==<br />
<br />
===Particle Swarm Optimization algorithm===<br />
<br />
The particle swarm optimization algorithm (PSO) is employed to optimized the parameters in a fixed mathematic model.In past several years, PSO has been successfully applied in optimizing the parameters for the non-linear system. It is demonstrated that PSO gets better results in a faster, cheaper way compared with other methods. The most important reason we choose to implement this algorithm into our software is that this algorithm is easy to realize parallelization. Since the most time-consuming part in our scheme is the optimization of parameters for a given topological structure. If we cannot find a efficient optimizer, it is impossible to deal with systems contains more than five or six nodes. parallelization of the optimization process will be implemented in our next version.<br />
<br />
=== Genetic Algorithm ===<br />
<br />
The genetic algorithm (GA) is employed to search the best topologis and the best interaction forms.It is a powerful method for complex optimization problems. It realizes an essential evolution process in a computer. Under a fitness function, the members of the population will be improved from generation to generation. And the population will fit the pressure much better by the intraspecific competition.It is suitable for our problems ,because it can be converged in a moderate generations and can give a population of best topologies, not only one by other algorithms.<br />
<br />
==Future==<br />
<br />
It is just the first step. We still have a lot of to realize the final goal. First, the link should be established between the interaction forms and the real particles, as the promoters, the proteins, the ligands and so on. We are trying to build a database to construct the links, but the experiments data now are far than enough. And there are still some problems in the measurement of the parameters. Second, the optimization space is too large for us to search. Our program should run for a long time to finish the whole job. The parallel computation is favorable here. So we will use the parallel computation to do the optimization in the next version. Third, the on-line version is also required as it will be more convenient to the users.<br />
|}<br />
<br />
|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
|}<br />
|}<br />
{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/WhyTeam:USTC Software/Why2009-10-21T16:12:38Z<p>Bigben: </p>
<hr />
<div>__NOTOC__<br />
{{USTCSW_Heading}}<br />
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<br /><br />
<font size = "5">Why?</font><br />
----<br />
|-<br />
|valign = "top" align = "justify" border = "0" width = "600px" bgcolor = "#F3F3F3"|<br />
These computational tools (detailed listed in figure below, Figure reproduced from [http://www.nature.com/nrm/journal/v10/n6/abs/nrm2698.html ''The second wave of synthetic biology: from modules to systems'']) are designed to facilitate the scientists in wet lab in purpose of saving time and cost. On the other hand, standardization components provide a powerful tool for engineering biological systems in lab even in future industrial factories. In other words, all the current efforts are put to assist the scientists and could never replace the intelligence of human beings who are the leading roles in designing experiments and mathematical models. <br />
<br />
Is it possible to move further to the steps of intelligence? Is it possible to generate the design protocol and list feasible biobricks? Is it possible to make design of biological networks a funny game even for laymen who know little about synthetic biology? Even not that further, is it possible to suggest different topologies of network that can achieve desired functions? Is it possible to tune an existing network to perform new functions? Is it possible to make a biological network more robust against uncertainties? <br />
<br />
Another unavoidable challenge is to fill the gap between dry design and wet experiment. Is it possible to guarantee our design solution biologically significant? Is it possible to propose several “strong” examples to illustrate availability and efficiency of our idea?<br />
<br />
Here, we try our best to challenge these seemingly impossibilities and make them possible. We hope our software could be cradle where amazing happens. We don't mean we are on the summit of pyramid of computational synthetic biology and it’s of little significance to say whose work is more important or not. Instead, a vast of collaborations are needed among computational scientists, biologists and engineers. As we described in our flowcharts, ABCs of ABCD, relevant tools are strongly needed to cope with difficulties we meet separately.<br />
<br />
[[Image:Computational_Software.png|center|480px|thumb|Computational_Software (Figure reproduced from [http://www.nature.com/nrm/journal/v10/n6/abs/nrm2698.html ''The second wave of synthetic biology: from modules to systems''])]]<br />
|}<br />
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|valign = "top"|<br />
{{USTCSW_SideBarR}}<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/StandardTeam:USTC Software/Standard2009-10-21T15:25:24Z<p>Bigben: /* Robustness Analysis */</p>
<hr />
<div>{{USTCSW_Heading}}<br />
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<br />
==The Angle==<br />
<br />
Devices by parts are constructed in a uniform way that is based on certain kind of biochemical reactions. The different responses to the same stimuli among these devices are due to the kinetic parameters which have close correlation with inherent chemical and physical property of parts particularly by directed evolution in project of USTC wet team. <br />
<br />
Here, we propose a new silico based standard for biobricks to facilitate the application in computer. We name it E-bricks in reciprocal to the concept of Biobrick. By applying our methods reversely to model devices on concerning static and dynamical properties, ODE model or frequency domain transfer function is established that is easy to drag and plug on a laptop like engineer did on CAD software.<br />
<br />
However, we are not only concerning on the simulation level but design issues: how to arrange existing device to construct a system that exhibit desired function.<br />
<br />
Thanks to the concept proposed by [endy_nbt], we try to establish a datasheet like the one in this paper. Considering the limit of current biobricks database, it is hard to construct sufficient and large database. While our USTC wet team is putting effort to following that standard, it’s lucky for us to obtain raw data that satisfies our model requirement. It is also be of great honor to assist our wet team. <br />
<br />
<br />
==Kinetic Parameters Identification==<br />
<br />
First of all, we shall clarify that, being dedicated to dry lab experiments, we naturally doesn't have as many incarnated Bio-Parts as usual wet labs do. <br />
<br />
In wet lab experiment, kinetic parameters are notorious for their difficulties to obtain quantitatively. To construct a well fabricated device, the kinetic parameters are crucial for an extensible parts. When certain parts are placed in the network, certain biochemical reactions with holding kinetic parameters are introduced. To identify kinetic parameters of basic devices determines the extensibility of devices. [https://2009.igem.org/Team:USTC/Modeling/Model-2 Model 2]<partinfo>K176126 DeepComponents</partinfo> is a subsystem of [https://2009.igem.org/Team:USTC/Modeling/Model-3 Model 3]<partinfo>K176066 DeepComponents</partinfo>. <br />
<br />
[[Image:wet2dry.png|center|500px|thumb|[https://2009.igem.org/Team:USTC/Modeling/Model-2 Model 2] and [https://2009.igem.org/Team:USTC/Modeling/Model-3 Model 3] from [https://2009.igem.org/Team:USTC/Modeling 2009 USTC Wet Team]]]<br />
<br />
==Robustness Analysis==<br />
<br />
In biological systems, kinetic parameters should be robust enough to resist uncertainties and noise. It is better to give a range of parameters in order to leave a design margin for users. Here, we propose [https://2009.igem.org/Team:USTC_Software/hoWAlgorithm#Global_Sensitivity_Analysis_.28GSA.29 robustness analysis algorithm] to determine the scope.<br />
<br />
After<br />
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==Database Structure==<br />
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==Our Proposal==<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/SafetyTeam:USTC Software/Safety2009-10-21T13:17:08Z<p>Bigben: /* Safety and Human Practices */</p>
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=Safety and Human Practices=<br />
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==Outlook==<br />
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An ambitious system we want to design for security is an artificial black box which people should work with by keys. The general idea to get the information from a working system is extracting the plasmid from the bacteria and sequencing the working parts. In this way, there will be less security. The bacteria will be a white box for everyone who gets it. Here the black boxes are necessary for the proteins or plasmids that may be harmful. So we are trying to design a bacteria that not easy to work and be extracted and sequenced.<br />
<br />
The first step, the controllable lysis system are introduced in the bacteria. And an operator system is employed as a switch to the lysis system. The lysis system will start without the ligand. A large library of specific interacting protein-ligand pairs with one template operator system can be built with computational design and directed evolution. In this way, only the owners of the bacteria know what the key is. So the bacteria itself will not grow and work, and at the same time the information of DNA is also destroyed by the lysis system. Our software can give a regulatory network to make the operator system stably open and close the lysis system.<br />
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The second step, the plasmid is restricted to work in the specific bacteria only, as it is hard to block the process of plasmid extraction and transform. A library of tRNA synthetases is necessary to change the translating processes to make the plasmid can not work in other bacteria. In this way, it is necessary to construct a platform to select tRNA synthetases mutation. A cell-free system is necessary, as the mutation may lead to the chaos of whole cell. And a time-dependent protein expression system can be designed by our software. And the plasmid can only working in a ligand-controlled specific cell environment.<br />
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In this way, we can construct a new platform to protect some harmful or potential harmful genes or systems.<br />
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==Q & A==<br />
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#Would any of your project ideas raise safety issues in terms of:<br />
#*researcher safety, <br />
#*public safety, or <br />
#*environmental safety?<br />
#Is there a local biosafety group, committee, or review board at your institution?<br />
#What does your local biosafety group think about your project?<br />
#Do any of the new BioBrick parts that you made this year raise any safety issues? <br />
#*If yes, did you document these issues in the Registry?<br />
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{{USTCSW_Foot}}</div>Bigbenhttp://2009.igem.org/Team:USTC_Software/StandardTeam:USTC Software/Standard2009-10-21T13:03:13Z<p>Bigben: /* Robustness Analysis */</p>
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==The Angle==<br />
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Devices by parts are constructed in a uniform way that is based on certain kind of biochemical reactions. The different responses to the same stimuli among these devices are due to the kinetic parameters which have close correlation with inherent chemical and physical property of parts particularly by directed evolution in project of USTC wet team. <br />
<br />
Here, we propose a new silico based standard for biobricks to facilitate the application in computer. We name it E-bricks in reciprocal to the concept of Biobrick. By applying our methods reversely to model devices on concerning static and dynamical properties, ODE model or frequency domain transfer function is established that is easy to drag and plug on a laptop like engineer did on CAD software.<br />
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However, we are not only concerning on the simulation level but design issues: how to arrange existing device to construct a system that exhibit desired function.<br />
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Thanks to the concept proposed by [endy_nbt], we try to establish a datasheet like the one in this paper. Considering the limit of current biobricks database, it is hard to construct sufficient and large database. While our USTC wet team is putting effort to following that standard, it’s lucky for us to obtain raw data that satisfies our model requirement. It is also be of great honor to assist our wet team. <br />
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==Kinetic Parameters Identification==<br />
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First of all, we shall clarify that, being dedicated to dry lab experiments, we naturally doesn't have as many incarnated Bio-Parts as usual wet labs do. <br />
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In wet lab experiment, kinetic parameters are notorious for their difficulties to obtain quantitatively. To construct a well fabricated device, the kinetic parameters are crucial for an extensible parts. When certain parts are placed in the network, certain biochemical reactions with holding kinetic parameters are introduced. To identify kinetic parameters of basic devices determines the extensibility of devices. [https://2009.igem.org/Team:USTC/Modeling/Model-2 Model 2]<partinfo>K176126 DeepComponents</partinfo> is a subsystem of [https://2009.igem.org/Team:USTC/Modeling/Model-3 Model 3]<partinfo>K176066 DeepComponents</partinfo>. <br />
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[[Image:wet2dry.png|center|500px|thumb|[https://2009.igem.org/Team:USTC/Modeling/Model-2 Model 2] and [https://2009.igem.org/Team:USTC/Modeling/Model-3 Model 3] from [https://2009.igem.org/Team:USTC/Modeling 2009 USTC Wet Team]]]<br />
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==Robustness Analysis==<br />
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In biological systems, kinetic parameters should be robust enough to resist uncertainties and noise. It is better to give a range of parameters in order to leave a design margin for users. Here, we propose [https://2009.igem.org/Team:USTC_Software/hoWAlgorithm#Global_Sensitivity_Analysis_.28GSA.29 robustness analysis algorithm] to determine the scope.<br />
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==Database Structure==<br />
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==Our Proposal==<br />
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