http://2009.igem.org/wiki/index.php?title=Special:Contributions/Yashpuranik&feed=atom&limit=50&target=Yashpuranik&year=&month=2009.igem.org - User contributions [en]2024-03-28T09:32:59ZFrom 2009.igem.orgMediaWiki 1.16.5http://2009.igem.org/Team:IIT_Bombay_India/ModelingTeam:IIT Bombay India/Modeling2009-10-22T02:09:17Z<p>Yashpuranik: /* Analysis of multiple feedback loops */</p>
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== '''Analysis of multiple feedback loops''' ==<br />
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'''Modeling Study'''<br />
<br />
We have developed models for the expression of copy number (as YFP) and lacI (as CFP) for the four constructs (zero feedback (open loop), single feedback (on copy number), single feedback (on LAcI) and double feedback (on both copy number and LacI). Three modeling strategies have been attempted.<br />
<br />
<br />
1. Detailed mechanistic model accounting for LacI binding to the promoter site and balance on the copy number and LacI concentration. Effect of IPTG on protein expression as measured by YFP was characterized and compared with model. Further the model was extended to represent synthesis of beta-gal expression and was related to growth on lactose. The model was able to capture the experimental observations. The simulations also indicated the burden versus growth for the various strains developed.<br />
<br />
<br />
2. A phenomenological model was developed to represent the four constructs and langevian approach was used to estimate the variability due to the stochastic process. <br />
<br />
<br />
3. The model was linearized around LacI expression and the system was represented in a block diagram to carry out the feedback analysis. Frequency response analysis using magnitude and phase Bode plots was used to characterize the effect of multiple feed-backs. Magnitude bode plot for the sensitivity function demonstrated that the noise was reduced for the multiple feedback system. External white noise was introduced into the block diagram to study its effect. All simulations were developed using simulink platform of MATLAB.<br />
<br />
<br />
[[Team:IIT_Bombay_India/DDM|Detailed Deterministic Model]]<br />
<br />
[[Team:IIT_Bombay_India/PSM|Phenomenological Stochastic Model]]<br />
<br />
[[Team:IIT_Bombay_India/CAM|Control Analysis Model]]<br />
<br />
|<br />
|}</div>Yashpuranikhttp://2009.igem.org/Team:IIT_Bombay_India/DDMTeam:IIT Bombay India/DDM2009-10-22T02:08:35Z<p>Yashpuranik: /* Detailed Deterministic Model */</p>
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== '''Detailed Deterministic Model''' ==<br />
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Detailed Deterministic Model<br />
<br />
'''Objective'''<br />
<br />
Here we wish to show how the dynamics of the cellular material (proteins and plasmids) changes with time and IPTG and also how the specific growth rate of the four constructs on lactose is controlled and maximized by use of multiple feedbacks. In this model quantification by simulation was done and later results were verified by experimental data. A concept of burden on cells and normalized growth rate is introduced to show that in multiple feedback loops helps in optimizing growth rate. <br />
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'''Primary Kinetics and Equations'''<br />
<br />
In our system we have the key components being plasmid copy number, fusion protein, yfp, lactose, IPTG and growth associated enzyme β-galactosidase. The E. coli genome inherently consists of β gal gene which has plac promoter. LacI interacts with lactose and IPTG and also with plac promoter.<br />
<br />
<br />
[[Image:abhinav1.jpg]]<br />
<br />
Assuming these 3 equilibrium reactions, we can now write differential equations for the components relating their concentrations with time. The total amount of plac promoter present in any strain could be given by the equation:<br />
<br />
[[Image:abhinav2.jpg]]<br />
<br />
Where ‘a’ is an integer which depends on the strain for which differential equation has been used to describe.(Total plac promoter, is the sum of concentration of free plac(fp) promoter and plac-LacI complex.<br />
<br />
<br />
<br />
[[Image:abhinav3.jpg]]<br />
<br />
LacI total equals cfp (because they are a fusion protein). LacI refers to unbounded free lacI in the medium.<br />
<br />
<br />
<br />
<br />
[[Image:abhinav4.jpg]]<br />
<br />
Note: here plac1, plac2, plac3 are the free plac associated with β-gal production, plasmid number and cfp-LacI protein. <br />
<br />
The differential equations are solved for two different conditions. Equations were first solved for 24 hours on other medium with different IPTG and no lactose. After 24 hours the equations were solved for the same value of IPTG but on different values of lactose.<br />
<br />
Equations for growth on no Lactose:<br />
<br />
<br />
<br />
[[Image:abhinav5.jpg]]<br />
<br />
Equations for growth on Lactose:<br />
<br />
<br />
<br />
[[Image:abhinav6.jpg]]<br />
<br />
[[Image:abhinav7.jpg]]<br />
<br />
<br />
'''Results'''<br />
<br />
We now define the cost that cell has to pay for growing in the Open loop and MIMO strains. In open loop, cell overproduces plasmid, LacI, Yfp and β-gal.<br />
In MIMO, it optimizes this load to as low as possible and is able to grow at higher specific growth rate. We define the burden on the cell by 2 different definitions:<br />
Definition 1:<br />
<br />
[[Image:pr5.jpg]]<br />
<br />
Here all maximum values are the maximum amount of the protein or plasmid produced by mutant strain. Other definition used for Burden is<br />
Definition 2<br />
<br />
[[Image:pr6.jpg]]<br />
<br />
The Normalized growth rate is<br />
<br />
[[Image:pr7.jpg]]<br />
<br />
Plots of Burden and Normalized growth rate at various Lactose show, that the strain 4 has been able to successfully reduce its burden and optimize its growth, whereas in strain 1 the overproduction occurs at the cost of reduced growth rate. At higher IPTG when MIMO strain behaves like Open loop it could be seen that burden on the cell increases.<br />
For cells growth, cell has to produce the β-gal. In order to produce β-gal, our mutant strains have been forced to produce LacI and YFP protein. Due to this, cells now have only a part of machinery working for cell division. This is the burden that cells have to pay for growing at a particular specific growth rate. <br />
<br />
<br />
[[Image:pr1.jpg]]<br />
<br />
[[Image:pr2.jpg]]<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
'''Conclusions'''<br />
<br />
<br />
1. The detailed model was developed to generate the dynamic profiles of the plasmid copy number, LacI, Yfp, β-gal, Lactose and biomass. Using the above model, we are able to correlate the simulation results with the experimentally obtained values. <br />
<br />
2. We also see that growth on lactose for strain 4 is highest among the 4 strains with lesser burden on the cell to produce the unnecessarily higher amount of protein for growth. <br />
<br />
3. We observe that as lactose concentration is increased within our simulation range, burden of the cell does not change. For strain 4, as lactose concentration increases, the normalized growth rate crosses the burden, indicating that cell has now optimized its growth for the corresponding burden. For strain 1, the increase in lactose does not have any such effect and burden is always above the normalized growth rate. As IPTG increases, burden on strain 4 increases, the growth rate now crosses the burden at an higher value of lactose. Also as IPTG increases growth rate of strain 1 also increases. <br />
<br />
<br />
The detailed methodology, system equations, results and discussion can be seen [[Media:Deterministic modelling.pdf|here]].<br />
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1. Specific growth rates determined at different conc. of Lactose for ptet A (SR1) and plac K(SR4) <br />
<br />
0.1g/l<br />
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0.5g/l<br />
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1g/l<br />
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1.5g/l<br />
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3.5g/l<br />
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2. Beta galactosidase expression determined. <br />
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3. Agar plate experiments was performed with SR1 and SR4 with different concentration of lactose.</div>Yashpuranikhttp://2009.igem.org/Week21Week212009-10-22T01:54:51Z<p>Yashpuranik: </p>
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1. Specific growth rates determined at different conc. of Lactose for ptet A (SR1) and plac K(SR4) <br />
<br />
0.1g/l<br />
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0.5g/l<br />
<br />
1g/l<br />
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1.5g/l<br />
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3.5g/l<br />
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2. Along with varying Lactose conc., expression was also checked at 50 and 100 micromolar IPTG conc. <br />
<br />
3. Beta galactosidase expression determined.</div>Yashpuranikhttp://2009.igem.org/Week22Week222009-10-22T01:53:25Z<p>Yashpuranik: </p>
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1. Specific growth rates determined at different conc. of Lactose for plac A (SR2) and ptet K(SR3) <br />
<br />
0.1g/l<br />
<br />
0.5g/l<br />
<br />
1g/l<br />
<br />
1.5g/l<br />
<br />
3.5g/l<br />
<br />
2. Along with varying Lactose conc., expression was also checked at 50 and 100 micromolar IPTG conc. <br />
<br />
3. Beta galactosidase expression determined.</div>Yashpuranikhttp://2009.igem.org/Week20Week202009-10-22T01:52:04Z<p>Yashpuranik: </p>
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Specific growth rate and beta galactosidase activity was measured for SR3 and SR4 on different conc. Of lactose on <br />
<br />
minimal media. <br />
<br />
The concentration used were same as the experiments of the previous week.</div>Yashpuranikhttp://2009.igem.org/Week19Week192009-10-22T01:51:34Z<p>Yashpuranik: </p>
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1. Specific growth rates determined at different conc. of Lactose for ptet A (SR1) and plac K(SR4) <br />
<br />
0.1g/l<br />
<br />
0.5g/l<br />
<br />
1g/l<br />
<br />
1.5g/l<br />
<br />
3.5g/l<br />
<br />
2. Beta galactosidase expression determined. <br />
<br />
1. Specific growth rates determined at different conc. of Lactose for plac A (SR2) and ptet K(SR3) <br />
<br />
0.1g/l<br />
<br />
0.5g/l<br />
<br />
1g/l<br />
<br />
1.5g/l<br />
<br />
3.5g/l<br />
<br />
2. Beta galactosidase expression determined.</div>Yashpuranikhttp://2009.igem.org/Week19Week192009-10-22T01:50:27Z<p>Yashpuranik: </p>
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1. Specific growth rates determined at different conc. of Lactose for ptet A (SR1) and plac K(SR4) <br />
<br />
0.1g/l<br />
<br />
0.5g/l<br />
<br />
1g/l<br />
<br />
1.5g/l<br />
<br />
3.5g/l<br />
<br />
2. Beta galactosidase expression determined. <br />
<br />
1. Specific growth rates determined at different conc. of Lactose for plac A (SR2) and ptet K(SR3) <br />
<br />
0.1g/l<br />
<br />
0.5g/l<br />
<br />
1g/l<br />
<br />
1.5g/l<br />
<br />
3.5g/l<br />
<br />
2. Beta galactosidase expression determined.</div>Yashpuranikhttp://2009.igem.org/Week18Week182009-10-22T01:48:38Z<p>Yashpuranik: </p>
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1. Growth curve was done for specific growth rate determination of all the four strains on Minimal medium.<br />
<br />
2. FACS was performed with all the four strains at different temperature to find out the effect of temperature <br />
<br />
on copy number of plasmid. <br />
<br />
3. FACS was performed for different conc. of IPTG from O to 100 micro molar to observe the linearity of FACS <br />
<br />
expression.</div>Yashpuranikhttp://2009.igem.org/Week17Week172009-10-22T01:48:00Z<p>Yashpuranik: </p>
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1. FACS for YFP at different IPTG concentrations. <br />
<br />
2. Dynamical study was also done at an interval of 2 hours.</div>Yashpuranikhttp://2009.igem.org/Week15Week152009-10-22T01:46:44Z<p>Yashpuranik: </p>
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1.Steady state FACS analysis was done for each strain .<br />
<br />
2.Prepared antibiotic and IPTG stocks, media for time course experiments with the construct</div>Yashpuranikhttp://2009.igem.org/Week12Week122009-10-22T01:45:39Z<p>Yashpuranik: </p>
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|}<br />
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<br />
{| background-color:#ffffff;" cellpadding="1.5" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
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| <br />
<br />
1.FACS with Host as Control .<br />
<br />
2.We got one new host strain which is lacI deleted at the same time both kanamycin and ampicillin sensitive. <br />
<br />
3.Competent cells were prepared from this strain.<br />
<br />
4.Transformations done with new host strain E.coli MG1655- some problem with ampicillin plates. There was some <br />
<br />
colonies on the control plate also. Problem thought was that there may be some contamination while preparing <br />
<br />
competent cells for the new hosts.</div>Yashpuranikhttp://2009.igem.org/Week10Week102009-10-22T01:44:58Z<p>Yashpuranik: </p>
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| <br />
<br />
Literature survey started to find out whether there are some strains available which can serve our purpose.<br />
<br />
1. FACS for tranformants with ampicillin resistance - CFP and YFP signals detected <br />
<br />
formation of two strains with the one that is ampicillin resistance.</div>Yashpuranikhttp://2009.igem.org/Week9Week92009-10-22T01:42:51Z<p>Yashpuranik: </p>
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| <br />
<br />
1. Cultured Host strain which will harbour the plasmid . The host strain is LacI deleted .This strain is kanamycin <br />
<br />
resistance.</div>Yashpuranikhttp://2009.igem.org/Week8Week82009-10-22T01:42:06Z<p>Yashpuranik: </p>
<hr />
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| <br />
<br />
1. Repeated FACS run of CFP and YFP with 100, 250, 500 and 1000 microM/ml IPTG <br />
<br />
2. Preparation of requirements for transformation. (0.1M cacl2 soln. , Ice cold centrifuge tubes.) Kept autoclaved <br />
<br />
eppendorf tubes and tips into freeze.<br />
<br />
3. Kanamycin stock 100X (X = 50 microg/ml)</div>Yashpuranikhttp://2009.igem.org/Week4Week42009-10-22T01:38:58Z<p>Yashpuranik: </p>
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| <br />
<br />
1. LB growth curve of CFP, YFP and Control strains<br />
<br />
2. M9 growth curve of CFP, YFP and Control strains.</div>Yashpuranikhttp://2009.igem.org/Week2Week22009-10-22T01:37:24Z<p>Yashpuranik: </p>
<hr />
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| <br />
<br />
<br />
<br />
1.LB Amp plates were made.<br />
<br />
2.Antibiotic stocks were made.<br />
<br />
Amp 1000X (X=100 microg/ml)<br />
<br />
Strep 1000X (X=500 microg/ml)<br />
<br />
3.Plated CFP, YFP and control strains to become familiar with FACS machine and FACS technique.</div>Yashpuranikhttp://2009.igem.org/Week1Week12009-10-22T01:36:01Z<p>Yashpuranik: </p>
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| <br />
<br />
1.LB and M9 Medium Preparation <br />
<br />
2.Ampicillin stock-100X (X=100 microg/ml) <br />
<br />
3.Growth Curve of strains having CFP and YFP on LB and M( medium.<br />
<br />
4.Trial FACS run with 100microM of IPTG for CFP and YFP (without controls)- signal obtained</div>Yashpuranikhttp://2009.igem.org/Team:IIT_Bombay_India/DDMTeam:IIT Bombay India/DDM2009-10-22T01:31:06Z<p>Yashpuranik: /* Detailed Deterministic Model */</p>
<hr />
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{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
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| <br />
<br />
== '''Detailed Deterministic Model''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
| <br />
<br />
<br />
'''Objective'''<br />
<br />
Here we wish to show how the dynamics of the cellular material (proteins and plasmids) changes with time and IPTG and also how the specific growth rate of the four constructs on lactose is controlled and maximized by use of multiple feedbacks. In this model quantification by simulation was done and later results were verified by experimental data. A concept of burden on cells and normalized growth rate is introduced to show that in multiple feedback loops helps in optimizing growth rate. <br />
<br />
<br />
'''Primary Kinetics and Equations'''<br />
<br />
In our system we have the key components being plasmid copy number, fusion protein, yfp, lactose, IPTG and growth associated enzyme β-galactosidase. The E. coli genome inherently consists of β gal gene which has plac promoter. LacI interacts with lactose and IPTG and also with plac promoter.<br />
<br />
<br />
[[Image:abhinav1.jpg]]<br />
<br />
Assuming these 3 equilibrium reactions, we can now write differential equations for the components relating their concentrations with time. The total amount of plac promoter present in any strain could be given by the equation:<br />
<br />
[[Image:abhinav2.jpg]]<br />
<br />
Where ‘a’ is an integer which depends on the strain for which differential equation has been used to describe.(Total plac promoter, is the sum of concentration of free plac(fp) promoter and plac-LacI complex.<br />
<br />
<br />
<br />
[[Image:abhinav3.jpg]]<br />
<br />
LacI total equals cfp (because they are a fusion protein). LacI refers to unbounded free lacI in the medium.<br />
<br />
<br />
<br />
<br />
[[Image:abhinav4.jpg]]<br />
<br />
Note: here plac1, plac2, plac3 are the free plac associated with β-gal production, plasmid number and cfp-LacI protein. <br />
<br />
The differential equations are solved for two different conditions. Equations were first solved for 24 hours on other medium with different IPTG and no lactose. After 24 hours the equations were solved for the same value of IPTG but on different values of lactose.<br />
<br />
Equations for growth on no Lactose:<br />
<br />
<br />
<br />
[[Image:abhinav5.jpg]]<br />
<br />
Equations for growth on Lactose:<br />
<br />
<br />
<br />
[[Image:abhinav6.jpg]]<br />
<br />
[[Image:abhinav7.jpg]]<br />
<br />
<br />
'''Results'''<br />
<br />
We now define the cost that cell has to pay for growing in the Open loop and MIMO strains. In open loop, cell overproduces plasmid, LacI, Yfp and β-gal.<br />
In MIMO, it optimizes this load to as low as possible and is able to grow at higher specific growth rate. We define the burden on the cell by 2 different definitions:<br />
Definition 1:<br />
<br />
[[Image:pr5.jpg]]<br />
<br />
Here all maximum values are the maximum amount of the protein or plasmid produced by mutant strain. Other definition used for Burden is<br />
Definition 2<br />
<br />
[[Image:pr6.jpg]]<br />
<br />
The Normalized growth rate is<br />
<br />
[[Image:pr7.jpg]]<br />
<br />
Plots of Burden and Normalized growth rate at various Lactose show, that the strain 4 has been able to successfully reduce its burden and optimize its growth, whereas in strain 1 the overproduction occurs at the cost of reduced growth rate. At higher IPTG when MIMO strain behaves like Open loop it could be seen that burden on the cell increases.<br />
For cells growth, cell has to produce the β-gal. In order to produce β-gal, our mutant strains have been forced to produce LacI and YFP protein. Due to this, cells now have only a part of machinery working for cell division. This is the burden that cells have to pay for growing at a particular specific growth rate. <br />
<br />
<br />
[[Image:pr1.jpg]]<br />
<br />
[[Image:pr2.jpg]]<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
'''Conclusions'''<br />
<br />
<br />
1. The detailed model was developed to generate the dynamic profiles of the plasmid copy number, LacI, Yfp, β-gal, Lactose and biomass. Using the above model, we are able to correlate the simulation results with the experimentally obtained values. <br />
<br />
2. We also see that growth on lactose for strain 4 is highest among the 4 strains with lesser burden on the cell to produce the unnecessarily higher amount of protein for growth. <br />
<br />
3. We observe that as lactose concentration is increased within our simulation range, burden of the cell does not change. For strain 4, as lactose concentration increases, the normalized growth rate crosses the burden, indicating that cell has now optimized its growth for the corresponding burden. For strain 1, the increase in lactose does not have any such effect and burden is always above the normalized growth rate. As IPTG increases, burden on strain 4 increases, the growth rate now crosses the burden at an higher value of lactose. Also as IPTG increases growth rate of strain 1 also increases. <br />
<br />
<br />
The detailed methodology, system equations, results and discussion can be seen [[Media:Deterministic modelling.pdf|here]].<br />
<br />
|<br />
|}</div>Yashpuranikhttp://2009.igem.org/Team:IIT_Bombay_India/TeamTeam:IIT Bombay India/Team2009-10-22T01:21:15Z<p>Yashpuranik: </p>
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<br />
<br />
'''<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="95%" align="center"<br />
!align="left"|<br />
<br />
Who we are <br />
----<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="95%" align="center"<br />
!align="left"|<br />
<br />
<br />
| Advisors:<br />
<br />
* Overall Leader: [https://igem.org/User_Information.cgi?user_id=4379 Prof. K. V. Venkatesh]<br />
* Graduate Student 1: [https://igem.org/User_Information.cgi?user_id=2363 Navneet Rai]<br />
* Graduate Student 2: [https://igem.org/User_Information.cgi?user_id=4436 Pushkar Malakar]<br />
* Systems' Engineering Analysis: [https://igem.org/User_Information.cgi?user_id=5312 Vinay A. Bavdekar]<br />
<br />
<br />
Undergrads:<br />
<br />
* Model Development and Analysis: [https://igem.org/User_Information.cgi?user_id=4451 Yash Puranik], [https://igem.org/User_Information.cgi?user_id=5493 Abhinav Jain] & [https://igem.org/User_Information.cgi?user_id=4452 Manish Shetty]<br />
* Experimental Work: [https://igem.org/User_Information.cgi?user_id=4470 Ankita Arora], [https://igem.org/User_Information.cgi?user_id=4476 Manish Kumar], [https://igem.org/User_Information.cgi?user_id=4478 Sudhir Pandey], [https://igem.org/User_Information.cgi?user_id=4483 Sonal Sethia], [https://igem.org/User_Information.cgi?user_id=4534 Supriya Khedkar] & [https://igem.org/User_Information.cgi?user_id=4542 Archana Bhide]<br />
<br />
|<br />
<gallery><br />
<br />
</gallery><br />
|}<br />
<br />
'''</div>Yashpuranikhttp://2009.igem.org/Team:IIT_Bombay_India/PSMTeam:IIT Bombay India/PSM2009-10-21T19:23:07Z<p>Yashpuranik: /* Phenomenological Stochastic Model */</p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
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|}<br />
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| <br />
<br />
== '''Phenomenological Stochastic Model''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
Stochastic Modelling for the system <br />
<br />
'''Objective'''<br />
To characterize the intrinsic noise present in the system for all the 4 strains.<br />
To compare the lac I expression levels and plasmid concentrations and the errors associated with them for each of the 4 strains, using a simplified phenomenological model.<br />
<br />
'''Model'''<br />
<br />
A simplified model for lacI expression and copy number regulation is developed.<br />
<br />
[[Image:Eq-1.jpg]]<br />
<br />
Where the terms C1 and C2 and C3 representing control action are:<br />
<br />
[[Image:Eq-2.jpg]]<br />
<br />
For open loop, none of the control actions exist, and hence C1=C2=1 and C3=0;<br />
<br />
For the strain with lacI regulation, C2=1, C1 and C3 are obtained from the equations above.<br />
<br />
For strain with plasmid regulation, C1=1,C2 and C3 are obtained from the equations above. <br />
<br />
For strain with multiple feedback, all the three terms, C1, C2 and C3 are obtained from equations above.<br />
<br />
<br />
'''Methodology'''<br />
<br />
Stochasticity is introduced in the system by randomly perturbing the kinetic parameters, K1,K2, K3 and K4 and k1, k2 and k4 from their mean values to a maximum limit of 30 % and carrying out numerous simulations to obtain the various trajectories possible. Hence the distributions so obtained for lacI and plasmid concentrations are characterized . The errors in these distributions are then compared for the 4 strains.<br />
<br />
<br />
'''Results'''<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
The qualitative behavior for all the 4 strains is similar.<br />
<br />
The strain with multiple feedback shows least expression while strain with no feedback shows maximum expression.<br />
<br />
The error bars are plotted above. The mean values for 100 runs and the errors associated with them are summarized below.<br />
<br />
[[Image:Table-1.jpg]]<br />
<br />
Thus, error decreases almost 6 times for the strain with multiple feedback as compared to the open loop strain. <br />
<br />
The error is almost similar for strains with only a single feedback, which is less than that for the open loop strain.<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
[[Image:Table-2.jpg]]<br />
<br />
The curves for plasmid concentration in the open loop strain and strain with lacI regulation are the same, since plasmid replication is unaffected by lacI regulation. <br />
<br />
The error in plasmid concentration is least in the strain with plasmid regulation, it is 1/3rd of the error in open loop strain.<br />
This can be attributed to the fact that the lacI feeds back to two control loops in strain with multiple feedback, and hence it does not regulate the plasmid concentration as effectively.<br />
<br />
'''Effect of IPTG on system:'''<br />
<br />
[[Image:Graph-3.jpg]]<br />
<br />
Increasing IPTG causes all systems to resemble open loop in their behavior, which is confirmed by their steady state concentration.<br />
The error values are summarized.<br />
<br />
[[Image:Table-3.jpg]]<br />
<br />
At high IPTG, the error and mean is almost similar for all strains. <br />
Note that we plot the total IPTG present in the system(free as well as complexed with IPTG). Hence the high values observed in the 3 strains.<br />
<br />
[[Image:Graph-4.jpg]]<br />
<br />
[[Image:Table-4.jpg]]<br />
<br />
Here again, the resemblance of the system with open loop is observed at high IPTG values.<br />
<br />
This is confirmed by the same mean and errors obtained at high IPTG values.<br />
<br />
Thus, we see that the strain with multiple feedback shows greater degree of control with reduced noise.<br />
<br />
Further we are attempting to study the differences on growth on lactose in the 4 strains by introducing stochasticity on the reduced model.<br />
<br />
<br />
<br />
<br />
|<br />
|}</div>Yashpuranikhttp://2009.igem.org/Team:IIT_Bombay_India/PSMTeam:IIT Bombay India/PSM2009-10-21T19:22:26Z<p>Yashpuranik: /* Phenomenological Stochastic Model */</p>
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!align="center"|[[Team:IIT_Bombay_India/Safety|Safety]]<br />
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<br />
== '''Phenomenological Stochastic Model''' ==<br />
|}<br />
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Stochastic Modelling for the system <br />
<br />
'''Objective'''<br />
To characterize the intrinsic noise present in the system for all the 4 strains.<br />
To compare the lac I expression levels and plasmid concentrations and the errors associated with them for each of the 4 strains, using a simplified phenomenological model.<br />
<br />
'''Model'''<br />
<br />
A simplified model for lacI expression and copy number regulation is developed.<br />
<br />
[[Image:Eq-1.jpg]]<br />
<br />
Where the terms C1 and C2 and C3 representing control action are:<br />
<br />
[[Image:Eq-2.jpg]]<br />
<br />
For open loop, none of the control actions exist, and hence C1=C2=1 and C3=0;<br />
<br />
For the strain with lacI regulation, C2=1, C1 and C3 are obtained from the equations above.<br />
<br />
For strain with plasmid regulation, C1=1,C2 and C3 are obtained from the equations above. <br />
<br />
For strain with multiple feedback, all the three terms, C1, C2 and C3 are obtained from equations above.<br />
<br />
<br />
'''Methodology'''<br />
<br />
Stochasticity is introduced in the system by randomly perturbing the kinetic parameters, K1,K2, K3 and K4 and k1, k2 and k4 from their mean values to a maximum limit of 30 % and carrying out numerous simulations to obtain the various trajectories possible. Hence the distributions so obtained for lacI and plasmid concentrations are characterized . The errors in these distributions are then compared for the 4 strains.<br />
<br />
<br />
'''Results'''<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
The qualitative behavior for all the 4 strains is similar.<br />
<br />
The strain with multiple feedback shows least expression while strain with no feedback shows maximum expression.<br />
<br />
The error bars are plotted above. The mean values for 100 runs and the errors associated with them are summarized below.<br />
<br />
[[Image:Table-1.jpg]]<br />
<br />
Thus, error decreases almost 6 times for the strain with multiple feedback as compared to the open loop strain. <br />
<br />
The error is almost similar for strains with only a single feedback, which is less than that for the open loop strain.<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
[[Image:Table-2.jpg]]<br />
<br />
The curves for plasmid concentration in the open loop strain and strain with lacI regulation are the same, since plasmid replication is unaffected by lacI regulation. <br />
<br />
The error in plasmid concentration is least in the strain with plasmid regulation, it is 1/3rd of the error in open loop strain.<br />
This can be attributed to the fact that the lacI feeds back to two control loops in strain with multiple feedback, and hence it does not regulate the plasmid concentration as effectively.<br />
<br />
Effect of IPTG on system:<br />
<br />
[[Image:Graph-3.jpg]]<br />
<br />
Increasing IPTG causes all systems to resemble open loop in their behavior, which is confirmed by their steady state concentration.<br />
The error values are summarized.<br />
<br />
[[Image:Table-3.jpg]]<br />
<br />
At high IPTG, the error and mean is almost similar for all strains. <br />
Note that we plot the total IPTG present in the system(free as well as complexed with IPTG). Hence the high values observed in the 3 strains.<br />
<br />
[[Image:Graph-4.jpg]]<br />
<br />
[[Image:Table-4.jpg]]<br />
<br />
Here again, the resemblance of the system with open loop is observed at high IPTG values.<br />
<br />
This is confirmed by the same mean and errors obtained at high IPTG values.<br />
<br />
Thus, we see that the strain with multiple feedback shows greater degree of control with reduced noise.<br />
<br />
Further we are attempting to study the differences on growth on lactose in the 4 strains by introducing stochasticity on the reduced model.<br />
<br />
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|}</div>Yashpuranikhttp://2009.igem.org/Team:IIT_Bombay_India/PSMTeam:IIT Bombay India/PSM2009-10-21T19:18:54Z<p>Yashpuranik: /* Phenomenological Stochastic Model */</p>
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!align="center"|[[Team:IIT_Bombay_India/Modeling|Modeling]]<br />
!align="center"|[[Team:IIT_Bombay_India/Notebook|Notebook]]<br />
!align="center"|[[Team:IIT_Bombay_India/Safety|Safety]]<br />
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{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
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| <br />
<br />
== '''Phenomenological Stochastic Model''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
Stochastic Modelling for the system <br />
<br />
'''Objective'''<br />
To characterize the intrinsic noise present in the system for all the 4 strains.<br />
To compare the lac I expression levels and plasmid concentrations and the errors associated with them for each of the 4 strains, using a simplified phenomenological model.<br />
<br />
'''Model'''<br />
<br />
A simplified model for lacI expression and copy number regulation is developed.<br />
<br />
[[Image:Eq-1.jpg]]<br />
<br />
Where the terms C1 and C2 and C3 representing control action are:<br />
<br />
[[Image:Eq-2.jpg]]<br />
<br />
For open loop, none of the control actions exist, and hence C1=C2=1 and C3=0;<br />
<br />
For the strain with lacI regulation, C2=1, C1 and C3 are obtained from the equations above.<br />
<br />
For strain with plasmid regulation, C1=1,C2 and C3 are obtained from the equations above. <br />
<br />
For strain with multiple feedback, all the three terms, C1, C2 and C3 are obtained from equations above.<br />
<br />
<br />
'''Methodology'''<br />
<br />
Stochasticity is introduced in the system by randomly perturbing the kinetic parameters, K1,K2, K3 and K4 and k1, k2 and k4 from their mean values to a maximum limit of 30 % and carrying out numerous simulations to obtain the various trajectories possible. Hence the distributions so obtained for lacI and plasmid concentrations are characterized . The errors in these distributions are then compared for the 4 strains.<br />
<br />
<br />
'''Results'''<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
Similar profile for plasmid concentration is plotted below:-<br />
The qualitative behavior for all the 4 strains is similar.<br />
The strain with multiple feedback shows least expression while strain with no feedback shows maximum expression.<br />
The error bars are plotted above. The mean values for 100 runs and the errors associated with them are summarized below.<br />
<br />
[[Image:Table-1.jpg]]<br />
<br />
Thus, error decreases almost 6 times for the strain with multiple feedback as compared to the open loop strain. <br />
The error is almost similar for strains with only a single feedback, which is less than that for the open loop strain.<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
[[Image:Table-2.jpg]]<br />
<br />
The curves for plasmid concentration in the open loop strain and strain with lacI regulation are the same, since plasmid replication is unaffected by lacI regulation. <br />
The error in plasmid concentration is least in the strain with plasmid regulation, it is 1/3rd of the error in open loop strain.<br />
This can be attributed to the fact that the lacI feeds back to two control loops in strain with multiple feedback, and hence it does not regulate the plasmid concentration as effectively.<br />
<br />
Effect of IPTG on system:<br />
<br />
[[Image:Graph-3.jpg]]<br />
<br />
Increasing IPTG causes all systems to resemble open loop in their behavior, which is confirmed by their steady state concentration.<br />
The error values are summarized.<br />
<br />
[[Image:Table-3.jpg]]<br />
<br />
At high IPTG, the error and mean is almost similar for all strains. <br />
Note that we plot the total IPTG present in the system(free as well as complexed with IPTG). Hence the high values observed in the 3 strains.<br />
<br />
[[Image:Graph-4.jpg]]<br />
<br />
[[Image:Table-4.jpg]]<br />
<br />
Here again, the resemblance of the system with open loop is observed at high IPTG values.<br />
This is confirmed by the same mean and errors obtained at high IPTG values.<br />
<br />
Thus, we see that the strain with multiple feedback shows greater degree of control with reduced noise.<br />
<br />
<br />
<br />
<br />
|<br />
|}</div>Yashpuranik