http://2009.igem.org/wiki/index.php?title=Special:Contributions/Pranayiitb&feed=atom&limit=50&target=Pranayiitb&year=&month=2009.igem.org - User contributions [en]2024-03-29T13:52:15ZFrom 2009.igem.orgMediaWiki 1.16.5http://2009.igem.org/Team:IIT_Bombay_India/ProjectTeam:IIT Bombay India/Project2009-10-22T02:44:59Z<p>Pranayiitb: </p>
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!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!align="center"|[[Team:IIT_Bombay_India/Modeling|Modeling]]<br />
!align="center"|[[Team:IIT_Bombay_India/Notebook|Notebook]]<br />
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{| background-color:#ffffff;" cellpadding="2" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
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| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
[[Image:final1.jpg]]<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
'''''Experimental'''''<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
'''Simulation'''<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
<br />
'''Experimental results'''<br />
<br />
<br />
<br />
1. '''Steady state value of YFP v/s IPTG:''' <br />
For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Here experimental results do not correlate with simulation results as strain 3 lies above strain 4.<br />
<br />
[[Image:final8.jpg]]<br />
<br />
'''2. Growth on Lactose for Strain 1 and 4:'''<br />
We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that standard deviation is less as compared to strain 1. We also have a comparison of the results obtained from simulation.<br />
<br />
[[Image:final6.jpg]]<br />
<br />
[[Image:final7.jpg]]<br />
<br />
[[Image:final2.jpg]]<br />
<br />
[[Image:final3.jpg]]<br />
<br />
<br />
<br />
3. '''Agar plate experiment:''' <br />
Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level.<br />
<br />
[[Image:final4.jpg]]<br />
<br />
[[Image:final5.jpg]]<br />
<br />
'''<br />
''Simulations''<br />
'''<br />
<br />
<br />
1. '''Detailed Deterministic models''':<br />
A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
<br />
2. '''Stochastic modeling'''<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
3. '''Control theory approach''' <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The magnitude bode plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
<br />
'''Conclusions'''<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
1. '''Experimental analysis of CFP:''' <br />
Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. '''Detailed model:''' <br />
Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4.''' Stochastic Analysis''':- <br />
To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. '''Control analysis:''' <br />
We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
Further updates and analysis will be presented [http://www.che.iitb.ac.in/online/people/faculty/core-faculty/k-v-venkatesh/igem-2009-updates here].<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/ProjectTeam:IIT Bombay India/Project2009-10-22T02:42:24Z<p>Pranayiitb: </p>
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!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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="2" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
[[Image:final1.jpg]]<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
<br />
'''''Experimental'''''<br />
<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
'''Simulation'''<br />
<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
'''Experimental results'''<br />
<br />
<br />
<br />
1. '''Steady state value of YFP v/s IPTG:''' <br />
For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Here experimental results do not correlate with simulation results as strain 3 lies above strain 4.<br />
<br />
[[Image:final8.jpg]]<br />
'''<br />
2. Growth on Lactose for Strain 1 and 4:''' <br />
We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that standard deviation is less as compared to strain 1. We also have a comparison of the results obtained from simulation.<br />
<br />
[[Image:final6.jpg]]<br />
<br />
[[Image:final7.jpg]]<br />
<br />
[[Image:final2.jpg]]<br />
<br />
[[Image:final3.jpg]]<br />
<br />
<br />
<br />
3. '''Agar plate experiment:''' <br />
Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level.<br />
<br />
[[Image:final4.jpg]]<br />
<br />
[[Image:final5.jpg]]<br />
<br />
'''<br />
''Simulations''<br />
'''<br />
<br />
<br />
1. '''Detailed Deterministic models''':<br />
A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
<br />
2. '''Stochastic modeling'''<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
3. '''Control theory approach''' <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The magnitude bode plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
'''Conclusions'''<br />
<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
<br />
1. '''Experimental analysis of CFP:''' <br />
Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. '''Detailed model:''' <br />
Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4.''' Stochastic Analysis''':- <br />
To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. '''Control analysis:''' <br />
We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
Further updates and analysis will be presented [http://www.che.iitb.ac.in/online/people/faculty/core-faculty/k-v-venkatesh/igem-2009-updates here].<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/ProjectTeam:IIT Bombay India/Project2009-10-22T02:40:33Z<p>Pranayiitb: </p>
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<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
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{| background-color:#ffffff;" cellpadding="2" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
[[Image:final1.jpg]]<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
<br />
'''''Experimental'''''<br />
<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
'''Simulation'''<br />
<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
'''Experimental results'''<br />
<br />
<br />
<br />
1. '''Steady state value of YFP v/s IPTG:''' <br />
For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Here experimental results do not correlate with simulation results as strain 3 lies above strain 4.<br />
<br />
[[Image:final8.jpg]]<br />
'''<br />
2. Growth on Lactose for Strain 1 and 4:''' <br />
We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that standard deviation is less as compared to strain 1. We also have a comparison of the results obtained from simulation.<br />
<br />
[[Image:final6.jpg]]<br />
<br />
[[Image:final7.jpg]]<br />
<br />
[[Image:final2.jpg]]<br />
<br />
[[Image:final3.jpg]]<br />
<br />
<br />
<br />
3. '''Agar plate experiment:''' <br />
Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level.<br />
<br />
[[Image:final4.jpg]]<br />
<br />
[[Image:final5.jpg]]<br />
<br />
'''<br />
''Simulations''<br />
'''<br />
<br />
<br />
1. '''Detailed Deterministic models''':<br />
A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
<br />
2. '''Stochastic modeling'''<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
3. '''Control theory approach''' <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The magnitude bode plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
'''Conclusions'''<br />
<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
<br />
1. '''Experimental analysis of CFP:''' <br />
Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. '''Detailed model:''' <br />
Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4.''' Stochastic Analysis''':- <br />
To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. '''Control analysis:''' <br />
We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
Further updates and analysis will be presented [[http://www.che.iitb.ac.in/online/people/faculty/core-faculty/k-v-venkatesh/igem-2009-updates|here]].<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/ProjectTeam:IIT Bombay India/Project2009-10-22T02:38:43Z<p>Pranayiitb: </p>
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!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
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{| background-color:#ffffff;" cellpadding="2" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
[[Image:final1.jpg]]<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
<br />
'''''Experimental'''''<br />
<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
'''Simulation'''<br />
<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
'''Experimental results'''<br />
<br />
<br />
<br />
1. '''Steady state value of YFP v/s IPTG:''' <br />
For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Due to lack of accurate rate constants the experimental results do not correlate with simulation results for strain 3 and strain 4 as expression profile in Strain-3 lies above that in strain-4.<br />
<br />
[[Image:final8.jpg]]<br />
'''<br />
2. Growth on Lactose for Strain 1 and 4:''' <br />
We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that the standard deviation is less for both in specific growth rate and in Beta-galactosidase expression as compared to that observed in strain 1. The simulations could correlate the experimental observations accuratly.<br />
<br />
[[Image:final6.jpg]]<br />
<br />
[[Image:final7.jpg]]<br />
<br />
[[Image:final2.jpg]]<br />
<br />
[[Image:final3.jpg]]<br />
<br />
<br />
<br />
3. '''Agar plate experiment:''' <br />
Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level. The percentage deviation was in the order of 35% in strain-1 as compared to only 10% in strain-4.<br />
<br />
[[Image:final4.jpg]]<br />
<br />
[[Image:final5.jpg]]<br />
<br />
'''<br />
''Simulations''<br />
'''<br />
<br />
<br />
1. '''Detailed Deterministic models''':<br />
A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
<br />
2. '''Stochastic modeling'''<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
3. '''Control theory approach''' <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The magnitude bode plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
'''Conclusions'''<br />
<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
<br />
1. '''Experimental analysis of CFP:''' <br />
Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. '''Detailed model:''' <br />
Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4.''' Stochastic Analysis''':- <br />
To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. '''Control analysis:''' <br />
We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
Further updates and analysis will be presented [http://www.che.iitb.ac.in/online/people/faculty/core-faculty/k-v-venkatesh/igem-2009-updates|here].<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/ModelingTeam:IIT Bombay India/Modeling2009-10-22T02:33:05Z<p>Pranayiitb: </p>
<hr />
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| <br />
<br />
== '''Analysis of multiple feedback loops''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
<br />
'''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>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/AnalysisTeam:IIT Bombay India/Analysis2009-10-22T02:31:01Z<p>Pranayiitb: </p>
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{| background-color:#ffffff;" cellpadding="1.5" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Experimental Studies''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
'''Objective'''<br />
<br />
1. Characterize the expression profile of synthetic network designed with multiple feedback loops.<br />
<br />
2. Characterize beta-galactosidase expression in the mutant strains of E.coli lacking lacI containing the designed synthetic genetic circuits.<br />
<br />
3. Phenotypic characterization of the transformed strains by quantifying growth on lactose<br />
<br />
<br />
'''Plasmid Developed'''<br />
<br />
1: BBa_K255001 - pLac.laci-cfp.pTet.yfp, present in pSB2K3.<br />
<br />
2: BBa_K255002 - pTet.laci-cfp.pTet.yfp, present in pSB2K3.<br />
<br />
3: BBa_K255003 - pLac.laci-cfp.pTet.yfp, present in pSB1A2<br />
<br />
4: BBa_K255004 - pTet.laci-cfp.pTet.yfp, present in pSB1A2.<br />
<br />
Above plasmids have been deposited in repository of standard biological parts, iGEM-2009<br />
<br />
<br />
'''Strains Developed'''<br />
<br />
Ecoli(MR1655,lacI deleted) strain was transformed individually with each plasmids by chemical methods.<br />
<br />
The strains were selected on the basis of their resistance to growth on Ampicillin and kanamycin. This resistance was provided to them by the respective plasmid which they have incorporated.<br />
<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
'''Experimental study'''<br />
<br />
1. Characterization of copy number by quantifying YFP for all the four strains developed.<br />
<br />
2. Characterization of YFP to see the effect of temperature on the copy number of plasmid.<br />
<br />
3. Growth studies on lactose for host strain (lacI deletion) and host strain transformed with synthetic genetic circuits having multiple feedback loops.<br />
<br />
4. Characterization of beta-galactosidase expression from host strain ( lacI deletion) and host strain transformed with synthetic genetic circuits having multiple feedback loops.<br />
<br />
<br />
'''Experimental Protocols'''<br />
<br />
Here is a detailed [https://2009.igem.org/Team:IIT_Bombay_India/protocol link] to experimental protocol.<br />
<br />
<br />
'''Results'''<br />
<br />
1. The YFP expression in Strain-1 (open loop) and strain 2 (SISO_LacI) was found to be nearly same at 0, 100, 200 and 500 micrometre of IPTG concentration. YFP expression for strain-3 (SISO_CN) increased by 10 fold on increasing IPTG concentration from 0 to 100 micrometre of IPTG. Thereafter it remains nearly constant. The variability in the distribution of YFP as characterized by FACS demonstrated that Strain-4 had the minimum variability in protein expression indicating lower noise. <br />
<br />
2. At low temperature (30 degree Celsius) the plasmid copy number decreased for all the strains but at 42 degree Celsius the plasmid copy number decreased for Strain 3 and Strain 4 but we could not find any difference in the copy number for strain 1 and strain 2 from 37 degree Celsius.<br />
<br />
3. The growth rate on lactose of Strain-1 was lower as compared to Strain-4. Further, the growth of Strain-4 was more sensitive to lower concentration than that observed in Strain-1. The variability in the growth rate was lower for strain-4 indicating that the multiple feedback loop yields robust protein expression which translates to stable growth rates. Agar plate experiments also demonstrated similar results.<br />
<br />
4. The beta-galactosidase expression of strain-4 was commensurate to the lactose concentration demonstrating that the multiple feedback yields optimal behavior. Strain-1 demonstrated lower beta-galactosidase activity due to higher LacI in the system. This added burden in strain-1 (open loop) reduced the growth rate.<br />
<br />
<br />
'''Conclusion'''<br />
<br />
In our iGEM -2009 project we have experimentally demonstrated the effect of multiple feedback loops on the gene expression using synthetic genetic circuits with none, one and two negative feedback loops. Experiments demonstrated that the system with multiple feedback loops was less noisy compared to others. The copy number was quantified by measuring YFP expression using FACS to obtain the mean expression and variability... The experimental studies demonstrated that the variability observed in the protein expression was propagated to the phenotypic level. Both agar plate experiments and growth rate measurements demonstrated lower variability for the strain with multiple feedback loops as compared to the open system. The growth experiment also demonstrated that the strain with multiple feedback loop design could optimally synthesize proteins to the availability of lactose thus minimizing burden of protein synthesis and maximizing growth rate.<br />
<br />
<br />
Complete Experimental results can be seen [[Media:detailed Experimental studies.pdf|here]].<br />
|<br />
<br />
|}</div>Pranayiitbhttp://2009.igem.org/File:Final1.jpgFile:Final1.jpg2009-10-22T02:28:42Z<p>Pranayiitb: uploaded a new version of "Image:Final1.jpg"</p>
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<div></div>Pranayiitbhttp://2009.igem.org/File:Final8.jpgFile:Final8.jpg2009-10-22T02:25:00Z<p>Pranayiitb: </p>
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{| background-color:#ffffff;" cellpadding="2" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
[[Image:final1.jpg]]<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
<br />
''Experimental''<br />
<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
''Simulation''<br />
<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
''Experimental results''<br />
<br />
<br />
<br />
1. Steady state value of YFP v/s IPTG: For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Here experimental results do not correlate with simulation results as strain 3 lies above strain 4.<br />
<br />
[[Image:final8.jpg]]<br />
<br />
2. Growth on Lactose for Strain 1 and 4: We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that standard deviation is less as compared to strain 1. We also have a comparison of the results obtained from simulation.<br />
<br />
[[Image:final6.jpg]]<br />
<br />
[[Image:final7.jpg]]<br />
<br />
[[Image:final2.jpg]]<br />
<br />
[[Image:final3.jpg]]<br />
<br />
<br />
<br />
3. Agar plate experiment: Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level.<br />
<br />
[[Image:final4.jpg]]<br />
<br />
[[Image:final5.jpg]]<br />
<br />
<br />
''Simulations''<br />
<br />
<br />
<br />
1. Detailed Deterministic models: A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
<br />
2. Stochastic modeling<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
3. Control theory approach <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The magnitude bode plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
'''Conclusions'''<br />
<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
<br />
1. Experimental analysis of CFP: Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. Detailed model: Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4. Stochastic Analysis:- To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. Control analysis: We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/File:Final5.jpgFile:Final5.jpg2009-10-22T02:09:17Z<p>Pranayiitb: </p>
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{| background-color:#ffffff;" cellpadding="2" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
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<br />
| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
[[Image:final1.jpg]]<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
<br />
''Experimental''<br />
<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
''Simulation''<br />
<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
''Experimental results''<br />
<br />
<br />
<br />
1. Steady state value of YFP v/s IPTG: For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Here experimental results do not correlate with simulation results as strain 3 lies above strain 4.<br />
<br />
2. Growth on Lactose for Strain 1 and 4: We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that standard deviation is less as compared to strain 1. We also have a comparison of the results obtained from simulation.<br />
<br />
[[Image:final2.jpg]]<br />
<br />
[[Image:final3.jpg]]<br />
<br />
<br />
<br />
3. Agar plate experiment: Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level.<br />
<br />
[[Image:final4.jpg]]<br />
<br />
[[Image:final5.jpg]]<br />
<br />
<br />
''Simulations''<br />
<br />
<br />
<br />
1. Detailed Deterministic models: A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
[[Image:pr3.jpg]]<br />
<br />
[[Image:pr4.jpg]]<br />
<br />
<br />
2. Stochastic modeling<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
[[Image:Graph-1.jpg]]<br />
<br />
[[Image:Graph-2.jpg]]<br />
<br />
3. Control theory approach <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
<br />
[[Image:shetty2.jpg]]<br />
<br />
The magnitude bode plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
'''Conclusions'''<br />
<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
<br />
1. Experimental analysis of CFP: Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. Detailed model: Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4. Stochastic Analysis:- To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. Control analysis: We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/ProjectTeam:IIT Bombay India/Project2009-10-22T01:53:13Z<p>Pranayiitb: </p>
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<br />
| <br />
<br />
== '''Analysis of multiple feed-backs in biological systems''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| '''Objective'''<br />
<br />
In our project, we wanted to quantify how the protein expression in a cell changes due to presence of multiple feedback loops. We developed 4 mutant strains of E. coli. Beta-galactosidase responsible for growth on lactose medium was then used to characterize the phenotypic property of specific growth rate. Experimental results were used to verify the simulated models.<br />
<br />
<br />
'''Our Constructs'''<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
<br />
'''Methodology'''<br />
<br />
<br />
''Experimental''<br />
----<br />
<br />
We transformed the four constructs in an E. coli strain with no intrinsic LacI. Using the 4 strains we characterized YFP expression, beta-galactosidase and Growth rate. We conducted our experiments in two parts, first growth on other medium and then growth on lactose media keeping IPTG constant. <br />
<br />
<br />
''Simulation''<br />
----<br />
<br />
In simulation we applied a gamut of simulation techniques to quantify our model. We developed a kinetics based model for the 4 strains and used it to quantify the dynamic and steady state profiles. Using Langevin approach, we applied stochastic model to simplified logistics equations. We linearised the dynamic model around a set point and converted the dynamic model to transfer function domain (s), we then did frequency response from control theory and generated the magnitude and phase Bode plot. <br />
<br />
<br />
'''Results'''<br />
<br />
''Experimental results''<br />
----<br />
<br />
<br />
1. Steady state value of YFP v/s IPTG: For Strain1 and 2, increase in IPTG, does not affect the YFP. For Strain 3 and 4, increase in IPTG increases YFP expressions. Here experimental results do not correlate with simulation results as strain 3 lies above strain 4.<br />
<br />
2. Growth on Lactose for Strain 1 and 4: We obtained specific growth rate and normalized beta-gal expression on lactose. In strain 4, we observe that standard deviation is less as compared to strain 1. We also have a comparison of the results obtained from simulation.<br />
<br />
3. Agar plate experiment: Strain-4 demonstrated higher colony forming unit as compared to strain-1. The increase was about 40%. The interesting fact was that the deviation observed in Strain-4 was less compared to that of Strain-1, reiterating the fact that the noise at the protein level was translated to the phenotypic level.<br />
<br />
<br />
''Simulations''<br />
----<br />
<br />
<br />
1. Detailed Deterministic models: A model was developed to accurately quantify the dynamic behavior of the all the strains. The specific growth on lactose, was able to correlate with the experimental data as shown above. Also a concept of burden was introduced and it was shown that strain 4 has optimized its protein concentration for maximizing growth.<br />
<br />
<br />
2. Stochastic modeling<br />
A phenomenological model was developed for expression of LacI and replication of copy number and stochasticity was introduced in the system using Langevin approach. The main aim of this exercise was to characterize the inherent noise present in the system, which was shown to greatly reduce for strain-4 as compared to strain-1. In the diagram shown the error bars at the end show how the noise varies dynamically in all the 4 strains.<br />
<br />
<br />
3. Control theory approach <br />
We have done frequency response analysis on the linear system using magnitude and phase Bode plots. <br />
The phase margin for strain 4 is 92.2 deg while phase margin for strain 3 is 56 deg. This indicates better ability in response to delays in production of LacI and replication of copy number.<br />
Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. <br />
The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.<br />
For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:<br />
The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. <br />
The magnitude plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.<br />
<br />
<br />
'''Conclusions'''<br />
<br />
<br />
We characterized a phenotypic property of a cell (growth) with the help of synthetic genetic circuits. We proved that the specific growth rate on lactose was optimized in the mutant strain containing multiple feedbacks. The noise or variance associated with the protein expression of a MIMO strain was comparatively lower than that of Open loop strain containing zero feedbacks.<br />
<br />
<br />
<br />
'''Future work'''<br />
<br />
<br />
1. Experimental analysis of CFP: Due to unavailability of cyan laser filter for FACs we were unable to do CFP expressions. By December 2009, we aim to generate CFP expression profiles for the four strains.<br />
<br />
2. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains <br />
<br />
3. Detailed model: Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;<br />
<br />
4. Stochastic Analysis:- To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.<br />
<br />
5. Control analysis: We have done the analysis for only one kind of feedback system. We could use different feedback <br />
systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here. <br />
<br />
<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/File:Strain1.jpgFile:Strain1.jpg2009-10-22T01:41:53Z<p>Pranayiitb: uploaded a new version of "Image:Strain1.jpg"</p>
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| <br />
<br />
== '''Control Theory Approach to Study Multiple Feedbacks on Lac-operon ''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
| Control Analysis Model<br />
<br />
<br />
'''Objectives'''<br />
<br />
1. Characterize the system.<br />
<br />
2. Linearize the system around a set-point on LacI.<br />
<br />
3. Obtain a linear model in transfer-function (s) domain.<br />
<br />
4. Frequency response analysis using magnitude and phase bode plots.<br />
<br />
5. Sensitivity analysis using magnitude bode plot for sensitivity function.<br />
<br />
6. Steps 2-5 for 1000μM IPTG.<br />
<br />
7. Add external noise in the system and tried to determine the reduction in the noise for the system with multiple feedbacks and open-loop system.<br />
<br />
<br />
'''Methodology'''<br />
<br />
We have 2 control levels. By combination, we have 4 different control loops or structures possible, expressed in 4 different strains. They are as follows:-<br />
<br />
'''Strain 1 (Open loop) with plasmid (BBa_K255004)'''<br />
<br />
It has got open loop without any feedback.re there is constitutive expression of LacI. <br />
<br />
<br />
'''Strain 2(Single Input Single Output with regulation on LacI [SISO_LacI] with plasmid (BBa_K255003))'''<br />
<br />
It has got a single negative feedback loop. So the expression of LacI is under regulation. Here also the copy number of the plasmid is fixed. <br />
<br />
<br />
'''Strain 3(Single Input Single Output with regulation on copy number [SISO_CN] with plasmid (BBa_K255002))'''<br />
<br />
It has got a single negative feedback loop on the feedback copy number. Here there is no control on the LacI expression. <br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO] with plasmid (BBa_K255001))'''<br />
<br />
It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression. <br />
<br />
<br />
The dynamic model for the system could be represented as given below:<br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
<br />
We linearize the system around a set-point on LacI and try to obtain a linear equation model around the setpoint. This enables us to separate the controllers from the system of equations. The controllers are designed as proportional-integral (PI) controllers. The process and controller parameters for the system were tuned in a manner as to obtain steady state and dynamic characteristics that closely match with experimental data. The utility of the multiple feedbacks was analysed using the frequency response tools of control systems’ theory using functions in MATLAB 7.8. We use bode plots to obtain the frequency response analysis for the multiple feedback and single feedback system. Further, we do frequency response analysis for high IPTG concentrations.<br />
<br />
The linearized system in transfer-function (s) domain is as given below: <br />
<br />
[[Image:shettynew.jpg]]<br />
<br />
<br />
We add external noise in the system using random noise block in SIMULINK in each of the differential equation blocks individually or together and compare the normalized standard deviations in steady-state LacI production for system with multiple feedbacks and open-loop system. The noise was given in relation to the steady-state value of copy number or LacI values such that standard deviation/steady-state value is constant for open loop and multiple-feedback systems.. With this we try to see whether external noise is attenuated in the system with multiple feedbacks.<br />
<br />
<br />
'''Results'''<br />
<br />
The magnitude and phase bode plots for the system is given below:<br />
<br />
[[Image:shetty2.jpg]]<br />
[[Image:shetty3.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system given in linear model. The green line represents Strain 3 with only C1(s), while blue line represents Strain 4 with both C1(s) and C2(s). The gain margin for both Strain 3 and Strain 4 is ∞.'' ''The phase margin is 92.2 degree for Strain 4 and 56 degree for Strain 3. The increased bandwidth from 0.00428 rad/min to 0.0255 rad/min indicates faster response and improved noise rejection.'' ''The Strain 3 has higher peak of 2.92 dB while Strain 4 has no peak, again indicating better noise-attentuation.<br />
''<br />
<br />
<br />
1. The phase margin for a distributed, multiple feedback system (DFS) is 92.2 degree, while it is 56 degree for a single, conventional feedback system (CFS).<br />
<br />
2. The bandwidth increases from 0.00428 rad/min to 0.0255 rad/min for Strain 3 to Strain 4. <br />
<br />
<br />
For system with IPTG concentration of 1000μM,<br />
<br />
<br />
[[Image:shetty4.jpg]]<br />
[[Image:shetty5.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system with 1000 µM IPTG for linear model given in Fig 2.'' ''The green line represents Strain 3 with only C1(s), while blue line represents Strain 4 with both C1(s) and C2(s).'' ''The gain margin for both Strain 3 and Strain 4 is ∞.'' ''The phase margin is 70 degree for Strain 4 and 64 degree for Strain 3.'' ''The bandwidth increase is not significant for Strain 4 from 0.0061 rad/min to 0.0078 rad/min indicates hardly any difference in noise rejection.'' ''The Strain 3 has higher peak of 1.62 dB while Strain 4 has a peak at 0.58 dB indicating a lower peak and a slight better performance in noise attentuation.'' <br />
<br />
1. The phase margin for Strain 3 and Strain 4 are 64 degree and 70 degree respectively.<br />
<br />
2. The bandwidth for Strain 3 and Strain 4 are 0.0061 rad/min and 0.0078 rad/min respectively.<br />
<br />
<br />
[[Image:shettynewnew.jpg]]<br />
<br />
''Fig: Simulink block model for LacI system with external noise.'' ''For noise in replication of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 62.5 for open-loop systems respectively.'' ''For noise in production of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 18779 for open-loop systems respectively.'' ''The standard-deviation/mean value of the LacI is used to characterize the noise at the output.''<br />
<br />
With external noise in the replication of copy number the normalised standard deviation is 43.67% for multiple-feedback system and 82.28% for open-loop system in terms of external white noise.<br />
<br />
With external noise in the production of LacI the normalised standard deviation is 136.5% for multiple-feedback system and 151.78% for open-loop system.<br />
<br />
With external noise in the production of LacI and the replication of copy number the normalised standard deviation is 44.59% for multiple-feedback system and 83.18% for open-loop system.<br />
<br />
<br />
<br />
'''Interpretation'''<br />
<br />
1. The increased phase margin for Strain 4 indicates that Strain 4 can take care of delays in production LacI directly and by virtue of production of multiple plasmid copies better than the Strain 3 which has regulation only on the plasmid copy number. <br />
<br />
2. This indicates faster expression of the protein LacI in the system with low noise.<br />
<br />
3. The increased bandwidth nearly 6 times for Strain 4 indicates a faster response and a better noise rejection over a wide range of frequencies indicating a far robust response as compared to Strain 3. <br />
<br />
4. For system with higher IPTG concentrations, IPTG takes away LacI, and thus acting as an inducer. This makes the system resemble open loop system more as compared to IPTG at lower concentrations.<br />
<br />
5. The phase margin of 70 degree and 64 degree for Strain 4 and Strain 3 respectively indicates the difference in ability to take care of delays in the two systems has reduced. The bandwidth increase for Strain 4 is not high as compared Strain 3, with IPTG concentration of 1000μM. Also, the bandwidth for Strain 4 with1000μM IPTG is far lower as compared to the bandwidth of Strain 4 with no IPTG. <br />
<br />
6. In presence of external noise, the multiple-feedback system attenuates noise at the output better than open-loop system. <br />
<br />
The detailed methodology, system equations, results and discussion can be seen [[Media:Control modelling.pdf|here]].<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/File:Strain1.jpgFile:Strain1.jpg2009-10-22T01:29:00Z<p>Pranayiitb: uploaded a new version of "Image:Strain1.jpg"</p>
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<div></div>Pranayiitbhttp://2009.igem.org/File:Detailed_Experimental_studies.pdfFile:Detailed Experimental studies.pdf2009-10-22T01:24:14Z<p>Pranayiitb: </p>
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<div></div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/AnalysisTeam:IIT Bombay India/Analysis2009-10-22T01:23:49Z<p>Pranayiitb: </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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!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
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{| background-color:#ffffff;" cellpadding="1.5" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Experimental Studies''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
'''Objective'''<br />
<br />
1. Characterize the expression profile of synthetic network designed with multiple feedback loops.<br />
<br />
2. Characterize beta-galactosidase expression in the mutant strains of E.coli lacking lacI containing the designed synthetic genetic circuits.<br />
<br />
3. Phenotypic characterization of the transformed strains by quantifying growth on lactose<br />
<br />
<br />
'''Plasmid Developed'''<br />
<br />
1: BBa_K255001 - for plac.laci-cfp.ptet.yfp, present in psb2k3.<br />
<br />
2: BBa_K255002 - for ptet.laci-cfp.ptet.yfp, present in psb2k3.<br />
<br />
3: BBa_K255003 - for plac.laci-cfp.ptet.yfp, present in psb1A2<br />
<br />
4: BBa_K255004 - for ptet.laci-cfp.ptet.yfp, present in psb1A2.<br />
<br />
Above plasmids have been deposited in repository of standard biological parts, iGEM-2009<br />
<br />
'''Strains Developed'''<br />
<br />
Ecoli(MR1655,lacI deleted) strain was transformed individually with each plasmids by chemical methods.<br />
<br />
The strains were selected on the basis of their resistance to growth on Ampicillin and kanamycin. This resistance was provided to them by the respective plasmid which they have incorporated.<br />
<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
'''Experimental study'''<br />
<br />
1. Characterization of copy number by quantifying YFP for all the four strains developed.<br />
<br />
2. Characterization of YFP to see the effect of temperature on the copy number of plasmid.<br />
<br />
3. Growth studies on lactose for host strain (lacI deletion) and host strain transformed with synthetic genetic circuits having multiple feedback loops.<br />
<br />
4. Characterization of beta-galactosidase expression from host strain ( lacI deletion) and host strain transformed with synthetic genetic circuits having multiple feedback loops.<br />
<br />
'''Experimental Protocols'''<br />
<br />
Here is a detailed [https://2009.igem.org/Team:IIT_Bombay_India/protocol link] to experimental protocol.<br />
<br />
'''Results'''<br />
<br />
1. The YFP expression in Strain-1 (open loop) and strain 2 (SISO_LacI) was found to be nearly same at 0, 100, 200 and 500 micrometre of IPTG concentration. YFP expression for strain-3 (SISO_CN) increased by 10 fold on increasing IPTG concentration from 0 to 100 micrometre of IPTG. Thereafter it remains nearly constant. The variability in the distribution of YFP as characterized by FACS demonstrated that Strain-4 had the minimum variability in protein expression indicating lower noise. <br />
<br />
2. At low temperature (30 degree Celsius) the plasmid copy number decreased for all the strains but at 42 degree Celsius the plasmid copy number decreased for Strain 3 and Strain 4 but we could not find any difference in the copy number for strain 1 and strain 2 from 37 degree Celsius.<br />
<br />
3. The growth rate on lactose of Strain-1 was lower as compared to Strain-4. Further, the growth of Strain-4 was more sensitive to lower concentration than that observed in Strain-1. The variability in the growth rate was lower for strain-4 indicating that the multiple feedback loop yields robust protein expression which translates to stable growth rates. Agar plate experiments also demonstrated similar results.<br />
<br />
4. The beta-galactosidase expression of strain-4 was commensurate to the lactose concentration demonstrating that the multiple feedback yields optimal behavior. Strain-1 demonstrated lower beta-galactosidase activity due to higher LacI in the system. This added burden in strain-1 (open loop) reduced the growth rate.<br />
<br />
'''Conclusion'''<br />
<br />
In our iGEM -2009 project we have experimentally demonstrated the effect of multiple feedback loops on the gene expression using synthetic genetic circuits with none, one and two negative feedback loops. Experiments demonstrated that the system with multiple feedback loops was less noisy compared to others. The copy number was quantified by measuring YFP expression using FACS to obtain the mean expression and variability... The experimental studies demonstrated that the variability observed in the protein expression was propagated to the phenotypic level. Both agar plate experiments and growth rate measurements demonstrated lower variability for the strain with multiple feedback loops as compared to the open system. The growth experiment also demonstrated that the strain with multiple feedback loop design could optimally synthesize proteins to the availability of lactose thus minimizing burden of protein synthesis and maximizing growth rate.<br />
<br />
<br />
Complete Experimental results can be seen [[Media:detailed Experimental studies.pdf|here]].<br />
|<br />
<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/AnalysisTeam:IIT Bombay India/Analysis2009-10-22T01:23:33Z<p>Pranayiitb: </p>
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!align="left"|<br />
<br />
| <br />
<br />
== '''Experimental Studies''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
'''Objective'''<br />
<br />
1. Characterize the expression profile of synthetic network designed with multiple feedback loops.<br />
<br />
2. Characterize beta-galactosidase expression in the mutant strains of E.coli lacking lacI containing the designed synthetic genetic circuits.<br />
<br />
3. Phenotypic characterization of the transformed strains by quantifying growth on lactose<br />
<br />
<br />
'''Plasmid Developed'''<br />
<br />
1: BBa_K255001 - for plac.laci-cfp.ptet.yfp, present in psb2k3.<br />
<br />
2: BBa_K255002 - for ptet.laci-cfp.ptet.yfp, present in psb2k3.<br />
<br />
3: BBa_K255003 - for plac.laci-cfp.ptet.yfp, present in psb1A2<br />
<br />
4: BBa_K255004 - for ptet.laci-cfp.ptet.yfp, present in psb1A2.<br />
<br />
Above plasmids have been deposited in repository of standard biological parts, iGEM-2009<br />
<br />
'''Strains Developed'''<br />
<br />
Ecoli(MR1655,lacI deleted) strain was transformed individually with each plasmids by chemical methods.<br />
<br />
The strains were selected on the basis of their resistance to growth on Ampicillin and kanamycin. This resistance was provided to them by the respective plasmid which they have incorporated.<br />
<br />
<br />
<br />
'''Strain 1 (Open Loop) with plasmid (BBa_K255004).''' It has got open loop without any feedback. Here there is constitutive expression of lacI. Here the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain1.jpg]]<br />
<br />
<br />
'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' It has got a single negative feedback loop.<br />
So the expression of lacI is under regulation. Here also the copy number of the plasmid is fixed.<br />
<br />
[[Image:Strain2.jpg]]<br />
<br />
<br />
'''Strain 3 (Single Input Single Output with regulation on copy number [SISO_CN]) with plasmid(BBa_K255002).''' It has got single negative feedback loop on the plasmid copy number . Here there is no control on the LacI expression.<br />
<br />
[[Image:Strain3.jpg]]<br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO]) with plasmid (BBa_K255001).''' It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression.<br />
<br />
[[Image:Strain4.jpg]] <br />
<br />
[[Image:Strain5.jpg]]<br />
<br />
<br />
'''Experimental study'''<br />
<br />
1. Characterization of copy number by quantifying YFP for all the four strains developed.<br />
<br />
2. Characterization of YFP to see the effect of temperature on the copy number of plasmid.<br />
<br />
3. Growth studies on lactose for host strain (lacI deletion) and host strain transformed with synthetic genetic circuits having multiple feedback loops.<br />
<br />
4. Characterization of beta-galactosidase expression from host strain ( lacI deletion) and host strain transformed with synthetic genetic circuits having multiple feedback loops.<br />
<br />
'''Experimental Protocols'''<br />
<br />
Here is a detailed [https://2009.igem.org/Team:IIT_Bombay_India/protocol link] to experimental protocol.<br />
<br />
'''Results'''<br />
<br />
1. The YFP expression in Strain-1 (open loop) and strain 2 (SISO_LacI) was found to be nearly same at 0, 100, 200 and 500 micrometre of IPTG concentration. YFP expression for strain-3 (SISO_CN) increased by 10 fold on increasing IPTG concentration from 0 to 100 micrometre of IPTG. Thereafter it remains nearly constant. The variability in the distribution of YFP as characterized by FACS demonstrated that Strain-4 had the minimum variability in protein expression indicating lower noise. <br />
<br />
2. At low temperature (30 degree Celsius) the plasmid copy number decreased for all the strains but at 42 degree Celsius the plasmid copy number decreased for Strain 3 and Strain 4 but we could not find any difference in the copy number for strain 1 and strain 2 from 37 degree Celsius.<br />
<br />
3. The growth rate on lactose of Strain-1 was lower as compared to Strain-4. Further, the growth of Strain-4 was more sensitive to lower concentration than that observed in Strain-1. The variability in the growth rate was lower for strain-4 indicating that the multiple feedback loop yields robust protein expression which translates to stable growth rates. Agar plate experiments also demonstrated similar results.<br />
<br />
4. The beta-galactosidase expression of strain-4 was commensurate to the lactose concentration demonstrating that the multiple feedback yields optimal behavior. Strain-1 demonstrated lower beta-galactosidase activity due to higher LacI in the system. This added burden in strain-1 (open loop) reduced the growth rate.<br />
<br />
'''Conclusion'''<br />
<br />
In our iGEM -2009 project we have experimentally demonstrated the effect of multiple feedback loops on the gene expression using synthetic genetic circuits with none, one and two negative feedback loops. Experiments demonstrated that the system with multiple feedback loops was less noisy compared to others. The copy number was quantified by measuring YFP expression using FACS to obtain the mean expression and variability... The experimental studies demonstrated that the variability observed in the protein expression was propagated to the phenotypic level. Both agar plate experiments and growth rate measurements demonstrated lower variability for the strain with multiple feedback loops as compared to the open system. The growth experiment also demonstrated that the strain with multiple feedback loop design could optimally synthesize proteins to the availability of lactose thus minimizing burden of protein synthesis and maximizing growth rate.<br />
<br />
Complete Experimental results can be seen [[Media:detailed Experimental studies.pdf|here]].<br />
|<br />
<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/collaborationTeam:IIT Bombay India/collaboration2009-10-22T01:19:42Z<p>Pranayiitb: /* Collaboration */</p>
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== '''Collaboration''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="3" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
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'''Experimental Collaboration'''<br />
<br />
IIT Madras team had problems in building assembly of parts by ligating together. We collaborated with IIT Madras team and helped them figure out the problem that might have caused the bottleneck in building constructs.<br />
<br />
<br />
'''Human Practices Collaboration'''<br />
<br />
We had discussions on Human Practices in synthetic biology. The surveys conducted by Team Valencia and Team TUDelft helped us in our discussions. Our team took part in the survey on human practices by Team Valencia. On account of all team members replying to this survey, our team was awarded ‘Collaboration Gold Medal. We also took part in the survey undertaken by Team TUDelft on reductionist approach in biology.</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/collaborationTeam:IIT Bombay India/collaboration2009-10-22T01:17:11Z<p>Pranayiitb: New page: {| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center" !align="center"|[[Team:IIT_Bombay_India|Home...</p>
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| <br />
<br />
== '''Collaboration''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
'''Experimental Collaboration'''<br />
<br />
IIT Madras team had problems in building assembly of parts by ligating together. We collaborated with IIT Madras team and helped them figure out the problem that might have caused the bottleneck in building constructs.<br />
<br />
<br />
'''Human Practices Collaboration'''<br />
<br />
We had discussions on Human Practices in synthetic biology. The surveys conducted by Team Valencia and Team TUDelft helped us in our discussions. Our team took part in the survey on human practices by Team Valencia. On account of all team members replying to this survey, our team was awarded ‘Collaboration Gold Medal. We also took part in the survey undertaken by Team TUDelft on reductionist approach in biology.</div>Pranayiitbhttp://2009.igem.org/File:Deterministic_modelling.pdfFile:Deterministic modelling.pdf2009-10-22T01:09:25Z<p>Pranayiitb: uploaded a new version of "Image:Deterministic modelling.pdf"</p>
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== '''Control Theory Approach to Study Multiple Feedbacks on Lac-operon ''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
| Control Analysis Model<br />
<br />
<br />
'''Objectives'''<br />
<br />
1. Characterize the system.<br />
<br />
2. Linearize the system around a set-point on LacI.<br />
<br />
3. Obtain a linear model in transfer-function (s) domain.<br />
<br />
4. Frequency response analysis using magnitude and phase bode plots.<br />
<br />
5. Sensitivity analysis using magnitude bode plot for sensitivity function.<br />
<br />
6. Steps 2-5 for 1000μM IPTG.<br />
<br />
7. Add external noise in the system and tried to determine the reduction in the noise for the system with multiple feedbacks and open-loop system.<br />
<br />
<br />
'''Methodology'''<br />
<br />
We have 2 control levels. By combination, we have 4 different control loops or structures possible, expressed in 4 different strains. They are as follows:-<br />
<br />
'''Strain 1 (Open loop) with plasmid (BBa_K255004)'''<br />
<br />
It has got open loop without any feedback.re there is constitutive expression of LacI. <br />
<br />
<br />
'''Strain 2(Single Input Single Output with regulation on LacI [SISO_LacI] with plasmid (BBa_K255003))'''<br />
<br />
It has got a single negative feedback loop. So the expression of LacI is under regulation. Here also the copy number of the plasmid is fixed. <br />
<br />
<br />
'''Strain 3(Single Input Single Output with regulation on copy number [SISO_CN] with plasmid (BBa_K255002))'''<br />
<br />
It has got a single negative feedback loop on the feedback copy number. Here there is no control on the LacI expression. <br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO] with plasmid (BBa_K255001))'''<br />
<br />
It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression. <br />
<br />
<br />
The dynamic model for the system could be represented as given below:<br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
<br />
We linearize the system around a set-point on LacI and try to obtain a linear equation model around the setpoint. This enables us to separate the controllers from the system of equations. The controllers are designed as proportional-integral (PI) controllers. The process and controller parameters for the system were tuned in a manner as to obtain steady state and dynamic characteristics that closely match with experimental data. The utility of the multiple feedbacks was analysed using the frequency response tools of control systems’ theory using functions in MATLAB 7.8. We use bode plots to obtain the frequency response analysis for the multiple feedback and single feedback system. Further, we do frequency response analysis for high IPTG concentrations.<br />
<br />
The linearized system in transfer-function (s) domain is as given below: <br />
<br />
[[Image:shettynew.jpg]]<br />
<br />
<br />
We add external noise in the system using random noise block in SIMULINK in each of the differential equation blocks individually or together and compare the normalized standard deviations in steady-state LacI production for system with multiple feedbacks and open-loop system. The noise was given in relation to the steady-state value of copy number or LacI values such that standard deviation/steady-state value is constant for open loop and multiple-feedback systems.. With this we try to see whether external noise is attenuated in the system with multiple feedbacks.<br />
<br />
<br />
'''Results'''<br />
<br />
The magnitude and phase bode plots for the system is given below:<br />
<br />
[[Image:shetty2.jpg]]<br />
[[Image:shetty3.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system given in linear model. The green line represents CFS with only C1(s), while blue line represents DFS with both C1(s) and C2(s). The gain margin for both CFS and DFS is ∞.'' ''The phase margin is 92.2 degree for DFS and 56o for CFS. The increased bandwidth from 0.00428 rad/min to 0.0255 rad/min indicates faster response and improved noise rejection.'' ''The CFS has higher peak of 2.92 dB while DFS has no peak, again indicating better noise-attentuation.<br />
''<br />
<br />
<br />
1. The phase margin for a distributed, multiple feedback system (DFS) is 92.2 degree, while it is 56 degree for a single, conventional feedback system (CFS).<br />
<br />
2. The bandwidth increases from 0.00428 rad/min to 0.0255 rad/min for CFS to DFS. <br />
<br />
<br />
For system with IPTG concentration of 1000μM,<br />
<br />
<br />
[[Image:shetty4.jpg]]<br />
[[Image:shetty5.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system with 1000 µM IPTG for linear model given in Fig 2.'' ''The green line represents CFS with only C1(s), while blue line represents DFS with both C1(s) and C2(s).'' ''The gain margin for both CFS and DFS is ∞.'' ''The phase margin is 70o for DFS and 64 degree for CFS.'' ''The bandwidth increase is not significant for DFS from 0.0061 rad/min to 0.0078 rad/min indicates hardly any difference in noise rejection.'' ''The CFS has higher peak of 1.62 dB while DFS has a peak at 0.58 dB indicating a lower peak and a slight better performance in noise attentuation.'' <br />
<br />
1. The phase margin for CFS and DFS are 64 degree and 70 degree respectively.<br />
<br />
2. The bandwidth for CFS and DFS are 0.0061 rad/min and 0.0078 rad/min respectively.<br />
<br />
<br />
[[Image:shettynewnew.jpg]]<br />
<br />
''Fig: Simulink block model for LacI system with external noise.'' ''For noise in replication of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 62.5 for open-loop systems respectively.'' ''For noise in production of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 18779 for open-loop systems respectively.'' ''The standard-deviation/mean value of the LacI is used to characterize the noise at the output.''<br />
<br />
With external noise in the replication of copy number the normalised standard deviation is 0.0138 for multiple-feedback system and 0.0260 for open-loop system.<br />
<br />
With external noise in the production of LacI the normalised standard deviation is 5.1499e-04 for multiple-feedback system and 5.7262e-04 for open-loop system.<br />
<br />
With external noise in the production of LacI and the replication of copy number the normalised standard deviation is 0.0141 for multiple-feedback system and 0.0263 for open-loop system.<br />
<br />
<br />
<br />
'''Interpretation'''<br />
<br />
1. The increased phase margin for DFS indicates that DFS can take care of delays in production LacI directly and by virtue of production of multiple plasmid copies better than the CFS which has regulation only on the plasmid copy number. <br />
<br />
2. This indicates faster expression of the protein LacI in the system with low noise.<br />
<br />
3. The increased bandwidth nearly 6 times for DFS indicates a faster response and a better noise rejection over a wide range of frequencies indicating a far robust response as compared to CFS. <br />
<br />
4. For system with higher IPTG concentrations, IPTG takes away LacI, and thus acting as an inducer. This makes the system resemble open loop system more as compared to IPTG at lower concentrations.<br />
<br />
5. The phase margin of 70o and 64ofor DFS and CFS respectively indicates the difference in ability to take care of delays in the two systems has reduced. The bandwidth increase for DFS is not high as compared CFS, with IPTG concentration of 1000μM. Also, the bandwidth for DFS with1000μM IPTG is far lower as compared to the bandwidth of DFS with no IPTG. <br />
<br />
6. In presence of external noise, the multiple-feedback system attenuates noise at the output better than open-loop system. <br />
<br />
The detailed methodology, system equations, results and discussion can be seen [[Media:Control modelling.pdf|here]].<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/CAMTeam:IIT Bombay India/CAM2009-10-22T01:02:36Z<p>Pranayiitb: </p>
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<br />
== '''Control Theory Approach to Study Multiple Feedbacks on Lac-operon ''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
| Control Analysis Model<br />
<br />
<br />
'''Objectives'''<br />
<br />
1. Characterize the system.<br />
<br />
2. Linearize the system around a set-point on LacI.<br />
<br />
3. Obtain a linear model in transfer-function (s) domain.<br />
<br />
4. Frequency response analysis using magnitude and phase bode plots.<br />
<br />
5. Sensitivity analysis using magnitude bode plot for sensitivity function.<br />
<br />
6. Steps 2-5 for 1000μM IPTG.<br />
<br />
7. Add external noise in the system and tried to determine the reduction in the noise for the system with multiple feedbacks and open-loop system.<br />
<br />
<br />
'''Methodology'''<br />
<br />
We have 2 control levels. By combination, we have 4 different control loops or structures possible, expressed in 4 different strains. They are as follows:-<br />
<br />
'''Strain 1 (Open loop) with plasmid (BBa_K255004)'''<br />
<br />
It has got open loop without any feedback.re there is constitutive expression of LacI. <br />
<br />
<br />
'''Strain 2(Single Input Single Output with regulation on LacI [SISO_LacI] with plasmid (BBa_K255003))'''<br />
<br />
It has got a single negative feedback loop. So the expression of LacI is under regulation. Here also the copy number of the plasmid is fixed. <br />
<br />
<br />
'''Strain 3(Single Input Single Output with regulation on copy number [SISO_CN] with plasmid (BBa_K255002))'''<br />
<br />
It has got a single negative feedback loop on the feedback copy number. Here there is no control on the LacI expression. <br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO] with plasmid (BBa_K255001))'''<br />
<br />
It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression. <br />
<br />
<br />
The dynamic model for the system could be represented as given below:<br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
<br />
We linearize the system around a set-point on LacI and try to obtain a linear equation model around the setpoint. This enables us to separate the controllers from the system of equations. The controllers are designed as proportional-integral (PI) controllers. The process and controller parameters for the system were tuned in a manner as to obtain steady state and dynamic characteristics that closely match with experimental data. The utility of the multiple feedbacks was analysed using the frequency response tools of control systems’ theory using functions in MATLAB 7.8. We use bode plots to obtain the frequency response analysis for the multiple feedback and single feedback system. Further, we do frequency response analysis for high IPTG concentrations.<br />
<br />
The linearized system in transfer-function (s) domain is as given below: <br />
<br />
[[Image:shettynew.jpg]]<br />
<br />
<br />
We add external noise in the system using random noise block in SIMULINK in each of the differential equation blocks individually or together and compare the normalized standard deviations in steady-state LacI production for system with multiple feedbacks and open-loop system. The noise was given in relation to the steady-state value of copy number or LacI values such that standard deviation/steady-state value is constant for open loop and multiple-feedback systems.. With this we try to see whether external noise is attenuated in the system with multiple feedbacks.<br />
<br />
<br />
'''Results'''<br />
<br />
The magnitude and phase bode plots for the system is given below:<br />
<br />
[[Image:shetty2.jpg]]<br />
[[Image:shetty3.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system given in linear model. The green line represents CFS with only C1(s), while blue line represents DFS with both C1(s) and C2(s). The gain margin for both CFS and DFS is ∞.'' ''The phase margin is 92.2 degree for DFS and 56o for CFS. The increased bandwidth from 0.00428 rad/min to 0.0255 rad/min indicates faster response and improved noise rejection.'' ''The CFS has higher peak of 2.92 dB while DFS has no peak, again indicating better noise-attentuation.<br />
''<br />
<br />
<br />
1. The phase margin for a distributed, multiple feedback system (DFS) is 92.2 degree, while it is 56 degree for a single, conventional feedback system (CFS).<br />
<br />
2. The bandwidth increases from 0.00428 rad/min to 0.0255 rad/min for CFS to DFS. <br />
<br />
<br />
For system with IPTG concentration of 1000μM,<br />
<br />
<br />
[[Image:shetty4.jpg]]<br />
[[Image:shetty5.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system with 1000 µM IPTG for linear model given in Fig 2.'' ''The green line represents CFS with only C1(s), while blue line represents DFS with both C1(s) and C2(s).'' ''The gain margin for both CFS and DFS is ∞.'' ''The phase margin is 70o for DFS and 64 degree for CFS.'' ''The bandwidth increase is not significant for DFS from 0.0061 rad/min to 0.0078 rad/min indicates hardly any difference in noise rejection.'' ''The CFS has higher peak of 1.62 dB while DFS has a peak at 0.58 dB indicating a lower peak and a slight better performance in noise attentuation.'' <br />
<br />
1. The phase margin for CFS and DFS are 64 degree and 70 degree respectively.<br />
<br />
2. The bandwidth for CFS and DFS are 0.0061 rad/min and 0.0078 rad/min respectively.<br />
<br />
<br />
[[Image:shettynewnew.jpg]]<br />
<br />
''Fig: Simulink block model for LacI system with external noise.'' ''For noise in replication of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 62.5 for open-loop systems respectively.'' ''For noise in production of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 18779 for open-loop systems respectively.'' ''The standard-deviation/mean value of the LacI is used to characterize the noise at the output.''<br />
<br />
With external noise in the replication of copy number the normalised standard deviation is 0.0138 for multiple-feedback system and 0.0260 for open-loop system.<br />
<br />
With external noise in the production of LacI the normalised standard deviation is 5.1499e-04 for multiple-feedback system and 5.7262e-04 for open-loop system.<br />
<br />
With external noise in the production of LacI and the replication of copy number the normalised standard deviation is 0.0141 for multiple-feedback system and 0.0263 for open-loop system.<br />
<br />
<br />
<br />
'''Interpretation'''<br />
<br />
1. The increased phase margin for DFS indicates that DFS can take care of delays in production LacI directly and by virtue of production of multiple plasmid copies better than the CFS which has regulation only on the plasmid copy number. <br />
<br />
2. This indicates faster expression of the protein LacI in the system with low noise.<br />
<br />
3. The increased bandwidth nearly 6 times for DFS indicates a faster response and a better noise rejection over a wide range of frequencies indicating a far robust response as compared to CFS. <br />
<br />
4. For system with higher IPTG concentrations, IPTG takes away LacI, and thus acting as an inducer. This makes the system resemble open loop system more as compared to IPTG at lower concentrations.<br />
<br />
5. The phase margin of 70o and 64ofor DFS and CFS respectively indicates the difference in ability to take care of delays in the two systems has reduced. The bandwidth increase for DFS is not high as compared CFS, with IPTG concentration of 1000μM. Also, the bandwidth for DFS with1000μM IPTG is far lower as compared to the bandwidth of DFS with no IPTG. <br />
<br />
6. In presence of external noise, the multiple-feedback system attenuates noise at the output better than open-loop system. <br />
<br />
The detailed methodology, system equations, results and discussion can be seen [Media:Control modelling.pdf|here]].<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/PSMTeam:IIT Bombay India/PSM2009-10-22T01:02:15Z<p>Pranayiitb: </p>
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<br />
== '''Phenomenological Stochastic Model''' ==<br />
|}<br />
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!align="left"|<br />
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| <br />
Stochastic Modelling for the system <br />
<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 />
The detailed methodology, system equations, results and discussion can be seen [[Media:Stochastic modelling.pdf|here]].<br />
<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/DDMTeam:IIT Bombay India/DDM2009-10-22T01:00:53Z<p>Pranayiitb: </p>
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<br />
== '''Detailed Deterministic Model''' ==<br />
|}<br />
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Detailed Molecular 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 />
<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>Pranayiitbhttp://2009.igem.org/File:Deterministic_modelling.pdfFile:Deterministic modelling.pdf2009-10-22T00:18:35Z<p>Pranayiitb: </p>
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<div></div>Pranayiitbhttp://2009.igem.org/File:Iitbombaylogo.jpgFile:Iitbombaylogo.jpg2009-10-22T00:15:26Z<p>Pranayiitb: uploaded a new version of "Image:Iitbombaylogo.jpg"</p>
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<div></div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:14:12Z<p>Pranayiitb: </p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<br />
|}<br />
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{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor: [[Image:iitbombaylogo.jpg]] Silver Sponsors: [[Image:DSIR LOGO1.jpg]]<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/File:Iitbombaylogo.jpgFile:Iitbombaylogo.jpg2009-10-22T00:13:32Z<p>Pranayiitb: uploaded a new version of "Image:Iitbombaylogo.jpg"</p>
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<div></div>Pranayiitbhttp://2009.igem.org/File:Iitbombaylogo.jpgFile:Iitbombaylogo.jpg2009-10-22T00:12:23Z<p>Pranayiitb: uploaded a new version of "Image:Iitbombaylogo.jpg"</p>
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<div></div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:09:36Z<p>Pranayiitb: /* Sponsors */</p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
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{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<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 />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor: [[Image:iitbombaylogo.jpg]] Silver Sponsors: [[Image:DSIR LOGO1.jpg]]<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:08:29Z<p>Pranayiitb: /* Sponsors */</p>
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<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<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 />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="20" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor: [[Image:iitbombaylogo.jpg]] Silver Sponsors: [[Image:DSIR LOGO1.jpg]]<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/File:DSIR_LOGO1.jpgFile:DSIR LOGO1.jpg2009-10-22T00:08:02Z<p>Pranayiitb: </p>
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<div></div>Pranayiitbhttp://2009.igem.org/File:Iitbombaylogo.jpgFile:Iitbombaylogo.jpg2009-10-22T00:07:47Z<p>Pranayiitb: </p>
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<div></div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:07:23Z<p>Pranayiitb: </p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<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 />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor: [[Image:iitbombaylogo.jpg]] Silver Sponsors: [[Image:DSIR LOGO1.jpg]]<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:04:41Z<p>Pranayiitb: </p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<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 />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor: [[Image:iitbombaylogo.jpg] Silver Sponsors: [Image:DSIR LOGO1.jpg]]<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:03:48Z<p>Pranayiitb: </p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<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 />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor: [[Image:iitbombaylogo.jpg]] Silver Sponsors: [[Image:DSIR LOGO1.jpg]]<br />
<br />
|<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:03:24Z<p>Pranayiitb: </p>
<hr />
<div>{| style="color:#000000;background-color:#ffffff;" cellpadding="6" cellspacing="3" border="0" bordercolor="#ffffff" width="65%" align="center"<br />
<br />
!align="center"|[[Team:IIT_Bombay_India|Home]]<br />
!align="center"|[[Team:IIT_Bombay_India/Team|The Team]]<br />
!align="center"|[[Team:IIT_Bombay_India/Project|The Project]]<br />
!align="center"|[[Team:IIT_Bombay_India/Analysis|Analysis]]<br />
!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 />
|}<br />
<br />
<br />
<br />
[[Image:IITB-Home.jpg]]<br />
<br />
{| background-color:#ffffff;" cellpadding="1" cellspacing="2" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| <br />
<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<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 />
== '''Sponsors''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Gold Sponsor : [[Image:iitbombaylogo.jpg]] | Silver Sponsors : [[Image:DSIR LOGO1.jpg]]<br />
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|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-22T00:00:09Z<p>Pranayiitb: </p>
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== '''Introduction''' ==<br />
|}<br />
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{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
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| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
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<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
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<br />
== '''Sponsors''' ==<br />
|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_IndiaTeam:IIT Bombay India2009-10-21T23:59:23Z<p>Pranayiitb: </p>
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<br />
== '''Introduction''' ==<br />
|}<br />
<br />
{| background-color:#ffffff;" cellpadding="5" cellspacing="1" border="0" bordercolor="#ffffff" width="90%" align="center"<br />
!align="left"|<br />
<br />
| Established in 1958, [http://www.iitb.ac.in IIT Bombay] is one of the most recognized centers of academic excellence in the country today. The excellence of its academic programs, a robust research and development program with parallel improvement in facilities and infrastructure have kept it at par with the best institutions in the world. The ideas on which such institutes are built evolve and change with national aspirations, national perspectives, and global trends. At IIT Bombay we are continuously seeking to extend the boundaries of our research in a sustained manner with clear cut executable goals, grounded solidly in national realities.<br />
<br />
<br />
This is our first year of participation and as such, we are pretty excited about the prospects. We are a group of students from the Chemical Engineering Department and from the School of Biosciences & Bioengineering. The most exciting aspect that we found about this competition was the interdisciplinary learning. A chemical reactor system invariably involves the design of control structures, and it is the design of these structures in a biological system that we wish to attain via our project.<br />
<br />
<br />
A major objective of synthetic biology is to unveil the inherent design principles prevailing in biological circuits. Multiple feedback loops (having both positive and negative regulation) are highly prevalent in biological systems. The relevance of such a design in biological systems is unclear. Our team has used synthetic biology approaches to answer these questions. Our team comprises of nine undergraduates, three graduate students as student mentors and two faculty mentors, one each from biology and engineering background. The project specifically deals with the analysis of the effect of single and multiple feedback loops on gene expression. This project involves theoretical and experimental studies. We have designed synthetic constructs to mimic multiple feedbacks. The focus of our experimental work is to visualize the effect of multiple feedback loops on the synthetic construct using single cell analysis. The project provides insights into the roles of multiple feedback loops in biological systems.<br />
|<br />
|}<br />
<br />
== '''Introduction''' ==</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/CAMTeam:IIT Bombay India/CAM2009-10-21T23:58:34Z<p>Pranayiitb: </p>
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== '''Control Theory Approach to Study Multiple Feedbacks on Lac-operon ''' ==<br />
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| Control Analysis Model<br />
<br />
<br />
'''Objectives'''<br />
<br />
1. Characterize the system.<br />
<br />
2. Linearize the system around a set-point on LacI.<br />
<br />
3. Obtain a linear model in transfer-function (s) domain.<br />
<br />
4. Frequency response analysis using magnitude and phase bode plots.<br />
<br />
5. Sensitivity analysis using magnitude bode plot for sensitivity function.<br />
<br />
6. Steps 2-5 for 1000μM IPTG.<br />
<br />
7. Add external noise in the system and tried to determine the reduction in the noise for the system with multiple feedbacks and open-loop system.<br />
<br />
<br />
'''Methodology'''<br />
<br />
We have 2 control levels. By combination, we have 4 different control loops or structures possible, expressed in 4 different strains. They are as follows:-<br />
<br />
'''Strain 1 (Open loop) with plasmid (BBa_K255004)'''<br />
<br />
It has got open loop without any feedback.re there is constitutive expression of LacI. <br />
<br />
<br />
'''Strain 2(Single Input Single Output with regulation on LacI [SISO_LacI] with plasmid (BBa_K255003))'''<br />
<br />
It has got a single negative feedback loop. So the expression of LacI is under regulation. Here also the copy number of the plasmid is fixed. <br />
<br />
<br />
'''Strain 3(Single Input Single Output with regulation on copy number [SISO_CN] with plasmid (BBa_K255002))'''<br />
<br />
It has got a single negative feedback loop on the feedback copy number. Here there is no control on the LacI expression. <br />
<br />
<br />
'''Strain 4 (Multiple Input Multiple Output with regulation on copy number and LacI [MIMO] with plasmid (BBa_K255001))'''<br />
<br />
It has dual negative feedback loop one on the plasmid copy number and second on the LacI expression. <br />
<br />
<br />
The dynamic model for the system could be represented as given below:<br />
<br />
[[Image:shetty1.jpg]]<br />
<br />
<br />
We linearize the system around a set-point on LacI and try to obtain a linear equation model around the setpoint. This enables us to separate the controllers from the system of equations. The controllers are designed as proportional-integral (PI) controllers. The process and controller parameters for the system were tuned in a manner as to obtain steady state and dynamic characteristics that closely match with experimental data. The utility of the multiple feedbacks was analysed using the frequency response tools of control systems’ theory using functions in MATLAB 7.8. We use bode plots to obtain the frequency response analysis for the multiple feedback and single feedback system. Further, we do frequency response analysis for high IPTG concentrations.<br />
<br />
The linearized system in transfer-function (s) domain is as given below: <br />
<br />
[[Image:shettynew.jpg]]<br />
<br />
<br />
We add external noise in the system using random noise block in SIMULINK in each of the differential equation blocks individually or together and compare the normalized standard deviations in steady-state LacI production for system with multiple feedbacks and open-loop system. The noise was given in relation to the steady-state value of copy number or LacI values such that standard deviation/steady-state value is constant for open loop and multiple-feedback systems.. With this we try to see whether external noise is attenuated in the system with multiple feedbacks.<br />
<br />
<br />
'''Results'''<br />
<br />
The magnitude and phase bode plots for the system is given below:<br />
<br />
[[Image:shetty2.jpg]]<br />
[[Image:shetty3.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system given in linear model. The green line represents CFS with only C1(s), while blue line represents DFS with both C1(s) and C2(s). The gain margin for both CFS and DFS is ∞.'' ''The phase margin is 92.2 degree for DFS and 56o for CFS. The increased bandwidth from 0.00428 rad/min to 0.0255 rad/min indicates faster response and improved noise rejection.'' ''The CFS has higher peak of 2.92 dB while DFS has no peak, again indicating better noise-attentuation.<br />
''<br />
<br />
<br />
1. The phase margin for a distributed, multiple feedback system (DFS) is 92.2 degree, while it is 56 degree for a single, conventional feedback system (CFS).<br />
<br />
2. The bandwidth increases from 0.00428 rad/min to 0.0255 rad/min for CFS to DFS. <br />
<br />
<br />
For system with IPTG concentration of 1000μM,<br />
<br />
<br />
[[Image:shetty4.jpg]]<br />
[[Image:shetty5.jpg]]<br />
''Fig: Magnitude, phase and sensitivity bode plots for LacI system with 1000 µM IPTG for linear model given in Fig 2.'' ''The green line represents CFS with only C1(s), while blue line represents DFS with both C1(s) and C2(s).'' ''The gain margin for both CFS and DFS is ∞.'' ''The phase margin is 70o for DFS and 64 degree for CFS.'' ''The bandwidth increase is not significant for DFS from 0.0061 rad/min to 0.0078 rad/min indicates hardly any difference in noise rejection.'' ''The CFS has higher peak of 1.62 dB while DFS has a peak at 0.58 dB indicating a lower peak and a slight better performance in noise attentuation.'' <br />
<br />
1. The phase margin for CFS and DFS are 64 degree and 70 degree respectively.<br />
<br />
2. The bandwidth for CFS and DFS are 0.0061 rad/min and 0.0078 rad/min respectively.<br />
<br />
<br />
[[Image:shettynewnew.jpg]]<br />
<br />
''Fig: Simulink block model for LacI system with external noise.'' ''For noise in replication of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 62.5 for open-loop systems respectively.'' ''For noise in production of plasmid copy number, mean is 0, and variance is 10 for multiple feedback and 18779 for open-loop systems respectively.'' ''The standard-deviation/mean value of the LacI is used to characterize the noise at the output.''<br />
<br />
With external noise in the replication of copy number the normalised standard deviation is 0.0138 for multiple-feedback system and 0.0260 for open-loop system.<br />
<br />
With external noise in the production of LacI the normalised standard deviation is 5.1499e-04 for multiple-feedback system and 5.7262e-04 for open-loop system.<br />
<br />
With external noise in the production of LacI and the replication of copy number the normalised standard deviation is 0.0141 for multiple-feedback system and 0.0263 for open-loop system.<br />
<br />
<br />
<br />
'''Interpretation'''<br />
<br />
1. The increased phase margin for DFS indicates that DFS can take care of delays in production LacI directly and by virtue of production of multiple plasmid copies better than the CFS which has regulation only on the plasmid copy number. <br />
<br />
2. This indicates faster expression of the protein LacI in the system with low noise.<br />
<br />
3. The increased bandwidth nearly 6 times for DFS indicates a faster response and a better noise rejection over a wide range of frequencies indicating a far robust response as compared to CFS. <br />
<br />
4. For system with higher IPTG concentrations, IPTG takes away LacI, and thus acting as an inducer. This makes the system resemble open loop system more as compared to IPTG at lower concentrations.<br />
<br />
5. The phase margin of 70o and 64ofor DFS and CFS respectively indicates the difference in ability to take care of delays in the two systems has reduced. The bandwidth increase for DFS is not high as compared CFS, with IPTG concentration of 1000μM. Also, the bandwidth for DFS with1000μM IPTG is far lower as compared to the bandwidth of DFS with no IPTG. <br />
<br />
6. In presence of external noise, the multiple-feedback system attenuates noise at the output better than open-loop system. <br />
<br />
A detailed review of all the Control analysis modelling attempted is available [[Media:Control modelling.pdf|here]].<br />
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|}</div>Pranayiitbhttp://2009.igem.org/Team:IIT_Bombay_India/PSMTeam:IIT Bombay India/PSM2009-10-21T23:57:13Z<p>Pranayiitb: </p>
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<br />
== '''Phenomenological Stochastic Model''' ==<br />
|}<br />
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| <br />
Stochastic Modelling for the system <br />
<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 />
A detailed review of all the Stochastic modelling attempted is available [[Media:Stochastic modelling.pdf|here]].<br />
<br />
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|<br />
|}</div>Pranayiitb