Team:IIT Bombay India/Project

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	Analysis of multiple feed-backs in biological systems

Objective

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.

Our Constructs

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.

Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003). 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.

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.

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.

Methodology

Experimental

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.

Simulation

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.

Results

Experimental results

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.

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.

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.

Simulations

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.

2. Stochastic modeling 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.

3. Control theory approach We have done frequency response analysis on the linear system using magnitude and phase Bode plots. 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. Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system. The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min. For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below: The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3. The magnitude plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.

Conclusions

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.

Future work

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.

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

3. Detailed model: Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;

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.

5. Control analysis: We have done the analysis for only one kind of feedback system. We could use different feedback systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here.

@@ Line 18: / Line 18: @@
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-== '''Multiple feed-backs in biological systems''' ==
+== '''Analysis of multiple feed-backs in biological systems''' ==
 |}
@@ Line 24: / Line 24: @@
 !align="left"|
-| '''Experimental Study'''
+| '''Objective'''
-The effect of multiple feedback loops on biological system is unclear. 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. The plasmids were designed using standard biobricks available using pLac and pTet promoters with inducible and fixed copy numbers. Experiments and modeling studies 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. Control feedback analysis demonstrated that gain margin increases and phase sensitivity indicated reduction in the noise due to multiple feedbacks. Growth experiments on lactose were also conducted to characterize the effect of synthetic network on the phenotypic response. The experiments and modeling 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.
+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.
+'''Our Constructs'''
-'''Modeling Study'''
-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.
+'''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.
-. 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.
+[[Image:Strain1.jpg]]
+'''Strain 2 (Single Input Single Output with regulation on LacI [SISO_LacI]) with plasmid (BBa_K255003).''' 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.
+[[Image:Strain2.jpg]]
+'''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.
+[[Image:Strain3.jpg]]
+'''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.
+[[Image:Strain4.jpg]]
+[[Image:Strain5.jpg]]
+'''Methodology'''
+''Experimental''
+----
+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.
+''Simulation''
+----
+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.
+'''Results'''
+''Experimental results''
+----
+.  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.
+. 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.
+. 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.
+''Simulations''
+----
+. 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.
+. Stochastic modeling
+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.
+. Control theory approach
+We have done frequency response analysis on the linear system using magnitude and phase Bode plots.
+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.
+Further, we have done magnitude bode plot for the sensitivity function to determine sensitivity of the system.
+The bandwidth for strain 4 is 0.0255 rad/min while bandwidth for strain 3 is 0.00428 rad/min.
+For system with 1000 µM IPTG, the magnitude and phase bode plots are given as below:
+The phase margin difference is not that significant. It is 70 deg for strain 4 and 64 deg for strain 3.
+The magnitude plot for the sensitivity function shows lower bandwidth of 0.0061 rad/min for strain 4 and 0.0078 rad/min.
+'''Conclusions'''
+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.
+'''Future work'''
+. 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.
+. More experimentation for different values of lactose and IPTG, to get more data for beta-gal expressions and growth rate for all 4 strains
+. Detailed model: Accurately finding the kinetic constants from literature and utilizing them to accurately correlate with the experimental results;
+. Stochastic Analysis:- To develop a simplified model for growth and to introduce stochasticity in the same and characterize the inherent noise in the system.
+. Control analysis: We have done the analysis for only one kind of feedback system. We could use different feedback
+systems characterized by different Hill-Coefficients and try to do further analysis on the same lines as the analysis done here.
-. A phenomenological model was developed to represent the four constructs and langevian approach was used to estimate the variability due to the stochastic process.
-. 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.
 |
 |}