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Analysis of multiple feedback loops

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.

1. Detailed mechanistic(deterministic) 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.

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.

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 control analysis simulations were developed using simulink platform of MATLAB.

A detailed summary for each of the models is provided at each of the links below.

Detailed Deterministic Model

Phenomenological Stochastic Model

Control Analysis Model