Assume the complete model for negative feedback, dX/dt = beta/(1+(X/K)^n)-alpah

Question

Assume the complete model for negative feedback, dX/dt = beta/(1+(X/K)^n)-alpah x. Use the provided quasi-stochastic solver (MATHEMATICA) or an equivalent script MATLAB and run a simulation several times to produce a distribution of steady states (for fixed parameter values). Plot the output X versus time. Compare the negative autoregulation steady state values distribution to that of a simple regulation. Note that you have to adjust the simple regulation parameters so that the mean values between the two distributions overlap. Plot the coefficient of variation of the negative autoregulation distribution versus K, beta, alpha, and n (i.e. 4 different plots).

Explanation / Answer

Cells regulate gene expression using networks of transcription interactions; it is of interest to discover the principles that govern the dynamical behavior of such networks. An important characteristic of these systems is the rise-time: the delay from the initiation of production until half maximal product concentration is reached. Here we employ synthetic gene circuits in Escherichia coli to measure the rise-times of non-self-regulated and of negatively autoregulated transcription units. Non-self-regulated units have a rise-time of one cell-cycle. We demonstrate experimentally that negative autoregulation feedback (also termed autogenous control) reduces the rise-time to about one fifth of a cell-cycle. This agrees with an analytical solution of a mathematical model for negative autoregulation. This may help in understanding the function of negative autoregulation, which appears in over 40% of known transcription factors in E.coli.

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