(302x) Stchastic Modelingof Genetic Toggle Switch and Noise-Induced Transitions

It has been envisioned that the ability to predict the function of genetic circuits will enhance the design of autonomous, programmable, complex regulatory genetic structures often referred as genetic applets. Acknowledging this fact an abundance of modeling techniques have emerged over the years delineating simple genetic structures in terms their constituents. Simpler systems like Escherichia Coli (E. Coli) in particular has grabbed the modelers imagination due to the desirable features of feedback inhibition, multi-stability, switching and oscillatory expression. The present work is an attempt to improvise existing models that fail to oblige to the crucial aspect of noise in genetic modeling.

The objective of this work is to analyze, model and simulate the gene expression mechanism by resorting to modern stochastic algorithms. The system involves two types of genes; the protein produced from the expression of one gene is capable of turning off the expression of the other gene. Rates of consumption of these proteins are assumed to be proportional to their concentrations. The master equation of this ?genetic toggle switch? is formulated using the probabilistic population balance around a particular state and by considering five mutually exclusive events. The efficacy of the present methodology is mainly attributable to the ability to derive the governing equations for the means, variances and covariance of the random variables by the method of system-size expansion of the nonlinear master equation. An alternative, more general approach for the derivation of the master equation and its expansion is also presented for comparison. Solving the resultant ordinary differential equations governing the means, variances and covariance simultaneously using the published data yields information concerning not only the means of the two populations of proteins but also the minimal uncertainties of the populations inherent in the expressions. It is also demonstrated that the probability of noise-induced transition from one steady state to another can be estimated based on the fluctuation envelopes derived from this procedure. The effects of internal noise induced transitions are then examined based on macroscopic solution and bifurcation analysis.