Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

Details Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation

2005-08-17

arxiv.org/abs/physics/0508112v1

Physics

Biological Physics

33 pages, submitted to The Journal of Chemical Physics

Scientific paper

10.1063/1.2149854

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy and of a state-dependent effective diffusion coefficient that characterize an unavailable effective Fokker-Planck equation. Additionally we illustrate the linking of equation-free techniques with continuation methods for performing a form of stochastic "bifurcation analysis"; estimation of mean switching times in the case of a bistable switch is also implemented in this equation-free context. The accuracy of our methods is tested by direct comparison with long-time stochastic simulations. This type of equation-free analysis appears to be a promising approach to computing features of the long-time, coarse-grained behavior of certain classes of complex stochastic models of gene regulatory networks, circumventing the need for long Monte Carlo simulations.

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