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

• Published in: The Journal of chemical physics 2006-02, Vol.124 (8), p.084106-084106
• Main Authors: Erban, Radek, Kevrekidis, Ioannis G, Adalsteinsson, David, Elston, Timothy C
• Format: Article
• Language: English
• Subjects: Algorithms; Computer Simulation; Gene Regulatory Networks; Models, Genetic; Monte Carlo Method; Stochastic Processes
• ISSN: 0021-9606; 1089-7690
• DOI: 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 Phi and of a state-dependent effective diffusion coefficient D 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.