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

摘要

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.