title: Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation.
abstract: 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.
authors.affiliation: Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom. erban@maths.ox.ac.uk
authors.forename: Radek
authors.initials: R
authors.lastname: Erban
authors.forename: Ioannis G
authors.initials: IG
authors.lastname: Kevrekidis
authors.forename: David
authors.initials: D
authors.lastname: Adalsteinsson
authors.forename: Timothy C
authors.initials: TC
authors.lastname: Elston
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D053263:Gene Regulatory Networks; D008957:Models, Genetic; D009010:Monte Carlo Method; D013269:Stochastic Processes