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

Radek Erban, Ioannis G. Kevrekidis, David Adalsteinsson, Timothy C. Elston

Research output: Contribution to journalArticle

66 Scopus citations

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 Φ 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.

Original languageEnglish (US)
Article number084106
JournalJournal of Chemical Physics
Volume124
Issue number8
DOIs
StatePublished - Mar 7 2006

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Fingerprint Dive into the research topics of 'Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation'. Together they form a unique fingerprint.

  • Cite this