@article{38576,
  keywords = {systems, dynamics, bifurcation-analysis, integration, simulation, algorithm, stochastic chemical-kinetics},
  author = {Erban and Kevrekidis and Adalsteinsson and Elston},
  title = {Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation},
  abstract = { <p>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.</p> },
  year = {2006},
  journal = {Journal of Chemical Physics},
  volume = {124},
  pages = {084106},
  month = {02/2006},
  isbn = {0021-9606},
  language = {English},
}