TY - JOUR

T1 - Gene regulatory networks

T2 - A coarse-grained, equation-free approach to multiscale computation

AU - Erban, Radek

AU - Kevrekidis, Ioannis G.

AU - Adalsteinsson, David

AU - Elston, Timothy C.

N1 - Funding Information:
One of the authors (I.G.K.) acknowledges partial support by DARPA and a NSF/ITR grant. Another author (R.E.) acknowledges partial support by the Biotechnology and Biological Sciences Research Council, University of Oxford and University of Minnesota. Another author (T.C.E.) also acknowledges support by DARPA (F30602-01-2-0579).

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

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U2 - 10.1063/1.2149854

DO - 10.1063/1.2149854

M3 - Article

C2 - 16512707

AN - SCOPUS:33751572545

VL - 124

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084106

ER -