dorsal/arxiv
View SchemaGene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
| Authors | Radek Erban, Ioannis G. Kevrekidis, David Adalsteinsson, Timothy C. Elston |
|---|---|
| Categories | |
| ArXiv ID | physics/0508112 |
| URL | https://arxiv.org/abs/physics/0508112 |
| DOI | 10.1063/1.2149854 |
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 and of a state-dependent effective diffusion coefficient 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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"abstract": "We present computer-assisted methods for analyzing stochastic models of gene\nregulatory networks. The main idea that underlies this equation-free analysis\nis the design and execution of appropriately-initialized short bursts of\nstochastic simulations; the results of these are processed to estimate\ncoarse-grained quantities of interest, such as mesoscopic transport\ncoefficients. In particular, using a simple model of a genetic toggle switch,\nwe illustrate the computation of an effective free energy and of a\nstate-dependent effective diffusion coefficient that characterize an\nunavailable effective Fokker-Planck equation. Additionally we illustrate the\nlinking of equation-free techniques with continuation methods for performing a\nform of stochastic \"bifurcation analysis\"; estimation of mean switching times\nin the case of a bistable switch is also implemented in this equation-free\ncontext. The accuracy of our methods is tested by direct comparison with\nlong-time stochastic simulations. This type of equation-free analysis appears\nto be a promising approach to computing features of the long-time,\ncoarse-grained behavior of certain classes of complex stochastic models of gene\nregulatory networks, circumventing the need for long Monte Carlo simulations.",
"arxiv_id": "physics/0508112",
"authors": [
"Radek Erban",
"Ioannis G. Kevrekidis",
"David Adalsteinsson",
"Timothy C. Elston"
],
"categories": [
"physics.bio-ph",
"physics.chem-ph",
"physics.comp-ph",
"q-bio.MN"
],
"doi": "10.1063/1.2149854",
"title": "Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation",
"url": "https://arxiv.org/abs/physics/0508112"
},
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