TY - JOUR

T1 - A constrained approach to multiscale stochastic simulation of chemically reacting systems

AU - Cotter, Simon L.

AU - Zygalakis, Konstantinos C.

AU - Kevrekidis, Ioannis G.

AU - Erban, Radek

N1 - Funding Information:
The research leading to these results has received funding from the European Research Council under the European Community's Seventh Framework Programme ( FP7/2007-2013 )/ERC Grant Agreement No. 239870. This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). The work of I.G.K. was partially supported by the US Department of Energy. Thanks also to Tomáš Vejchodský for useful conversations regarding the assembly and solution within the finite element method. RE would also like to thank Somerville College, University of Oxford, for a Fulford Junior Research Fellowship.

PY - 2011/9/7

Y1 - 2011/9/7

N2 - Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.

AB - Stochastic simulation of coupled chemical reactions is often computationally intensive, especially if a chemical system contains reactions occurring on different time scales. In this paper, we introduce a multiscale methodology suitable to address this problem, assuming that the evolution of the slow species in the system is well approximated by a Langevin process. It is based on the conditional stochastic simulation algorithm (CSSA) which samples from the conditional distribution of the suitably defined fast variables, given values for the slow variables. In the constrained multiscale algorithm (CMA) a single realization of the CSSA is then used for each value of the slow variable to approximate the effective drift and diffusion terms, in a similar manner to the constrained mean-force computations in other applications such as molecular dynamics. We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems.

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U2 - 10.1063/1.3624333

DO - 10.1063/1.3624333

M3 - Article

C2 - 21913748

AN - SCOPUS:80052808364

SN - 0021-9606

VL - 135

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 9

M1 - 094102

ER -