A constrained approach to multiscale stochastic simulation of chemically reacting systems

Type
Article

Authors
Cotter, Simon L.
Zygalakis, Konstantinos C.
Kevrekidis, Ioannis G.
Erban, Radek

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2011-09-02

Print Publication Date
2011-09-07

Date
2011-09-02

Abstract
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. © 2011 American Institute of Physics.

Citation
Cotter SL, Zygalakis KC, Kevrekidis IG, Erban R (2011) A constrained approach to multiscale stochastic simulation of chemically reacting systems. J Chem Phys 135: 094102. Available: http://dx.doi.org/10.1063/1.3624333.

Acknowledgements
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.

Publisher
AIP Publishing

Journal
The Journal of Chemical Physics

DOI
10.1063/1.3624333

PubMed ID
21913748

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