Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates

作者: Weinan E , Di Liu , Eric Vanden-Eijnden

DOI: 10.1063/1.2109987

关键词: Convergence (routing)Kinetic energyScale (ratio)AlgorithmMarkov processComputer scienceStochastic processStochastic simulationTau-leapingSimple (abstract algebra)

摘要: An efficient simulation algorithm for chemical kinetic systems with disparate rates is proposed. This new quite general, and it amounts to a simple seamless modification of the classical stochastic (SSA), also known as Gillespie [J. Comput. Phys. 22, 403 (1976); J. Chem. 81, 2340 (1977)] algorithm. The basic idea use an outer SSA simulate slow processes computed from inner which simulates fast reactions. Averaging theorems Markov can be used identify variables in system well effective dynamics over time scale, even though itself does not rely on such information. nested easily generalized more than two separated scales. Convergence efficiency are discussed using established error estimates illustrated through examples.

参考文章(15)
Eric Vanden-Eijnden, NUMERICAL TECHNIQUES FOR MULTI-SCALE DYNAMICAL SYSTEMS WITH STOCHASTIC EFFECTS ⁄ Communications in Mathematical Sciences. ,vol. 1, pp. 385- 391 ,(2003) , 10.4310/CMS.2003.V1.N2.A11
Bjorn Engquist, Yen-Hsi Tsai, Heterogeneous multiscale methods for stiff ordinary differential equations Mathematics of Computation. ,vol. 74, pp. 1707- 1742 ,(2005) , 10.1090/S0025-5718-05-01745-X
Christopher V. Rao, Adam P. Arkin, Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm The Journal of Chemical Physics. ,vol. 118, pp. 4999- 5010 ,(2003) , 10.1063/1.1545446
Yang Cao, Daniel T. Gillespie, Linda R. Petzold, The Slow-Scale Stochastic Simulation Algorithm Journal of Chemical Physics. ,vol. 122, pp. 014116- 014116 ,(2005) , 10.1063/1.1824902
Weinan E, Analysis of the heterogeneous multiscale method for ordinary differential equations Communications in Mathematical Sciences. ,vol. 1, pp. 423- 436 ,(2003) , 10.4310/CMS.2003.V1.N3.A3
K. Takahashi, K. Kaizu, B. Hu, M. Tomita, A multi-algorithm, multi-timescale method for cell simulation Bioinformatics. ,vol. 20, pp. 538- 546 ,(2004) , 10.1093/BIOINFORMATICS/BTG442
Eric L. Haseltine, James B. Rawlings, Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics Journal of Chemical Physics. ,vol. 117, pp. 6959- 6969 ,(2002) , 10.1063/1.1505860
A.B. Bortz, M.H. Kalos, J.L. Lebowitz, A new algorithm for Monte Carlo simulation of Ising spin systems Journal of Computational Physics. ,vol. 17, pp. 10- 18 ,(1975) , 10.1016/0021-9991(75)90060-1
R. Srivastava, M. S. Peterson, W. E. Bentley, Stochastic kinetic analysis of the Escherichia coli stress circuit using σ32-targeted antisense Biotechnology and Bioengineering. ,vol. 75, pp. 120- 129 ,(2001) , 10.1002/BIT.1171