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Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions.
J Chem Phys 2005; 122(5):54103JC

Abstract

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Authors+Show Affiliations

Department of Chemical Engineering and Materials Science, and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455, USA.No affiliation info available

Pub Type(s)

Journal Article
Research Support, N.I.H., Extramural
Research Support, Non-U.S. Gov't
Research Support, U.S. Gov't, Non-P.H.S.
Research Support, U.S. Gov't, P.H.S.

Language

eng

PubMed ID

15740306

Citation

Salis, Howard, and Yiannis Kaznessis. "Accurate Hybrid Stochastic Simulation of a System of Coupled Chemical or Biochemical Reactions." The Journal of Chemical Physics, vol. 122, no. 5, 2005, p. 54103.
Salis H, Kaznessis Y. Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J Chem Phys. 2005;122(5):54103.
Salis, H., & Kaznessis, Y. (2005). Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. The Journal of Chemical Physics, 122(5), p. 54103.
Salis H, Kaznessis Y. Accurate Hybrid Stochastic Simulation of a System of Coupled Chemical or Biochemical Reactions. J Chem Phys. 2005 Feb 1;122(5):54103. PubMed PMID: 15740306.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. AU - Salis,Howard, AU - Kaznessis,Yiannis, PY - 2005/3/3/pubmed PY - 2006/5/18/medline PY - 2005/3/3/entrez SP - 54103 EP - 54103 JF - The Journal of chemical physics JO - J Chem Phys VL - 122 IS - 5 N2 - The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations. SN - 0021-9606 UR - https://www.unboundmedicine.com/medline/citation/15740306/Accurate_hybrid_stochastic_simulation_of_a_system_of_coupled_chemical_or_biochemical_reactions_ L2 - https://dx.doi.org/10.1063/1.1835951 DB - PRIME DP - Unbound Medicine ER -