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Efficient exact stochastic simulation of chemical systems with many species and many channels (2000)
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| Venue: | J. Phys. Chem. A |
| Citations: | 427 - 5 self |
BibTeX
@ARTICLE{Gibson00efficientexact,
author = {Michael A. Gibson and Jehoshua Bruck},
title = {Efficient exact stochastic simulation of chemical systems with many species and many channels},
journal = {J. Phys. Chem. A},
year = {2000},
volume = {104},
pages = {1876--1889}
}
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Abstract
There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more common, systems with very small numbers of molecules are important in some applications (e.g., in small biological cells or in surface processes). In both views, most complicated systems with multiple reaction channels and multiple chemical species cannot be solved analytically. There are exact numerical simulation methods to simulate trajectories of discrete, stochastic systems, (methods that are rigorously equivalent to the Master Equation approach) but these do not scale well to systems with many reaction pathways. This paper presents the Next Reaction Method, an exact algorithm to simulate coupled chemical reactions that is also efficient: it (a) uses only a single random number per simulation event, and (b) takes time proportional to the logarithm of the number of reactions, not to the number of reactions itself. The Next Reaction Method is extended to include timedependent rate constants and non-Markov processes and is applied to a sample application in biology (the lysis/lysogeny decision circuit of lambda phage). The performance of the Next Reaction Method on this application is compared with one standard method and an optimized version of that standard method. 1.
Keyphrases
efficient exact stochastic simulation many channel many specie chemical system next reaction method standard method exact numerical simulation method chemical equation lambda phage simulation event fundamental way master equation approach surface process complicated system differential equation exact algorithm multiple chemical specie small biological cell lysis lysogeny decision circuit coupled system sample application stochastic process small number optimized version non-markov process many reaction pathway single random number multiple reaction channel stochastic system coupled chemical reaction timedependent rate constant
