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Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

Gibson, Michael A. and Bruck, Jehoshua (2000) Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. Journal of Physical Chemistry A, 104 (9). pp. 1876-1889. ISSN 1089-5639. http://resolver.caltech.edu/CaltechAUTHORS:20170719-082029624

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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 time-dependent 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.


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http://dx.doi.org/10.1021/jp993732qDOIArticle
http://pubs.acs.org/doi/abs/10.1021/jp993732qPublisherArticle
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Additional Information:© 2000 American Chemical Society. Received 19 October 1999. Published online 15 February 2000. Published in print 1 March 2000. The authors thank Daniel Gillespie and Tau-Mu Yi for their careful reading of an earlier version of this paper. We also appreciate several comments from the anonymous reviewers that improved the clarity of this paper. Supported in part by ONR grant N00014-97-1-0293, by a JPL-CISM grant, by NSF Young Investigator Award CCR-9457811, and by a Sloan Research Fellowship.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-97-1-0293
NSFCCR-9457811
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20170719-082029624
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170719-082029624
Official Citation:Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels Michael A. Gibson and Jehoshua Bruck The Journal of Physical Chemistry A 2000 104 (9), 1876-1889 DOI: 10.1021/jp993732q
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79188
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:19 Jul 2017 16:44
Last Modified:19 Jul 2017 16:44

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