A moment closure method for stochastic reaction networks

Chang Hyeong Lee, Kyeong Hun Kim, Pilwon Kim

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82 Citations (Scopus)


In this paper we present a moment closure method for stochastically modeled chemical or biochemical reaction networks. We derive a system of differential equations which describes the dynamics of means and all central moments from a chemical master equation. Truncating the system for the central moments at a certain moment term and using Taylor approximation, we obtain explicit representations of means and covariances and even higher central moments in recursive forms. This enables us to deal with the moments in successive differential equations and use conventional numerical methods for their approximations. Furthermore, we estimate the errors in the means and central moments generated by the approximation method. We also find the moments at equilibrium by solving truncated algebraic equations. We show in examples that numerical solutions based on the moment closure method are accurate and efficient by comparing the results to those of stochastic simulation algorithms.

Original languageEnglish
Article number134107
JournalJournal of Chemical Physics
Issue number13
Publication statusPublished - 2009

Bibliographical note

Funding Information:
C.H.L. would like to thank Professor Hans G. Othmer and Professor Roger Lui for early discussions on this subject. K.-H.K. would like to acknowledge that this work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MEST) (Grant No. R01-2008-000-20010-0).

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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