Modeling stochasticity in biochemical reaction networks

P. H. Constantino, M. Vlysidis, P. Smadbeck, Y. N. Kaznessis

Research output: Contribution to journalReview articlepeer-review

8 Scopus citations


Small biomolecular systems are inherently stochastic. Indeed, fluctuations of molecular species are substantial in living organisms and may result in significant variation in cellular phenotypes. The chemical master equation (CME) is the most detailed mathematical model that can describe stochastic behaviors. However, because of its complexity the CME has been solved for only few, very small reaction networks. As a result, the contribution of CME-based approaches to biology has been very limited. In this review we discuss the approach of solving CME by a set of differential equations of probability moments, called moment equations. We present different approaches to produce and to solve these equations, emphasizing the use of factorial moments and the zero information entropy closure scheme. We also provide information on the stability analysis of stochastic systems. Finally, we speculate on the utility of CME-based modeling formalisms, especially in the context of synthetic biology efforts.

Original languageEnglish (US)
Article number093001
JournalJournal of Physics D: Applied Physics
Issue number9
StatePublished - Feb 1 2016

Bibliographical note

Publisher Copyright:
© 2016 IOP Publishing Ltd.


  • biological systems
  • modeling
  • stochastic


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