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Nonlinear Langevin model with product stochasticity for biological networks: The case of the Schnakenberg model

Journal of Systems Science and Complexity volume 23, pages 896–905 (2010)Cite this article

Abstract

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. This paper studies the simple Schnakenberg model consisting of three reversible reactions and two molecular species whose concentrations vary. To reduce the residual errors from the conventional formulation of the Langevin equation, the authors propose to explicitly model the effective coupling between macroscopic concentrations of different molecular species. The results show that this formulation is effective in correcting residual errors from the original uncoupled Langevin equation and can approximate the underlying chemical master equation very accurately.

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Author information

Affiliations

  1. Ministry of Education Key Laboratory of Systems Biomedicine, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai, 200240, China

    Youfang Cao & Jie Liang

  2. Department of Bioengineering, University of Illinois at Chicago, Chicago, USA

    Youfang Cao & Jie Liang

Authors
  1. Youfang Cao
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  2. Jie Liang
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Corresponding author

Correspondence to Youfang Cao.

Additional information

The research is supported by phase II 985 Project under Grant No. T226208001, NIH under Grant No. GM079804-01A1 and GM081682, NSF under Grant No. DBI-0646035 and DMS-0800257, and ONR under Grant No. N00014-09-1-0028.

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Cao, Y., Liang, J. Nonlinear Langevin model with product stochasticity for biological networks: The case of the Schnakenberg model. J Syst Sci Complex 23, 896–905 (2010). https://doi.org/10.1007/s11424-010-0213-0

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  • DOI: https://doi.org/10.1007/s11424-010-0213-0

Key words

  • Langevin equation
  • master equation
  • noise
  • Schnakenberg model