Journal of Mathematical Biology

, Volume 65, Issue 3, pp 493–520 | Cite as

Multiscale stochastic modelling of gene expression

  • Pavol Bokes
  • John R. King
  • Andrew T. A. Wood
  • Matthew Loose


Stochastic phenomena in gene regulatory networks can be modelled by the chemical master equation for gene products such as mRNA and proteins. If some of these elements are present in significantly higher amounts than the rest, or if some of the reactions between these elements are substantially faster than others, it is often possible to reduce the master equation to a simpler problem using asymptotic methods. We present examples of such a procedure and analyse the relationship between the reduced models and the original.


Stochastic gene expression Master equation Singular perturbation methods System size expansion 

Mathematics Subject Classification (2000)

92C40 60J25 34E15 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Pavol Bokes
    • 1
    • 2
  • John R. King
    • 1
  • Andrew T. A. Wood
    • 1
  • Matthew Loose
    • 3
  1. 1.Centre for Mathematical Medicine and Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  2. 2.Department of Applied Mathematics and StatisticsComenius UniversityBratislavaSlovakia
  3. 3.Institute of Genetics, Queen’s Medical CentreUniversity of NottinghamNottinghamUK

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