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Journal of Mathematical Biology

, Volume 64, Issue 5, pp 829–854 | Cite as

Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression

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

Abstract

Gene expression at the single-cell level incorporates reaction mechanisms which are intrinsically stochastic as they involve molecular species present at low copy numbers. The dynamics of these mechanisms can be described quantitatively using stochastic master-equation modelling; in this paper we study a generic gene-expression model of this kind which explicitly includes the representations of the processes of transcription and translation. For this model we determine the generating function of the steady-state distribution of mRNA and protein counts and characterise the underlying probability law using a combination of analytic, asymptotic and numerical approaches, finding that the distribution may assume a number of qualitatively distinct forms. The results of the analysis are suitable for comparison with single-molecule resolution gene-expression data emerging from recent experimental studies.

Keywords

Stochastic modelling Gene expression Master equation Generating function 

Mathematics Subject Classification (2000)

92C40 60J27 

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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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