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

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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.

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Author notes

  1. Pavol Bokes

    Present address: Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, Bratislava, 842 48, Slovakia

Authors and Affiliations

  1. Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK

    Pavol Bokes, John R. King & Andrew T. A. Wood

  2. Institute of Genetics, Queen’s Medical Centre, University of Nottingham, Nottingham, NG7 2UH, UK

    Matthew Loose

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  1. Pavol Bokes
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  2. John R. King
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  3. Andrew T. A. Wood
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  4. Matthew Loose
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Correspondence to Pavol Bokes.

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Bokes, P., King, J.R., Wood, A.T.A. et al. Exact and approximate distributions of protein and mRNA levels in the low-copy regime of gene expression. J. Math. Biol. 64, 829–854 (2012). https://doi.org/10.1007/s00285-011-0433-5

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  • DOI: https://doi.org/10.1007/s00285-011-0433-5

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