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Multimodality and Flexibility of Stochastic Gene Expression

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Abstract

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

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Acknowledgements

Work supported by FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo, Brazil) and by the USP-COFECUB 2008-2012 program.

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Authors and Affiliations

  1. Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, Cidade Universitária, São Paulo, SP, Brazil, CEP: 05508-090

    Guilherme da Costa Pereira Innocentini & Michael Forger

  2. Escola de Artes, Ciências e Humanidades, Universidade de São Paulo, Av. Arlindo Béttio, 1000, Ermelino Matarazzo, São Paulo, SP, Brazil, CEP: 03828-000

    Alexandre Ferreira Ramos

  3. IMNP, UMR 5235, Université de Montpellier 2, Pl. E. Bataillon, Bat. 24, 34095, Montpellier Cedex 5, France

    Ovidiu Radulescu

  4. Instituto de Física de São Carlos, Universidade de São Paulo, Av. Trabalhador São-Carlense, 400, São Carlos, SP, Brazil, CEP: 13566-590

    José Eduardo Martinho Hornos

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  1. Guilherme da Costa Pereira Innocentini
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  2. Michael Forger
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  3. Alexandre Ferreira Ramos
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Correspondence to Guilherme da Costa Pereira Innocentini.

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Innocentini, G.d.C.P., Forger, M., Ramos, A.F. et al. Multimodality and Flexibility of Stochastic Gene Expression. Bull Math Biol 75, 2600–2630 (2013). https://doi.org/10.1007/s11538-013-9909-3

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  • DOI: https://doi.org/10.1007/s11538-013-9909-3

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