Bulletin of Mathematical Biology

, Volume 75, Issue 12, pp 2600–2630 | Cite as

Multimodality and Flexibility of Stochastic Gene Expression

  • Guilherme da Costa Pereira InnocentiniEmail author
  • Michael Forger
  • Alexandre Ferreira Ramos
  • Ovidiu Radulescu
  • José Eduardo Martinho Hornos
Original Article


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.


Gene expression Stochasticity Noise reduction 



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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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Guilherme da Costa Pereira Innocentini
    • 1
    Email author
  • Michael Forger
    • 1
  • Alexandre Ferreira Ramos
    • 2
  • Ovidiu Radulescu
    • 3
  • José Eduardo Martinho Hornos
    • 4
  1. 1.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.Escola de Artes, Ciências e HumanidadesUniversidade de São PauloSão PauloBrazil
  3. 3.IMNP, UMR 5235Université de Montpellier 2Montpellier Cedex 5France
  4. 4.Instituto de Física de São CarlosUniversidade de São PauloSão CarlosBrazil

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