Bulletin of Mathematical Biology

, Volume 78, Issue 1, pp 110–131 | Cite as

Protein Synthesis Driven by Dynamical Stochastic Transcription

  • Guilherme C. P. InnocentiniEmail author
  • Michael Forger
  • Ovidiu Radulescu
  • Fernando Antoneli
Original Article


In this manuscript, we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations, while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time-dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.


Gene expression Stochasticity Exact solutions  Dynamics 

Mathematics Subject Classification




We would like to thank the referees for their insights. Work supported by FAPESP, SP, Brazil (G. I., contract 2012/04723-4) and CNPq, Brazil (G. I., contract 202238/2014-8; M. F., contract 307238/2011-3; F. A., contract 306362/2012-0). O. R. thanks CNRS and LABEX Epigenmed for support.


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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  • Guilherme C. P. Innocentini
    • 1
    • 2
    Email author
  • Michael Forger
    • 1
  • Ovidiu Radulescu
    • 2
  • Fernando Antoneli
    • 3
  1. 1.Departamento de Matemática Aplicada, Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil
  2. 2.DIMNP, UMR 5235Université de Montpellier 2Montpellier Cedex 5France
  3. 3.Laboratório de Genômica Evolutiva e Biocomplexidade & DISEscola Paulista de Medicina, Universidade Federal de São PauloSão PauloBrazil

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