Bulletin of Mathematical Biology

, Volume 75, Issue 2, pp 351–371 | Cite as

Transcriptional Bursting Diversifies the Behaviour of a Toggle Switch: Hybrid Simulation of Stochastic Gene Expression

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


Hybrid models for gene expression combine stochastic and deterministic representations of the underlying biophysical mechanisms. According to one of the simplest hybrid formalisms, protein molecules are produced in randomly occurring bursts of a randomly distributed size while they are degraded deterministically. Here, we use this particular formalism to study two key regulatory motifs—the autoregulation loop and the toggle switch. The distribution of burst times is determined and used as a basis for the development of exact simulation algorithms for gene expression dynamics. For the autoregulation loop, the simulations are compared to an analytic solution of a master equation. Simulations of the toggle switch reveal a number of qualitatively distinct scenarios with implications for the modelling of cell-fate selection.


Gene expression Stochastic hybrid models 



P. Bokes was supported by the European Commission under Marie Curie Early Stage Researcher Training (contract no. MEST-CT-2005-020723) and also by the Slovak Research and Development Agency (contract no. APVV-0134-10). J. King gratefully acknowledges the funding of the BBSRC/EPSRC (reference no. BB/D008522/1) and of the Royal Society and Wolfson Foundation.


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Copyright information

© Society for Mathematical Biology 2013

Authors and Affiliations

  • Pavol Bokes
    • 1
  • John R. King
    • 2
  • Andrew T. A. Wood
    • 2
  • Matthew Loose
    • 3
  1. 1.Department of Applied Mathematics and StatisticsComenius UniversityBratislavaSlovakia
  2. 2.Centre for Mathematical Medicine and Biology, School of Mathematical SciencesUniversity of NottinghamNottinghamUK
  3. 3.Institute of Genetics, Queen’s Medical CentreUniversity of NottinghamNottinghamUK

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