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

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Abstract

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.

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Notes

  1. Alternatively, n>0 could be required in place of a 1>0, with a 1<0 corresponding to positive feedback.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Comenius University, Mlynská dolina, Bratislava, 842 48, Slovakia

    Pavol Bokes

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

    John R. King & Andrew T. A. Wood

  3. 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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Correspondence to Pavol Bokes.

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Bokes, P., King, J.R., Wood, A.T.A. et al. Transcriptional Bursting Diversifies the Behaviour of a Toggle Switch: Hybrid Simulation of Stochastic Gene Expression. Bull Math Biol 75, 351–371 (2013). https://doi.org/10.1007/s11538-013-9811-z

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  • DOI: https://doi.org/10.1007/s11538-013-9811-z

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