Transcriptional Bursting Diversifies the Behaviour of a Toggle Switch: Hybrid Simulation of Stochastic Gene Expression
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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.
KeywordsGene 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.
- Alon, U. (2007). An introduction to systems biology: design principles of biological circuits. London: Chapman & Hall/CRC. Google Scholar
- Andrecut, M., & Kauffman, S. A. (2006). Noise in genetic toggle switch models. J. Int. Bioinform, 23. Google Scholar
- Bokes, P. (2010). Genetic regulatory networks. PhD thesis, University of Nottingham. Google Scholar
- Bokes, P., King, J. R., Wood, A. T. A., & Loose, M. (2012). Multiscale stochastic modelling of gene expression. J. Math. Biol. Google Scholar
- Cox, D. R., & Oakes, D. (1984). Analysis of survival data. Boca Raton: Chapman & Hall/CRC. Google Scholar
- Keener, J., & Sneyd, J. (2008). Mathematical physiology: cellular physiology. Berlin: Springer. Google Scholar
- Lei, J., Mackey, M. C., Yvinec, R., & Zhuge, C. (2012). Adiabatic reduction of a piecewise deterministic Markov model of stochastic gene expression with bursting transcription. arXiv:1202.5411.
- Newby, J. M. (2011). Isolating intrinsic noise sources in a stochastic genetic switch. arXiv:1111.1415.
- van Kampen, N. G. (2006). Stochastic processes in physics and chemistry. Amsterdam: Elsevier. Google Scholar