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Singh, Abhyudai; Hespanha, João P.

Stochastic hybrid systems for studying biochemical processes. (English) Zbl 1211.37117

Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 368, No. 1930, 4995-5011 (2010).
Summary: Many protein and mRNA species occur at low molecular counts within cells, and hence are subject to large stochastic fluctuations in copy numbers over time. Development of computationally tractable frameworks for modelling stochastic fluctuations in population counts is essential to understand how noise at the cellular level affects biological function and phenotype. We show that stochastic hybrid systems (SHSs) provide a convenient framework for modelling the time evolution of population counts of different chemical species involved in a set of biochemical reactions. We illustrate recently developed techniques that allow fast computations of the statistical moments of the population count, without having to run computationally expensive Monte Carlo simulations of the biochemical reactions. Finally, we review different examples from the literature that illustrate the benefits of using SHSs for modelling biochemical processes.

Cited in 21 Documents

MSC:

37N25 Dynamical systems in biology
92C40 Biochemistry, molecular biology
34F05 Ordinary differential equations and systems with randomness
92E20 Classical flows, reactions, etc. in chemistry

Keywords:

stochastic hybrid systems; stochastic chemical kinetics; moment closure; gene regulatory networks; gene autoregulation; negative feedback

Software:

StochDynTools
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