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Multivariate normal approximation for the stochastic simulation algorithm: limit theorem and applications. (English) Zbl 1352.92067

Pauleve, Loic (ed.) et al., Post-proceedings of the 5th international workshop on static analysis and systems biology (SASB 2014), Munich, Germany, September 10, 2014. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 316, 67-82 (2015).
Summary: Stochastic approaches in systems biology are being used increasingly to model the heterogeneity and the intrinsic stochasticity of living systems, especially at the single-cell level. The stochastic simulation algorithm – also known as the Gillespie algorithm – is currently the most widely used method to simulate the time course of a system of bio-chemical reactions in a stochastic way. In this article, we present a central limit theorem for the Gillespie stochastic trajectories when the living system has reached a steady-state, that is when the internal bio-molecules concentrations are assumed to be at equilibrium. It appears that the stochastic behavior in steady-state is entirely characterized by the stoichiometry matrix of the system and a single vector of reaction probabilities. We propose several applications of this result such as deriving multivariate confidence regions for the time course of the system and a constraints-based approach which extends the flux balance analysis framework to the stochastic case.
For the entire collection see [Zbl 1329.92010].

MSC:

92C42 Systems biology, networks
60F05 Central limit and other weak theorems
60G50 Sums of independent random variables; random walks
62H99 Multivariate analysis
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