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bioRxiv · 10.1101/360123

Stationary Equations for Non-Markovian Biochemical Systems

Zhang, J.·Zhou, T.
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Abstract

We develop a new approach for stochastic analysis of biochemical reaction systems with arbitrary distributions of waiting times between reaction events. Specifically, we derive a stationary generalized chemical master equation for a non-Markovian reaction network. Importantly, this equation allows to transform the original non-Markovian problem into a Markovian one by introducing a mean reaction propensity function for every reaction in the network. Furthermore, we derive a stationary generalized linear noise approximation for the non-Markovian system, which is convenient to the direct estimation of the stationary noise in state variables. These derived equations can have broad applications, and exemplars of two representative non-Markovian models provide evidence of their applicability.

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Zhang, J., Zhou, T.. 2018-07-03. Stationary Equations for Non-Markovian Biochemical Systems. https://doi.org/10.1101/360123

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