What is it about?
The stationary or equilibrium state of a chemically reacting system is the state how the system stabilises after a longer time period. Computing this for stochastic models is only possible under special circumstances. We collected all methods we found in the literature which make this possible. Building on these, we compared the dose-response properties of four gene regulatory systems. We developed a delicate mathematical technique for computing a marginal distribution through summing a product-form distribution with conservation.
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Why is it important?
This paper is a treasure trove for anybody who wants to implement a stochastic simulation of a fast-slow chemical system and wants to use the quasi-steady-state assumption for the fast timescale to speed up the computation. This is underlined by over 11,800 recorded accesses on the publisher's website.
Perspectives
My paper with Peter Pfaffelhuber in Stochastic Models (The stationary distribution of a Markov jump process glued together from two state spaces at two vertices) is a pure theory paper motivated by the drive to extend these results.
Dr Bence Mélykúti
Albert-Ludwigs-Universitat Freiburg
Read the Original
This page is a summary of: Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks, Journal of The Royal Society Interface, June 2014, Royal Society Publishing,
DOI: 10.1098/rsif.2014.0054.
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Contributors
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