BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:The system-size expansion of the chemical master equation: develop ments in the past 5 years - Ramon Grima (University of Edinburgh) DTSTART:20160408T104500Z DTEND:20160408T113000Z UID:TALK65301@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Co-author: Philipp Thomas (Imperial College London)
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The system-size expansion of the master equation\, first d eveloped by van Kampen\, is a well known approximation technique for deter ministically monostable systems. Its use has been mostly restricted to the lowest order terms of this expansion which lead to the deterministic rate equations and the linear-noise approximation (LNA). I will here describe recent developments concerning the system-size expansion\, including (i) i ts use to obtain a general non-Gaussian expression for the probability dis tribution solution of the chemical master equation\; (ii) clarification of the meaning of higher-order terms beyond the LNA and their use in stochas tic models of intracellular biochemistry\; (iii) the convergence of the ex pansion\, at a fixed system-size\, as one considers an increasing number o f terms\; (iv) extension of the expansion to describe gene-regulatory syst ems which exhibit noise-induced multimodality\; (v) the conditions under w hich the LNA is exact up to second-order moments\; (v i) the relationship between the system-size expansion\, the chemical Fokker-Planck equation an d moment-closure approximations.

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