Dresden 2020 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 57: Poster: Statistical Physics; Critical Phenomena; Stochastic Thermodynamics; Extreme Events; Data Analytics
DY 57.6: Poster
Thursday, March 19, 2020, 15:00–18:00, P1C
Capturing large fluctuations in the dynamics of biochemical reaction networks — •Maximilian Kurjahn1, Ander Movilla2, and Peter Sollich1,2 — 1University of Göttingen, Institute for Theoretical Physics, 37077 Göttingen, Germany — 2Department of Mathematics, King's College London, Strand, London WC2R 2LS, UK
Biological systems such as gene expression and metabolism can often be described by chemical reaction networks. Their dynamics is governed by a chemical master equation that cannot be solved analytically, so approximations are necessary. Standard approaches such as the linear noise approximation predict Gaussian fluctuations into the unphysical regime of negative concentrations, particularly when small mean molecule numbers lead to large fluctuations.
We present an alternative approach that works with Poisson fluctuations and is based on a Doi-Peliti coherent state path integral representation of the dynamics. To this we apply the Plefka expansion, a systematic approximation technique from the physics of glasses.
Up to first order the standard mass action kinetics are recovered that describe the dynamics for large molecule numbers. An accurate description in the large fluctuation regime of low copy numbers is obtained by a second order Plefka expansion. The method can be taken further by constraining as order parameters not just first moments but also second moments, i.e. time correlations.
We demonstrate the approach on simple but paradigmatic reaction networks from systems biology, comparing with the results of mass action kinetics and full stochastic simulations.