Regensburg 2022 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 28: Extreme Events, Glasses and Miscellaneous

DY 28.7: Vortrag

Mittwoch, 7. September 2022, 12:45–13:00, H19

Accurate dynamics from memory in chemical reactions with small copy numbers — •Moshir Harsh and Peter Sollich — Institut für Theoretische Physik, Georg-August-Universität Göttingen

Chemical reactions in the regime of small copy numbers of species such as gene regulation or protein interaction networks show large fluctuations, making mean field solutions as given by mass action kinetics unreliable. Accurate calculations of the one and two-time quantities of these stochastic processes remain a challenging problem; numerical solutions to the master equation or stochastic simulations can be deployed, but these are computationally intensive and do not allow likelihood inference from dynamical trajectories.

Here, we present a method that captures the fluctuations beyond mean field using self-consistently determined memory: by integrating information from the past we can systematically improve our approximation for the dynamics of chemical reactions. This memory is not added ad-hoc, but can be shown to arise naturally by considering the effective action of the Doi-Peliti field theory of chemical reactions. The effective action is treated perturbatively but we can self-consistently resum a very large class of diagrams resulting in a stable expansion. We demonstrate this method and its accuracy on single and multi-species binary reactions across a range of parameter values. We show how this approach also opens a route to making inferences from experimentally measured dynamics.