BPCPPDYSOE21 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 9: Statistical Physics 2 - organized by Barbara Drossel (Darmstadt), Sabine Klapp (Berlin) und Thomas Speck (Mainz)

DY 9.1: Vortrag

Montag, 22. März 2021, 11:00–11:20, DYb

Path integral approach to strong fluctuations in chemical reaction network dynamics using the Plefka expansion — •Moshir Harsh and Peter Sollich — Institut für Theoretische Physik, Georg-August-Universität, Göttingen, Germany

Biochemical reaction networks such as gene regulation, protein interaction and signalling pathways involve the participation of just a few copies of some key molecular species. With the advent of modern capabilities in live quantitative fluorescence microscopy and spectroscopy, the dynamics of a number of molecular species in these networks can be observed experimentally. However, inferring dynamical parameters from such data remains a challenge as the trajectories of low copy number species show large fluctuations, causing approximate approaches like the Fokker-Planck equation and moment closure to fail in this regime, while the in principle exact master equation has no general analytical solution.

Here we present an alternative method based on constructing the path integral for the dynamics of a generic reaction network, which is then treated within a Gaussian approximation by constraining the first and the second order statistics of the field variables using the systematic Plefka expansion of the dynamical free energy. We develop the method to treat any system of reactions in full generality and show its applicability and accuracy across a range of example systems. The approximate path integral can also form the basis for making inferences from experimentally measured dynamics.