Waves in a Stochastic Cell Motility Model

TL;DR

This paper derives and analyzes a mesoscopic stochastic reaction-diffusion model for actin wave dynamics in cells, showing it better captures microscopic behavior than deterministic models and aids understanding of experimental observations.

Contribution

The work introduces a mesoscopic stochastic model (Chemical Langevin Equation) for cell actin waves, bridging microscopic and macroscopic descriptions with improved analytical and simulation capabilities.

Findings

Stochastic patterns from the model align with experimental actin wave dynamics.

The mesoscopic model captures microscopic behavior more accurately than deterministic equations.

The approach facilitates mathematical analysis and numerical simulations of cellular wave phenomena.

Abstract

In Bhattacharya et al. (Science Advances, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied. Both at the microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reaction-diffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction-diffusion system, or Chemical Langevin Equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction-diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.