Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries

TL;DR

This paper introduces a particle-based simulation algorithm for stochastic reaction-diffusion systems within moving cellular boundaries, revealing effects like superdiffusion and altered reaction rates that are often overlooked.

Contribution

The authors develop an intuitive algorithm for simulating diffusion on moving boundaries, validated against PDE solutions, and demonstrate its impact on reaction dynamics in dividing cells.

Findings

Moving boundaries induce superdiffusive motion.

Reaction rates become time-inhomogeneous due to boundary movement.

Simulations show significant effects in dividing yeast cells.

Abstract

Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and can highly bias conclusions from simulation studies. In this work, we present an intuitive algorithm for particle-based diffusion in and on moving boundaries, for both point particles and spherical particles. We first benchmark in appropriate scenarios our proposed stochastic method against solutions of partial differential equations, and further demonstrate that moving boundaries can give rise to super diffusive motion as well as time-inhomogeneous reaction rates. Finally, we conduct a numerical experiment representing photobleaching of diffusing fluorescent proteins in dividing Saccharomyces cerevisiae cells to demonstrate that moving boundaries might cause important effects neglected in previously published studies.