Generation and motion of interfaces in a mass-conserving reaction-diffusion system
Abstract
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is analyzed in the limit of slow surface diffusion. Using the tools of formal asymptotics and calculus of variations, we study the characteristic wave-pinning behavior of this system on three dynamical timescales. On the short timescale, generation of an interface separating high- and low-concentration domains is established under suitable conditions. Intermediate timescale dynamics is shown to lead to a uniform growth or shrinking of these domains to sizes which are fixed by global parameters. Finally, the long time dynamics reduces to area-preserving geodesic curvature flow that may lead to multi-interface steady state solutions. These results provide a foundation for studying cell polarization and related phenomena in biologically relevant geometries.
Cite
@article{arxiv.2210.00585,
title = {Generation and motion of interfaces in a mass-conserving reaction-diffusion system},
author = {Pearson W. Miller and Daniel Fortunato and Matteo Novaga and Stanislav Y. Shvartsman and Cyrill B. Muratov},
journal= {arXiv preprint arXiv:2210.00585},
year = {2022}
}