"Generation and Motion of Interfaces in a Mass-Conserving Reaction-Diff" by Pearson W. Miller, Daniel Fortunato et al.
 

Generation and Motion of Interfaces in a Mass-Conserving Reaction-Diffusion System

Document Type

Article

Publication Date

1-1-2023

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 are shown to lead to a uniform growth or shrinking of these domains to sizes that are fixed by global parameters. Finally, the long timescale dynamics reduce 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.

Identifier

85173527148 (Scopus)

Publication Title

SIAM Journal on Applied Dynamical Systems

External Full Text Location

https://doi.org/10.1137/22M152548X

e-ISSN

15360040

First Page

2408

Last Page

2431

Issue

3

Volume

22

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