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

Pearson W. Miller, Daniel Fortunato, Matteo Novaga, Stanislav Y. Shvartsman, Cyrill B. Muratov

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)2408-2431
Number of pages24
JournalSIAM Journal on Applied Dynamical Systems
Volume22
Issue number3
DOIs
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation

Keywords

  • Laplace-Beltrami operator
  • long-time behavior
  • pattern formation
  • reaction-diffusion
  • singular perturbations

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