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 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.
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Published In
SIAM Journal on Applied Dynamical Systems
Pages: 2408 - 2431
DOI: 10.1137/22M152548X
ISSN (online): 1536-0040
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© 2023 Society for Industrial and Applied Mathematics.
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Submitted: 28 September 2022
Accepted: 10 May 2023
Published online: 14 August 2023
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