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arXiv · 2210.00585

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
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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.

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Pearson W. Miller, Daniel Fortunato, Matteo Novaga, Stanislav Y. Shvartsman, Cyrill B. Muratov. 2022-10-02. Generation and motion of interfaces in a mass-conserving reaction-diffusion system. https://arxiv.org/abs/2210.00585

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