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
Recommended Citation
Miller, Pearson W.; Fortunato, Daniel; Novaga, Matteo; Shvartsman, Stanislav Y.; and Muratov, Cyrill B., "Generation and Motion of Interfaces in a Mass-Conserving Reaction-Diffusion System" (2023). Faculty Publications. 2227.
https://digitalcommons.njit.edu/fac_pubs/2227