A Cahn--Hilliard Model for Cell Motility
| Autor: | Antoine Mellet, Nicolas Meunier, Alessandro Cucchi |
|---|---|
| Přispěvatelé: | Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), University of Maryland [College Park], University of Maryland System, Laboratoire de Mathématiques et Modélisation d'Evry (LaMME), Université d'Évry-Val-d'Essonne (UEVE)-ENSIIE-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE) |
| Rok vydání: | 2020 |
| Předmět: |
Interface model
Applied Mathematics Mathematical analysis Motility sharp interface limit 01 natural sciences Quantitative Biology::Cell Behavior 010101 applied mathematics Computational Mathematics Dimension (vector space) hysteresis phenomena Sharp interface nonlinear fourth order parabolic equations Limit (mathematics) [MATH]Mathematics [math] 0101 mathematics Cahn-Hilliard equations Hele-Shaw free boundary problems Analysis Mathematics |
| Zdroj: | SIAM Journal on Mathematical Analysis SIAM Journal on Mathematical Analysis, 2020, 52 (4), pp.3843-3880. ⟨10.1137/19M1267969⟩ |
| ISSN: | 1095-7154 0036-1410 |
| DOI: | 10.1137/19m1267969 |
| Popis: | International audience; We introduce and study a diffuse interface model describing cell motility. We provide a detailed rigorous analysis of the model in dimension 1 and formally derive the sharp interface limit in any dimension. The model integrates the most important physical processes involved in cell motility, such as incompressibility, internal stresses exerted by the cytoskeleton seen as an active gel, and dynamic contact lines. The resulting nonlinear system couples a degenerate fourth order parabolic equation of Cahn-Hilliard type for the phase variable with a convection-reaction-diffusion equation for the active potential. The sharp interface limit leads to a Hele-Shaw type free boundary problem which includes the effects of surface tension and an additional destabilizing term at the free boundary. This additional term can be seen as a nonlinear Robin type boundary condition with the "wrong" sign. Such a boundary condition reflects the active nature of the cell, e.g., protrusion formation. We rigorously investigate the properties of this model in one dimension and prove the appearance of nontrivial traveling wave solutions for the limit problem when the key physical parameter exceeds a certain critical value. Although minimal, this new Hele-Shaw model, with Robin's unconventional boundary condition, is rich enough to describe the universal property of migrating cells that has been recently described by various theoretical biophysical models. |
| Databáze: | OpenAIRE |
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