Comptes Rendus
no. 10
Partial differential equations
Phase-field model of cell motility: Traveling waves and sharp interface limit
[Modèle de champ de phase pour la migration cellulaire : ondes progressives et limite de type interface mince]

Présenté par : Haïm Brézis

Leonid Berlyand1 ; Mykhailo Potomkin1 ; Volodymyr Rybalko2
1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
2 Mathematical Division, B. Verkin Institute for Low Temperature, Physics and Engineering of National Academy of Sciences of Ukraine, 47 Nauka Ave., 61103, Kharkiv, Ukraine
Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 986-992.

Nous présentons dans cet article des résultats récents sur l'analyse asymptotique d'un modèle EDP pour la migration de cellules eucaryotes. Nous dérivons formellement l'équation limite pour l'interface, qui décrit le mouvement de la membrane cellulaire. Dans le cas unidimensionnel, nous justifions cette limite de façon rigoureuse, et nous observons numériquement quelques propriétés surprenantes, comme par exemple une discontinuité dans les vitesses à l'interface et un phénomène d'hystérésis. Nous montrons l'apparition d'ondes de propagation non triviales quand le paramètre physique clé dépasse un certain seuil.

In this paper, we report our recent results on the asymptotic analysis of a PDE model for the motility of an eukaryotic cell. We formally derive the sharp interface limit, which describes the motion of the cell membrane. In the 1D case, we rigorously justify the limit, and, using numerical simulations, observe some surprising features, such as discontinuity of interface velocities and hysteresis. We show that nontrivial traveling wave solutions appear when the key physical parameter exceeds a critical value.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.09.001

Leonid Berlyand 1 ; Mykhailo Potomkin 1 ; Volodymyr Rybalko 2

1 Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
2 Mathematical Division, B. Verkin Institute for Low Temperature, Physics and Engineering of National Academy of Sciences of Ukraine, 47 Nauka Ave., 61103, Kharkiv, Ukraine 
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Leonid Berlyand; Mykhailo Potomkin; Volodymyr Rybalko. Phase-field model of cell motility: Traveling waves and sharp interface limit. Comptes Rendus. Mathématique, Volume 354 (2016) no. 10, pp. 986-992. doi : 10.1016/j.crma.2016.09.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.09.001/

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