Analysis of a non-local and non-linear Fokker-Planck model for cell crawling migrationReport as inadecuate




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1 MAP5 - MAP5 - Mathématiques Appliquées à Paris 5 2 LM-Orsay - Laboratoire de Mathématiques d-Orsay 3 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

Abstract : Cell movement has essential functions in development, immunity and cancer. Various cell migration patterns have been reported and a general rule has recently emerged, the so-called UCSP Universal Coupling between cell Speed and cell Persistence, 30. This rule says that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to migration speed. In 30, the advection of polarity cues by a dynamic actin cytoskeleton undergoing flows at the cellular scale was proposed as a first explanation of this universal coupling. Here, following ideas proposed in 30, we present and study a simple model to describe motility initiation in crawling cells. It consists of a non-linear and non-local Fokker-Planck equation, with a coupling involving the trace value on the boundary. In the one-dimensional case we characterize the following behaviours: solutions are global if the mass is below the critical mass, and they can blow-up in finite time above the critical mass. In addition, we prove a quantitative convergence result using relative entropy techniques.

Keywords : asymptotic convergence Keller-Segel system. entropy method Cell polarisation global existence blow-up





Author: Christèle Etchegaray - Nicolas Meunier - Raphael Voituriez -

Source: https://hal.archives-ouvertes.fr/



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