Analysis of a non-local and non-linear Fokker-Planck model for cell crawling migration

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.
Type de document :
Pré-publication, Document de travail
2016
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Dernière modification le : mardi 10 octobre 2017 - 11:22:05
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  • HAL Id : hal-01437108, version 1
  • ARXIV : 1701.06862

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Christèle Etchegaray, Nicolas Meunier, Raphael Voituriez. Analysis of a non-local and non-linear Fokker-Planck model for cell crawling migration. 2016. 〈hal-01437108〉

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