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.
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https://hal.archives-ouvertes.fr/hal-01437108
Contributor : Christèle Etchegaray <>
Submitted on : Thursday, December 12, 2019 - 2:02:09 PM
Last modification on : Monday, January 13, 2020 - 1:12:12 AM

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  • HAL Id : hal-01437108, version 2
  • ARXIV : 1701.06862

Citation

Christèle Etchegaray, Nicolas Meunier, Raphael Voituriez. Analysis of a non-local and non-linear Fokker-Planck model for cell crawling migration. 2016. ⟨hal-01437108v2⟩

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