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.
Keywords
Cite
@article{arxiv.1701.06862,
title = {Analysis of a non-local and non-linear Fokker-Planck model for cell crawling migration},
author = {Christèle Etchegaray and Nicolas Meunier and Raphael Voituriez},
journal= {arXiv preprint arXiv:1701.06862},
year = {2019}
}