Appears in collection : 2022 - T1 - WS1 - Tissue growth and movement

In this talk, I will present a deterministic model of single-cell migration based on a fluid description of the intracellular actin cytoskeleton, and on its interaction with a molecular specie. The problem writes as a reaction-advection-diffusion for the molecular dynamics, and a Darcy law coupled with a Poisson problem for the fluid. A Dirichlet boundary condition on the fluid pressure accounts for both the molecular regulation and the active behavior of the cytoskeleton. The model accounts for both static and motile behaviors, as shown from mathematical analysis and numerical simulations. Furthermore, by adding stochastic fluctuations in the molecular advection term, the model provides numerical trajectories that share key-properties with their experimental counterparts. This is a joint work with Nicolas Meunier (LaMME, Évry) and Raphaël Voituriez (LJP, LPTMC, Sorbonne université).