Free boundary problem for cell protrusion formations: theoretical and numerical aspects - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Mathematical Biology Year : 2016

Free boundary problem for cell protrusion formations: theoretical and numerical aspects

Abstract

In this paper, a free boundary problem for cell protrusion formation is studied theoretically and numerically. The cell membrane is precisely described thanks to a level set function, whose motion is due to specific signalling pathways. The aim is to model the chemical interactions between the cell and its environment, in the process of invadopodia or pseudopodia formation. The model consists of Laplace equation with Dirichlet condition inside the cell coupled to Laplace equation with Neumann condition in the outer domain. The actin polymerization is accounted for as the gradient of the inner signal, which drives the motion of the interface. We prove the well-posedness of our free boundary problem under a sign condition on the datum. This criterion ensures the consistency of the model, and provides conditions to focus on for any enrichment of the model. We then propose a new first order Cartesian finite-difference method to solve the problem. We eventually exhibit the main biological features that can be accounted for by the model: the formation of thin and elongated protrusions as for invadopodia, or larger protrusion as for pseudopodia, depending on the source term in the equation. The model provides the theoretical and numerical grounds for single cell migration modeling, whose formulation is valid in 2D and 3D. In particular, specific chemical reactions that occured at the cell membrane could be precisely described in forthcoming works.
Fichier principal
Vignette du fichier
subm_paperJMB-v2-R1.pdf (15.26 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01412264 , version 1 (08-12-2016)

Identifiers

Cite

Olivier Gallinato, Masahito Ohta, Clair Poignard, Takashi Suzuki. Free boundary problem for cell protrusion formations: theoretical and numerical aspects. Journal of Mathematical Biology, 2016, ⟨10.1007/s00285-016-1080-7⟩. ⟨hal-01412264⟩
247 View
115 Download

Altmetric

Share

Gmail Facebook X LinkedIn More