Modelling adhesion-independent cell migration

Gaspard Jankowiak (1) , Diane Peurichard (2, 3) , Anne Reversat (4) , Christian Schmeiser (5) , Michael Sixt (4)

1 RICAM - Johann Radon Institute for Computational and Applied Mathematics
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]
5 Fakultät für Mathematik [Wien]

A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net polymerization or depoly-merization in the cortex is modelled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility.

Mots clés: Weak solutions; Cell motility modelling; Cellular cortex; Variational methods; Actin polymerization

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Gaspard Jankowiak, Diane Peurichard, Anne Reversat, Christian Schmeiser, Michael Sixt. Modelling adhesion-independent cell migration. Mathematical Models and Methods in Applied Sciences, In press, ⟨10.1142/S021820252050013X⟩. ⟨hal-02076901v2⟩