Nonlocal models of cell-cell adhesion and their Cahn-Hilliard approximation #

Carles Falcó, Ruth E Baker, José A Carrillo

15:10 Monday in 2Q49.

Part of the Dynamics of reaction-transport systems session.

Abstract #

Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes. Adhesive forces are highly linked to the cell geometry and often, continuum models represent these by nonlocal attractive interactions. In this talk, I will explain how such models can be approximated by Cahn-Hilliard type equations in the limit of short-range interactions. The resulting model is local, resembling a thin-film type equation, and numerical simulations in one and two dimensions reveal that it still shows the diversity of patterns observed both in experiments and in previously used nonlocal models. In addition, it also has the advantage of having explicit stationary solutions, which provides a direct link between the model parameters and the differential adhesion hypothesis.