Modelling cell segregation and border sharpening between distinct cell populations: from microscopic to macroscopic models
The organisation of biological tissues during development is accompanied by the formation of sharp borders between distinct cell populations. The maintenance of this cell segregation is key in adult tissue homeostatis, and its disruption can lead tumor cells to spread and form metastasis. In this talk, we first present an agent-based model featuring two cell types, each cell being modelled as a point particle interacting with its close neighbors via local cross-links modeled by springs that are randomly created and destructed (inter- and intra- species interactions). We then derive a macroscopic model from the agent-based formulation. In the mean field limit, assuming large number of particles and links as well as propagation of chaos, the corresponding kinetic system consists of two equations for the individual particle distribution function and two equations for the link densities. In the large-scale limit and in the regime where link creation/destruction frequency is very large, the link density distributions become local functions of the particle distribution densities. The latter evolve through aggregation diffusion equations. By addressing the stability of a homogeneous distribution of particles for Hookean repulsive potentials, we obtain precise conditions for the phase transition, which link the system’s segregation ability to the model parameters and give further insight into the cell segregation processes.