Abstract

Cell migration and adhesion are essential processes that take place during development. Cells migrate to their target sites, and cell-to-cell adhesion enables cells to aggregate and form cohesive tissues. Both are crucial, not only for the proper development of the body structure and organs, but also for tissue homeostasis and repair, and for the invasion of cancerous tumours. Mathematical modelling and numerical simulation provides a means to explore current hypotheses for the roles of migration and adhesion: to put them into a concrete framework where they may be tested and refined, and experimentally testable predictions made.

We consider a one-dimensional stochastic, lattice-based model of cell-to-cell adhesion. We examine behaviour at the mesoscopic individual cell level, but also look at the average macroscopic behaviour of the system. We also consider how to implement this model on a growing domain (as in development) – finding that the traditional box-splitting method for domain growth presents several problems, we develop our own growth simulation method.