Adhesion-driven patterning in collective cell behaviour

Cellular adhesion is a fundamental mechanism underlying diverse collective cell behaviours, from tissue self-organisation in developmental biology to the formation of directional queues that guide cell migration. Modelling such interactions has also proven mathematically rich, motivating the use of continuum partial differential equation models that capture adhesion through nonlocal interaction kernels. These models can, for instance, reproduce classical cell-sorting patterns arising from differential adhesion in mixtures of cell populations. In this talk, we briefly review such models and explain how a local approximation of nonlocal aggregation–diffusion equations can be derived in the limit of short-range interactions. We then discuss recent advances in the field and highlight new results on pattern formation driven by adhesive interactions in migrating and proliferating cell populations, as well as in systems of nonreciprocally interacting cells.