A continuum approach to modelling cell-cell adhesion.

Cells adhere to each other through the binding of cell adhesion molecules at the cell surface. This process, known as cell-cell adhesion, is fundamental in many areas of biology, including early embryo development, tissue homeostasis and tumour growth. In this paper we develop a new continuous mathematical model of this phenomenon by considering the movement of cells in response to the adhesive forces generated through binding. We demonstrate that our model predicts the aggregation behaviour of a disassociated adhesive cell population. Further, when the model is extended to represent the interactions between multiple populations, we demonstrate that it is capable of replicating the different types of cell sorting behaviour observed experimentally. The resulting pattern formation is a direct consequence of the relative strengths of self-population and cross-population adhesive bonds in the model. While cell sorting behaviour has been captured previously with discrete approaches, it has not, until now, been observed with a fully continuous model.