Cellular adhesions are one of the fundamental biological interactions between cells and their surroundings. However, the continuum modelling of cellular adhesions has remained mathematically challenging.
In 2006 Armstrong et al proposed a mathematical model in the form of an integro partial differential equation. This model was successful at replicating Steinbergs cell sorting experiments and since has been used in models of cancer invasion and morphogenesis.
In this talk we derive models of cell-cell adhesion from an underlying stochastic random walk. Through this derivation we are able to include micro biological properties in the model. It is shown that a particular choice of these properties yields the original Armstrong model.