Continuous models for cell-cell adhesion.

Cell adhesion is the binding of a cell to another cell or to an extracellular matrix component. This process is essential in organ formation during embryonic development and in maintaining multicellular structure. Armstrong et al. (2006) [J. Theor. Biol. 243, pp. 98-113] proposed a nonlocal advection-diffusion system as a possible continuous mathematical model for cell-cell adhesion. Although the system is attractive and challenging, it gives biologically unrealistic numerical solutions under certain situations. We identify the problems and change underlying idea of cell movement from "cells move randomly" to "cells move from high to low pressure regions". Then we provide a modified continuous model for cell-cell adhesion. Numerical experiments illustrate that the modified model is able to replicate not only Steinberg׳s cell sorting experiments but also some phenomena which cannot be captured at all by Armstrong-Painter-Sherratt model.