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| 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, Painter and Sherratt [J. Theor. Biol. 243 (2006), 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. We identify and remedy the problems, and provide a new continuous model for cell-cell adhesion. Our model replicates some phenomena which can not be captured at all by Armstrong-Painter-Sherratt model. |
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