  In this paper we are interested in a degenerate parabolic system of
reaction-diffusion equations arising in biology when studying cell adhesion at
the protein level. In this modeling the unknown is the couple of the
distribution laws of the freely diffusing proteins and of the fixed ones. Under
sufficient conditions on the aggregation and unbinding probabilities, we prove
the existence of solution of the considered system, as well as their
positivity, boundedness and uniqueness. Moreover, we discuss the stability of
the equilibrium solution. Finally, we show that the simpler and particular
choice of an affine aggregation function and of a constant unbinding
probability do not lead to pattern formation as expected in the application.
These analytical results are also supported by some numerical simulation.
