We consider the polarization of a cell in response to an outer signal. The mathematical model consists of a diffusion equation in the inner volume coupled to a reaction diffusion system on the cell membrane. In a certain asymptotic limit we rigorously prove the convergence towards a generalized obstacle problem. In term of this limit system we derive conditions for the onset of polarization. The results will be mainly presented for the stationary case, we will briefly discuss some extensions to the time-dependent case.

(This is joint work with Barbara Niethammer, Juan Velazquez, and Anna Logioti)