  Signaling molecules play an important role for many cellular functions. We
investigate here a general system of two membrane reaction-diffusion equations
coupled to a diffusion equation inside the cell by a Robin-type boundary
condition and a flux term in the membrane equations. A specific model of this
form was recently proposed by the authors for the GTPase cycle in cells. We
investigate here a putative role of diffusive instabilities in cell
polarization. By a linearized stability analysis we identify two different
mechanisms. The first resembles a classical Turing instability for the membrane
subsystem and requires (unrealistically) large differences in the lateral
diffusion of activator and substrate. The second possibility on the other hand
is induced by the difference in cytosolic and lateral diffusion and appears
much more realistic. We complement our theoretical analysis by numerical
simulations that confirm the new stability mechanism and allow to investigate
the evolution beyond the regime where the linearization applies.
