Influence of specific ionic diffusion on the protein self-aggregation instability

Transcellular currents are involved in the generation of spatial order during the growth of numerous biological cells. A dynamic instability triggered by the aggregation of the proteins may be at the origin of the symmetry breaking. An analysis in terms of a semi-microscopic model is performed. It reveals that the dynamics of the ion transferred by the mobile proteins, pumps or channels, is of paramount importance. The diffusion currents play a crucial role in the critical behaviour, even if the instability mechanism is of electric origin. When the diffusion coefficients of the different species are different, our results do not agree with those of the classical cable formalism