Electric field induced propagating structures in a model of spatio-temporal signalling

The conditions are established for the onset of convective instabilities in a general two-variable reaction–diffusion–advection system in which one of the reactant species is immobile. These results are applied in detail to predict the effects of applying electric fields in a model for cellular calcium wave propagation based on the calcium-induced calcium-release (CICR) mechanism. Extensive numerical simulations of this model are described and these show that spatial structures can be generated entirely through applying electric fields at the parameter values determined by the general theory. These structures take the form of propagating wave packets, and can be either relatively simple or have complex dynamics, depending on the kinetic parameters.