Dynamical structures in binary media of potassium-driven neurons.

According to the conventional approach neural ensembles are modeled with fixed ionic concentrations in the extracellular environment. However, in some cases the extracellular concentration of potassium ions cannot be regarded as constant. Such cases represent specific chemical pathway for neurons to interact and can influence strongly the behavior of single neurons and of large ensembles. The released chemical agent diffuses in the external medium and lowers thresholds of individual excitable units. We address this problem by studying simplified excitable units given by a modified FitzHugh-Nagumo dynamics. In our model the neurons interact only chemically via the released and diffusing potassium in the surrounding nonactive medium and are permanently affected by noise. First, we study the dynamics of a single excitable unit embedded in the extracellular matter. That leads to a number of noise-induced effects such as self-modulation of firing rate in an individual neuron. After the consideration of two coupled neurons we consider the spatially extended situation. By holding parameters of the neuron fixed, various patterns appear ranging from spirals and traveling waves to oscillons and inverted structures depending on the parameters of the medium.