Spatial electrical patterns in simulated neuronal dendrites

Steady state longitudinal distributions of (a) the density of channels conducting an inward transmembrane current of cations, (b) the submembrane concentrations of these cations, and (c) the resting membrane potential, were investigated in a phenomenological model of a cylinder-shaped dendritic process of the neuron. It was found that spatially non-uniform patterns of these distributions occur only if one of the following conditions held (i) an increase in the intracellular concentration of cations conducting an inward passive transmembrane current amplified the active efflux of those cations by the pump and attenuated their passive influx through the voltage dependent channels, with amplification of the efflux lower than attenuation of the influx; (ii) molecules of mobile channels bore a negative electrophoretic charge exposed to the intracellular space and were subject to lateral electrodiffusion in the membrane; (iii) the cations induced a further release of cations from intracellular stores. Numerical simulation studies of the membrane with Na and K channels and Na/K pumps with conditions (i) and (ii) have demonstrated the possibility of the creation of inhomogeneous patterns in the neurites. These inhomogeneous patterns are dissipative structures (DSs), and they can be spatially periodic.