Effects of tapering geometry and inhomogeneous ion channel distribution in a neuron model

Recent experiments have produced direct evidence on the existence of various dendritic voltage-gated ion channels, indicating that these neuronal components are not just a passive medium for the propagation of synaptic excitation but a putative source of neuronal excitability that is reflected in the activity patterns occurring on the soma. In order to study possible changes in neuronal excitability when the distribution of dendritic voltage-activated channels is non-uniform, and the dendritic geometry is not necessarily cylindric, we have developed a neuron model that incorporates two voltage-activated currents [I(Na) and I(K)], and in which space-dependent distributions of the system parameters can be treated in a mathematically simple and efficient way. Simulation results with the model showed that both linearly and exponentially tapering geometries led to marked anisotropy of the propagation of excitation, favouring the soma-to-dendrite direction. Exponentially decaying densities of dendritic voltage-activated channels, with appropriate choice of the parameters, induced bistable behaviour between the normal resting state and an intrinsic, sustained oscillation with cylindric as well as linear and exponential tapering dendritic geometry. Bistability could not be evoked when the model was reduced to a space-independent one (point-like soma). These results suggest that both tapering dendritic geometry and inhomogeneous distribution of ion channels may crucially affect the propagation and integration of synaptic potentials, and that changes in dendritic channel densities might underlie pathological electrophysiological activities.