Information processing in neurons with nonlinear characteristics.

Abstract

A mathematical model of dendritic neurons is derived directly from electrophysiological data on nonlinear current-voltage characteristics of nerve membranes, taking account of the neuron's morphology, the anatomic structure of the dendritic tree and of the fact that signals are processed through neurons in both discrete and continuous form. The model neuron (a generalization of FitzHugh's BVP-model) and its equivalent electric circuit are described by a nonlinear partial differential equation of third order supplemented by appropriate boundary conditions. Dynamic and information processing properties of the neuron are discussed in physical and mathematical terms. It is shown that information processing in a large class of neurons can be described as a stability phenomenon. Relations between the neuron's output impulse frequency and the amplitude of the post-synaptic potential are derived which are in very good agreement with experiment. Jump effects, rhythmic discharges and neuronal activities such as bur...