A mathematical model of the effects of spatio-temporal patterns of dendritic input potentials on neuronal somatic potentials

A mathematical model of a neuron was developed to investigate the effects of various spatio-temporal patterns of miniature dendritic input potentials on neuronal somatic potentials. The model treats spatio-temporal dendritic activation patterns as the input or forcing function in the non-homogeneous cable equation. The theoretical somatic potentials resulting from several different spatio-temporal input patterns were generated on an IBM 360/75 computer. The model allows the investigation of the theoretical effects of activations at several different synaptic sites, of repeated activations at one or more sites, and of changes in various parameters. The time-to-peak and amplitude of individual excitatory postsynaptic potentials, distance of synapses from the soma, and interactivation interval for repeated activations at the same synapse were among the parameters investigated. Not only the order of activations at different synaptic sites was important, but the time intervals between activations were shown to be important. For a given order of activations at different synapses, optimum time intervals between activations were demonstrated, with respect to the resulting peak somatic potentials. Possible consequences of some hypothetical learning and memory mechanisms upon neuronal excitability were discussed. It was also shown that a deterministic model can generate theoretical curves which appear to be almost of a random nature with respect to the observed numbers and amplitudes of peaks of individual EPSPs. The conditions for the appearance of extra peaks were discussed.This paper describes work done as a portion of G.M.B.'s Ph. D. thesis in biomathematics at N.C. State University, and was supported by Public Health Service Grant No. GM-678 from the National Institute of General Medical Sciences.