Synaptic transmission in a model for stochastic neural activity.

A stochastic model equation for nerve membrane depolarization is derived which incorporates properties of synaptic transmission with a Rall-Eccles circuit for a trigger zone. If input processes are Poisson the depolarization is a Markov process for which equations for the moments of the interspike interval can be written down. An analytic result for the mean interval is obtained in a special case. The effect of the excitatory reversal potential is considerable if it is not too far from threshold and if the interspike interval is long. Computer simulations were performed when inhibitory and excitatory inputs are active. A substantial amount of inhibition leads to an exceedingly long tail in the density of the interspike time. With excitation only the interspike interval is often an approximately lognormal random variable. A coefficient of variation greater than one is often a consequence of relatively strong inhibition. Inferences can be made on the nature of the synaptic input from the statistics and density of the time between spikes. The inhibitory reversal potential usually has a relatively small effect except when the frequency of inhibition is large. An appendix contains the model equations in the case of an arbitrary distribution of postsynaptic potential amplitudes.