A new stochastic model for auditory-nerve discharge.

This paper investigates the mechanisms for history-dependent probability of eight-nerve discharge, which is modeled as the probability that the excitatory postsynaptic potential (EPSP) process crosses afferent membrane threshold, with the discharge history dependence due to the dependence of postsynaptic threshold voltage on time since previous action potential. The model parameters are the Poisson intensity alpha t of vesicle release, the duration epsilon and probability density PV(upsilon) of single-vesicle EPSP's, and the threshold voltage curve theta (tau) for spiking. It is proven that the infinitesimal conditional probabilities of discharge exhibit two distinct behaviors. The first is associated with the time tau = T D, exactly the time the neuron releases from absolute refractory where there is no intensity [theta(tau) = infinity, for tau < T D]. At this time the neuron has a nonzero probability of discharge [symbol:see text] (T D) = lim delta-->0 Pr(Nt,t+delta = 1/t - wNt = T D). The second regime corresponds to the time since previous spike being greater than dead time, tau > T D, during which time the intensity exists lambda t(tau) = lim delta-->0(1/delta) Pr(Nt,t+delta = 1/t - wNt = tau > T D). The fact that there is a nonzero probability of discharge following passage from the absolute refractory period predicts the nonmonotonic hazard intensity seen in high spontaneous neurons [R. P. Gaumond, Ph.D. thesis, Washington University, St. Louis (1980)] and high driven rate neurons. It is shown that for the lowest range of vesicle release intensities where the vesicle-release-rate/membrane-integration-time product alpha t epsilon small, the nonzero probability of discharge at a point is approximately equal to 0. The discharge intensity is dominated by a term linear in vesicle release intensity: lambda t(tau) approximately alpha t exp(-integral of t-epsilon t alpha sigma d sigma) integral of theta (tau) infinity Pv(upsilon)d upsilon. This is precisely the Siebert-Gaumond intensity product form with monotonic recovered discharge probability. At high vesicle release rates, such as for driven rate responses, the nonzero probability of discharging at a point becomes of nonsignificant size, and the intensity of discharge grows nonlinearly with alpha t, implying the product model does not hold. The model is demonstrated via the analysis of auditory nerve fibers from the cat.