New method for analyzing the synchronization of synaptic input and spike output in neural systems

Abstract

We present a new technique for analyzing the probability distribution of output spikes for the integrate and fire model. Using this method we investigate models with arbitrary synaptic response functions and the results, which are compared with numerical simulations, are exact in the limit of a large number of small amplitude inputs. We apply this method to the synchronization problem, in which the relationship between the spread in arrival times of the inputs (the temporal jitter of the synaptic input) and the resultant spread in the times at which the output spikes are generated (output jitter) is analyzed. The results indicate that the ratio of the output jitter to the input jitter is consistently less than one and that it decreases for increasing numbers of inputs, in agreement with earlier studies. We identify the variation in the spike generating thresholds of the neurons and the variation in the number of active inputs as being important factors that determine the timing jitter in layered networks, in addition to those identified previously.