Correlation analysis of stimulus-evoked changes in excitability of spontaneously firing neurons

Abstract

1. Theoretical expressions for the cross-correlation function are described which relate the output spike train of a neuron to an input spike train. The cross-correlation function is related to a convolution integral of two functions: 1) a waiting-time density, which describes the probability of observing the next succeeding output spike given an arbitrary input; and 2) a conditional output autocorrelation function, which contains information related to the statistical properties of the output spike train itself, and to the carry-over of the effects of an input to subsequent intervals. 2. The primary synaptic effect appears in the cross-correlation function as a distorted version of the derivative of the PSP. Depending on the duration of the evoked excitability change, as compared to the mean output interspike interval, periodicities due to the spontaneous activity of the cell appear to a greater or lesser extent in the cross-correlation. 3. To estimate underlying excitability changes using correlation techniques, one must estimate both the cross- and the conditional output autocorrelation functions. In cases when the excitability changes are short and do not carry forward to subsequent intervals, the more readily estimated unconditional output autocorrelation can be used in place of the conditional correlation.