Spike-triggered averages for passive and resonant neurons receiving filtered excitatory and inhibitory synaptic drive

A path-integral approach is developed for the analysis of spike-triggered-average quantities in neurons with voltage-gated subthreshold currents. Using a linearization procedure to reduce the models to the generalized integrate-and-fire form, analytical expressions are obtained in an experimentally relevant limit of fluctuation-driven firing. The influences of voltage-gated channels as well as excitatory and inhibitory synaptic filtering are shown to affect significantly the neuronal dynamics prior to the spike. Analytical forms are given for all relevant physiological quantities, such as the mean voltage triggered to the spike, mean current flowing through voltage-gated channels and the mean excitatory and inhibitory conductance wave forms prior to a spike. The mathematical results are shown to be in good agreement with numerical simulations of the underlying non-linear conductance-based models. The method promises to provide a useful analytical tool for the prediction and interpretation of the temporal structure of spike-triggered averages measured experimentally.