New technique for analyzing integrate and fire neurons

Abstract By integrating over the distribution of arrival times of the afferent postsynaptic potentials (PSPs), the probability density of the summed potential is calculated. An output spike is generated when the potential reaches threshold, and the probability density of output spikes (the first-passage density) is calculated. This “integrated-input” technique enables the investigation of models that incorporate the decay of the membrane potential and rise time of the synaptic current. PSPs with a distribution of amplitudes, including inhibitory PSPs, are also analyzed. The results are exact in the limit of large numbers of small amplitude inputs.