Finite Post Synaptic Potentials Cause a Fast Neuronal Response

A generic property of the communication between neurons is the exchange of pulses at discrete time points, the action potentials. However, the prevalent theory of spiking neuronal networks of integrate-and-fire model neurons relies on two assumptions: the superposition of many afferent synaptic impulses is approximated by Gaussian white noise, equivalent to a vanishing magnitude of the synaptic impulses, and the transfer of time varying signals by neurons is assessable by linearization. Going beyond both approximations, we find that in the presence of synaptic impulses the response to transient inputs differs qualitatively from previous predictions. It is instantaneous rather than exhibiting low-pass characteristics, depends non-linearly on the amplitude of the impulse, is asymmetric for excitation and inhibition and is promoted by a characteristic level of synaptic background noise. These findings resolve contradictions between the earlier theory and experimental observations. Here we review the recent theoretical progress that enabled these insights. We explain why the membrane potential near threshold is sensitive to properties of the afferent noise and show how this shapes the neural response. A further extension of the theory to time evolution in discrete steps quantifies simulation artifacts and yields improved methods to cross check results.