LETTER Communicated by Brent Doiron Response of Integrate-and-Fire Neurons to Noisy Inputs Filtered by Synapses with Arbitrary Timescales: Firing Rate and Correlations

Delivery of neurotransmitter produces on a synapse a current that flows through the membrane and gets transmitted into the soma of the neu-ron, where it is integrated. The decay time of the current depends on the synaptic receptor’s type and ranges from a few (e.g., AMPA receptors) to a few hundredmilliseconds (e.g., NMDA receptors). The role of the variety of synaptic timescales, several of them coexisting in the same neuron, is at present not understood. A prime question to answer is which is the effect of temporal filtering at different timescales of the incoming spike trains on the neuron’s response. Here, based on our previous work on lin-ear synaptic filtering, we build a general theory for the stationary firing response of integrate-and-fire (IF) neurons receiving stochastic inputs fil-tered by one, two, ormultiple synaptic channels, each characterized by an arbitrary timescale. The formalism applies to arbitrary IF model neurons and arbitrary forms of input noise (i.e., not required to be gaussian or to have small amplitude), as well as to any form of synaptic filtering (linea