# Exact firing time statistics of neurons driven by discrete inhibitory noise

## TL;DR

This paper derives exact statistical measures for neuron firing times under inhibitory noise, accounting for both small and large synaptic inputs, and applies to heterogeneous neuron populations.

## Contribution

It provides exact analytical results for firing rate, variability, and spectrum of neurons influenced by inhibitory synaptic inputs, including finite amplitude effects.

## Key findings

- Exact firing rate and variability formulas derived
- Results applicable to finite and large synaptic inputs
- Methods extend to heterogeneous neuron populations

## Abstract

Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of inhibitory stimulation on the firing time statistics, we consider Leaky Integrate-and-Fire neurons subject to inhibitory instantaneous post-synaptic potentials. In particular, we report exact results for the firing rate, the coefficient of variation and the spike train spectrum for various synaptic weight distributions. Our results are not limited to stimulations of infinitesimal amplitude, but they apply as well to finite amplitude post-synaptic potentials, thus being able to capture the effect of rare and large spikes. The developed methods are able to reproduce also the average firing properties of heterogeneous neuronal populations.