Firing statistics of inhibitory neuron with delayed feedback. I. Output ISI probability density

TL;DR

This paper analytically and numerically investigates how delayed inhibitory feedback influences the firing statistics of neurons, revealing significant changes in output ISI distributions and bimodality, with implications for understanding neuronal activity.

Contribution

It provides the first exact analytical expressions for output ISI density in inhibitory neurons with delayed feedback and compares these with numerical results for different neuron models.

Findings

Output ISI densities become bimodal with feedback.

Delayed inhibitory feedback does not significantly change ISI coefficient of variation.

Neuronal firing statistics are radically altered by inhibitory delayed feedback.

Abstract

Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a delay. We investigate here, how does the presence of inhibitory feedback affect the output firing statistics. Using binding neuron (BN) as a model, we derive analytically the exact expressions for the output interspike intervals (ISI) probability density, mean output ISI and coefficient of variation as functions of model's parameters for the case of threshold 2. Using the leaky integrate-and-fire (LIF) model, as well as the BN model with higher thresholds, these statistical quantities are found numerically. In contrast to the previously studied situation of no feedback, the ISI probability densities found here both for BN and LIF neuron become bimodal and have discontinuity of jump type. Nevertheless, the presence of inhibitory delayed feedback was not found to affect substantially the output ISI coefficient of variation. The ISI coefficient of variation found ranges between 0.5 and 1. It is concluded that introduction of delayed inhibitory feedback can radically change neuronal output firing statistics. This statistics is as well distinct from what was found previously (Vidybida & Kravchuk, 2009) by a similar method for excitatory neuron with delayed feedback.