Influence of inhibitory synapses on the criticality of excitable neuronal networks

TL;DR

This paper analyzes how inhibitory synapses influence the criticality and dynamic range of excitable neuronal networks, providing analytical expressions for critical points and revealing excitatory-inhibitory balance effects.

Contribution

It introduces analytical formulas for the critical points of neuronal networks considering inhibitory effects and explores their impact on dynamic range and activity regimes.

Findings

Critical points depend on synaptic intensities and network parameters.

Dynamic range is maximized at specific critical points.

Excitatory and inhibitory inputs balance in large networks.

Abstract

In this work, we study the dynamic range of a neuronal network of excitable neurons with excitatory and inhibitory synapses. We obtain an analytical expression for the critical point as a function of the excitatory and inhibitory synaptic intensities. We also determine an analytical expression that gives the critical point value in which the maximal dynamic range occurs. Depending on the mean connection degree and coupl\-ing weights, the critical points can exhibit ceasing or ceaseless dynamics. However, the dynamic range is equal in both cases. We observe that the external stimulus mask some effects of self-sustained activity (ceaseless dynamic) in the region where the dynamic range is calculated. In these regions, the firing rate is the same for ceaseless dynamics and ceasing activity. Furthermore, we verify that excitatory and inhibitory inputs are approximately equal for a network with a large number of connections, showing excitatory-inhibitory balance as reported experimentally.