Death and rebirth of neural activity in sparse inhibitory networks

TL;DR

This paper investigates how inhibition in sparse neural networks can both suppress and promote neural activity, revealing a transition point and explaining the underlying mechanisms through mean field analysis, with implications for understanding neuronal dynamics.

Contribution

It introduces a mean field model that explains the reversal of inhibition effects in sparse networks and characterizes the transition from suppression to rebirth of neural activity.

Findings

Inhibition can both suppress and promote neural activity depending on network sparsity.

A transition point exists where the number of active neurons reaches a minimum.

Slow synapses induce irregular bursting dynamics consistent with experimental data.

Abstract

In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons' death). However, the random pruning of the connections is able to reverse the action of inhibition, i.e. in a sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons' rebirth). Thus the number of firing neurons reveals a minimum at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by the neurons with higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving an analytic mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, the system passes from a perfectly regular evolution to an irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.