Self-organized critical balanced networks: a unified framework

TL;DR

This paper introduces a mean-field model that unifies the understanding of asynchronous irregular and critical neuronal activity states, showing how balanced inhibition and excitation lead to power-law avalanches and self-organized quasi-criticality.

Contribution

It generalizes previous integrate-and-fire models to demonstrate a phase transition at synaptic balance, explaining diverse brain activity states and the emergence of critical dynamics.

Findings

Power-law neuronal avalanches occur at the critical synaptic ratio g_c ≈ 4.

Balanced networks exhibit four typical synchronous activity states.

Homeostatic mechanisms lead to self-organized quasi-critical activity.

Abstract

Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire network of Brunel (2000). We show that the point with balanced inhibitory/excitatory synaptic weight ratio $g_c \approx 4$ corresponds to a second order absorbing phase transition usual in self-organized critical (SOC) models. At the synaptic balance point $g_c$, the network exhibits power-law neuronal avalanches with the usual exponents, whereas for nonzero external field the system displays the four usual synchronicity states of balanced networks. We add homeostatic inhibition and firing rate adaption and obtain a self-organized quasi-critical balanced state with avalanches and AI-like activity. Our model might explain why different inhibition levels are obtained in different experimental conditions and for different regions of the brain, since at least two dynamical mechanisms are necessary to obtain a truly balanced state, without which the network may hover in different regions of the presented theoretical phase diagram.