Balance of excitation and inhibition determines 1/f power spectrum in neuronal networks

TL;DR

This study shows that the balance of excitation and inhibition in neuronal networks influences the 1/f power spectrum, with about 30% inhibition leading to a spectrum similar to that observed in resting brain activity, linking network dynamics to criticality.

Contribution

It demonstrates how the inhibitory-excitatory balance affects the spectral scaling exponent in neuronal networks, providing insights into criticality and potential pathological markers.

Findings

Scaling exponent $eta$ depends on inhibitory synapse percentage.

Purely excitatory networks exhibit $eta$ close to 2.

Approximately 30% inhibition yields $eta$ around 1.

Abstract

The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies have shown that avalanche dynamics at criticality corresponds to some specific balance of excitation and inhibition, thus suggesting that this is a basic feature of the critical state of neuronal networks. In particular, a lack of inhibition significantly alters the temporal structure of the spontaneous avalanche activity and leads to an anomalous abundance of large avalanches. Here we study the relationship between network inhibition and the scaling exponent $\beta$ of the power spectral density (PSD) of avalanche activity in a neuronal network model inspired in Self-Organized Criticality (SOC). We find that this scaling exponent depends on the percentage of inhibitory synapses and tends to the value $\beta = 1$ for a percentage of about 30%. More specifically, $\beta$ is close to $2$, namely brownian noise, for purely excitatory networks and decreases towards values in the interval $[1,1.4]$ as the percentage of inhibitory synapses ranges between 20 and 30%, in agreement with experimental findings. These results indicate that the level of inhibition affects the frequency spectrum of resting brain activity and suggest the analysis of the PSD scaling behavior as a possible tool to study pathological conditions.