Highly connected neurons spike less frequently in balanced networks

TL;DR

This paper uses a heterogeneous mean-field theory to show that in balanced neuronal networks, neurons with more connections tend to spike less frequently, aligning with experimental data and highlighting the importance of connectivity heterogeneity.

Contribution

It introduces a heterogeneous mean-field approach to analyze how in-degree and out-degree connectivity patterns affect neuronal spiking activity in balanced networks.

Findings

Highly connected neurons spike less frequently.

Heterogeneous out-degrees can restore balance in networks.

Results align with recent experimental observations.

Abstract

Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs on average and spiking activity is driven by transient breaks in this balance. Most previous studies of balanced networks assume a homogeneous or distance-dependent connectivity structure, but connectivity in biological cortical networks is more intricate. We use a heterogeneous mean-field theory of balanced networks to show that heterogeneous in-degrees can break balance, but balance can be restored by heterogeneous out-degrees that are correlated with in-degrees. In all examples considered, we find that highly connected neurons spike less frequently, consistent with recent experimental observations.