Emergence of irregular activity in networks of strongly coupled conductance-based neurons

TL;DR

This paper demonstrates that irregular activity and broad rate distributions in conductance-based neural networks emerge through a drift-diffusion balance mechanism when synaptic strength scales as 1/log(K), differing from the classical balanced state model.

Contribution

It introduces a new regime for conductance-based networks where irregular activity arises without fine tuning, with synaptic strength scaling as 1/log(K), expanding the understanding of neural network dynamics.

Findings

Irregular activity emerges with synapses of order 1/log(K)

Current fluctuations are suppressed in this regime

Network response properties depend on input size and are testable experimentally

Abstract

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive firing. In networks of neurons with current-based synapses, the balanced state emerges dynamically if coupling is strong, i.e. if the mean number of synapses per neuron $K$ is large and synaptic efficacy is of order $1/\sqrt{K}$. When synapses are conductance-based, current fluctuations are suppressed when coupling is strong, questioning the applicability of the balanced state idea to biological neural networks. We analyze networks of strongly coupled conductance-based neurons and show that asynchronous irregular activity and broad distributions of rates emerge if synapses are of order $1/\log(K)$. In such networks, unlike in the standard balanced state model, current fluctuations are small and firing is maintained by a drift-diffusion balance. This balance emerges dynamically, without fine tuning, if inputs are smaller than a critical value, which depends on synaptic time constants and coupling strength, and is significantly more robust to connection heterogeneities than the classical balanced state model. Our analysis makes experimentally testable predictions of how the network response properties should evolve as input increases.