An Analytically Solvable Model of Firing Rate Heterogeneity in Balanced State Networks

TL;DR

This paper introduces an exactly solvable model of firing rate heterogeneity in balanced neural networks, enabling precise analysis of how neuronal and synaptic properties influence activity distributions.

Contribution

It presents a mathematically tractable balanced-state network model using the Gauss-Rice neuron, allowing exact calculation of firing rate distributions and incorporation of multiple neuronal populations.

Findings

Exact firing rate distribution calculation for balanced networks

Model accommodates multiple neuron types and synaptic receptors

Provides insights into the impact of neuron and synapse properties on activity heterogeneity

Abstract

Distributions of neuronal activity within cortical circuits are often found to display highly skewed shapes with many neurons emitting action potentials at low or vanishing rates, while some are active at high rates. Theoretical studies were able to reproduce such distributions, but come with a lack of mathematical tractability, preventing a deeper understanding of the impact of model parameters. In this study, using the Gauss-Rice neuron model, we present a balanced-state cortical circuit model for which the firing rate distribution can be exactly calculated. It offers selfconsistent solutions to recurrent neuronal networks and allows for the combination of multiple neuronal populations, with single or multiple synaptic receptors (e.g. AMPA and NMDA in excitatory populations), paving the way for a deeper understanding of how firing rate distributions are impacted by single neuron or synaptic properties.