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Distributions of neuronal activity within cortical circuits are often foundto display highly skewed shapes with many neurons emitting action potentials atlow or vanishing rates, while some are active at high rates. Theoreticalstudies were able to reproduce such distributions, but come with a lack ofmathematical tractability, preventing a deeper understanding of the impact ofmodel parameters. In this study, using the Gauss-Rice neuron model, we presenta balanced-state cortical circuit model for which the firing rate distributioncan be exactly calculated. It offers selfconsistent solutions to recurrentneuronal networks and allows for the combination of multiple neuronalpopulations, with single or multiple synaptic receptors (e.g. AMPA and NMDA inexcitatory populations), paving the way for a deeper understanding of howfiring rate distributions are impacted by single neuron or synaptic properties.

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