Field-theoretic approach to compartmental neuronal networks: impact of dendritic calcium spike-dependent bursting

TL;DR

This paper develops a field-theoretic model for compartmental neuronal networks, revealing how dendritic calcium spikes influence collective activity and phase transitions in neural populations.

Contribution

It introduces a novel statistical field-theoretic approach for modeling complex compartmental neurons with multiple spike types, extending mean-field theory to these systems.

Findings

Exact mean-field limit maps networks to a marked point process.

Compartmentalized connectivity affects the phase diagram and metastability.

Dendritic calcium spikes significantly influence network activity states.

Abstract

Neurons are spatially extended cells; different parts of a neuron have specific voltage dynamics. Important types of neurons even generate different spikes in different parts of the cell. Neurons' inputs are also often spatially compartmentalized, with different sources targeting different locations on the cell. Classic mean-field theories for neural population activity, however, rely on point-neuron models with at most one type of spike. Here, we develop a statistical field-theoretic approach to understanding collective activity in networks of compartmental neurons, including those generating multiple types of spikes. We use this to examine simple models of networks with thick-tufted layer 5 pyramidal cells, which generate calcium spikes in their apical dendrite when dendritic depolarization coincides with a back-propagating somatic spike. In the weakly-coupled regime, we uncover an exact mean-field limit for these networks that maps them to a marked point process. We use this mean-field limit to compare the impact of compartmentalized recurrent excitatory and inhibitory connectivity on the equilibrium phase diagram. This exposes regions of metastability between various activity states, including activity with silent vs active dendrites, with and without inhibitory activity, and oscillations.