Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses

TL;DR

This paper analyzes how electric synapses influence collective neural dynamics and spike train statistics in conductance-based Integrate-and-Fire networks, providing explicit formulas and connections to existing models.

Contribution

It introduces an explicit formula for the spike train Gibbs distribution in conductance-based IF networks with electric synapses, linking to maximum entropy and GLM models.

Findings

Electric synapses significantly affect spike train correlations.

The model provides explicit formulas for spike train statistics.

Connections to existing statistical models are established.

Abstract

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or Generalized Linear Models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.