How well do reduced models capture the dynamics in models of interacting neurons ?

TL;DR

This paper evaluates how effectively simplified reduced models replicate the complex dynamics of interacting neuron networks, highlighting the roles of spike correlations and nonlinearities in discrepancies.

Contribution

It introduces stochastic neuron models and compares them with simple reduced models, identifying key mechanisms behind differences in firing rate predictions.

Findings

Correlations in spiking cause discrepancies in firing rates.

Nonlinearities in membrane potential dynamics contribute to model differences.

Random walk models effectively reproduce membrane potential fluctuations.

Abstract

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models were investigated, and mechanisms leading to these discrepancies were identified. Chief among them is correlations in spiking, or partial synchronization, working in concert with "nonlinearities" in the time evolution of membrane potentials. Additionally, simple random walk models and their first passage times were shown to reproduce well fluctuations in neuronal membrane potentials and interspike times.