Mind the Last Spike -- Firing Rate Models for Mesoscopic Populations of Spiking Neurons

TL;DR

This paper advocates for the refractory density method as a powerful framework to develop more accurate and biologically grounded firing rate models for mesoscopic neural populations, addressing limitations of traditional models.

Contribution

It introduces the RDM as a systematic way to derive rate models from detailed neuron dynamics, including finite-size effects and nonstationary behavior.

Findings

RDM enables derivation of efficient population density equations for GIF neurons.

The theory predicts nonstationary neural population dynamics.

Extension to finite-size populations allows more realistic modeling.

Abstract

The dominant modeling framework for understanding cortical computations are heuristic firing rate models. Despite their success, these models fall short to capture spike synchronization effects, to link to biophysical parameters and to describe finite-size fluctuations. In this opinion article, we propose that the refractory density method (RDM), also known as age-structured population dynamics or quasi-renewal theory, yields a powerful theoretical framework to build rate-based models for mesoscopic neural populations from realistic neuron dynamics at the microscopic level. We review recent advances achieved by the RDM to obtain efficient population density equations for networks of generalized integrate-and-fire (GIF) neurons -- a class of neuron models that has been successfully fitted to various cell types. The theory not only predicts the nonstationary dynamics of large populations of neurons but also permits an extension to finite-size populations and a systematic reduction to low-dimensional rate dynamics. The new types of rate models will allow a re-examination of models of cortical computations under biological constraints.