Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons

TL;DR

This paper investigates how excitability, a key feature of biological signaling, emerges in large networks of quadratic integrate-and-fire neurons, revealing that population-level excitability mirrors single-cell mechanisms through a new theoretical framework.

Contribution

It introduces a comprehensive framework for understanding excitability in large neural populations, extending single-cell canard analysis to complex network structures including sparse networks.

Findings

Population excitability thresholds are similar to single-cell thresholds.

The Ott-Antonsen ansatz effectively describes large network dynamics.

The framework applies to both mean-field reducible and sparse networks.

Abstract

From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. Here, we show that the mechanism of excitability in large networks and mean-field descriptions of coupled quadratic integrate-and-fire (QIF) cells mirrors that of the individual components. We initially exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical analysis and numerical computations to develop a novel and comprehensive framework for excitability in large populations, applicable not only to models amenable to Ott-Antonsen reduction, but also to networks without a closed-form mean-field limit, in particular sparse networks.