Rhythmogenic neuronal networks, pacemakers, and k-cores

TL;DR

This paper investigates how the connectivity structure of a minimal neuronal network model influences the emergence of pacemakers and burst termination, revealing fundamental differences from mean-field predictions.

Contribution

It demonstrates that network connectivity properties determine pacemaker locations and burst termination, highlighting the importance of k-core structures in neuronal dynamics.

Findings

Connectivity determines emergent pacemakers.

K-core clusters control burst termination.

Differences from mean-field theory predictions.

Abstract

Neuronal networks are controlled by a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a minimal model of the preBotzinger complex, a small neuronal network that controls the breathing rhythm of mammals through periodic firing bursts. We show that the properties of a such a randomly connected network of identical excitatory neurons are fundamentally different from those of uniformly connected neuronal networks as described by mean-field theory. We show that (i) the connectivity properties of the networks determines the location of emergent pacemakers that trigger the firing bursts and (ii) that the collective desensitization that terminates the firing bursts is determined again by the network connectivity, through k-core clusters of neurons.