Rhythmogenic neuronal networks, emergent leaders, and k-cores.

Neuronal network behavior results from a combination of the dynamics of individual neurons and the connectivity of the network that links them together. We study a simplified model, based on the proposal of Feldman and Del Negro (FDN) [Nat. Rev. Neurosci. 7, 232 (2006)], of the preBötzinger Complex, a small neuronal network that participates in the control of the mammalian breathing rhythm through periodic firing bursts. The dynamics of this randomly connected network of identical excitatory neurons differ from those of a uniformly connected one. Specifically, network connectivity determines the identity of emergent leader neurons that trigger the firing bursts. When neuronal desensitization is controlled by the number of input signals to the neurons (as proposed by FDN), the network's collective desensitization--required for successful burst termination--is mediated by k-core clusters of neurons.