NEURAL EXCITABILITY, SPIKING AND BURSTING

TLDR

The authors review how bifurcation mechanisms generate neuronal spikes and extend the classification of neural bursters using geometric bifurcation theory. They analyze spike generation and bursting by applying geometric bifurcation theory to characterize saddle‑node and Andronov–Hopf bifurcations and to classify new burster types. They find that the bifurcation type dictates neuro‑computational behavior—saddle‑node cells act as integrators with all‑or‑none spikes, while Andronov–Hopf cells act as resonators with frequency‑selective firing—and that different burster types can synchronize and process information in distinct ways.

Abstract

Bifurcation mechanisms involved in the generation of action potentials (spikes) by neurons are reviewed here. We show how the type of bifurcation determines the neuro-computational properties of the cells. For example, when the rest state is near a saddle-node bifurcation, the cell can fire all-or-none spikes with an arbitrary low frequency, it has a well-defined threshold manifold, and it acts as an integrator; i.e. the higher the frequency of incoming pulses, the sooner it fires. In contrast, when the rest state is near an Andronov–Hopf bifurcation, the cell fires in a certain frequency range, its spikes are not all-or-none, it does not have a well-defined threshold manifold, it can fire in response to an inhibitory pulse, and it acts as a resonator; i.e. it responds preferentially to a certain (resonant) frequency of the input. Increasing the input frequency may actually delay or terminate its firing. We also describe the phenomenon of neural bursting, and we use geometric bifurcation theory to extend the existing classification of bursters, including many new types. We discuss how the type of burster defines its neuro-computational properties, and we show that different bursters can interact, synchronize and process information differently.