Neural Excitability, Spiking and Bursting

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.

In vivo conditions influence the coding of stimulus features by bursts of action potentials

“…Burst firing is seen ubiquitously in the central nervous system and can be caused by a multitude of intrinsic and network mechanisms (Rinzel 1987;Wang and Rinzel 1995;Izhikevich 2000;Doiron et al 2002). As such, an important question pertains to whether differences in the mechanisms that give rise to burst firing can also give rise to differences in sensory coding.…”

“…the firing of packets of action potentials followed by quiescence) which is seen ubiquitously in the CNS (Krahe and Gabbiani 2004). Although the intrinsic and network mechanisms that give rise to burst firing are generally well understood (Izhikevich 2000;Sherman and Guillery 2002;Krahe and Gabbiani 2004), the functional role of burst firing is less well understood. In particular, it has been proposed that bursts, when treated as a single event, can signal the presence of particular stimulus features Metzner et al 1998;Sherman 2001;Sherman and Guillery 2002;Chacron et al 2004a;Lesica and Stanley 2004;Oswald et al 2004).…”

To Burst or Not to Burst?

“…Moreover, neurons at the same stage of processing can often be subdivided into bursting and tonically firing subgroups (Goldberg, 2000;Bastian and Nguyenkim, 2001). Although the particular dynamics that can lead to bursting behavior are generally well understood (Wang and Rinzel, 1995;Izhikevich, 2000), their role in sensory processing remains poorly understood. Furthermore, the relative computational advantages of bursting and tonically firing neurons have not been clearly established.…”

From Spikers to Bursters Via Coupling: Help From Heterogeneity

“…As δ increases, the homoclinic bifurcation moves into the right saddle-node and disappears at a codimension-2 Takens-Bogdanov bifurcation (indicated by the lower bullet). At this point, a second Hopf bifurcation appears on the upper branch, and square-wave bursting turns into tapered (fold/Hopf) bursting (de Vries, 1998;Izhikevich, 2000). As δ increases still further, bursting gives way to relaxation oscillators when the rightmost Hopf bifurcation moves to the left of the left saddle-node and out of the region of bistability.…”

“…The β-cell and respiratory models both belong to the class of 'square-wave' or 'fold-homoclinic' bursters (Izhikevich, 2000); another widely-studied member of this class is the Hindmarsh-Rose caricature of thalamic neurons (Hindmarsh and Rose, 1984). Bursting in this class of models requires two fundamental elements.…”