Abstract

Midbrain dopamine neurons exhibit a novel type of bursting that we call “inverted square wave bursting” when exposed to Ca2+-activated small conductance (SK) K+ channel blockers in vitro. This type of bursting has three phases: hyperpolarized silence, spiking, and depolarization block. We find that two slow variables are required for this type of bursting, and we show that the three-dimensional bifurcation diagram for inverted square wave bursting is a folded surface with upper (depolarized) and lower (hyperpolarized) branches. The activation of the L-type Ca2+ channel largely supports the separation between these branches. Spiking is initiated at a saddle node on an invariant circle bifurcation at the folded edge of the lower branch and the trajectory spirals around the unstable fixed points on the upper branch. Spiking is terminated at a supercritical Hopf bifurcation, but the trajectory remains on the upper branch until it hits a saddle node on the upper folded edge and drops to the lower branch. The two slow variables contribute as follows. A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking. The slow activation of the ether-a-go-go-related (ERG) K+ current is largely responsible for termination of the depolarized plateau. The mechanisms and slow processes identified herein may contribute to bursting as well as entry into and recovery from the depolarization block to different degrees in different subpopulations of dopamine neurons in vivo.

Highlights

  • The activity of midbrain dopamine neurons, as reflected in levels of extracellular dopamine concentration and the fMRI BOLD signals in their target areas, is hypothesized to represent a reward prediction error [1] or, alternatively, confidence in a prediction of a desired outcome [2]

  • We propose that special dynamic mechanisms for bursting are not required to achieve a temporary acceleration in frequency, the intrinsic currents that characterize dopamine neurons provide burst mechanisms that may be harnessed as needed to facilitate single or multiple bursts

  • We confirmed that a calciumdriven, approximately sinusoidal, slow oscillatory potentials (SOP) can be obtained when bath application of TTX is simulated by setting gNa = 0 (Fig. 1d) to block spiking

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Summary

Introduction

The activity of midbrain dopamine neurons, as reflected in levels of extracellular dopamine concentration and the fMRI BOLD signals in their target areas, is hypothesized to represent a reward prediction error [1] or, alternatively, confidence in a prediction of a desired outcome [2]. The firing pattern of dopamine neurons affects dopaminergic signaling; for example, electrical stimulation of dopaminergic cells at 40 Hz is much more effective in elevating dopamine extracellular concentration in rat striatum [3] than the same number of stimuli applied at 10 Hz. Dopamine (DA) neurons are regular pacemakers at 1–7 Hz in vitro [4, 5], but in vivo exhibit different firing patterns, including regular single-spiking, irregular single-spiking and burst firing both in freely moving [6] and anesthetized [7] rats. Bursts are associated in awake animals with reward-related stimuli [10, 11], and they are referred to as a phasic signal in contrast to the tonic signal mediated by single-spike firing

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