Implications of cellular models of dopamine neurons for disease.

This review addresses the present state of single-cell models of the firing pattern of midbrain dopamine neurons and the insights that can be gained from these models into the underlying mechanisms for diseases such as Parkinson's, addiction, and schizophrenia. We will explain the analytical technique of separation of time scales and show how it can produce insights into mechanisms using simplified single-compartment models. We also use morphologically realistic multicompartmental models to address spatially heterogeneous aspects of neural signaling and neural metabolism.

Hyperbolic chaos of standing wave patterns generated parametrically by a modulated pump source.

We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales 1:3.

Exploring neuronal bistability at the depolarization block.

Many neurons display bistability--coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to be involved in short-term memory in particular by allowing a brief signal to elicit long-lasting changes in firing. In this paper, we focus on bistability that allows for a choice between tonic spiking and depolarization block in a wide range of the depolarization levels.

Regulation of firing frequency in a computational model of a midbrain dopaminergic neuron.

Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo.

Transient high-frequency firing in a coupled-oscillator model of the mesencephalic dopaminergic neuron.

Dopaminergic neurons of the midbrain fire spontaneously at rates <10/s and ordinarily will not exceed this range even when driven with somatic current injection. When driven at higher rates, these cells undergo spike failure through depolarization block. During spontaneous bursting of dopaminergic neurons in vivo, bursts related to reward expectation in behaving animals, and bursts generated by dendritic application of N-methyl-d-aspartate (NMDA) agonists, transient firing attains rates well above this range.