Characterization of the currents underlying rhythmic firing in mammalian dopaminergic neurons

Abstract

A mathematical model of midbrain dopamine neurons has been developed in order to understand the mechanisms underlying two types of calcium-dependent firing patterns that these cells exhibit in vitro. The first is the regular, pacemaker-like firing exhibited in a slice preparation, and the second is a burst firing pattern sometimes exhibited in the presence of apamin. Since both types of oscillations are blocked by nifedipine, we have focused on the slow calcium dynamics underlying these firing modes. The underlying oscillations in membrane potential are best observed when action potentials are blocked by the application of TTX. This converts the regular single-spike firing mode to a slow oscillatory potentials (SOP) and apamin-induced bursting to a slow square-wave oscillation. We hypothesize that the SOP results from the interplay between the L-type calcium current ($I\sb{Ca,L}$) and the apamin-sensitive calcium-activated potassium current ($I\sb{K,Ca,SK}$). We further hypothesize that the square-wave oscillation results from the alternating voltage activation and calcium inactivation of $I\sb{Ca,L}$. Our model consists of two components: (a) a Hodgkin-Huxley-type membrane model, and (b) a fluid compartment model. A material balance on $Ca\sp{2+}$ is provided in the cytosolic fluid compartment, while calcium concentration is considered constant in the extracellular compartment. Model parameters were determined using both voltage-clamp and calcium imaging data from the literature. In addition to modeling the SOP and square-wave oscillations in DA neurons, the model provides reasonable mimicry of the experimentally observed graded modification of the amplitude and frequency of the SOP in response to injected current, as well as the elongation of the plateau duration of the square wave oscillations in response to calcium chelation.