Calcium Dynamics Underlying Pacemaker-Like and Burst Firing Oscillations in Midbrain Dopaminergic Neurons: A Computational Study

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Abstract
A mathematical model of midbrain dopamine neurons has been developed 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. Because 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 potential (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 (ICa,L) and the apamin-sensitive calcium-activated potassium current ( IK,Ca,SK). We further hypothesize that the square-wave oscillation results from the alternating voltage activation and calcium inactivation of ICa,L. Our model consists of two components: a Hodgkin-Huxley-type membrane model and a fluid compartment model. A material balance on Ca2+is provided in the cytosolic fluid compartment, whereas 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 dopaminergic neurons, the model provides reasonable mimicry of the experimentally observed response of SOPs to TEA application and elongation of the plateau duration of the square-wave oscillations in response to calcium chelation.