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 (I(Ca,L)) and the apamin-sensitive calcium-activated potassium current (I(K,Ca,SK)). We further hypothesize that the square-wave oscillation results from the alternating voltage activation and calcium inactivation of I(Ca,L). Our model consists of two components: a Hodgkin-Huxley-type membrane model and a fluid compartment model. A material balance on Ca(2+) 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.
Dopaminergic local circuit neurons in the retina (DA cells) show robust, spontaneous, tetrodotoxin-sensitive pacemaking. To investigate the mechanism underlying this behavior, we characterized the sodium current and a subset of the potassium currents in the cells in voltage-clamp experiments. We found that there is a persistent component of the sodium current in DA cells which activates at more depolarized potentials than the transient component of the current. The transient component was completely inactivated at -50 mV, but DA cells remained able to fire spontaneous action potentials when potassium channels were partially blocked and the membrane potential remained above -40 mV. Based on these electrophysiological data, we developed a reduced computer model that reproduced the major features of DA cells. In simulations at the physiological resting potential, the persistent component of the sodium current was both necessary and sufficient to account for spontaneous activity, and the major contribution of the transient component of the sodium current was to initiate the depolarization of the model cell during the interspike interval. When tonic inhibition was simulated by lowering the input impedance of the model cell, the transient component played a larger role.
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