Calcium dynamics underlying pacemaker-like and burst firing oscillations in midbrain dopaminergic neurons: A computational study

A mathematical model of midbrain dopamine neurons has been developed to und erstand the mechanisms underlying two types of calcium-dependent firing pat terns that these cells exhibit in vitro. The first is the regular, pacemake r-like firing exhibited in a slice preparation, and the second is a burst f iring pattern sometimes exhibited in the presence of apamin. Because both t ypes of oscillations are blocked by nifedipine, we have focused on the slow calcium dynamics underlying these firing modes. The underlying oscillation s in membrane potential are best observed when action potentials are blocke d 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,I-L) and the apamin-sen sitive calcium-activated potassium current (I-K,I-Ca,I-SK). We further hypo thesize that the square-wave oscillation results from the alternating volta ge activation and calcium inactivation of I-Ca,I-L. Our model consists of t wo components: a Hodgkin-Huxley-type membrane model and a fluid compartment model. A material balance on Ca2+ is provided in the cytosolic fluid compa rtment, whereas calcium concentration is considered constant in the extrace llular compartment. Model parameters were determined using both voltage-cla mp and calcium-imaging data from the literature. In addition to modeling th e SOP and square-wave oscillations in dopaminergic neurons, the model provi des reasonable mimicry of the experimentally observed response of SOPs to T EA application and elongation of the plateau duration of the square-wave os cillations in response to calcium chelation.