Coupled oscillator model of the dopaminergic neuron of the substantia nigra

Calcium imaging using fura-2 and whole cell recording revealed the effective location of the oscillator mechanism on dopaminergic neurons of the substantia nigra, pars compacta, in slices from rats aged 15-20 days. As previously reported, dopaminergic neurons fired in a slow rhythmic single spiking pattern. The underlying membrane potential oscillation survived blockade of sodium currents with TTX and was enhanced by blockade of voltage-sensitive potassium currents with TEA. Calcium levels increased during the subthreshold depolarizing phase of the membrane potential oscillation and peaked at the onset of the hyperpolarizing phase as expected if the pacemaker potential were due to a low-threshold calcium current and the hyperpolarizing phase to calcium-dependent potassium current. Calcium oscillations were synchronous in the dendrites and soma and were greater in the dendrites than in the soma. Average calcium levels in the dendrites overshot steady-state levels and decayed over the course of seconds after the oscillation was resumed after having been halted by hyperpolarizing currents. Average calcium levels in the soma increased slowly, taking many cycles to achieve steady state. Voltage clamp with calcium imaging revealed the voltage dependence of the somatic calcium current without the artifacts of incomplete spatial voltage control. This showed that the calcium current had little or no inactivation and was half-maximal at -40 to -30 mV. The time constant of calcium removal was measured by the return of calcium to resting levels and depended on diameter. The calcium sensitivity of the calcium-dependent potassium current was estimated by plotting the slow tail current against calcium concentration during the decay of calcium to resting levels at -60 mV. A single compartment model of the dopaminergic neuron consisting of a noninactivating low-threshold calcium current, a calcium-dependent potassium current, and a small leak current reproduced most features of the membrane potential oscillations. The same currents much more accurately reproduced the calcium transients when distributed uniformly along a tapering cable in a multicompartment model. This model represented the dopaminergic neuron as a set of electrically coupled oscillators with different natural frequencies. Each frequency was determined by the surface area to volume ratio of the compartment. This model could account for additional features of the dopaminergic neurons seen in slices, such as slow adaptation of oscillation frequency and may produce irregular firing under different coupling conditions.