Midbrain dopaminergic (DA) neurons sustain important physiological functions such as control of motricity and signalling of positive error in reward prediction in the mesolimbic system. Under physiological conditions, DA neurons can switch between three distinct modes: tonic (pacemaker), irregular, and burst firing. The nature of the channels involved in the low frequency pacemaking of DA neurons is still highly discussed. Indeed, whereas many studies have shown that L-type calcium channels are critical for this spontaneous activity, others, including ours, have observed little effect of a blockade of these channels on this firing pattern. Therefore, the respective contribution of calcium and sodium channels in pacemaking remains unclear. However, it is commonly accepted that low-frequency spontaneous firing requires oscillations in the cytoplasmic free calcium concentration. In this paper, we use a mathematical analysis to extract the mechanisms underlying the spontaneous activity of dopaminergic neurons. For this purpose, we develop a basic model of a dopaminergic neuron, where we consider the minimal set of conductances that are able to reproduce the firing patterns exhibited by these cells.

We find that pacemaker firing in dopaminergic neurons is mainly sustained by the cooperation of sodium and L-type calcium channels, whereas variations of the intracellular calcium concentration play a major role in the rate of this spontaneous firing pattern. On the basis of this mechanism, we identify potential causes for the experimental discrepancies mentioned above, using the simple model of a dopaminergic neuron as well as the quantitative model. We observe that neurons only differing by less than 1% in their maximal sodium conductance might react oppositely to a blockade of L-type calcium channels. Experiments performed in rat brain slices confirm that L-type calcium and sodium channels cooperate to generate pacemaking in these neurons.