How modeling can reconcile apparently discrepant experimental results: the case of pacemaking in dopaminergic neurons

Abstract

Midbrain dopaminergic neurons are endowed with endogenous slow pacemaking properties. In recent years, many different groups have studied the basis for this phenomenon, often with conflicting conclusions. In particular, the role of a slowly-inactivating L-type calcium channel in the depolarizing phase between spikes is controversial, and the analysis of slow oscillatory potential (SOP) recordings during the blockade of sodium channels has led to conflicting conclusions. Based on a minimal model of a dopaminergic neuron, our analysis suggests that the same experimental protocol may lead to drastically different observations in almost identical neurons. For example, complete L-type calcium channel blockade eliminates spontaneous firing or has almost no effect in two neurons differing by less than 1% in their maximal sodium conductance. The same prediction can be reproduced in a state of the art detailed model of a dopaminergic neuron. Some of these predictions are confirmed experimentally using single-cell recordings in brain slices. Our minimal model exhibits SOPs when sodium channels are blocked, these SOPs being uncorrelated with the spiking activity, as has been shown experimentally. We also show that block of a specific conductance (in this case, the SK conductance) can have a different effect on these two oscillatory behaviors (pacemaking and SOPs), despite the fact that they have the same initiating mechanism. These results highlight the fact that computational approaches, besides their well known confirmatory and predictive interests in neurophysiology, may also be useful to resolve apparent discrepancies between experimental results.

Figure 1. Equivalent circuit diagram of the model.

The model is composed of one compartment containing the conductances shown, in parallel with a membrane capacitance.

Figure 2. Comparison of the behavior of the detailed model (left) and of the minimal model (middle) in in vitro and in vivo-like conditions with experimental data obtained from dopaminergic neurons (right).

In each case, the neuron fires regularly in single spikes in vitro, and an inhibition of calcium-activated potassium channels induces burst firing in vivo. Experimental data are from Seutin (unpublished)(upper panel) and Drion (unpublished)(lower panel).

Figure 3. Analysis of the spontaneous activity of the minimal model.

(A) Variations of the membrane potential (top) and the intracellular calcium concentration (bottom) over time. (B) Sketch of the bifurcation diagram of the minimal model, with as the bifurcation parameter. The gray part corresponds to negative values of , which is non physiological. denotes the steady-state curve for each value of the bifurcation parameters. The dotted part of shows its unstable part. HB denotes a Hopf bifurcation and SN a saddle-node bifurcation. The trajectory of the membrane potential is plotted in red.

Figure 4. Cooperation between sodium and calcium channels in the generation of spontaneous activity in the minimal model and in the detailed model.

The center panels show the type of pacemaker activity according to the value of sodium and L-type calcium conductances. The white zone represents the couples of conductances which result in a hyperpolarized state of the cell and the dark blue zone accounts for pacemaking. Each insert shows the behavior of the model in control condition and during a blockade of L-type calcium channels or sodium channels for a particular set of conductances. The pacemaker behavior of the model strongly relies on the values of both the sodium and the L-type calcium conductances.

Figure 5. Effect of sodium and L-type calcium channel blockade on the firing of SNc dopaminergic neurons in vitro.

(A1) Extracellular recording of a DA cell in control conditions (left) and after application of 20 M nifedipine (right). (A2) Same as (A1) after a 80 reduction of the sodium conductance by the superfusion of 30 nM TTX. (B) Evolution of the mean firing rate (samples of 2 minutes) of a DA cell over time. (C) Mean firing frequency (N = 6) for each condition (mean sem). A simultaneous application of TTX and nifedipine affects the firing of the cells more strongly, as compared to the application of either of the two compounds alone. All experiments were performed in the presence of blockers of synaptic transmission. Note that the superfusion of the blockers produces an excitation of the neurons, which can be attributed to the block of inhibitory D2 autoreceptors. *P0.05, **P0.01, ***P0.001.

Figure 6. Ability of a N-type, but not of a T-type calcium current, to drive pacemaker activity in the absence of all other calcium channels in the detailed model.

(A) Variations of the membrane potential of the modeled neuron over time when all calcium currents are blocked, in the presence of N-type calcium channels and in the presence of T-type calcium channels, from left to right, respectively. (B) Same as (A), but during an inhibition of sodium channels. N-type calcium channels in sufficient density are able to generate an oscillatory behavior, contrary to T-type calcium channels.

Figure 7. Analysis of the effect of SK channel blockade on the spontaneous activity of the minimal model.

(A and B) Variations of the membrane potential over time (top) and sketch of the bifurcation diagram of the minimal model (bottom, with as the bifurcation parameter) in the presence and in the absence of SK channels. The grey part corresponds to negative values of , which are non physiological. denotes the steady-state curve for each value of the bifurcation parameters. The dotted part of shows its unstable part. HB denotes a Hopf bifurcation and SN denotes a saddle-node bifurcation. Trajectories of the membrane potential are plotted in red. (C and D) Same as (A and B) but when sodium channels are blocked. The frequency of SOPs is almost halved, whereas the frequency of spikes is barely affected. This simulations were performed in the absence of noise, which would induce irregularities in the absence of SK channels.

Figure 8. Comparison of the pacemaking (“spikes”) and slow oscillatory potentials (“SOPs”) in the minimal model.

Note that the simulations have been performed using in vitro-like conditions (low amplitude noise). (A) Interspike interval histograms (ISIh's) of a set of modeled cells in the presence (left) and in the absence (right) of SK channels. The light blue bars account for spikes in control conditions and the dark blue bars for SOP oscillations during sodium channel blockade. (B) Comparison of the rate of spikes and SOPs for different values of and . (C) Plot of successive spike intervals (light blue) or successive SOP intervals (dark blue) of a set of modeled cells. Although they are driven by the same mechanisms, spikes and SOPs are not correlated. Moreover, SOPs are more sensitive to the noise.