Conceived and designed the experiments: GD RS VS. Performed the experiments: GD LM. Analyzed the data: GD LM RS VS. Contributed reagents/materials/analysis tools: GD. Wrote the paper: GD RS VS.
The authors have declared that no competing interests exist.
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.
Dopamine is a neurotransmitter which plays important roles in the control of voluntary movement, motivation and reward, attention, and learning. Dysfunction of midbrain dopaminergic systems is involved in various diseases such as Parkinson's disease, schizophrenia and drug abuse. This underlines the importance of a tight regulation of dopamine levels in the brain. At the cellular level, the release of dopamine is directly correlated to the type of electrical activity (the firing pattern) of nerve cells that produce it, the so-called “dopaminergic neurons”. Therefore, an in depth understanding of the mechanisms underlying the electrical behavior of dopaminergic neurons is of critical importance to find new strategies for the treatment of diseases that result from dysfunction of this system.
Midbrain dopaminergic (DA) neurons sustain important physiological functions such as control of movement
The nature of the channels involved in the low frequency pacemaking of DA neurons is still strongly 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 (see
Reference | Nature of the preparation | Agent used | Observed effect |
Nedergaard et al., 1993 | Slices from adult guinea-pigs, SNc, intracellular recordings. | nifedipine ( |
Cessation of firing at undisclosed concentration. |
Mercuri et al., 1994 | Slices from adult Wistar rats, SNc and lateral VTA, intracellular recordings. | nifedipine and nimodipine ( |
Decrease in the firing rate of about 50 |
Puopolo et al., 2007 | Acutely dissociated neurons from the SNc of juvenile (16 day-old) mice, whole cell recordings. | Cessation of firing in all neurons (17/17).Firing rate decreased in 9/17 neurons.Firing rate decreased in 10/14 neurons. | |
Chan et al., 2007 | Slices from juvenile mice (younger than P21), SNc, cell-attached and whole-cell recordings.Slices from young adult mice (older than P28), SNc, cell-attached and whole cell recordings. | isradipine ( |
“Firing largely unaffected” (but firing reduced by an |
Guzman et al., 2009 | Slices from both juvenile and young adult mice, SNc, cell-attached and whole cell recordings | isradipine ( |
Firing unaffected. |
Putzier et al., 2009 | Slices from juvenile rats (younger than P21), SNc, whole cell recordings | nimodipine ( |
Cessation of firing. |
Khaliq and Bean, 2010 | Slices from both juvenile and young adult mice, medial VTA, whole cell recordings | Firing increased three-fold. | |
Seutin et al., unpublished | Slices from adult ( |
nifedipine ( |
Firing unaffected (N = 5).Variable effects, no clear trend (N = 5). |
SNc: substantia nigra, pars compacta; VTA : ventral tegmental area. Rodents are classified as juvenile (
In the presence of the sodium channel blocker tetrodotoxin (TTX), DA neurons also exhibit slow oscillatory potentials (SOPs)
In this paper, we use a mathematical analysis to extract the mechanisms underlying the spontaneous activity of DA neurons. For this purpose, we develop a minimal model of a DA neuron, in which we include the minimal set of conductances that are able to reproduce the firing patterns exhibited by these cells (see below). This minimal model is able to exhibit pacemaker firing in the absence of synaptic afferents, and to switch from a low frequency single-spike firing to bursting when SK channels are blocked in the presence of excitatory inputs, as reported experimentally
The main conclusion of our analysis is that pacemaker firing in DA neurons is sustained by the cooperation of sodium and L-type calcium channels (and more modestly N-type or P/Q-type calcium channels
As a secondary conclusion, our model shows that, even though the initiation of SOPs and spikes is sustained by the same mechanism, these oscillatory patterns are not correlated, which is in agreement with experimental results
In order to extract the essential mechanisms of pacemaking of DA neurons, we developed a minimal model endowed with the minimal set of conductances which is necessary to reproduce the firing patterns of these cells. The conductances present in the model are shown in
The model is composed of one compartment containing the conductances shown, in parallel with a membrane capacitance.
The proposed minimal model is able to reproduce the firing patterns exhibited by DA neurons, namely pacemaker firing
In each case, the neuron fires regularly in single spikes
The frequency of the spontaneous activity is limited by calcium influx. Indeed, a rise of the cytoplasmic calcium concentration strongly reduces the excitability of the cell. Therefore, to ensure a calcium entry (resp. exit) during the spike generation (resp. between two successive spikes), one or several types of calcium channels (resp. calcium pumps) must be present. Moreover, in order to generate a spontaneous activity even in the absence of calcium-activated potassium channels (as is observed in DA neurons
In the absence of synaptic inputs, DA neurons fire spontaneously in a very regular manner
(
The mechanisms involved in the pacemaker activity of the minimal model can be fully understood using bifurcation analysis. The bifurcation diagram shown in
The low threshold in
The important consequences of this cooperation are illustrated in
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.
Panels
In order to confirm that the spontaneous initiation of spikes in DA neurons is mainly sustained by the cooperation between sodium and L-type calcium channels, we performed extracellular recordings (additional to those reported in
We next tested the effect of 20
(
These recordings were performed on eleven neurons. In one case, nifedipine completely inhibited the spontaneous activity of the cell. In four other cells, nifedipine produced little effect, whereas TTX completely suppressed the firing (not shown). In the six other neurons, coapplication of nifedipine and TTX inhibited the firing to a greater extent than either agent alone. Indeed, an ANOVA test showed that the firing rate of the neurons was different in the four experimental conditions (synaptic blockers alone, +nifedipine, +TTX, +TTX and nifedipine, F
The fact that L-type calcium channels and sodium channels can cooperatively drive the pacemaker activity of DA neurons can be explained by comparing the I-V curves of the two currents (Supplementary
This similarity is observed in the detailed model as well (Supplementary
(
Our minimal model also sheds light on the mechanisms of, and related controversies on, slow oscillatory potentials (SOPs). Indeed, it has experimentally been shown that SNc DA neurons exhibit SOPs during application of TTX
In addition, it has been reported that block of the SK current on TTX-treated DA neurons strongly affects the shape of SOPs. Namely, this manipulation significantly increases the duration of the depolarizing and hyperpolarizing phases
For a sufficiently high value of
(
In contrast, sodium channel blockade has a critical impact on the high threshold. Indeed, the Hopf bifurcation which defines the high threshold in pacemaking vanishes when sodium channels are blocked. As a consequence, the high threshold of SOPs is defined at the right saddle-node bifurcation, which is masked by the Hopf bifurcation in control conditions. This implies that, whereas the depolarization mechanism is identical in spikes and SOPs, the repolarization mechanisms are different.
This difference has significant consequences on the model behavior, all consistent with experimental data:
SK channel blockade has little effect on the left saddle-node bifurcation but a dramatic effect on the right one (compare
There is no reason to expect a strong correlation between spikes and SOPs.
Note that the simulations have been performed using
In addition, Guzman et. al recently showed that spikes are much more regular than SOPs in DA neurons
These results show that a lack of correlation between spikes and SOPs does not necessarily imply that the generating mechanism of these two oscillatory behaviors is different. Therefore, this experimental observation may not be used to dismiss a role of L-type calcium channels in the generation of spikes in DA neurons.
In spite of many experimental studies, the precise mechanisms underlying the spontaneous initiation of spikes in DA neurons are still largely debated in the literature. Using our minimal model as well as a detailed model of a DA neuron, we extracted two critical parameters for the low frequency spontaneous firing.
Firstly, low-frequency single-spike firing and high-frequency intra-bursts firing have to be sustained by two dynamics operating on different time scales. Fast firing is limited by the refractory period of action potentials, which is fixed by the kinetics of voltage-gated channels. On the other hand, the dynamics that are the most likely to limit the rate of low-frequency firing are the variations of the intracellular calcium concentration. Indeed, an accumulation of calcium in the cytoplasm strongly reduces the excitability of the cells, through the inactivation of depolarizing currents (i.e. L-type calcium currents) and the activation of hyperpolarizing currents (i.e. calcium pumps and SK channels). This is in agreement with experimental data, which show that replacement of calcium with either cobalt
Secondly, the spontaneous initiation of action potentials in DA neurons is the result of the cooperation between various depolarizing currents. In agreement with the experimental results of Putzier et al.
The most contradictory experimental results obtained on DA neurons are probably those concerning the role of L-type calcium channels in the spontaneous initiation of spikes
Such subtle differences in conductance parameters are quite likely to occur in various experimental conditions. For example, it has recently been shown that there are quantitative differences between DA neurons from the SNc and the VTA in terms of density of these conductances
A second source of contradictory experimental results might be the difference between the preparations that are used in different laboratories. For instance, in the case of DA neurons, in which the initial segment is often remote from the soma
SOPs exhibited by DA neurons during blockade of sodium channels have been largely studied
DA neuron electrophysiology has been modeled by several groups
There are some conceptual differences between our minimal model and some earlier models. For example, the calcium current included in the Wilson and Callaway model
One limitation of our minimal model is that it is essentially qualitative and does not take into account the very specifics of DA neurons. However, because of its generality, our model could be a starting point to analyze similar firing patterns of a number of other cell types. Finally, our analysis demonstrates the value of a simplified model to reconcile apparently contradictory experimental observations.
All procedures were carried out in accordance with guidelines of the European Communities Council Directive of 24 November 1986 (86 609 EEC) and were accepted by the Ethics Committee for Animal Use of the University of Liège (protocol 86).
The model follows the common equation
The equation giving the membrane potential variations over time is as follows:
All the ionic currents equations follow a Hodgkin-Huxley scheme
The values of the parameters used for the simulations are given in
Parameter | Value |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Simulations were performed using the Neuron software, which is freely available for download at
Bifurcation diagrams were drawn both using the graphical Matlab package matcont (which is freely available for download at
Adult (200–250 g) male Wistar rats were housed in groups of three or four, supplied with food and water ad libitum, and maintained on a 12 hour light/dark cycle.
Rats were anesthetized with chloral hydrate (400 mg/kg, i.p) and decapitated. The brain was extracted out of the skull in less than 1 min and cooled in ice-cold (
Horizontal slices (400
Action potentials (amplitude: 200 to 1000
Electrophysiological criteria were used in order to identify DA neurons. In vitro, these neurons exhibit a very regular firing pattern and long (
Only one cell was studied per slice. All recordings were made in the substantia nigra pars compacta area. Drugs were applied by superfusion at known concentrations using three-way taps. Each concentration was applied for at least 10 min to ensure that the drug concentration reached equilibrium in the tissue. Drug effects were quantified by calculating the mean firing frequency over the 5 last minutes of the control period and over the last minute during which the drug was superfused. Synaptic blockers were superfused throughout all experiments unless stated otherwise. Neurons whose firing rate varied by more than 5
The activity of DA neurons was recorded in control conditions for 5 minutes. Synaptic blockers (10
The sources of the drugs used were as follows. CGP55845, CNQX, MK801, TTX and Nifedipine were obtained from Tocris Cookson (Bristol, UK). SR95531 was obtained from Sigma (St Louis, MO, USA). Sulpiride was a gift from Sanofi-Aventis.
Experimental data were analyzed with a global ANOVA test for correlated values, followed by Tukey's post-hoc tests for comparisons between groups.
Cooperation between sodium and calcium channels in the generation of spontaneous activity in the detailed model. The center panel shows the type of pacemaker activity according to the sodium and L-type calcium conductances. The white zone represent the couples of conductances which results to a spontaneous hyperpolarization of the cell and the dark blue zone account 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, respectively. The pacemaker behavior of the model strongly relies on the values of both the sodium and the L-type calcium conductances.
(EPS)
Effect of synaptic blockers and a D2 receptor agonist on the firing rate of SNc DA neurons in brain slices. (A) Mean firing frequency (samples of 2 minutes) of the recorded cells over time (mean
(EPS)
I-V curves of various depolarizing currents in the two models. I-V curves of sodium channels (in red) and of L-type calcium channels (in black) of the minimal model (A) and of the detailed model (B). For the detailed model, I-V curves of N-type (in blue) and T-type (in dotted black) calcium channels are also plotted. The only current which has a significantly different half-activation potential as compared to the L-type calcium current is the T-type calcium current.
(EPS)
Analysis of the slow oscillatory potentials of the minimal model. (A) Variations of the membrane potential (top) and of the intracellular calcium concentration (bottom) over time. (B) Sketch of the bifurcation diagram of the minimal model, with
(EPS)
Comparison of the calcium dynamics during pacemaking and slow oscillatory potentials. (A and B) Evolution of membrane potential (top) and calcium oscillations (bottom) over time in control conditions and during a sodium blockade, respectively. (C) Variations of intracellular calcium concentrations during both oscillatory patterns.
(EPS)
Effect of sodium channel density on the response of the detailed model to calcium channel blockade. Response of the detailed model to an inhibition of all calcium channels for two slightly different values of sodium channel density. (A and B) Variations of the membrane potential over time in control conditions (left) and after the blockade of all calcium channels (right) for two different sodium conductances. Note how dramatically the value of
(EPS)
The authors gratefully acknowledge several constructive discussions with Drs. Margaret Rice (New York University), Dominique Engel (University of Liege) and Pierre Maquet (University of Liege). They also gratefully acknowledge Maxime Bonjean (Salk Institute for Biomedical Studies) for his contribution to the implementation of the detailed model.