Abstract
The level of expression of ion channels has been demonstrated to vary over a threefold to fourfold range from neuron to neuron, although the expression of distinct channels may be strongly correlated in the same neurons. We demonstrate that variability and covariation also apply to the biophysical properties of ion channels. We show that, in rat substantia nigra pars compacta dopaminergic neurons, the voltage dependences of the A-type (IA) and H-type (IH) currents exhibit a high degree of cell-to-cell variability, although they are strongly correlated in these cells. Our data also demonstrate that this cell-to-cell covariability of voltage dependences is sensitive to cytosolic cAMP and calcium levels. Finally, using dynamic clamp, we demonstrate that covarying IA and IH voltage dependences increases the dynamic range of rebound firing while covarying their amplitudes has a homeostatic effect on rebound firing. We propose that the covariation of voltage dependences of ion channels represents a flexible and energy-efficient way of tuning firing in neurons.
Introduction
The ability of any specific ion channel to participate in a given firing feature (e.g., spike duration, spike amplitude, burst duration, rebound properties) has been studied and described in many different neuronal types in numerous invertebrate and vertebrate species (Hille, 2001). More recently, experimental and theoretical studies have suggested that whenever multiple currents contribute to the same firing feature, numerous solutions are available to cells to achieve the same output (Goldman et al., 2001; MacLean et al., 2003; Prinz et al., 2004; Burdakov, 2005; Swensen and Bean, 2005; Marder and Goaillard, 2006; Schulz et al., 2006; Puopolo et al., 2007; Taylor et al., 2009; Hudson and Prinz, 2010; Marder and Taylor, 2011). In mouse cerebellar Purkinje cells, knocking down the Nav1.6 sodium channel does not significantly disrupt bursting behavior because the effect of knocking down this channel is partially compensated by an increase in amplitude of a low-threshold calcium current (Swensen and Bean, 2005). In the lobster stomatogastric nervous system, microinjecting pacemaker neurons with mRNA encoding for the Shal channel [carrying the rapidly inactivating A-type (IA) potassium current] does not modify spontaneous bursting because the increase in IA is compensated by a correlated increase in the amplitude of the hyperpolarization-activated H-type (IH) cationic current (MacLean et al., 2003).
These studies using artificial manipulations of ion channel expression have led to the hypothesis that coregulation of properties of functionally overlapping ion channels in unperturbed neurons may constitute a powerful mechanism for precisely defining specific firing patterns and maintaining them over the lifetime of a neuron (Marder and Goaillard, 2006). Consistent with this hypothesis, recent studies performed in the invertebrate nervous system have demonstrated that numerous ion channels/currents display correlated levels of expression/amplitude in unperturbed populations of neurons (MacLean et al., 2005; Schulz et al., 2006, 2007; Khorkova and Golowasch, 2007; Goaillard et al., 2009; Tobin et al., 2009; Temporal et al., 2011). Moreover, some of these correlations in ion channel properties were demonstrated to be cell-type specific and strongly predict the functional output of the neuron (Schulz et al., 2007; Goaillard et al., 2009). Yet little is known about whether coregulation of ion channels occurs in unperturbed mammalian neurons, and whether they involve biophysical properties and/or the level of expression/amplitude of channels/currents.
We studied rebound firing in substantia nigra pars compacta (SNc) dopaminergic neurons and analyzed the respective involvement of IH and IA in this firing feature. First, we demonstrate that these two currents have opposite and complementary influences on rebound delay. We show that the voltage dependences of IH and IA are highly variable from cell to cell but are strongly positively correlated in the same cells. We then demonstrate that intracellular cAMP and calcium levels strongly alter the covariation of IA and IH voltage dependences. Strikingly, increasing cAMP in the presence of a fast calcium chelator induces a coordinated shift in the voltage dependences and reduces their variability. Finally, we show that covarying the maximum conductances of these currents stabilizes rebound firing, while covarying the voltage dependences of the currents according to their biological distribution increases the dynamic range of rebound firing. We suggest that covariation of voltage dependences provides a flexible and efficient way of tuning rebound firing.
Materials and Methods
Midbrain slice preparation.
Acute slices were prepared from P16–P22 Wistar rats of either sex. All experiments were performed according to the European and institutional guidelines for the care and use of laboratory animals (Council Directive 86/609/EEC and French National Research Council). Rats were anesthetized with halothane (Nicholas Piramal India) and decapitated. The brain was immersed briefly in oxygenated ice-cold low-calcium artificial CSF (aCSF) containing the following (in mm): 125 NaCl, 25 NaHCO3, 2.5 KCl, 1.25 NaH2PO4, 0.5 CaCl2, 4 MgCl2, and 25 glucose, pH 7.4, oxygenated with 95% O2/5% CO2 gas. The cortices were removed and then coronal midbrain slices (250 μm) were cut in ice-cold oxygenated low-calcium aCSF on a vibratome (Leica VT 1200S). Following 30–45 min incubation in oxygenated low-calcium aCSF at 32°C, the acute slices were then incubated for a minimum of 30 min in oxygenated aCSF (containing in mm: 125 NaCl, 25 NaHCO3, 2.5 KCl, 1.25 NaH2PO4, 2 CaCl2, 2 MgCl2, and 25 glucose, pH 7.4, oxygenated with 95% O2/5% CO2 gas) at room temperature before electrophysiological recordings.
Drugs.
We used kynurenate (2 mm, Sigma-Aldrich), picrotoxin (100 μm, Sigma-Aldrich), tetrodotoxin (TTX; 1 μm, Alomone Labs), ZD7288 (3 and 30 μm, Tocris Bioscience), Androctonus mauretanicus mauretanicus toxin 3 (AmmTX3, 3 nm–2 μm), 1,2-bis(2-aminophenoxy) ethane-N,N,N′,N′-tetra-acetic acid (BAPTA; 5 or 10 mm, Tocris Bioscience), 2′,5′-dideoxy adenosine 3′-triphosphate tetrasodium (ddA; 20 μm, Sigma-Aldrich), and 8-Bromo-cAMP sodium salt (8-Br-cAMP; 25 μm, Tocris Bioscience). Kynurenate, picrotoxin, tetrodotoxin, ZD7288, and AmmTX3 were used to block excitatory synaptic activity, inhibitory synaptic activity (current-clamp recordings), the TTX-sensitive sodium currents (voltage-clamp recordings), and the IH and IA currents, respectively, and were bath applied via continuous perfusion in aCSF, except for concentrations of AmmTX3 ≥30 nm (which were applied directly into the bath with the bath perfusion briefly arrested until the toxin took effect). BAPTA, ddA, and 8-Bromo-cAMP were present in the patch pipette solution.
Electrophysiology recordings and analysis.
All recordings (342 cells in current-clamp, voltage-clamp, or dynamic clamp) were performed on midbrain slices continuously superfused with oxygenated aCSF at 30–32°C. Picrotoxin and kynurenate were systematically added to the aCSF for all recordings to prevent contamination of the intrinsically generated activity by glutamatergic and GABAergic spontaneous synaptic activity. Patch pipettes (1.8–2.5 MΩ for voltage-clamp recordings) were pulled from borosilicate glass (GC150TF-10 for voltage-clamp, Harvard Apparatus) on a DMZ-Universal Puller (Zeitz Instruments) and filled with a patch solution containing the following (in mm): 20 KCl, 10 HEPES, 10 EGTA, 2 MgCl2, 2 Na-ATP, and 120 K-gluconate, pH 7.4, 290–300 mOsm. Whole-cell recordings were made from SNc dopaminergic neurons visualized using infrared differential interference contrast videomicroscopy (QImaging Retiga camera; Olympus BX51WI microscope), and were identified based on their location, large size (soma >30 μm; see Fig. 1A), and electrophysiological profile (regular slow pacemaking activity, large spike half-width, large sag in response to hyperpolarizing current steps; see Fig. 1C,D). Tyrosine-hydroxylase immunolabeling in 73 neurobiotin (0.05% in patch solution; Vector Labs) tracer-filled cells confirmed this electrophysiological identification (see Fig. 1B). Briefly, slices were fixed with 4% paraformaldehyde overnight at 4°C and were immunolabeled (protocol modified from Wolfart et al., 2001) with sheep antityrosine hydroxylase (Millipore; 1:9000), followed by donkey anti-sheep Alexa Fluor 488 (Invitrogen; 1:1000; 2 μg/ml) and Streptavadin Alexa Fluor 594 (Invitrogen; 1:12,000; 166.7 ng/ml).
For voltage-clamp experiments, only whole-cell recordings with an uncompensated series resistance <7 MΩ (compensated 85–90%) were included in the analysis. For current-clamp pharmacology experiments, higher series resistances were tolerated as long as the bridge compensation was properly adjusted to 100%. Liquid junction potential (+13.2 mV) and capacitive currents were compensated on-line. To ensure that variability in voltage measurements was not due to the slow appearance of offset potentials during the recording, offset potentials were measured after removing the pipette from the neuron. Offset values were negligible (≤1 mV) and therefore not corrected for. Recordings were acquired at 10 kHz and were filtered with a low-pass filter (Bessel characteristic 2.9 kHz cutoff frequency). For current-clamp recordings, 1 s hyperpolarizing current steps were injected to elicit a hyperpolarization-induced sag (due to IH activation). Short synaptic-like hyperpolarizing currents were also injected to mimic a single GABAergic input (diexponential inputs; 4.6 ms rising time constant, 47.4 ms decaying time constant) (Tanaka et al., 2009). For proper comparison of rebound properties across cells and pharmacological conditions, long hyperpolarizing current steps were adjusted to obtain an average voltage value of either −84.9 ± 1.8 mV or −71.9 ± 1.3 mV at the end of the hyperpolarizing pulse in all cells, and short synaptic-like hyperpolarizing inputs were adjusted to obtain an average voltage value of −84.9 ± 2.1 mV or −71.9 ± 1.5 mV at the peak of the hyperpolarization. Vkink was defined as the voltage point where the voltage first derivative reaches a plateau (corresponding to the start of the linear phase II).
For voltage-clamp recordings of IA and IH, tetrodotoxin was also added to the aCSF. The total potassium current was elicited by 500 ms voltage steps from a holding voltage of −100 mV to test potential between −80 and −5 mV (500 ms, 5 mV increments). The delayed rectifier potassium current was elicited by a protocol consisting of a 500 ms prestep at −50/−40 mV (to fully inactivate IA) followed by voltage steps between −50/−40 and 10 mV (500 ms, 5 mV increments). The IA current was then isolated by subtraction (total potassium current − delayed rectifier current). The peak of the isolate IA measured during the incremental pulses between −80 mV and −5 mV was then divided by potassium driving force with a reversal potential of −100 mV. Peak conductance was then plotted against the voltage of the corresponding voltage step and was fitted with a Boltzmann function as follows:
where I0 is basal current, Imax is the maximal current, V is voltage, V50 is half-activation voltage, and b scales the voltage sensitivity of activation/inactivation.
IA V50 and IA b were extracted from this analysis. IA time constant of activation and inactivation were obtained using a diexponential fit (exponential rise to maximum and exponential decay) of the current. To assess IA inactivation properties, 500 ms voltage steps were applied from −40 to −120 mV (in increments of −5 mV) followed by a 500 ms voltage step at −40 mV. Then, the peak current measured during the pulse to −40 mV was plotted against the voltage of the conditioning prepulses to obtain the inactivation curve of IA. Data were fitted with a Boltzmann function (four-parameter sigmoidal function, see equation), and V50 and b were extracted from this analysis.
A two-step voltage-clamp protocol was used to determine the voltage-dependent activation of IH. A prepulse to various holding potentials from −60 to −130 mV (increments of −5 mV associated with progressive decrements in step duration) was used to activate IH to different extents. A subsequent pulse to −130 or −120 mV was used to measure the degree of activation of IH independent of changes in driving force. Finally, the amplitude of IH measured during the pulse to −130 or −120 mV was plotted against the voltage of the prepulse, and the data were fitted using the Boltzmann function equation. V50, b, and IH Imax were extracted from this analysis. IH time constant of activation was obtained using single exponential fits of the current at the different voltage steps.
Dynamic-clamp recordings and analysis.
To model IH and IA, all the parameters for the conductance definitions were extracted from our voltage-clamp recordings (see Tables 1, 2; Fig. 7). The voltage dependence of the time constant of IH activation (IH τm) was fitted with a four-parameter peak Gaussian equation (see Fig. 7B; n = 27, average fit) and the values of the holding potential at the peak of the Gaussian fit were extracted (see Tables 1, 2, Vτ) and plotted against the IH activation V50 values. As there was a significant positive correlation between Vτ and IH activation V50 (linear regression, R = 0.84, p < 0.001, n = 27), when IH activation V50 was shifted in the modeled IH, Vτ was shifted accordingly. The voltage dependencies of IA time constant of activation (IA τm) and inactivation (IA τh) were fitted with a Boltzmann function (four-parameter sigmoidal function, see equation; n = 19; see Fig. 7C,D, average fit). However, there was no correlation between the IA τm or IA τh V50 values and the IA activation and inactivation V50 values, respectively (R = 0.07, p = 0.79, n = 19; R = 0.07, p = 0.81, n = 19, respectively). Thus, for the model of IA, IA τm and IA τh were not shifted in conjunction with the activation and inactivation curves of IA. For the data presented in Figure 9C, values of injected maximum conductances (gmA, gmH) were normalized to the input conductance to account for the shunting effect of background membrane conductances on the efficiency of injected conductances. Input conductance was measured using a hyperpolarizing current-clamp pulse after complete blockade of IA and IH.
To inject the models of IA and IH, we used the SM-2 software developed by Hugh Robinson (Robinson, 2008) (Cambridge Conductance), which runs on a scriptable digital-signal-processing (DSP)-based system for dynamic conductance injection. Conductance definitions for IH and IA were compiled and downloaded from the PC to a P-25M DSP board (Innovative Integration), which executes the conductance injection with a sampling rate of 40 KHz over a 2 V range with a resolution of 0.1 mV.
Data acquisition and analysis.
Data were acquired using an EPC 10 USB patch-clamp amplifier (HEKA) and the Patchmaster software acquisition interface (HEKA). Analysis was performed using FitMaster v2x30 (Heka) and Igor Pro (version 6.0, WaveMetrics). The statistical analysis, performed according to the distribution properties of the data, included linear regression, multiple linear regression, product moment (Pearson), rank order correlation (Spearman), unpaired t test, Mann–Whitney, paired t test, Fisher test (for variance comparison), one-way ANOVA, standard sigmoidal fitting procedure, and Gaussian fitting procedure (all conducted using SigmaPlot 10.0, Jandel Scientific), with p < 0.05 considered to be statistically significant. Figures were prepared using SigmaPlot, GraphPad Prism 5, Igor Pro, Photoshop CS4, and Adobe Illustrator CS4. Unless otherwise stated, data are presented as mean ± SEM in figures and as mean ± SD in the main text.
Results
Dissecting the rebound properties of SNc dopaminergic neurons
To investigate the roles of IA and IH in the rebound properties of SNc dopaminergic neurons, we first performed a detailed current-clamp analysis of these neurons in P16–P22 rat acute midbrain slices. SNc dopaminergic neurons were identified based on their location, size, and morphology (Fig. 1A) and their characteristic electrophysiological properties (Kita et al., 1986; Grace and Onn, 1989; Kitai et al., 1999) (Fig. 1C). In 72 of 73 cells, the dopaminergic identity was confirmed by post hoc tyrosine hydroxylase (a dopamine synthesis enzyme) immunolabeling (Fig. 1B). Consistent with the numerous studies performed on this preparation (Kita et al., 1986; Grace and Onn, 1989; Kitai et al., 1999; Nedergaard, 1999; Liss et al., 2001; Putzier et al., 2009), most dopaminergic neurons displayed low-frequency pacemaker activity (mean frequency, 1.41 ± 0.75 Hz, n = 116), with slow action potentials (mean half-width, 1.56 ± 0.38 ms, n = 125; Fig. 1C), and a characteristic response to long hyperpolarizing current steps consisting of a large voltage sag (>30 mV) during current injection and a biphasic repolarization after hyperpolarization is released (Fig. 1D). While the sag is thought to be essentially the consequence of the activation of IH (Franz et al., 2000; Neuhoff et al., 2002), the biphasic rebound most likely reveals the influence of IA at subthreshold potentials (Kita et al., 1986; Nedergaard, 1999). The rebound was separated into two successive phases based on its voltage trajectory (Fig. 1E): an immediate repolarization phase after release from hyperpolarization (phase I) leading to a kink (Vkink is the membrane potential at this point), from which arises a slow repolarization phase (phase II), leading to spike threshold. While the duration of phase I was not correlated with rebound delay, both Vkink and the slope of repolarization during phase II (phase II slope) showed significant correlations with rebound delay [Vkink vs log(rebound delay), R = −0.648, p < 0.001, n = 118; log(phase II slope) vs log(rebound delay), R = −0.963, p < 0.001, n = 118, Pearson; Fig. 1F,G]. Vkink and phase II slope also shared a significant positive correlation, such that phase II slope increased when Vkink depolarized [log(phase II slope) vs Vkink, R = 0.592, p < 0.001, n = 138, Pearson], suggesting that these two parameters may be mediated by common mechanisms.
Identification of SNc dopaminergic neurons and dissection of rebound properties. A, Infrared image of a dopaminergic neuron and the patch pipette. B, Left, Fluorescent streptavidin labeling of a neuron filled with neurobiotin. Right, Tyrosine hydroxylase immunolabeling of the same neuron. C, Characteristic electrophysiological properties of SNc dopaminergic neurons. Top row, Left, Current-clamp recording showing the typical pacemaker tonic firing of a dopaminergic neuron. Right, Histogram of the log-normal distribution of the interspike interval (inverse of the instantaneous frequency). Bottom row, Left, Current-clamp recording showing the typical slow action potential waveform of a dopaminergic neuron. Right, Histogram of the log-normal distribution of action potential half-width. Dashed lines indicate −60 mV. D, Rebound waveform in SNc dopaminergic neurons. Top, Current-clamp recording of a typical response of a neuron to a 1 s hyperpolarizing current step leading to −120 mV, showing the clear kink in the repolarization. The gray trace represents the current step from 0 to −125 pA. Bottom, The rebound elicited by short diexponential synaptic-like pulses also displayed a biphasic repolarization. The gray trace represents the −287 pA current injection. E, Expanded version corresponding to the gray box in D. Two phases of repolarization (phase I, phase II) are distinguished based on the rate of repolarization. The transition point was named “kink” and the corresponding voltage Vkink. F, Scatter plots summarizing the correlation between rebound delay and Vkink. Top, Scatter plot showing the relationship between rebound delay elicited by 1 s steps (gray circles) or short synaptic-like (black circles) hyperpolarizing stimuli. Bottom, Scatter plot illustrating the significant correlation between log (rebound delay) and Vkink for long hyperpolarizations (R, p, and n values are on the plot). G, Scatter plots summarizing the correlation between rebound delay and phase II slope. Top, Scatter plot showing the relationship between rebound delay and phase II slope elicited by 1 s (gray circles) or short synaptic-like (black circles) hyperpolarizing pulses. Bottom, Scatter plot illustrating the significant correlation between log (rebound delay) and log (phase II slope) for long hyperpolarizations (R, p, and n values are on the plot). Scale bars: A, B, 20 μm. Calibration: C, Top, 20 mV, 1 s; C, Bottom, 20 mV, 2 ms; D, Top, 20 mV, 200 ms; D, Bottom, 20 mV, 200 ms; E, 20 mV, 20 ms.
Although long hyperpolarizing current steps such as those used here (1 s duration, leading to voltages of −84.0 ± 1.8 mV at the end of the pulse) constitute the typical protocol used to analyze rebound properties (Harris-Warrick et al., 1995; Neuhoff et al., 2002), we wanted to determine whether such rebound behavior could be triggered by more “physiological” stimuli. As GABAergic synaptic inputs represent >70% of the total number of synaptic inputs received by SNc dopaminergic neurons (Tepper and Lee, 2007), we also used short current injections reproducing the waveform of a GABAergic IPSC (Tanaka et al., 2009; scaled to reach a peak hyperpolarization of −84.9 ± 2.1 mV; Fig. 1D). Although these events were shorter and induced a milder hyperpolarization than the 1 s current step, they triggered a very similar biphasic rebound (Fig. 1D). Moreover, the quantitative relationships between Vkink, phase II slope, and rebound delay for the short synaptic-like hyperpolarizations lay along the same distribution as those observed for long hyperpolarizations (Fig. 1F,G).
IA and IH have opposite and complementary effects on rebound firing
To determine the precise contribution of IA and IH to the rebound properties, we tested the effect of specific blockers of the channels underlying these currents in dopaminergic neurons. In SNc dopaminergic neurons, IA and IH are carried by the long isoform of the potassium Kv4.3 channel (Liss et al., 2001; Hahn et al., 2003) and by subunits 2, 3, and 4 of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, respectively (Franz et al., 2000; Neuhoff et al., 2002). While ZD7288 was used to block IH (Neuhoff et al., 2002; Chan et al., 2007), we used the scorpion toxin AmmTX3, a pore-blocker for the Kv4 channel family (Vacher et al., 2002, 2004), to block IA (Fig. 2). In SNc dopaminergic neurons, nanomolar concentrations of AmmTX3 selectively blocked IA and increased spontaneous pacemaking frequency (Fig. 2, p < 0.01, n = 9, paired t test), as expected for IA blockers in these cells (Nedergaard, 1999; Liss et al., 2001; Putzier et al., 2009). We used nonsaturating concentrations of AmmTX3 (300 nm) and ZD7288 (3 μm), which suppress 60–85% of either current but did not disrupt the characteristic biphasic waveform of the rebound (Fig. 3). AmmTX3 and ZD7288 were applied consecutively to neurons in randomized order. As their effects were consistent with respect to the induced changes in rebound delay, phase II slope, and Vkink for all hyperpolarizing protocols independent of the order in which they were applied, the data were pooled into before and after AmmTX3/ZD7288 application datasets.
Characterization of AmmTX3 activity in SNc dopaminergic neurons. A, AmmTX3 blocks IA without modifying gating properties. Left, Voltage-clamp recordings of IA (step to −40 mV from holding potentials of −40, −60, −70, and −80 mV shown beneath traces) obtained from the same neuron in control conditions (top, black traces) and in the presence of 100 nm AmmTX3 (bottom, gray traces). Right, Inactivation curves corresponding to the traces presented on the left. Note that AmmTX3 only reduces the amplitude of the current without modifying the inactivation properties. B, Dose–response curve of the effect of AmmTX3 on IA amplitude in SNc dopaminergic neurons in acute brain slices. Numbers above the points indicate the number of cells used for the quantification of the effect of the toxin at different concentrations. C, 300–600 nm AmmTX3 blocks IA but does not affect the delayed rectifier potassium current (n = 5) or IH (n = 4). Top, Voltage-clamp recordings of IA (left, step to −40 mV from a −100 mV prestep shown beneath traces) and the delayed rectifier potassium current (right, step to −10 mV from a −40 mV prestep shown beneath traces) from the same neuron in control (black traces) and in the presence of 300 nm AmmTX3 (gray traces). Bottom, Voltage-clamp recordings of IA (left, step to −40 mV from a −100 mV prestep shown beneath traces) and IH (right, step to −110 mV from a −60 mV prestep shown beneath traces) from the same neuron in control (black traces) and in the presence of 300 nm AmmTX3 (gray traces). Note that while IA is almost completely abolished by toxin application, the potassium-delayed rectifier current and IH are not affected. D, AmmTX3 has the expected effect of IA blockers on spontaneous pacemaker activity. Top and Middle, Current-clamp recordings of spontaneous activity in a neuron in control condition (top) and in the presence of 300 nm AmmTX3 (middle). Bottom, Scatter plot showing the significant increase in spontaneous frequency induced by 300 nm AmmTX3 in nine SNc dopaminergic neurons. Dashed lines indicate −60 mV (current-clamp) or 0 pA (voltage-clamp). **p < 0.01. Calibration: A, 2 nA, 100 ms; C, Top right and left, 2 nA, 200 ms; C, Bottom left, 1 nA, 100 ms; C, Bottom right, 250 pA, 500 ms; D, 20 mV, 2.5 s.
Effects of specific blockers of IA and IH on rebound properties. A, Rebound response induced by a 1 s hyperpolarizing pulse (−84.0 mV at the end of the pulse) in control (top trace), in the presence of 300 nm AmmTX3 (middle trace), and in the presence of AmmTX3 + 3 μm ZD7288 (bottom trace). Bottom, Bar plot showing the average rebound delay values before and after the application of AmmTX3 and ZD7288. B, Rebound response induced by a 1 s hyperpolarizing pulse (−71.9 mV at the end of the pulse) in control (top trace), in the presence of 3 μm ZD7288 (middle trace), and in the presence of ZD7288 + 300 nm AmmTX3 (bottom trace). Bottom, Bar plot showing the average rebound delay before and after the application of AmmTX3 and ZD7288. C, Same experimental protocol as in A, but using short synaptic-like hyperpolarizations (−84.9 mV at the peak) to induce the rebound. Bottom, Bar plot showing the average rebound delay before and after AmmTX3 and ZD7288 application. D, Same experimental protocol as in B, but using short synaptic-like hyperpolarizations (−71.9 mV at the peak) to induce the rebound. Bottom, Bar plot showing the average rebound delay values before and after AmmTX3 and ZD7288 application. The gray traces in A–D represent the current stimulus. *p < 0.05, **p < 0.01, ***p < 0.001. Dashed lines in traces indicate −60 mV. Calibration: A–D, 20 mV, 500 ms.
ZD7288 and AmmTX3 induced opposite changes in rebound firing in response to both long and short synaptic-like hyperpolarizations leading to voltages of −84.0 at the end and −84.9 at the peak of the pulse, respectively (Fig. 3A,C). When using long hyperpolarizing steps, AmmTX3 significantly decreased rebound delay (p < 0.001, n = 14, paired t test), increased phase II slope (p = 0.007, n = 9, paired t test), and depolarized Vkink (p = 0.001, n = 9, paired t test), while ZD7288 significantly delayed rebound firing (p < 0.001, n = 22, paired t test), decreased phase II slope (p < 0.001, n = 18, paired t test), and hyperpolarized Vkink (p = 0.003, n = 18, paired t test; Fig. 3A; see Fig. 8D), consistent with previous observations (Neuhoff et al., 2002). These effects were consistent with the correlations between Vkink, phase II slope, and rebound delay described earlier (Fig. 1F,G). AmmTX3 and ZD7288 also significantly decreased (p < 0.001, n = 6, paired t test) and increased (p = 0.023, n = 14, paired t test) rebound delay, respectively, after short synaptic-like hyperpolarizations (Fig. 3C). As the hyperpolarizing protocols used so far could potentially enhance IH involvement in the rebound responses, we also induced rebound firing using hyperpolarizations that resulted in voltages of −71.9 ± 1.3 and −71.9 ± 1.5 mV at the end of the pulse for long hyperpolarizations and at the peak for the short hyperpolarizations, respectively (Fig. 3B,D). These milder hyperpolarizations are equivalent to the trough voltage recorded during spontaneous pacemaking (−72.1 ± 4.4 mV, n = 162) and induce a weaker activation of IH (Fig. 3B,D). Even in these conditions, AmmTX3 and ZD7288 significantly decreased and increased rebound delay, respectively, for both long (p < 0.001, n = 8, paired t test; p < 0.001, n = 13, paired t test) and short hyperpolarizations (p < 0.05, n = 5, paired t test; p < 0.05, n = 8, paired t test; Fig. 3B,D). Moreover, the magnitude of the effects of ZD7288 and AmmTX3 on rebound delay was not statistically different between the −84 and −72 mV long and short hyperpolarization protocols (one-way ANOVA; p = 0.24, p = 0.40, respectively; Fig. 3). These results confirm that common biophysical mechanisms involving predominantly IA and IH underlie rebound firing, and suggest that IA and IH complementarity may be involved in physiological responses to inhibitory inputs.
Variability and correlations in the biophysical properties of IA and IH
To determine the biophysical basis of the strong functional complementarity of IA and IH, we measured the amplitude, voltage dependence, and kinetics of IH and IA in 109 SNc dopaminergic neurons. We first observed that dopaminergic neurons exhibit widely different IA and IH amplitudes and voltage dependences (Fig. 4A–C). While variability in the amplitude of currents (Fig. 4B) has already been described for various currents in many systems (including IA and IH in SNc neurons) (Liss et al., 2001; Golowasch et al., 2002; Neuhoff et al., 2002; MacLean et al., 2005; Swensen and Bean, 2005; Schulz et al., 2006, 2007; Khorkova and Golowasch, 2007; Goaillard et al., 2009; Temporal et al., 2011), we found that other properties, such as voltage dependence, can also display a high degree of variability from cell to cell (Fig. 4C). The variability in voltage dependence [represented by the activation and inactivation midpoints (V50)] and amplitude was independent of age (age vs IH activation V50 or IA inactivation V50: R = −0.164, p = 0.098, n = 104, Pearson; or R = −0.24, p = 0.168, n = 125, Pearson; age vs IH or IA amplitude: R = −0.07, p = 0.48, n = 84, Spearman; or R = 0.058, p = 0.747, n = 33, Spearman, respectively) and of the input resistance of the neurons (input resistance vs IH activation V50 or IA inactivation V50: R = 0.114, p = 0.294, n = 86, Spearman; or R = 0.0852, p = 0.38, n = 108, Spearman; input resistance vs IH or IA amplitude: R = −0.0543, p = 0.647, n = 73, Spearman; or R = −0.227, p = 0.226, n = 30, Spearman, respectively). Various studies have shown that the inactivation and activation properties of the Kv4 channels can be regulated either independently (Anderson et al., 2010) or in a coordinated manner (Hoffman and Johnston, 1998; Yu et al., 1999; Levy et al., 2010). We measured IA activation properties in a subset of neurons (n = 32) and found that the half-inactivation and the half-activation voltages of IA were positively correlated (R = 0.418, p = 0.017, Pearson). Consistent with the coordinated shift in IA inactivation and activation V50 values, IA amplitude measured at −40 mV was found to be negatively correlated with IA inactivation V50 in the whole population (Fig. 5D, gray circles; R = −0.614, p < 0.001, n = 83, Spearman), as less current is generated at a given potential when the activation curve shifts toward depolarized potentials.
Variability and covariation of IA and IH biophysical properties. A, Top, Voltage-clamp recordings of IH in two dopaminergic neurons in response to hyperpolarizing pulses at −80, −100, and −120 mV from a holding potential of −60 mV, followed by a pulse at −130 mV. Bottom, Voltage-clamp recordings of IA in the same cells in response to a depolarizing pulse to −60, −50, and −40 mV from a holding potential of −100 mV. Dashed lines indicate 0 pA. B, Scatter plots showing the variability in amplitude of IH maximum current recorded at −130 mV (left) and IA recorded at −40 mV (right). Black and gray lines indicate the mean and SD, respectively. C, Scatter plots showing the variability in the voltage dependence of activation of IH (left) and inactivation of IA (right). Black and gray lines indicate the mean and SD, respectively. D, Left, IH activation (dashed line) and IA inactivation (solid line) curves corresponding to the cells presented in A. Right, Scatter plot showing the significant positive correlation between IH activation and IA inactivation V50 values. In B–D, the black and gray circles correspond to the voltage-clamp recordings of the two neurons presented in A. E, Left, Scatter plot showing the relationships between the time after breaking into whole-cell configuration and IA inactivation (small empty circles) or IH activation (small gray circles) V50 values for the cells presented in Figure 4D, right. Large circles represent the average values of IA inactivation (black) and IH activation (gray) V50 values for each 5 min time window following break-in to whole-cell configuration (the n for each 5 min time window is indicated at the top and bottom of the plot). Note the lack of a significant correlation between IA inactivation V50 values and time following break-in, and the significant correlation between the time following break-in and IH activation V50 values (R, p, and n values are indicated on the plot). Right, Plot showing no change between the average IA inactivation V50 values in the same cells (n = 10) recorded immediately after obtaining whole-cell configuration (0–1 min) and again after 9–16 min. Calibration: A, Top, 500 pA, 2 s; Bottom, 4 nA, 200 ms. Error bars represent SD.
IA and IH covariation of voltage dependences is sensitive to cytosolic calcium and cAMP concentrations. A, Scatter and box plots illustrating the effect of BAPTA on IH activation and IA inactivation voltages. Compared with the control population (A–C, gray circles/boxes; n = 109 and 95 for IA inactivation and IH activation V50 values, respectively), the addition of 5 mm BAPTA to the patch pipette (white circles/boxes) significantly depolarizes the inactivation V50 of IA (n = 22), but not the activation V50 of IH (n = 22). The replacement of EGTA with 10 mm BAPTA in the patch pipette (black circles/boxes) significantly depolarizes both IA inactivation and IH activation V50 values (n = 38 and 35, respectively). B, Scatter and box plots showing the effects of ddA and 8-Br-cAMP on IA inactivation and IH activation V50 values. ddA (white circles/boxes) significantly hyperpolarized IH activation V50 (n = 22), but did not significantly shift IA inactivation V50 (n = 28). 8-Br-cAMP (black circles/boxes) significantly depolarized both IA inactivation (n = 21) and IH activation (n = 17) V50 values. C, Scatter and box plots illustrating the effect of the coapplication of 10 mm BAPTA and 8-Br-cAMP on IA inactivation and IH activation V50 values. Data show that 10 mm BAPTA/8-Br-cAMP (black circles/boxes) significantly depolarized IA inactivation (n = 24) and IH activation (n = 22) V50 values (black asterisks), and also significantly reduced the variability (gray asterisks, F test) for both IA inactivation and IH activation V50 values compared with the control population. D, Scatter plot illustrating the negative linear regression (R = −0.663, p < 0.001) present between IA inactivation V50 and the amplitude of IA measured at −40 mV in the control population (gray circles), and the alignment of the average values for the control population (large gray circle), 5 mm BAPTA (white square), 10 mm BAPTA (black square), and 10 mm BAPTA/8-Br-cAMP conditions (gray diamond) along this regression line. Box-and-whisker plots in A–C represent the median value and first and third quartiles (box), and the minimum and maximum values of the distribution (whiskers). Error bars in D represent SD. *p < 0.05, **p < 0.01, ***p < 0.001.
We then wondered whether the functional complementarity between IA and IH could emerge from the coregulation of some of their biophysical properties. Studies mostly performed on invertebrates have shown that the amplitude of IA and IH or the levels of expression of the channels carrying IA and IH are positively correlated in various cell types (MacLean et al., 2005; Schulz et al., 2007; Tobin et al., 2009; Cao and Oertel, 2011). As the large amplitude of IA (>20 nA) in SNc dopaminergic neurons prevents an accurate measurement of the maximum conductance of the current in most SNc dopaminergic neurons, we were able to determine the maximum conductances of both IA and IH in a small subset of neurons (n = 23), and did not observe a statistically significant correlation between these parameters (R = 0.258, p = 0.242, n = 22, Spearman). Surprisingly, though, measuring IH activation properties and IA inactivation properties revealed that their voltage dependences were positively correlated (R = 0.613, p < 0.001, n = 85, Pearson; Fig. 4D). In addition, there was also a significant positive correlation between IH activation V50 and IA activation V50 (R = 0.459, p = 0.0315, n = 22, Spearman). When the time of recording following breaking into whole-cell configuration was compared with IA inactivation V50, there was no significant change over time (R = 0.131, p = 0.232, n = 85, Spearman; Fig. 4E). Rundown experiments verified that IA inactivation V50 values did not change over time during whole-cell recording in the same cells: IA was measured immediately following break-in and again after 9–16 min (p = 0.573, n = 10, paired t test; Fig. 4E). However, there was a small but significant hyperpolarization of IH activation V50 over time (−0.32 mV/min, R = 0.343, p = 0.001, n = 85, Spearman; Fig. 4E), as has been previously reported (Zolles et al., 2006). Nevertheless, significant variability was present for IH activation and IA inactivation V50 values recorded within 5 min of obtaining whole-cell configuration (Fig. 4E). Importantly, despite the slight hyperpolarization of IH over time, there was a significant correlation between IH and IA V50 values in subsamples of cells from narrow time windows at the beginning (1–7.5 min, R = 0.673, p < 0.001, n = 31, Spearman), middle (8–11 min, R = 0.532, p = 0.0013, n = 34, Spearman), or end (11.5–19 min, R = 0.692, p < 0.001, n = 20, Spearman) of the time range. These data demonstrate that cytoplasmic dialysis was not responsible for the variability of IA inactivation and IH activation V50 values or their covariation.
IH and IA covariation of voltage dependences is sensitive to cAMP and calcium levels
We then considered the potential molecular machinery underlying the IA and IH covariation in voltage dependences. Kv4.3 channels in the SNc dopaminergic neurons are associated with the calcium-sensitive auxiliary subunit KChip3.1 (Liss et al., 2001). Thus, IA properties might be modulated by calcium variations (An et al., 2000), as has been demonstrated in other cell types (Patel et al., 2002; Anderson et al., 2010). Furthermore, two of the three subunits responsible for IH in SNc dopaminergic neurons (HCN2 and HCN4; Franz et al., 2000) are very sensitive to cAMP variations (Biel et al., 2009), and two out of the three adenylyl cyclases detected in the SNc dopaminergic neurons are inhibited by calcium (Chan et al., 2007). Therefore, we investigated whether locking intracellular calcium and cAMP levels could induce a coordinated shift of IA and IH voltage dependences and/or reduce the variability of their covariation.
Cells recorded with the fast calcium chelator BAPTA (5 mm) added to the control intracellular solution exhibited IA inactivation V50 values slightly depolarized compared with the control population (average of −69.91 ± 3.07 vs −73.18 ± 4.48, p < 0.001, n = 22 vs n = 109, Mann–Whitney), but no significant change in IH activation V50 values (p = 0.64, n = 22 vs n = 95, Mann–Whitney; Fig. 5A). However, using an intracellular solution containing 10 mm BAPTA and no EGTA resulted in a larger depolarization of IA inactivation V50 (−64.81 ± 2.13 vs −73.18 ± 4.48, p < 0.001, n = 38 vs n = 109, unpaired t test) and a slight but significant depolarization of IH activation V50 (−90.78 ± 3.16 vs −92.72 ± 4.24, p = 0.015, n = 35 vs n = 95, unpaired t test; Fig. 5A). Interestingly, the IA inactivation V50 values measured in 10 mm BAPTA were located within the range recorded in control condition, but clustered at the depolarized edge of the range.
To manipulate the cytosolic cAMP levels, we first used a nonselective adenylyl cyclase inhibitor ddA (20 μm) to induce a decrease in cAMP concentration (Chan et al., 2007). While ddA induced a significant hyperpolarization of IH activation V50 values (−94.8 ± 3.55 vs −92.72 ± 4.24, p = 0.0186, n = 22 vs n = 95, Mann–Whitney), IA inactivation V50 values were unaffected (p = 0.19, Mann–Whitney; Fig. 5B). We then used the nondegradable cAMP analog 8-Br-cAMP (25 μm) to artificially increase the cytosolic cAMP level, resulting in a significant depolarization of both IH activation V50 (−80.23 ± 3.5 vs −92.72 ± 4.24, p < 0.001, n = 17 vs n = 95, Mann–Whitney) and IA inactivation V50 values (−69.99 ± 2.58 vs −73.18 ± 4.48, p < 0.001, n = 21 vs n = 109, Mann–Whitney; Fig. 5B).
These experiments demonstrate that IA and IH are affected by changes in both cytosolic calcium and cAMP, with IA being more sensitive to calcium manipulation while IH is more sensitive to cAMP manipulation. As dopaminergic SNc neurons possess the molecular machinery to enable cross talk between the cAMP and calcium signaling pathways (Chan et al., 2007), we also tested the effect of combining 10 mm BAPTA with 8-Br-cAMP. This condition resulted in a dramatic depolarization of both IA inactivation V50 (−65.96 ± 2.07 vs −73.18 ± 4.48, p < 0.001, n = 24 vs n = 109, Mann–Whitney) and IH activation V50 (−80.12 ± 2.69 vs −92.72 ± 4.24, p < 0.001, n = 24 vs n = 95, Mann–Whitney; Fig. 5C). Most interestingly, combining BAPTA and 8-Br-cAMP was associated with a significant reduction in the variability of IA inactivation (Fisher test to compare variances, F = 4.7, p < 0.001) and IH activation (F = 2.49, p = 0.015) V50 values (Fig. 5C), effectively restricting the covariation of IH and IA voltage dependencies to a small region of the parameter space. While the values recorded in control condition covered a range of 23.0 and 23.4 mV for IA inactivation and IH activation V50 values, respectively, the values recorded in BAPTA plus 8-Br-cAMP were clustered in a range of 7.9 and 10.2 mV, respectively. Moreover, these values aligned with the distribution of values recorded in the control population. These data strongly suggest that the variability in IH and IA V50 values is partly due to the cell-to-cell variability in the local levels of calcium and cAMP. Additionally, this observation demonstrates that the large variability in IH and IA voltage dependences in control condition is not a consequence of uncompensated offsets, as this measurement error would be independent of pharmacological agents. Interestingly, the depolarization and restricted variability of the values obtained in BAPTA plus 8-Br-cAMP were not associated with an increase in input resistance compared with control, therefore ruling out space-clamp errors as the source of variability in voltage dependence of IA and IH. Furthermore, in experimental conditions in which IA inactivation was significantly depolarized (5 mm BAPTA, 10 mm BAPTA, BAPTA plus 8-Br-cAMP), the amplitude of IA measured at −40 mV was also significantly reduced, consistent with a coordinated depolarization of both IA activation and inactivation curves (Fig. 5D). Although other signaling pathways may be involved in the modulation of IA and IH biophysical properties, these experiments demonstrate that the covariability of IA and IH voltage dependences is sensitive to local calcium and cAMP levels.
IH and IA biophysical properties quantitatively determine rebound properties
What is the relationship between the different phases of the rebound and the biophysical properties of IA and IH? Since rebound firing and the properties of IA and IH were measured in the same neurons, we were able to determine whether specific properties of these currents correlated with rebound parameters. Both IA inactivation and IH activation V50 values positively correlated with Vkink (Fig. 6A, Pearson), while the IA time constant of inactivation (IA τh) negatively correlated with phase II slope (R = −0.533, p < 0.001, n = 88; Fig. 6B, Pearson performed on log transforms of the variables) and with rebound delay (R = 0.511, p < 0.001, n = 72, Pearson on log transforms). However, both IA inactivation and IH activation V50 values were not correlated with the action potential threshold (R = 0.186, p = 0.105, n = 77, Pearson, and R = 0.105, p = 0.402, n = 66, Pearson, respectively; Fig. 6C) or peak voltage (R = 0.178, p = 0.122, n = 77, Pearson; or R = 0.0259, p = 0.837, n = 66, Pearson, respectively; Fig. 6D). The lack of correlation between the voltage dependences of IH and IA and other voltage properties in the same cells is also important as it rules out the possibility that uncompensated voltage offsets might be responsible for the covariations in IH and IA voltage dependences. Although these results suggest that the variations in IA and IH biophysical properties may modulate the rebound profile, they do not demonstrate a causal relationship.
Summary of correlations between IA and IH biophysical properties and firing parameters. A, Scatter plot showing the significant positive correlations between the Vkink and IA inactivation (black) and IH activation (gray) V50 values. Gray lines indicate the linear regressions for IA and IH V50 values (R, p, and n values are at the top left and bottom right of the plot), respectively. B, Scatter plot illustrating the significant correlation between IA τh and phase II slope. The gray line (inset) indicates the linear regression between the log transforms of the variables. C, Scatter plot representing the absence of correlations between action potential threshold and IA (black) and IH (gray) V50 values. The dashed gray line indicates the linear regressions (R, p, and n values are on the plot). D, Scatter plot representing the absence of correlations between action potential peak and IA (black) and IH (gray) V50 values. The dashed gray line indicates the linear regressions (R, p, and n values are on the plot).
Thus, we used the dynamic-clamp technique to determine whether these correlations between IA and IH biophysical properties and the rebound parameters represented causal relationships. The dynamic-clamp-simulated IA and IH were injected into neurons after complete blockade of the endogenous IA and IH by saturating concentrations of AmmTX3 (2 μm) and ZD7288 (30 μm; Fig. 7F). All the parameters used in the dynamic-clamp experiments were extracted from the voltage-clamp measurements presented in Figure 4 (Fig. 7A–D; Tables 1, 2). It is important to note that no specific adjustment of biophysical parameters was performed to reproduce the effects of the currents on rebound firing. The traces in Figure 7E show that these parameters precisely reproduced the voltage-clamp recordings obtained for the biological currents. Using these nonadjusted parameters also accurately reproduced the rebound behavior observed in unperturbed SNc dopaminergic neurons (Fig. 7F). Indeed, simulating the average parameters of IA and IH yielded Vkink and phase II slope values very similar to the average values observed in current-clamp in unperturbed neurons (Vkink = −66.87 ± 1.0 vs −66.4 ± 3.9 mV, n = 10 vs n = 118, p = 0.31, Mann–Whitney; phase II slope = 62.72 ± 8.99 vs 57.4 ± 23.9 mV/s, n = 10 vs n = 118, p = 0.13, Mann–Whitney). This is particularly interesting since one of the drawbacks of the dynamic-clamp technique is that the simulated conductances are injected at a single point (in our case, the soma). If the currents characterized in voltage-clamp are mostly located far from the soma, space-clamp errors will contaminate the voltage-clamp measurements, and the simulation of these erroneous currents with dynamic clamp will not accurately reproduce the firing behavior observed in current-clamp in the unperturbed neurons (Storm et al., 2009). Our results argue that the biophysical properties of IA and IH in dopaminergic neurons can be accurately determined using whole-cell somatic recordings, and their influence on firing can be accurately tested using somatic dynamic clamp. Consistent with this, immunohistochemical labeling (Liss et al., 2001; and in our laboratory, data not shown) and voltage-clamp recordings from nucleated patches (Liss et al., 2001) and dissociated neurons (Puopolo et al., 2007) have also unambiguously demonstrated that IH and IA currents are present at high densities at the soma of SNc dopaminergic neurons. Moreover, since highly nonlinear relationships cannot be captured by averaging data (Golowasch et al., 2002; Marder and Taylor, 2011), reproducing the average firing behavior with dynamic-clamp-simulated average IA and IH suggests that the correlations between the biophysical properties of these currents are mostly linear or close to linearity.
Dynamic-clamp simulation of IA and IH reproduces rebound profile. A, Activation curves of IH and IA and inactivation curve of IA from the biological currents used for the dynamic clamp. B, Voltage dependence of the time constant of activation of IH. The black line indicates the Gaussian fit of the experimental measures of the time constant of activation of IH (gray circles, n = 27) used for the dynamic-clamp model. C, D, Voltage dependence of the time constants of activation (C) and inactivation (D) of IA. The black line indicates the sigmoidal fit of the experimental values (gray circles, n = 19) used for the dynamic-clamp model. E, Experimental traces (gray) and dynamic-clamp simulation (black) of IH (voltage steps to −80, −100, −120 mV from −60 mV) and IA (steps to −60, −50, −40 mV from −100 mV). F, Current-clamp recordings showing the rebound profile of a neuron in control condition (gray trace, top left and right), after complete blockade of IA and IH (2 μm AmmTX3, 30 μm ZD7288, bottom left), and after injection of the simulated IA and IH (black trace, top right). Bottom right, Dynamic-clamp IH (upper gray trace) and IA (lower gray trace) currents injected into the neuron during the rebound protocol. The black trace (bottom right) corresponds to the sum of the two currents. Dashed lines indicate −60 mV (current-clamp) or 0 pA (voltage clamp, dynamic clamp). Calibration: E, Top, 500 pA, 2 s; E, Bottom, 2 nA, 200 ms; F, 20 mV/100 pA, 250 ms. See Table 1.
Equations and parameters used for the dynamic-clamp models of IA and IH
Covariation of IA and IH voltage dependences
To validate the dynamic-clamp system, we simulated the AmmTX3 and ZD7288 pharmacology experiments by reducing the injected conductances (gmA or gmH) to 20% of their original values (Fig. 8A–D). Reducing gmA or gmH qualitatively and quantitatively reproduced the effects of partial inhibition of IA and IH on all rebound parameters (Fig. 8D): reducing gmA significantly decreased rebound delay (p < 0.001, n = 5, paired t test), increased phase II slope (p = 0.002, n = 5, paired t test), and depolarized Vkink (p = 0.045, n = 5, paired t test), while reducing gmH significantly increased rebound delay (p < 0.001, n = 5, paired t test), decreased phase II slope (p < 0.001, n = 5), and hyperpolarized Vkink (p < 0.001, n = 5; Fig. 8D). It is especially striking that the dynamic clamp not only qualitatively reproduces the effects of AmmTX3 and ZD7288 on rebound parameters but also produces quantitative effects extremely similar to the effects of the toxins (Fig. 8D, left and right columns).
Dynamic clamp reproduces the effects of partial inhibition of IA and IH. A, Rebound profile (top, black trace) of a neuron in response to the injection of average IA (100% gmA, bottom, light gray trace) and IH (100% gmH, bottom, black trace) conductances. B, Rebound profile in the same neuron (top, black trace) with 20% gmA and 100% gmH. C, Rebound profile in the same neuron (top, black trace) with 20% gmH and 100% gmA. D, Left column, Bar plots summarizing the effects of reducing gmA (20% gmA) or gmH (20% gmH) on rebound delay, phase II slope, and Vkink. Right column (shaded box), Bar plots summarizing the effect of blocking 60–85% of the IA and IH currents with AmmTX3 and ZD7288, respectively, on the different rebound parameters. The bar plots showing the effect of AmmTX3 and ZD7288 on rebound delay were also presented in Figure 3A. Dashed lines indicate −60 mV (current-clamp) or 0 pA (dynamic clamp). *p < 0.05, **p < 0.01, ***p < 0.001.
Covarying the amplitudes or the voltage dependences of IH and IA induces opposite effects on rebound delay
The covariation in amplitude of IA and IH has been proposed to represent a homeostatic mechanism (MacLean et al., 2003, 2005; Cao and Oertel, 2011). Our pharmacology experiments and their dynamic-clamp replicates indeed demonstrate that these two currents have opposite and complementary effects on rebound properties in dopaminergic neurons (Figs. 3, 8), suggesting that the covariation of their amplitudes should stabilize rebound properties. To demonstrate and quantify this principle, we simulated various combinations of gmA and gmH and analyzed the variations in rebound delays associated with these different sets of parameters (Fig. 9). We found that while different ratios of gmA/gmH yielded different values of rebound delay, modifying gmA and gmH while keeping the ratio constant (independent of its original value) tended to maintain the rebound delay value (Fig. 9C, gray lines). For example, modifying only gmA while keeping gmH constant induced a more pronounced change in delay than if both conductances were scaled together (Fig. 9A,B, traces 1–3). From these experiments, we were also able to determine the direction of maximum sensitivity of rebound delay in the parameter space (the optimal coordinated changes in gmA and gmH yielding maximal changes in delay): decreasing gmH by approximately threefold while increasing gmA by approximately fourfold (Fig. 9C, dotted line). Therefore, maintaining a constant ratio between IA and IH maximum conductances had a stabilizing (or homeostatic) effect on rebound properties.
Effects of varying gmA and gmH on rebound delay. A, Example traces showing the rebound profile (top traces) of the same neuron in response to the dynamic-clamp injection (IH, bottom black trace; IA, bottom gray trace; total injected current, bottom color trace) of various combinations of gmH and gmA: (1) 1 * gmH, 1 * gmA, (2) 2 * gmH, 2 * gmA, and (3) 1 * gmH, 2 * gmA with gmH = 16.6 nS and gmA = 380 nS. The numbers are used to identify the corresponding traces and points in B and C. B, Expanded superimposed current-clamp (top) and dynamic-clamp (bottom) traces corresponding to the traces shown in A. C, Summary bubble plot showing the effect of varying gmA and gmH on rebound delay. Increasing delay is coded by both color and size of the bubble: small blue bubbles correspond to short delays while big red bubbles correspond to long delays. Gray lines indicate constant ratio directions in parameter space. The dashed line corresponds to the direction of best sensitivity of delay in parameter space calculated by multiple linear regression of delay versus gmA and gmH (delay = 270 + 8.4 * gmA − 146 * gmH). In this plot, gmA and gmH were normalized to the input conductance of the neuron and do not have dimensions. Dashed lines indicate −60 mV (current-clamp) or 0 pA (dynamic clamp). Calibration: A, Top, 20 mV; A, Bottom, 200 pA 500 ms; B, Top, 20 mV; B, Bottom, 200 pA, 150 ms.
To determine what functional impact the covariation of voltage dependences observed in our voltage-clamp experiments (Fig. 4D) might have, we also tested different combinations of IA and IH V50 values inside or outside the biological distribution of values while using average values for gmA and gmH (Table 2) and keeping them constant (Fig. 10). Only IH activation V50 and IA inactivation V50 are represented, but IA activation V50 was also modified accordingly since it was found to be significantly correlated with IH activation V50 and IA inactivation V50 in voltage-clamp recordings. We specifically tested three combinations of values along the biological distribution centered on the mean of IA and IH V50 values (−73 ± 7.5 mV, −92.5 ± 4.35 mv, respectively; Fig. 10, conditions 1, 2, and 3), and compared these to a set of combinations equidistant and orthogonal to the biological distribution (Fig. 10, conditions 4 and 5). Interestingly, we found that the “biological” combinations of values were associated with a large variation in rebound delay (condition 1 vs 2, p = 0.013, n = 5; condition 3 vs 2, p = 0.028, n = 5, paired t test; Fig. 10) while “nonbiological” orthogonal combinations were associated with no significant change in rebound delay (condition 4 vs 2, p = 0.256, n = 5; condition 5 vs 2, p = 0.84, paired t test; Fig. 10). When using “biological” combinations, the changes in rebound delay were associated with changes in Vkink and phase II slope (Fig. 10B, example traces) consistent with the correlations observed in our voltage-clamp recordings (Fig. 6): hyperpolarizing the V50 values of IA and IH induced a significant hyperpolarization of the Vkink (average of −72.4 vs −66.9 mV, p < 0.001, n = 5, paired t test) and a decrease in phase II slope (45.9 vs 65.7 mV/s, p = 0.002, n = 5, paired t test), while depolarizing the V50 values had opposite and significant effects on Vkink (−61.2 vs −66.9 mV, p < 0.001, n = 5, paired t test) and phase II slope (82.8 vs 65.7 mV/s, p < 0.001, n = 5, paired t test). In contrast, for the orthogonal distribution, only the combination of depolarized IA and hyperpolarized IH (Fig. 10, condition 5) was associated with a slight depolarizing shift of Vkink (−65 vs −66.9 mV, p = 0.03, n = 5, paired t test). All other values were not significantly different from those obtained with the mean combination. Although the voltage dependences of other currents may covary with IA and IH V50 values in the biological population, these experiments demonstrate that the isolated covariation of IA and IH voltage dependences (while all other endogenous currents are not modified) is sufficient to accurately reproduce the correlations observed between the properties of IA and IH and the rebound profile in the biological population (Fig. 6). Thus, IA and IH properties have a critical influence on the response to inhibitory stimuli, independent of the variations in properties of other voltage-dependent currents.
Effects of covarying IH and IA voltage dependences on rebound delay. A, Left, Example current-clamp traces showing the rebound profile in the same neuron in response to the dynamic-clamp injection of “biological” combinations of voltage dependences of IA and IH (traces 1–3 correspond to depolarized, average biological values, and hyperpolarized V50 values, respectively; see C, corresponding points). Right, Example current-clamp traces showing the rebound profile in the same neuron in response to the dynamic-clamp injection of nonbiological “orthogonal” combinations of voltage dependences of IA and IH (traces 5, 2, and 4 correspond to hyperpolarized IH V50 and depolarized IA V50, average biological V50 values, and depolarized IH V50 and hyperpolarized IA V50 respectively; see corresponding points in C). B, Expanded current-clamp (top) and dynamic-clamp (bottom) traces corresponding to the traces presented in A. C, Summary bubble plot showing the effect of varying IA and IH voltage dependences on rebound delay. Variations in delay are coded by the size of the black bubbles. Filled light-gray circles correspond to the biological distribution of V50 values (Fig. 4D) and the gray line indicates the linear regression of these values. The dashed line corresponds to the direction orthogonal to the biological distribution. Numbers correspond to the traces presented in A and B. Asterisks indicate significant differences in delay compared with the mean value (2). ns, Nonsignificant. Calibration: A, 20 mV, 250 ms; B, Top, 20 mV; Bottom, 200 pA, 100 ms. Dashed lines indicate −60 mV (current-clamp) or 0 pA (dynamic clamp).
Unlike the covariation of maximum conductances, the covariation of voltage dependences seems to essentially have a “nonhomeostatic” effect on rebound properties as it enhances the dynamic range of rebound values. Moreover, Figure 11 clearly shows that covarying the voltage dependences of IA and IH along the biological distribution (>15 mV and 8.7 mV, respectively) induced a similar change in rebound delay as changing gmA/gmH by fourfold, suggesting that covarying the voltage dependences of IA and IH constitutes a much more efficient way of tuning rebound delay.
Comparing the effects of varying IH and IA voltage dependences or maximum conductances. Bubble plot showing the variations in normalized rebound delay (bubble diameter) associated with variable ratios of gmA/gmH (horizontally aligned bubbles) and the three different biological combinations of covarying voltage dependences of IH and IA (vertically aligned bubbles). Note that the changes in delay induced by a fourfold change in gmA/gmH and by a 15/8.7 mV shift in voltage dependences are of similar magnitude (small bubbles vs large bubbles).
Discussion
In the present study, we show that IA and IH voltage dependences are highly variable from cell to cell but strongly correlated in SNc dopaminergic neurons, and that this covariation is sensitive to calcium and cAMP levels. Furthermore, we demonstrate that this covariation plays a critical role in tuning rebound delay as it confers synergistic functional effects to otherwise antagonistic currents. This is the first time that the covariation of voltage dependences of two distinct currents has been demonstrated, that signals involved in the covariation have been identified, and that the functional influence of this covariation on firing has been quantified.
Variability and covariation of biophysical properties of IA and IH in SNc dopaminergic neurons
Variability in the properties of ion channels is a physiological phenomenon observed in numerous systems (Liss et al., 2001; Golowasch et al., 2002; Neuhoff et al., 2002; MacLean et al., 2005; Swensen and Bean, 2005; Schulz et al., 2006, 2007; Khorkova and Golowasch, 2007; Goaillard et al., 2009; Temporal et al., 2011). So far, a threefold to fourfold range of variability has been reported mainly at the level of ion channel expression or current amplitude. We describe a high degree of variability in the amplitudes and voltage dependences of IA and IH and a significant covariation of their voltage dependences (Fig. 4). Studies have reported similar levels of variability in the amplitude of IA (Liss et al., 2001) and IH (Neuhoff et al., 2002) in mouse SNc dopaminergic neurons. Furthermore, consistent with invertebrate studies (Schulz et al., 2006), Liss et al. (2001) found that the amplitude of the IA current scaled linearly with the level of expression of the Kv4.3 channel that underlies it. Our data are also consistent with previous reports of variability in the amplitude of IH (measured at −120 mV) in SNc neurons associated with a high degree of variability in rebound delay: cells with a large IH (due to a depolarized activation voltage and/or high density of channels) tended to have faster rebounds (Neuhoff et al., 2002). Moreover, a recent study demonstrated that wortmannin [an inhibitor of phosphatidylinositol-4,5-bisphosphate (PIP2) synthesis] induced a negative shift in the voltage dependence of IH associated with an increase in rebound delay in SNc dopaminergic neurons (Zolles et al., 2006).
Functional impact of the covariation on physiological activity patterns
Our dynamic-clamp experiments directly demonstrate that the covariation of the voltage dependences of IA and IH powerfully modifies rebound delay in SNc dopaminergic neurons (Fig. 10) and could play a critical role in shaping the response of these neurons to inhibitory inputs. Indeed, 70% of the synaptic inputs received by SNc dopaminergic neurons are GABAergic (Tepper and Lee, 2007), while dopamine release between neighboring cells is also responsible for long hyperpolarizations (Vandecasteele et al., 2008). A recent study using dynamic clamp in SNc dopaminergic neurons demonstrated that their response to trains of simulated GABAergic inputs was influenced by IH properties (Tateno and Robinson, 2011). The partial inhibition of IA and IH (Figs. 3, 8) also clearly showed the involvement of these two currents in rebound responses to short (single simulated GABAergic-like event) or longer (1 s current step) hyperpolarizing stimuli, even for mild hyperpolarizations. IA and IH have also been reported to be involved in pacemaking activity in SNc neurons (Liss et al., 2001; Seutin et al., 2001; Neuhoff et al., 2002; Okamoto et al., 2006; Zolles et al., 2006; Chan et al., 2007; Puopolo et al., 2007; Guzman et al., 2009; Putzier et al., 2009; Tateno and Robinson, 2011). Although we did not investigate relationships between IA and IH and spontaneous activity, it is likely that the covariation of voltage dependences would also influence pacemaking activity. Studies have reported that changing IH voltage dependence or amplitude induced significant changes in pacemaking frequency in SNc dopaminergic neurons (Zolles et al., 2006; Tateno and Robinson, 2011). Thus, the covariation of voltage dependences may also be relevant to understanding the regulation of SNc dopaminergic neuron firing in general.
Several studies indicate that the SNc dopaminergic neurons are heterogeneous, and that the intrinsic properties of these neurons may depend on (1) the localization of the neurons within the SNc or on their projection sites (Lammel et al., 2008; Liss and Roeper, 2008) or (2) the expression of the calcium-binding protein calbindin (Neuhoff et al., 2002). We found no relationship between IA and IH voltage dependences and the localization of the neurons in the SNc (for both mediolateral and rostrocaudal axes, n = 47 and 33, respectively; data not shown). Nonetheless, part of the variability in IH, IA, and rebound firing properties may be associated with the functional diversity of dopaminergic SNc neurons (Neuhoff et al., 2002; Lammel et al., 2008; Liss and Roeper, 2008).
Mechanisms underlying the covariation of voltage dependences
Our results demonstrate that calcium and cAMP potently modify the covariation of IA and IH voltage dependences (Fig. 6). The effects of BAPTA on IA and 8-Br-cAMP on IH are consistent with the well documented sensitivity of these currents to calcium and cAMP, respectively (Birnbaum et al., 2004; Sergeant et al., 2005; Zolles et al., 2006; Biel et al., 2009; Anderson et al., 2010). In addition, our data demonstrated a milder converse sensitivity of IH and IA to calcium and cAMP manipulation, respectively (Fig. 5). These data are consistent with the results from Chan et al. (2007) demonstrating that two of the three adenylyl cyclases expressed in SNc dopaminergic neurons are calcium-inhibited. Thus, the depolarization of IH V50 values by BAPTA is probably due to the release of the calcium inhibition on the adenylyl cyclases and subsequent increase in cAMP. Conversely, little evidence is available regarding Kv4 modulation by the cAMP signaling pathway (Hoffman and Johnston, 1998; Yang et al., 2001; Lin et al., 2010). Hoffman and Johnston (1998) demonstrated that IA inactivation and activation curves in hippocampal pyramidal neurons are depolarized by the cAMP-mediated activation of protein kinase A. Although pyramidal cells express only Kv4.2 (Chen et al., 2006), the high level of homology between Kv4.2 and Kv4.3 (including several phosphorylation sites) strongly suggests that Kv4.3 shares cAMP sensitivity (Schrader et al., 2002). Another study performed on SNc dopaminergic neurons also suggested that IA amplitude is modulated by cAMP through MAPK activation (Yang et al., 2001). Finally, the application of BAPTA plus 8-Br-cAMP not only shifted IA and IH voltage dependences in a coordinated manner, but also dramatically reduced their variability (Fig. 5C). Altogether, these data suggest that the covariation of IA and IH voltage dependences is strongly dependent on calcium and cAMP. However, we do not conclude that these are the only signals involved in the covariation in voltage dependences. For example, as both HCN and Kv4 channels have been shown to be sensitive to PIP2, this signaling pathway may also be involved (Oliver et al., 2004; Zolles et al., 2006).
Although our experiments were performed using globally imposed changes in calcium and cAMP, these signals are most likely confined to submembrane microcompartments in physiological conditions. As the fast calcium chelator BAPTA (producing local calcium buffering), but not EGTA, was able to significantly reduce the variability in IA and IH V50 values (Fig. 5), local calcium variations are likely involved in the covariation of IA/IH. Consistent with these results, Anderson et al. (2010) demonstrated that the Cav3-mediated modulation of IA inactivation properties in cerebellar granule cells was also blocked by 10 mm BAPTA but not by 10 mm EGTA. Subsequently, they showed that the Cav3 calcium channel modulation of IA relied on the formation of protein complexes comprising Kv4.2, KChip3.1, and Cav3 (Anderson et al., 2010). A similar molecular organization might be involved in the covariation of IA and IH voltage dependences in SNc dopaminergic neurons.
Coregulating conductances versus voltage dependences: homeostasis versus signal tuning?
Our dynamic-clamp results and other studies (MacLean et al., 2003; Cao and Oertel, 2011) demonstrate that IH and IA compensate each other and that firing properties are conserved when a constant gmA/gmH ratio between the two currents is maintained (Fig. 9). Therefore, the frequent correlation in the levels of mRNA for the channels carrying IH and IA (or in the current amplitude) in crustaceans (MacLean et al., 2005; Khorkova and Golowasch, 2007; Schulz et al., 2007; Tobin et al., 2009; Temporal et al., 2011) can be interpreted as a homeostatic mechanism. We demonstrated that a stable gmA/gmH ratio in SNc dopaminergic neurons indeed maintained rebound properties (Fig. 9) while the covariation in voltage dependences maximized the dynamic range of rebound delays (Fig. 10). Furthermore, our results show that covarying voltage dependences within the biological range of values has the same effect on rebound delay as changing the ratio between IH and IA maximum conductances by a factor of four (Fig. 11). This is especially striking since the range of values of V50 values used for the dynamic-clamp experiments covered only two-thirds of the total range observed in the voltage-clamp experiments. These values are also within the range of amplitudes of modulator-induced shifts in voltage dependence previously reported for IA (Harris-Warrick et al., 1995; Yu et al., 1999; Birnbaum et al., 2004; Levy et al., 2010) or IH (Harris-Warrick et al., 1995; Zolles et al., 2006; Biel et al., 2009). Data obtained in SNc dopaminergic neurons (Liss et al., 2001) and in invertebrates (MacLean et al., 2003; Schulz et al., 2006, 2007; Tobin et al., 2009; Temporal et al., 2011) suggest that changing the ratio of maximum conductances may rely on changing the levels of expression of the underlying channels. Alternatively, it could involve internalization of channels and/or degradation of channel proteins or mRNAs. However, such processes would be energy expensive and occur on a minute-to-hour time scale. Covarying voltage dependences represents a highly computationally efficient and energy-efficient way of tuning rebound properties. As the covariation of voltage dependences of IA and IH involves small signaling molecules (including calcium and cAMP) that can exhibit rapid dynamics, this covariation also provides a highly flexible way of tuning rebound properties. Therefore, in any given neuronal type, the appropriate firing pattern may be approximately achieved (coarse tuning) by coregulation of the expression of functionally overlapping ion channels (such as Kv4.3 and HCN in SNc dopaminergic neurons), with the coregulation of gating properties allowing for a secondary flexible fine-tuning of firing. Whether this tuning would occur in response to acute external signals, such as neurotransmitters or neuromodulators, or in response to chronic changes in excitability, is yet to be determined.
Footnotes
This work was funded by Institut National de la Santé et de la Recherche Médicale (Avenir Grant to J.-M.G., postdoctoral fellowship to J.A.), the Fyssen Foundation (J.-M.G.), Conseil Général des Bouches du Rhône CG13 (J.-M.G.), the National Health and Medical Research Council of Australia (postdoctoral overseas training fellowship 544940 to A.W.) and the Foundation pour la Recherche Médicale (postdoctoral fellowship to A.W.). We thank Armand Tasmadjian and Martial Dufour for technical assistance; Dr. Hélène Vacher, Dr. Fabien Tell, and Dr. Dominique Debanne for helpful discussions on the experiments; and Dr. Dominique Debanne, Dr. Michael Seagar, and Dr. Eve Marder for helpful comments on the manuscript.
The authors declare no competing financial interest.
- Correspondence should be addressed to Jean-Marc Goaillard, Avenir group Homeostasis of Excitability and Neuromodulation, Institute National de la Santé et de la Recherche Médicale UMR1072, Marseille 13015, France. jean-marc.goaillard{at}univ-amu.fr
