Loosely bound Zn2+ ions are increasingly recognized as potential modulators of synaptic plasticity and neuronal excitability under normal and pathophysiological conditions. Cav2.3 voltage-gated Ca2+ channels are among the most sensitive targets of Zn2+ and are therefore likely to be involved in the neuromodulatory actions of endogenous Zn2+. Although histidine residues on the external side of domain I have been implicated in the effects on Cav2.3 channel gating, the exact mechanisms involved in channel modulation remain incompletely understood. Here, we use a combination of electrophysiological recordings, modification of histidine residues, and computational modeling to analyze Zn2+-induced changes in Cav2.3 channel function. Our most important findings are that multiple high- and low-affinity mechanisms contribute to the net Zn2+ action, that Zn2+ can either inhibit or stimulate Ca2+ influx through Cav2.3 channels depending on resting membrane potential, and that Zn2+ effects may persist for some time even after cessation of the Zn2+ signal. Computer simulations show that (1) most salient features of Cav2.3 channel gating in the absence of trace metals can be reproduced by an obligatory model in which activation of two voltage sensors is necessary to open the pore; and (2) most, but not all, of the effects of Zn2+ can be accounted for by assuming that Zn2+ binding to a first site is associated with an electrostatic modification and mechanical slowing of one of the voltage sensors, whereas Zn2+ binding to a second, lower-affinity site blocks the channel and modifies the opening and closing transitions. While still far from complete, our model provides a first quantitative framework for understanding Zn2+ effects on Cav2.3 channel function and a step toward the application of computational approaches for predicting the complex actions of Zn2+ on neuronal excitability.

Introduction

Voltage-gated Ca2+ channels (VGGCs) participate in neuronal signaling and provide the key link between electrical signals and various nonelectrical processes, such as neurotransmitter release, transcription, and muscle contraction (Catterall, 1998; Hofmann et al., 1999; Neumaier et al., 2015). Their modulation by foreign (i.e., non-Ca2+) inorganic cations has proven instrumental in identifying the mechanisms underlying Ca2+-selective flux and may have important (patho)physiological implications. For example, the d-block metal ions Zn2+ and Cu2+ have been identified as endogenous modulators of neuronal transmission and synaptic plasticity and implicated in a number of pathophysiological conditions (Frederickson et al., 2000, 2005; Mathie et al., 2006). Cav2.3 channels, which are thought to be involved in synaptic transmission (Gasparini et al., 2001), action potential burst firing, and oscillatory activity (Christie et al., 1995; Magee and Carruth, 1999), are among the most sensitive targets for Zn2+ and Cu2+ currently known (Kang et al., 2007; Shcheglovitov et al., 2012). In addition, these channels have an expression pattern that coincides with the spatial distribution of loosely bound Zn2+ ions in the brain (Sochivko et al., 2002; Weiergräber et al., 2006b), suggesting that they could represent a main mediator for the reported anticonvulsive effects of endogenous Zn2+. Although nonconserved histidine residues in the voltage-sensor module (VSM) of domain I have been convincingly implicated in the effects of Zn2+ on Cav2.3 channel gating (Fig. 1 A; Kang et al., 2007; Shcheglovitov et al., 2012), the exact mechanisms involved and the potential role of additional metal binding sites remain incompletely understood. Here, we have used metal ion–buffered solutions, different experimental conditions, and computational modeling to explore the effects of Zn2+ on Cav2.3 channel function over a wide range of free Zn2+ concentrations. Based on our data, we have developed a Markov model that accounts for most salient features of Cav2.3 channel gating in the absence of trace metals and also reproduces their alteration by a range of Zn2+ concentrations previously estimated to be (patho)physiologically relevant. In addition, our results provide novel insights into the dependence of Zn2+ effects on the ionic conditions and reveal that changes in the neuronal resting membrane potential (RMP) could profoundly influence and even invert the net Zn2+ action from inhibition to stimulation. Taken together, our work provides a first quantitative framework for understanding Zn2+ effects on Cav2.3 channel function and a step toward the application of computational approaches for understanding the complex actions of Zn2+ on neuronal excitability and their dependence on the prevailing neuronal properties and ionic conditions.

Materials and methods

Cell culture

Human embryonic kidney (HEK293) cells stably transfected with human Cav2.3d and β3 Ca2+-channel subunits (Mehrke et al., 1997; Nakashima et al., 1998) were cultured under normal growth conditions (37°C and 5% CO2) in Dulbecco’s modified Eagle medium (Sigma-Aldrich) supplemented with 10% FCS and antibiotics (1% penicillin-streptomycin and selection markers; 1 mg ml−1 geneticin [G-418] and 200 µg ml−1 hygromycin B). Cells were routinely passaged twice a week using 0.05% trypsin/0.02% EDTA. For electrophysiological recordings, cells were seeded on nitric acid–washed glass coverslips and used within 24–48 h after plating.

Chemicals

HEPES (Pharmagrade), Tricine (Pharmagrade), La(III)chloride heptahydrate (99.999%), TEA chloride, Chelex 100 (sodium form), Zn(II)chloride (99.999%), pyruvic acid (98%), ATP, oxaloacetic acid, FBS, hygromycin B, geneticin, penicillin-streptomycin, hydrochloric acid (TraceSelect), and 70% nitric acid (ACS reagent) were purchased from Sigma-Aldrich. Anhydrous ethanol, diethylpyrocarbonate (high purity), sodium hydroxide 30% solution (suprapur), sodium chloride (puratronic, 99.999%; AlfaAesar), potassium chloride (puratronic, 99.997%; AlfaAesar) cesium chloride (99.999%; AlfaAesar), calcium chloride (99.99%; AlfaAesar), 50% cesium hydroxide solution (99.9%; AlfaAesar), D-glucose (AnalaR Normapur), and potassium hydroxide (99.98%) were purchased from VWR. 1,000 mM stock solutions of diethyl pyrocarbonate (DEPC) in anhydrous ethanol were prepared on the day of the experiments, kept on ice, and diluted into standard external solution immediately before use.

Preparation of buffered Zn2+ solutions

To avoid trace metal contamination and reduce uncertainties with regard to free metal ion concentrations in our recording solutions, we employed suitable labware and sample handling procedures, which have been outlined in detail in a previous publication (Neumaier et al., 2017). Briefly, all solutions were prepared using type 1 ultrapure water (Purelab Flex 2 by ELGA Labwater), metal-free pipette tips, and reagents of the highest purity available (see previous section). All containers used for preparation and storage were made from polymethylpentene, polystyrene, or low-density polyethylene and pretreated by a comprehensive cleaning procedure that involved rinses with alcohol, successive soaking in dilute (10%) hydrochloric and nitric acid, and extensive washes with type 1 ultrapure water. Before the addition of multivalent cations or chelators, all solutions were treated with the metal-chelating ion exchange resin Chelex 100 to remove adventitious metal ions. For most experiments, Tricine (10 mM) was used as a dual proton and metal ion buffer to prepare buffered Zn2+ solutions (solutions 1–3A in Table S1). Free Zn2+ concentrations above the useful range for buffering with Tricine were prepared in a HEPES-buffered background solution (solutions 1–3B in Table S1). There was no difference in the electrophysiological properties recorded in Tricine- versus HEPES-buffered solutions, suggesting that our methods were sufficient to reduce trace metal contamination below the limits for detection. To facilitate fast and complete reversal of metal ion effects during washout, however, the HEPES-buffered solution used for control recordings and washout was supplemented with 0.1 mM of the trace metal chelator diethylenetriaminepentaacetic acid. In all cases, pH-, temperature-, and ionic strength–corrected free metal ion concentrations were calculated with the general-purpose speciation software Visual MINTEQ and constants reported previously (Mohamed, 2007; Goldberg et al., 2002; Khalil et al., 2009). Apart from Zn2+ binding by Tricine, these calculations took into account the formation of hydroxide species and the (weak) binding by Tricine of Ca2+ ions so as to ensure that the estimated free Ca2+ concentration was the same in HEPES- and Tricine-buffered solutions.

Ionic and gating current recordings

Cells were voltage clamped using the whole-cell configuration of the patch-clamp technique (Hamill et al., 1981). Pipettes were prepared from thick-walled borosilicate glass capillaries (1.5/0.84 mm OD/ID; World Precision Instruments) using a P97 Micropipette puller (Sutter Instruments). Resistance of the resulting electrodes was between 1.5 and 6.5 MΩ when filled with standard internal solution. The bath was connected to ground via 140 mM sodium chloride agar bridges. Currents were sampled at 20 or 50 kHz and filtered at 10 kHz using an EPC9 amplifier (HEKA) controlled with HEKA’s Pulse software. Leak and capacitive currents were subtracted online using a –P/5 (for ionic currents) or –P/8 (for gating currents) protocol. Series resistance was compensated electronically by ≤90% and continuously monitored throughout the measurements. All experiments were performed at room temperature (20–22°C) and, unless noted otherwise, from a holding potential of −80 mV for ionic current recordings or −100 mV for gating current recordings. During the experiments, cells were constantly perfused with external solution at a rate of ∼2–4 ml min−1 using a gravity-driven perfusion system controlled by manual precision flow regulators (Sarstedt). The standard external solution for ionic current recordings contained (in mM) 120 NaCl, 5 KCl, 20 TEA chloride, 10 D-glucose, 10 Tricine, and 2.8/5.8 CaCl2 or 10 HEPES and 2.3/4.5 CaCl2 (= 2/4 mM free Ca2+; for details, see Table S1) with the pH adjusted to 7.4 using NaOH or HCl and osmolarity of 297–314 mOsm. Gating currents were recorded in the same HEPES-buffered solution but with 4 mM free MgCl2 (instead of CaCl2) and 0.1 mM free La3+ (0.2 mM LaCl3 + 0.1 mM EDTA) to block ionic currents. Ca2+ substitution by Mg2+ did not alter channel voltage dependence (Fig. S1 A), whereas 100 µM free La3+ shifted it by 8.3 ± 0.7 mV (n = 6 cells) to more depolarized test potentials (Fig. S1 B), which was taken into account by assuming a 10-mV shift during fitting.

The standard internal solution was composed of (in mM) 130 CsCl, 5 oxaloacetic acid, 5 creatine, 5 pyruvic acid, 10 EGTA, 10 HEPES, and 4 MgATP with the pH adjusted to 7.3 using CsOH and osmolarity of 275–295 mOsm. It was filtered through 0.2-µm surfactant-free cellulose acetate membranes (Corning) and kept on ice between the recordings. The liquid junction potential between internal and external solution (calculated using the JPcalc algorithm in pClamp 10; Molecular Devices) was ∼5 mV. Since no correction for the liquid junction potential was done, all voltages shown were actually 5 mV more negative.

Whole-cell protocols

During the experiments, currents were routinely monitored by application at 0.03 Hz of a 30-ms test pulse to +10 mV followed by 10-ms repolarization at −50 mV to record well-resolved tail currents. To construct steady-state I-V relationships, peak currents recorded with a protocol consisting of 25-ms test pulses to potentials between −80 mV and +60 mV (10-mV increments at 0.1 Hz) were normalized by the cell capacitance or maximum current amplitude under control conditions and plotted as a function of the test-pulse potential. Tail-current amplitudes recorded during repolarization to −50 mV at the end of the voltage steps were normalized to the maximum tail-current amplitude and plotted as a function of the prepulse potential to construct isochronous activation curves. Gating currents were recorded with the same protocol, except that the holding potential was −100 mV, the test pulse duration was reduced to 20 ms, and repolarization was also to −100 mV.

Instantaneous I-V (II-V) relationships were obtained with a protocol consisting of a fixed 10-ms prepulse to +60 mV followed by 40-ms test pulses to potentials between −80 mV and +60 mV (10-mV increments at 0.1 Hz). Instantaneous (tail) current amplitudes recorded during the test pulses were normalized by the cell capacitance or maximum tail current amplitude under control conditions and plotted as a function of the test-pulse potential.

The fraction of channels available for activation from different holding potentials was assessed by a protocol consisting of 2-s conditioning prepulses at potentials between −120 mV and +10 mV (10-mV increments at 0.1 Hz) followed by a fixed 35-ms test pulse to +10 mV. To construct prepulse inactivation (PPI) curves, peak current amplitudes recorded during the test pulse were normalized by the maximum amplitude and plotted as a function of the prepulse potential.

Data analysis and statistics

Leak-subtracted current traces were directly analyzed with PulseFit (HEKA) or exported for further processing with Microsoft Excel 2010 and OriginLab Pro (version 9; OriginLab).

I-V relationships were fitted with a combined Ohm–Boltzmann equation: 
I=(VmVrev)×Gmax/{1+exp[(VmV0.5)/k]},
(1)
where I is the (normalized) peak current density measured at the test potential Vm, Vrev the apparent reversal potential, Gmax the maximum slope conductance, V0.5 the voltage eliciting half-maximal inward currents, and k the slope factor. Isochronous activation and PPI curves were fitted with single Boltzmann equations: 
I/Imax=A2+(A1A2)/{1+exp[(VmV0.5)/k]},
(2)
where I/Imax is the normalized current corresponding to the prepulse potential Vm, V0.5 is the voltage of half-maximal activation (V0.5act) or inactivation (V0.5inact), k the activation (kact) or inactivation (kinact) slope factor, and A1 and A2 the initial and final values, respectively. Activation time constants were determined by single exponential functions fit to the rising phase of currents, which started when the current amplitude had reached 20% of its final value. Inactivation during 400-ms voltage steps was biexponential, but the slower time constant was often too slow to be determined reliably (τslow > 200–700 ms depending on the test potential), so that inactivation time constants were determined using a single exponential function with variable offset fitted to the decaying phase of currents. Tail current decay over a wide voltage range was quantified by the sum of up to three exponential functions, where the two faster time constants presumably reflect deactivation and the third, slowest time constant corresponds to inactivation. Weighted deactivation time constants were calculated according to the following equation: 
τw=(A1×τ1+A2×τ2)/(A1+A2),
(3)
where τw is the weighted time-constant, A1 and τ1 are the relative amplitude and time-constant of the first exponential component and A2 and τ2 the relative amplitude and time-constant of the second exponential component. All fits were performed using the Levenberg-Marquardt least-squares algorithm and the goodness of fits was judged based on residual plots and adjusted χ2 values. Smooth curves in the figures represent fits to average data whereas values given in the text are average data from fits to individual measurements. Values in the text and figures are expressed as mean ± SEM based on n, the number of independent experiments. Boxplots show median, upper and lower quartiles (box), minimum and maximum values (whiskers), and individual data points (dots). Numerical values for the parameters characterizing monotonic concentration-response curves were obtained from fits of the data with a standard sigmoid saturation curve of the form: 
Y=A1+(A2A1)/{1+10[(logKZnX)×h]},
(4a)
where X is the logarithm of the free Zn2+ concentration that produces the effect Y, A1 is the bottom asymptote, A2 the top asymptote or maximum effect (Emax), KZn the free Zn2+ concentration producing 50% of the Emax (= apparent dissociation constant for Zn2+), and h the Hill slope. Biphasic concentration–response curves were fitted with a combination of two sigmoid saturation curves of the form 
Y=A1+(A2A1){p1+10[(logKZn1X)×h1]+1p1+10[(logKZn2X)×h2]},
(4b)
where X is the logarithm of the free Zn2+ concentration that produces the effect Y, A1 and A2 are the bottom and top asymptotes, KZn1 and KZn2 the free Zn2+ concentrations producing 50% of the Emax is mediated by the two components, h1 and h2 the corresponding Hill slopes, and p the proportion of maximum response due to the more potent component. Unless noted otherwise, the Hill slopes were fixed to 1 (but see Limitations).

To indicate experimental uncertainty, we assumed a Gaussian distribution of the fit parameters and used 84% confidence intervals (CIs), so that the probability that two CIs abut or overlap if there really is no difference should be roughly equal to or smaller than P = 0.05, respectively (Austin and Hux, 2002). In all other cases, statistical significance was assessed with OriginLab Pro 9 using a repeated-measures ANOVA followed by Bonferroni's post hoc analysis when comparing mean values from the same cells or a one-way ANOVA followed by Bonferroni's post hoc analysis when comparing multiple independent mean values. Homogeneity of variances between groups was tested using Levene’s test for equality of variances on the squared deviations. In the case of heteroscedastic data (P < 0.05 in Levene’s test and ratio of largest to smallest variance ≥4), statistical significance was assessed with Minitab (version 17; Minitab) using Welch’s ANOVA and the Games-Howell multiple comparison method.

Modeling and simulations

Model development, optimization, and simulations were performed using the NEURON version 7.6.2 simulation environment (Carnevale and Hines, 2006). Kinetic equations were written and solved directly using KINETIC methods of the NMODL language in NEURON.

The rates of Zn2+ interaction with different sites were defined in terms of a simple, bimolecular reaction: 
kon=[Zn]×dZn
(5a)
and 
koff=dZn×KZn,
(5b)
where [Zn] is the free Zn2+ concentration, dZn is the rate of complex formation between Zn2+ and the site, and KZn is the affinity of the site for Zn2+.

For parameter optimization and whole-cell simulations, we constructed an in silico one-compartmental model of a HEK293 cell with diameter and length of 21.851 µm, which corresponds to a sphere with surface area of 1,500 µm2. Temperature, specific membrane capacitance, and cytoplasmic resistivity were set to 22°C, 1 µF/cm2, and 60 Ω×cm, respectively. All simulations were performed using the default integration strategy with an implicit fixed time step of 25 µs.

For kinetic modeling, mean current traces (in pA/pF) were calculated from all control recordings performed with the voltage protocols shown in Fig. 15, C–F and converted to mA/cm2 assuming a specific membrane capacitance of 1 µF/cm2. The model shown in Fig. 15 A was then simultaneously fitted to the whole set of experimental traces using the nonlinear least-squares minimization method included in NEURON (Multiple Run Fitter [MRF] subroutine), which is based on the principal axis method described by Brent (1976). Approximately equal weighting of current traces recorded with different protocols was achieved by scaling the error values reported by each MRF generator until it was close to the value reported by all other MRF generators.

Macroscopic ion currents (in mA/cm2) were calculated according to 
Iion=Po×n×p×ghk(Vm,Cai,Cao),
(6)
where PO is the faction of channels in the four open states, n is the number of channels per square centimeter, p is the single-channel permeability, and ghk is the Goldman–Hodgkin–Katz current equation. The single-channel permeability was assumed to be 7.5 × 10−14 cm3s−1, and the number of channels per square centimeter was set to values between 1.15 × 1010 and 1.40 × 1010 to account for differences in expression levels between experiments performed with the different voltage protocols.

Macroscopic gating currents were calculated as the product of the number of channels and the sum, over all pairs of states, of the charge movement between states times the fraction of channels in each state times the transition rate between the states. Some of the optimizations were run on the Neuroscience Gateway (Sivagnanam et al., 2013). Source code for the model reported in this paper and several scripts for running simulations are available in ModelDB (McDougal et al., 2017) at http://modeldb.yale.edu/261714.

Online supplemental material

Fig. S1 shows the effects of Ca2+ substitution with Mg2+ or 100 µM free La3+ on Cav2.3 channel voltage dependence. Fig. S2 shows evidence for fast and slow components of charge movement observed in our gating current recordings. Fig. S3 compares experimental and simulated Cav2.3 channel biophysical properties in the absence of metal ions. Table S1 lists the composition of all external solutions used in the electrophysiological recordings. Table S2 presents the absolute effects of 5.4 μm free Zn2+ on Cav2.3 channel gating under different experimental conditions. Table S3 lists the relative effects of vatious free Zn2+ concentrations on Cav2.3 channel gating under different experimental conditions. Table S4 shows Emax and KZn values obtained from Zn2+ concentration-response data under different experimental conditions. Table S5 shows global KZn values for high-affinity shift and slowing.

Results

We reassessed the action of Zn2+ on Cav2.3 channel function under near-physiological ionic conditions with either 2 or 4 mM free Ca2+ as the charge carrier and at two different pH values. To identify gating effects caused by binding to the putative metal binding site in domain I, some recordings were performed after carbethoxylation of extracellular histidine residues with DEPC (Fig. 1 B). Unless noted otherwise, all recordings were performed at room temperature (20–22°C) and from a holding potential of −80 mV. The key electrophysiological properties as a function of the experimental conditions in the absence of Zn2+ or other trace metals (control recordings with Tricine or HEPES + diethylenetriaminepentaacetic acid) are summarized in Table 1. In the first part of the Results, we will briefly describe the hallmarks of Cav2.3 channel modulation by low micromolar Zn2+ levels and their dependence on time, voltage, ionic conditions, and Zn2+ interaction with histidine residues. In the second and third parts, we will summarize their rather complex dependence on Zn2+ concentration and try to delineate effects mediated by high- and low-affinity binding. The fourth part briefly describes the development of a model for Cav2.3 channel gating in the absence of trace metals, while the last part deals with our approach to model the major Zn2+ effects on Cav2.3 channel gating.

Cav2.3 channel modulation by low micromolar Zn2+ concentrations

Fig. 2 exemplifies the effects of 5.4 µM Zn2+ on macroscopic currents carried by 4 mM free Ca2+ at pH 7.4. Currents were evoked by step depolarization to different test potentials and repolarization to −50 mV (Fig. 2 A, I-V protocol), a fixed test pulse following 2-s prepulses at different conditioning potentials (Fig. 2 B, PPI protocol), or repolarization to different test potentials following a fixed depolarizing prepulse to open the channels (Fig. 2 C, II-V protocol). Zn2+-induced suppression was strong and steeply voltage dependent when recorded with the I-V protocol, as reflected in a shift of the I-V curve to more depolarized test potentials (Fig. 2, A and D). The same concentration of Zn2+ produced almost no changes in currents measured with the II-V protocol (Fig. 2, C and E).

Zn2+ shifts and alters channel voltage dependence

Fig. 2 F shows isochronous activation and inactivation curves, constructed from tail currents recorded with the I-V protocol or from the fraction of current available for activation recorded with the PPI protocol, respectively. Application of 5.4 µM Zn2+ produced a depolarizing shift of both activation and inactivation voltage dependence by almost 10 mV (Fig. 2 G), which was completely reversed during washout with Zn2+-free solution (Fig. 2 F). The shift was paralleled by a decreased slope of the activation curve, as reflected in a moderate but significant and selective increase of the activation slope factor by ∼10–15% (Fig. 2 H).

Zn2+ slows macroscopic current kinetics

Apart from altering channel voltage dependence, Zn2+ produced a dramatic slowing of current kinetics that is most evident when inspecting scaled I-V current traces (Fig. 3 A). Fig. 4 A summarizes the effects of 5.4 µM Zn2+ on the time course of macroscopic activation (right) and deactivation (left) at various test potentials, quantified by fitting exponential functions to the rising phase of I-V currents (Fig. 2 A and Fig. 3 A) or the decaying phase of II-V currents (Fig. 2 C and Fig. 3 B), respectively. It can be seen that the effects on activation kinetics were much more pronounced than would be expected based on the voltage shift described above. Thus, after correction for the expected effects of a 10-mV shift on activation kinetics, 5.4 µM Zn2+ still slowed current activation almost twofold and over the whole voltage range examined.

On the other hand, Zn2+ had no effects on deactivation time constants except for a minor increase at intermediate test potentials (Fig. 4 A), which could reflect the depolarizing shift in channel voltage dependence. Interestingly, inspection of scaled II-V current traces near the threshold voltage for macroscopic activation still revealed a clear acceleration of tail-current decay (Fig. 3 B), which was related to neither changes in deactivation time constants nor faster inactivation (Fig. 4 B). Instead, the faster tail-current decay in the presence of Zn2+ appeared to result almost entirely from a depolarizing shift in the relative amplitude of both processes, which markedly increased the apparent contribution of deactivation to total tail-current decay at depolarized test potentials (Fig. 4 C). Indeed, when the time course of inactivation was examined using 400-ms voltage steps, Zn2+ actually slowed down both fast and slow components of current decay recorded near the half-activation voltage (Fig. 3 A). However, there was no effect on the limiting decay rate reached at depolarized test potentials (Fig. 4 D) or on the time constants for recovery from inactivation at −80 mV (data not shown), suggesting that the underlying microscopic inactivation rates were unaffected. Because macroscopic inactivation is thought to derive most of its voltage dependence from the voltage dependence of activation, the observed shift in inactivation voltage dependence might have been a consequence of the Zn2+-induced changes in activation gating (but see Modeling the effects of Zn2+ on Cav2.3 channel gating).

Zn2+ effects depend on the holding potential

Regardless of the underlying mechanism, the shift of the inactivation curve (Fig. 2 F) suggested that Zn2+ increases the availability for activation after prepulses at intermediate test potentials, in which case its effects could be influenced by the RMP. To test this assumption, we compared the effects of Zn2+ on currents evoked by step depolarization from different holding potentials. As illustrated in Fig. 5, Ca2+ currents evoked from voltages that provide full availability (i.e., less than or equal to −80 mV) were rapidly inhibited and slowed by application of 5.4 µM free Zn2+ and quickly returned to their control amplitude and kinetics during washout (Fig. 5, A, B, and D), indicating that Zn2+ application and washout were complete in <30 s. Currents evoked from more depolarized holding potentials displayed the same rapid slowing, but suppression was diminished and followed by a paradoxical increase of current amplitudes in the maintained presence of Zn2+ (Fig. 5 A), during which the kinetic slowing persisted (Fig. 5 B). For example, currents evoked from a holding potential of −60 mV were reduced to 85 ± 3% of their initial amplitude 30 s after application of 5.4 µM Zn2+ but then progressively increased to reach a steady-state level at 128 ± 7% of their control amplitude after 240 s in the maintained presence of Zn2+ (Fig. 5, A and C). Subsequent washout of Zn2+ rapidly restored the normal activation kinetics (Fig. 5 B) and led to overrecovery of current amplitudes beyond their initial level, which was followed by a gradual return toward the control amplitude. The same but less pronounced effects were observed when the free Zn2+ concentration was reduced to 2.3 µM (data not shown). In principle, Zn2+-induced stimulation that gets evident as the holding potential becomes more depolarized would be consistent with a shift in the voltage dependence of inactivation, which should increase availability near the voltage of half-maximal inactivation. However, considering the slow time course of current increase, most of the observed stimulation could not be explained by the increase in availability measured after 2-s prepulses. To roughly separate the two opposing effects of Zn2+, the difference in peak current amplitudes between the last test pulse delivered in the presence of Zn2+ and the first test pulse delivered after starting washout was taken as a measure for the degree of Zn2+-induced suppression and used to correct the original peak current amplitudes measured in the presence of Zn2+. Fig. 6 A illustrates the magnitude and time course of current stimulation thus obtained at different holding potentials (top) and also indicates the estimated magnitude of suppression (bottom), which showed no dependence on holding potential. Fig. 6 B compares the current increase after 240 s in the presence of Zn2+ from Fig. 6 A with the increase in availability determined using the PPI protocol. Both effects exhibited the bell-shaped voltage dependence that would be expected for a shift in inactivation, but the slow changes peaked at ∼30 mV more negative holding potentials. A possible explanation for these findings could be that Zn2+ also shifts a process like ultraslow voltage-dependent inactivation, which occurs at more negative holding potentials and with time constants for development and recovery in the order of minutes (Boyett et al., 1994; Yasuda et al., 2004). True steady-state inactivation curves that reflect such processes could not be obtained, as the long prepulse durations necessary were neither practical nor tolerated by the cells. However, a testable prediction of the above assumption is that the time course of recovery from inactivation produced by a hyperpolarizing shift in holding potential equivalent to the Zn2+-induced depolarizing shift in activation voltage dependence should roughly match that of Zn2+-induced stimulation at the same holding potential. Fig. 6 C shows data from a recording where the holding potential was changed from −60 mV to −70 mV and back to −60 mV as indicated. Neither the time course (Fig. 6 D) nor the degree (Fig. 6 E) of current increase were significantly different from the values for Zn2+-induced stimulation at the same holding potential, suggesting that the latter effect was also due to slow recovery from holding potential–dependent inactivation.

Zn2+ effects depend on histidine residues

Previous studies have linked both pH- and metal-induced changes in Cav2.3 channel gating to histidine residues making up the proposed metal binding site in domain I (Fig. 1 A; Cens et al., 2011; Kang et al., 2007; Shcheglovitov et al., 2012). Because divalent cations often compete with each other and protons for binding to the histidine imidazole ring, one of our aims was to assess how changes in the ionic conditions or histidine modification influence Zn2+-induced modulation. As illustrated in Fig. 7, A–D and Table S2, reducing the concentration of Ca2+ (from 4 to 2 mM) or moderate acidification (from pH 7.4 to 7.0) significantly increased or decreased, respectively, the changes in activation voltage dependence and kinetics produced by 5.4 µM Zn2+, suggesting that Ca2+ and protons both counteract the effects of Zn2+ on gating. The pH reduction also significantly slowed and shifted activation under control conditions (Table 1), indicating that protonation of residues in the Zn2+ site could produce gating effects similar to Zn2+ binding.

Pretreatment with the histidine-modifying agent DEPC almost completely prevented the Zn2+-induced shift (Fig. 7 C) and slowing (Fig. 7, B and D), confirming that both effects are related to interaction with histidine residues, presumably located in the proposed metal ion binding site. In addition, DEPC produced gating effects opposite to those exerted by Zn2+ and selectively stimulated Cav2.3 channel activation in the absence of trace metal ions, as reflected in a significant shift of the activation curve by ∼9 mV toward more negative test potentials and accelerated activation kinetics under control conditions (Table 1).

Finally, DEPC pretreatment also prevented the Zn2+-induced increase of the activation slope factor (Fig. 7 E), but several observations indicated that the underlying mechanism may differ from that mediating the shift and slowing. First, pH reduction reproduced the other gating effects of Zn2+ as described above but had no effect on the slope of the activation curve under control conditions (Table 1). Second, manipulation of the Ca2+ concentration or of the pH of the extracellular solution significantly altered the other gating effects of Zn2+ (Fig. 7, A–D) but had no effect on the Zn2+-induced changes in kact (Fig. 7 E). Third, while DEPC pretreatment produced effects opposite to the shift and slowing, it reproduced Zn2+-induced changes in the slope of the activation curve, as reflected in a significant increase of kact in pretreated cells under control conditions (Table 1).

Concentration dependence of Zn2+-induced gating changes

To further corroborate and extent the above findings, we performed additional experiments with a wide range of free Zn2+ levels. Fig. 8 A, Fig. 9 A, and Fig. 10 A show concentration–response curves, which were constructed by plotting the indicated Zn2+-induced gating changes as a function of the logarithm of the free Zn2+ concentration and fitted with one (Eq. 4a) or a combination of two (Eq. 4b) sigmoid saturation curves. Best-fit values and CIs for apparent dissociation constants (KZn) and Emax values obtained under the different experimental conditions are summarized below each plot (Fig. 8, B and C; Fig. 9, B and C; and Fig. 10, B and C) and in Table S4.

Micromolar Zn2+ concentrations slow and shift by multiple mechanisms

The concentration–response curves for the Zn2+-induced shift in activation voltage dependence were clearly biphasic under all experimental conditions examined, revealing the existence of two separable components with vastly different affinities (Fig. 8). They could be well described by a combination of two simple saturation curves with Hill slopes of 1 (Eq. 4b), indicating that Zn2+ may exert its effects through interaction with at least two independent sites. The concentration dependence for changes in inactivation voltage dependence (not shown, but see Table S4) and for the (shift-corrected) Zn2+-induced slowing (Fig. 9) had a very similar overall appearance, comprising both high- and low-affinity components. On the other hand, effects on the slope of the activation curve showed a less complex dependence on Zn2+ concentration that could be well described by a single saturation curve (Fig. 10; Eq. 4a). To better delineate the various effects and their differential dependence on Zn2+ concentration, Fig. 11 A compares high- and low-affinity KZn values for shift and slowing and the KZn value for changes in the slope of the activation curve obtained with 4 mM free Ca2+ (pH 7.4). It can be seen that there was no significant difference between the KZn values for high-affinity shift and slowing, supporting the notion that both effects reflect Zn2+ binding to a common site. To obtain a single apparent dissociation constant, we simultaneously refitted the effects on channel voltage dependence and kinetics with a global KZn value for the high-affinity component (high-affinity 1 in Fig. 11 A) and all other parameters fixed to the values shown in Table S4. The Zn2+ concentration for half-maximal shift and slowing thus obtained for recordings performed with 4 mM Ca2+ was 4.4 µM, with an 84% CI ranging from 4.2 to 4.6 µM (Fig. 11, A and B; and Table S5). Under the same experimental conditions, the apparent KZn value was approximately four times higher for effects on the slope of the activation curve (high-affinity 2 in Fig. 11, A and C; and ratio kact in Table S4), >40 times higher for the low-affinity slowing (low-affinity 1 in Fig. 11, A and D; and low-affinity ratio τact in Table S4), and ∼200 times higher for the low-affinity shift in channel voltage dependence (low-affinity 2 in Fig. 11, A and E; and low-affinity ΔV0.5act and ΔV0.5inact in Table S4), indicating that there are either multiple Zn2+ sites and/or differences in the coupling between Zn2+ binding and its various functional consequences.

Hallmarks of high-affinity shift and slowing

Pretreatment with DEPC completely eliminated the high-affinity slowing (Fig. 9) and significantly decreased the maximum shift mediated by the high-affinity component, which produced, at most, a 3-mV shift (Fig. 8) in pretreated cells. Based on these two findings, DEPC pretreatment antagonized high-affinity Zn2+ binding noncompetitively, which is consistent with a disruption of the putative metal binding site by irreversible carbethoxylation of one or more histidine residues.

Reducing the concentration of Ca2+ or moderate acidification significantly decreased or increased respectively, the global apparent KZn value for high-affinity shift and slowing (Fig. 8, Fig. 9, and Fig. 11 B; and Table S5), supporting the notion that there is competition for binding among Zn2+, Ca2+, and protons. In addition, the increase in proton concentration was associated with a significant decrease of the Emax values for high-affinity shift and slowing (Fig. 8, Fig. 9, and Fig. 11 B). The latter could only partly be accounted for by the moderate gating effects of pH reduction observed under control conditions (∼2-mV shift and 1.2-fold slowing; Table 1), suggesting that protonation of the high-affinity site is either less effective than Zn2+-binding in altering channel gating (i.e., protons could act as Fweak partial agonists, possibly due to their lower charge) or that protons also reduce Zn2+ binding noncompetitively.

On the other hand, reducing the Ca2+ concentration had no clear effects on the maximum gating changes mediated by high-affinity binding (Fig. 8, Fig. 9, and Fig. 11 B) or activation gating under control conditions (Table 1), suggesting that Ca2+ acts as competitive antagonist that binds to the high-affinity site and displaces Zn2+ ions without altering channel gating.

DEPC pretreatment also prevented and partly reversed the direction of changes in kact, but this effect differed from the shift and slowing in that it was completely unaffected by changes in the concentration of Ca2+ (Fig. 10 and Fig. 11 C). It was also more sensitive to moderate acidification, which significantly increased the apparent dissociation constant for effects on kact approximately threefold but also significantly increased the Emax (Fig. 10, B and C).

Low-affinity shift and slowing have distinct concentration dependencies

Low-affinity shift and slowing were much less affected by DEPC pretreatment (Fig. 8, Fig. 9, and Fig. 11, D and E; and Table S4), suggesting that histidine residues are not involved in these effects. The apparent KZn value for the shift obtained in recordings performed with 4 mM Ca2+ was 790 µM (CI, 660–950 µM), which is significantly higher than the KZn value for low-affinity slowing of 180 µM (CI, 60–530 µM). For comparison, the corresponding values after pretreatment with DEPC were 640 µM (CI, 500–820 µM) for the low-affinity shift and 140 µM (CI, 120–160 µM) for the low-affinity slowing, respectively (Fig. 11 A). The two effects were also differently affected by moderate acidification, which significantly reduced the KZn and Emax values for low-affinity shift (Fig. 8 and Fig. 11 E), but not slowing (Fig. 9 and Fig. 11 D). Reducing the concentration of Ca2+ affected neither the low-affinity shift nor the low-affinity slowing (Fig. 8, Fig. 9, and Fig. 11, D–E). Taken together, these findings are in good agreement with previous studies showing that Zn2+ and other d-block metal ions slow activation, often without altering channel voltage dependence, in several VGCCs lacking critical histidine residues in domain I (Magistretti et al., 2001, 2003; Castelli et al., 2003; Park et al., 2015). Interestingly, most of these studies also found a less marked but significant metal-induced slowing of ICa deactivation speed (Magistretti et al., 2003; Castelli et al., 2003), an effect that was also observed in the present study (Fig. 12). Under normal conditions (i.e., 2 or 4 mM Ca2+, pH 7.4), a clear slowing was only visible at the highest free Zn2+ concentrations examined (Fig. 12 B), most likely because the Zn2+-induced depolarizing shift tended to accelerate deactivation at a given test potential, thereby counteracting and masking any potential slowing. Thus, as illustrated in Fig. 12, A and B, the deactivation slowing became much more pronounced and evident already at low micromolar Zn2+ levels after DEPC pretreatment and, to some extent, pH reduction, both of which strongly reduced the shift in channel voltage dependence.

Concentration dependence of Zn2+-induced changes in permeation

While the site of action for high-affinity shift and slowing of Cav2.3 channel currents by Zn2+, Ni2+, and Cu2+ is relatively well established, much less is known about the location of additional, lower-affinity sites for d-block metal ions, which appear to be present in most or all high-voltage activated (HVA) Ca2+ channels (Neumaier et al., 2015). Since all of these cations can more or less effectively obstruct the ion-conducting pore, and Ca2+ channel gating is well known to be influenced by the permeability of charge-carrying ions, it has been proposed that the slowing is independent of the time course and voltage dependence of pore block per se (i.e., not a consequence of time- and voltage-dependent unblock during the test pulses) but related to an allosteric modification of channel gating, induced by binding of metals to their blocking site (Castelli et al., 2003). Block of single HVA Ca2+ channels has been shown to occur on a rapid timescale (Winegar et al., 1991), so that II-V current suppression should provide a reasonable measure for the degree of pore block. To assess the apparent voltage dependence of Cav2.3 channel block by Zn2+, we therefore determined apparent KZn values for II-V current suppression and plotted them as a function of the test potential (Fig. 13, A and B; but see below). As a simple voltage-independent measure for the degree of “instantaneous” block, we also quantified Zn2+ effects on II-V currents in terms of the slope conductance between −40 and +20 mV (GII-V; Fig. 13 C and Table S4). Finally, for comparison with previous work, the degree of “steady-state” block measured with the I-V protocol was quantified based on changes in Gmax (Table S4).

Although the concentration dependencies exhibited some clear discontinuities at intermediate Zn2+ concentrations, they could be reasonably well approximated by a combination of two simple saturation isotherms, the best-fit values of which are shown in Table S4 and described in more detail in the following sections.

High-affinity binding to histidine residues may also affect conduction

Apparent dissociation constants for high-affinity II-V current suppression showed no clear dependence on the test potential and could be well described with a single, shared KZn value of 16 µM (CI, 14–20 µM; Fig. 13 A, right), which is in good agreement with the high-affinity KZn value 12 μm (CI, 9–17 μm; Table S4) obtained when the effects were quantified in terms of changes in GII-V. Suppression mediated by high-affinity binding was incomplete at all test potentials examined (Fig. 13 B), indicating that it is not related to physical obstruction of the ion-conducting pore. In addition, its contribution to total suppression was sensitive to acidification or DEPC pretreatment (Fig. 13 B), suggesting an involvement of histidine residues and possibly other protonation sites. However, while slower activation and faster deactivation due to the Zn2+-induced gating changes may have contributed to a scaling down of instantaneous currents, high-affinity II-V current suppression per se could not be explained by the shift and slowing alone, since it was most prominent at Zn2+ concentrations where activation at the prepulse voltage was still complete in under 10 ms (which was the duration of the activating prepulse). In addition, the corresponding KZn value was significantly higher than the KZn for shift and slowing but almost identical to that for the changes in kact (Table S4; see also next section), possibly pointing to a common site of action.

Evidence for a link between pore block and low-affinity changes in gating

KZn values for low-affinity II-V current suppression were much higher and exhibited a shallow voltage dependence matching the expectations for Ca2+ channel block by d-block metal ions (Fig. 13 A). For example, under our standard recording conditions, the logarithm of the KZn values between −80 and 10 mV could be well described by a straight line KZn(Vm) = 443 × exp(−0.015 × Vm), indicating that block decreased approximately e-fold per 77 mV with hyperpolarization. In the context of a model where blocking Zn2+ ions enter the electric field (compare Woodhull, 1973), the intercept of the line should provide the zero-voltage KZn value (443 µM; CI, 299–592) and the slope should be equal to zδF/RT, where z is blocker valence (i.e., +2 for Zn2+) and δ is the fraction of the voltage drop at the blocking site. The value of δ = 0.19 obtained from the above equations corresponds to a blocking site located at ∼20% of the potential drop from the membrane surface, which is in good agreement with previous findings on the voltage dependence of Zn2+ block in native HVA Ca2+ channels (Winegar et al., 1991). At test potentials more depolarized than 10 mV however, block started to decrease with depolarization, indicating that the voltage dependence is more complex. Moreover, DEPC pretreatment or moderate acidification increased or decreased, respectively, the Zn2+ affinity at zero voltage, while both reduced the apparent voltage dependence of block (Fig. 13 A). A more important observation is illustrated in Fig. 14, which compares logKZn values for the various Zn2+-induced gating changes (left) with those for block at −50 mV (i.e., the test potential where tail currents for activation curves were determined) or 10 mV (i.e., the test potential where the activation slowing was quantified) and that for high-affinity (voltage-independent) suppression of II-V currents. It can be seen that KZn values for low-affinity shift and slowing were not significantly different from the KZn values for block at −50 mV or 10 mV, respectively. Hence, while the low-affinity gating effects could clearly not be accounted for by the shallow voltage dependence of block per se, it seems conceivable that they could be linked to occupation of the blocking site by Zn2+. Also note that, as described in the preceding section, the voltage-independent KZn value for high-affinity II-V current suppression was almost identical to that obtained for the Zn2+-induced changes in kact.

A Markov model of Cav2.3 channel gating in the absence of trace metals

To better resolve and separate specific effects of Zn2+ on channel gating, we developed a Markov model for Cav2.3 channels as described below and applied a global fitting procedure, whereby the model was simultaneously fitted to the whole set of recordings obtained under control conditions (4 mM Ca2+ at pH 7.4). Because ionic currents alone provide little information on transitions between closed states, the model was further constrained with gating currents (Fig. S2 A), recorded after blocking ion conduction by substitution of Ca2+ with Mg2+ and addition of 200 µM La3+ + 100 µM EDTA (i.e., 100 µM free La3+). The total dataset used for fitting included gating currents recorded at 15 different test potentials, short I-V currents (25 ms) recorded at 15 different test potentials, long I-V currents (400 ms) recorded at 10 different test potentials, II-V currents recorded at 13 different test potentials, and PPI currents recorded at 14 different test potentials.

The topology of the model (Fig. 15 A) was chosen based on the following structural and functional considerations: VGCCs are heterotetrameric proteins composed of four nonidentical VSMs and a central pore region (Fig. 1 A). Optical tracking of voltage-sensor movement by voltage-clamp fluorometry (VCF) in voltage-gated sodium and calcium channels indicates that activation of the individual VSMs is probabilistic in nature and largely governed by their respective steady-state and kinetic properties (Chanda and Bezanilla, 2002; Pantazis et al., 2014). To reflect these findings, horizontal transitions in Fig. 15 A are voltage dependent and correspond to movement of the four nonidentical voltage sensors (rows 1–4 in Fig. 15 B) and pore opening or closing (row 5 in Fig. 15 B), respectively. The voltage sensors operate in parallel and are independent of each other, with one simplifying assumption as described below. The rates for voltage-dependent transitions between two states were expressed in terms of the transition-state theory and are given by​ 
kfw=keq×exp[z×x×(VmVeq)×F/RT]
(7a)
and 
kbw=keq×exp[z×(1x)×(VmVeq)×F/RT],
(7b)
where kfw and kbw are the values of the forward and backward rates at the test potential Vm, keq is the value of the forward and backward rates at the test potential Veq, z is the effective valence of the gating charge associated with the transition, x is the relative position of the energy barrier in the membrane, and F, R, and T have their usual thermodynamic meaning (Brog-Graham, 1991).

In voltage-gated sodium channels, activation of the VSMs in domain I-III is associated with rapid charge movement and obligatorily precedes channel opening (Chanda and Bezanilla, 2002), while activation of the VSM in domain I-V is correlated with a slow component of charge movement and gives rise to a short-lived second open state that precedes inactivation (Chen et al., 1996; Capes et al., 2013; Goldschen-Ohm et al., 2013). Much less is known about VGCCs, but mutational studies (Beyl et al., 2016; García et al., 1997) and optical tracking of voltage-sensor movement by VCF (Pantazis et al., 2014; Savalli et al., 2016; Flucher, 2016) indicate that activation of two or three VSMs may be sufficient for pore opening. Consistent with these findings, Cav2.3 channel gating currents showed a significant fraction of charge movement that was too slow to be associated with channel opening (Fig. S2 B). We tested obligatory models in which activation of 2–4 VSMs is required for channel opening and found that the whole set of ionic and gating current recordings could only be described by a model where activation of two VSMs is obligatory for channel opening, with the simplifying assumption that these VSMs activate in a specific sequence. Based on the role of the VSM that activates first for simulated Zn2+-induced modulation (see next section), we have tentatively assigned these two VSMs the numbers 1 and 2, noting that our data are not sufficient to conclusively relate them to specific protein domains (but see A model of Cav2.3 channel gating and Zn2+-induced modulation and Limitations). The resulting model has a total of four conductive states, which is consistent with experimental evidence for multiple Ca2+ channel open states (Fass and Levitan, 1996; Schneider et al., 1994; Nakayama and Brading, 1993). In analogy to sodium channels, the VSMs not obligatory for channel opening have been proposed to play a role for coupling of activation to voltage-dependent inactivation (Pantazis et al., 2014; Flucher, 2016), a process that has been shown or is thought to be state rather than truly voltage dependent in VGCCs (Neumaier et al., 2015). Therefore, vertical transitions in the model are voltage independent and correspond to entry into and return from fast (Fig. 15 A, middle) and slow (Fig. 15 A, bottom) inactivated states. As the VSMs in the model could not be related to specific domains of the channel protein and data on the coupling between voltage-sensor movement and voltage-dependent inactivation is not available, the state dependence of inactivation was determined empirically by fixing fast and slow inactivation and deinactivation time constants to experimentally determined values and adding or removing inactivated states until the model reproduced both the time-course and steady-state voltage dependence of inactivation. Microscopic reversibility was imposed by defining transition rates between inactivated states as being identical to those of the (parallel) transitions between closed states.

The individual transitions of the model and optimized parameter values obtained from fits to the control recordings are listed in Fig. 15 B. Fig. 15, C–F compare recorded families of current traces evoked with the voltage protocols depicted above (black) and simulations (blue) performed with the optimized parameter values. For further comparison, the simulated currents were analyzed in the same way as the experimental data, and the results are plotted together in Fig. S3. The model accounted for all salient features of the control data, including the time course of macroscopic current activation, deactivation, and inactivation (Fig. 15, C–F); the shape and position of the I-V curve (Fig. S3 A); the relatively sharp separation between voltage-dependent activation and inactivation (Fig. S3 B); the bell-shaped voltage dependence of activation and deactivation time constants (Fig. S3 D); and the fast and slow gating current components (Fig. 15 C, top).

Modeling the effects of Zn2+ on Cav2.3 channel gating

Lacking data from, for example, VCF, the voltage sensors in our model could obviously not be related to specific domains in the channel protein. However, preliminary tests with the model showed that only manipulation of one set of voltage-dependent transitions (i.e., kfw1/kbw1 in Fig. 15 B) could qualitatively reproduce the selective slowing of activation gating observed experimentally, while changes in the other transition had either little effect on activation kinetics (kfw3/kbw3 and kfw4/kbw4) or affected the deactivation kinetics in a way that was inconsistent with the experimental data (kfw2/kbw2 and ko/kc). With this is mind, we first extended our model by including Zn2+ binding to a first site (site 1) with a resulting modification of voltage sensor 1 in the model to simulate the Zn2+-induced high-affinity changes in activation gating.

To this end, each state in the model was connected to a corresponding Zn-bound state, with rates for binding (kon1) and unbinding (koff1) at site 1 defined in terms of a simple, bimolecular reaction (Eq. 5a and Eq. 5b). To simulate Zn2+-induced changes in gating rates, we adopted the shift and scaling procedure first introduced by Elinder and Arhem (2003) and assumed that the rate constants for movement of voltage sensor 1 in metal-bound channels can be expressed by modification of Eq. 7a and Eq. 7b into 
kfw1=Aoff1×keq×exp[z1×x1×(VmVeq1Voff1)×F/RT]
(8a)
and 
kbw1=Aoff1×keq×exp[z1×(1x1)×(VmVeq1Voff1)×F/RT],
(8b)
where Voff1 is a voltage offset that accounts for the electrostatic effects of a bound metal ion on the local electric field at sensor 1 and Aoff is a slowing factor that accounts for the mechanical effects of a bound metal ion on sensor 1 and corresponds to adding an energy barrier of ΔW = kT × ln(Aoff−1).

Pore block and the low-affinity slowing of activation and deactivation were implemented by including a second, lower-affinity Zn2+ blocking site, with rates for binding (kon2) and unbinding (koff2) defined as above (Eq. 5a and Eq. 5b). Channels with Zn2+ bound to site 2 were assumed to be nonconductive (i.e., blocked) and their rates for opening and closing slowed by an unidentified allosteric mechanism implemented as slowing factor Aoff2. For simplicity, block was assumed to be voltage independent and restricted to activated closed and open channel states.

Fig. 16, Fig. 17, and Fig. 18 show results from simulations for a Zn2+ concentration of 5.4 µM performed with the extended model and parameter values shown in Table 2. It can be seen that, despite the many simplifying assumptions, the model reproduced almost exactly the corresponding experimental data, with much stronger suppression of I-V versus II-V currents (Fig. 16, A and C–E), a depolarizing shift of the activation voltage dependence (Fig. 16 F), a dramatic slowing of macroscopic activation with little change in deactivation time constants (Fig. 17, A and B; and Fig. 18 A), and an apparent acceleration of tail-current decay measured with the II-V protocol at depolarized test potentials (Figs. 17 B and 18 C). In addition, simulated Zn2+-modified currents showed the same apparent slowing of inactivation kinetics near the half-activation voltage as observed experimentally (Fig. 17 A; and Fig. 18, B and D) and a similar shift of the inactivation voltage dependence (Fig. 16 F), supporting the assumption that these effects could result from activation–inactivation coupling rather than Zn2+-induced changes in the microscopic inactivation rates. The model underestimated the magnitude of II-V current suppression at low Zn2+ concentrations and overestimated it at high Zn2+ concentrations, which is not surprising given that we have neglected the voltage dependence of block and the high-affinity component of II-V current suppression. However, the predicted concentration dependence of I-V current suppression, quantified in terms of the Gmax, was in good agreement with the experimental data (Fig. 16 G). Even more importantly, the model qualitatively and quantitatively reproduced the concentration dependence of Zn2+ effects on activation voltage dependence (Fig. 19 A), macroscopic activation (Fig. 19 B), and deactivation kinetics (Fig. 19 D) in the range of physiologically relevant Zn2+ concentrations. Interestingly, the model also reproduced the small but significant and Zn2+-concentration–dependent increase in apparent Vrev (Fig. 19 C), indicating that this effect was not related to true changes in, for example, equilibrium potentials or selectivity and highlighting the ineptness of Vrev as a measure for true Vrev values under conditions that alter channel voltage dependence. It also qualitatively reproduced the concentration dependence of changes in inactivation voltage dependence, although it did underestimate the degree of shift (Fig. 19 E), which could reflect the arbitrary state dependence of inactivation and/or the disregard of ultraslow inactivation processes. On the other hand, the model did clearly not account for the reduced steepness of the activation curve (Fig. 19 F), even though it did predict a minor increase of kact at the highest free Zn2+ concentration. Taken together, this is consistent with our findings that the mechanism underlying the changes in kact is somewhat different from that involved in the shift and slowing.

Discussion

Endogenous, loosely bound Zn2+ ions are increasingly recognized as potential modulators of neuronal excitability, and Zn2+ dis-homeostasis has been implicated in a number of pathophysiological conditions (Frederickson et al., 2000, 2005; Mathie et al., 2006). Owing to a high-affinity trace metal–binding site in their domain I VSM (Fig. 1 A), which is not conserved in other HVA VGCCs, Cav2.3 channels are among the most sensitive targets for Zn2+ and certain other trace metals currently known (Kang et al., 2007; Shcheglovitov et al., 2012). Here, we performed an in-depth assessment of Zn2+-induced modulation of cloned human Cav2.3 + β3 channels over a wide range of Zn2+ concentrations and used a preliminary Markov model to test whether the results can be accounted for by different biophysical mechanisms. Our most important and novel findings are (1) that low micromolar Zn2+ concentrations could both inhibit or stimulate Ca2+ influx through Cav2.3 channels depending on RMP (Figs. 5 and 6); (2) that multiple high- and low-affinity mechanisms of Zn2+ action exist, which can be distinguished based on their concentration dependence, sensitivity to the experimental conditions, and correlation with pore block (Figs. 7, 8, 9, 10, 11, 12, 13, and 14); and (3) that most, but not all, of the observed effects can be described by a simplified model that involves Zn2+ binding to a first site with an associated electrostatic modification and mechanical slowing of one of the voltage sensors and Zn2+ binding to a second, lower-affinity site, which blocks the channel and modifies the opening and closing transitions (Figs. 16, 17, 18, and 19). In the following sections, we will try to reconcile our findings with previous results and discuss potential implications with regard to the underlying sites, briefly consider our proposed model and potential (patho)physiological implications, and finally address some inherent limitations of our work.

Evidence for multiple mechanisms of Zn2+ action

Various previous studies have investigated the effects of Zn2+ and other trace metals on native or cloned VGCCs, all of which are thought to be more or less potently blocked by these cations. With regard to cloned Cav2.3 channels, (sub)micromolar concentrations of Zn2+, Cu2+, and Ni2+ have also been shown to produce depolarizing shifts in channel voltage dependence, a reduced sensitivity toward depolarization, and a pronounced slowing of macroscopic activation (Zamponi et al., 1996; Shcheglovitov et al., 2012; Kang et al., 2007), resembling their action on native R-type currents in cortical (Castelli et al., 2003; Magistretti et al., 2003) and dorsal root ganglion neurons (Shcheglovitov et al., 2012). Our present findings reveal that the Zn2+-induced gating changes can be separated into multiple components with distinct concentration dependencies, which comprise a common high-affinity component for shift and slowing (KZn ∼2–3 µM with 2 mM Ca2+), a second high-affinity component for the changes in activation voltage sensitivity (KZn ∼15–40 µM with 2 mM Ca2+), and two lower-affinity components for shift (KZn >500 µM with 2 mM Ca2+) and slowing (KZn ∼50–170 µM with 2 mM Ca2+).

High-affinity shift and slowing

To delineate effects mediated by Zn2+ binding to histidine residues, we used DEPC pretreatment, which effectively prevented the high-affinity shift and slowing. This is consistent with molecular cloning studies showing that the effects of Zn2+, Cu2+, and Ni2+ are all diminished by mutation of histidine residues located in the IS1-IS2 (His111) and IS3-IS4 (His179 and His183) loops (Fig. 1 A; Kang et al., 2007; Shcheglovitov et al., 2012). In particular, substitution of two loop histidines has previously been shown to reduce the activation shift induced by 7 µM Zn2+ from 13 mV in WT channels to 3 mV in mutant channels (with 1 mM Ca2+; Shcheglovitov et al., 2012). Considering that interpolation of our own data to the same free Zn2+ concentration gives a shift of 11 or 13 mV (with 4 or 2 mM Ca2+) for untreated and 3 mV (with 4 mM Ca2+) for DEPC-treated channels, it seems justified to conclude that high-affinity shift and slowing reflect Zn2+ interaction with the proposed metal binding site and that DEPC mainly acted by modification of histidine residues in the same site (but see Limitations). Moderate acidification significantly reduced apparent Zn2+ affinity and maximum Zn2+ effects and produced gating changes similar to Zn2+ under control conditions, which is consistent with previous results showing that metal ions and protons both alter Cav2.3 channel gating by interaction with the known loop histidines (Cens et al., 2011; Shcheglovitov et al., 2012). In view of our findings, protons could act as partial agonists that are less effective than Zn2+ in altering channel gating, whereas the effects of Ca2+ on apparent Zn2+ affinity are consistent with a competitive antagonism.

Unexpectedly, low micromolar Zn2+ concentrations also stimulated Cav2.3 channel currents evoked from moderately depolarized holding potentials, which may have important (patho)physiological implications (see (Patho)physiological implications). Development and reversal of this effect were much slower than Zn2+-induced suppression but could be reproduced by a change in holding potential approximately equal to the shift in channel voltage dependence, suggesting that they reflect equilibration of a slow coupled inactivation process rather than slow Zn2+ binding/unbinding at a distinct, stimulatory site.

High-affinity changes in slope factor

Another unexpected finding was that the KZn for high-affinity shift and slowing (4.2–4.6 µM) is roughly four times smaller than the KZn for changes in voltage sensitivity (16–22 µM), even though both effects were sensitive to histidine modification. In principle, this could reflect the fact that Zn2+ preferentially affects the charge movement of only one of the four pseudosubunits. However, we also found that (1) DEPC produces effects opposite to the Zn2+-induced shift and slowing but mimics Zn2+ effects on the activation slope factor under control conditions, (2) shift and slowing show a different dependence on the experimental conditions than the changes in the slope of the activation curve, and (3) the proposed model quantitatively accounts for the shift and slowing, but not for the increase in slope factor. In addition, the KZn for changes in slope factor coincided almost exactly with the KZn for a voltage-independent decrease of II-V currents (14–20 µM) that was also sensitive to DEPC pretreatment. The underlying mechanism remains to be firmly established, but it is tempting to speculate that Zn2+ mimics the proton-induced decrease in Cav2.3 channel unitary conductance described in a previous study, which has been linked to a histidine residue in one of the pore loops (Fig. 1 A) and is also accompanied by an increased slope factor (Cens et al., 2011). However, DEPC sensitivity alone does not necessarily prove a role of histidine residues, and the fact that acidification actually increased the maximum changes in slope factor could point to the involvement of other amino acid residues (see Limitations). In any case, the moderate magnitude of the slope changes even at saturating Zn2+ concentrations (∼1.7-fold increase in kact) suggests that reduced voltage sensitivity does not significantly contribute to the net Zn2+ action, which is also supported by our modeling results.

Low-affinity slowing

Our findings also indicate that an unidentified, DEPC-resistant site with lower Zn2+ affinity contributes to the slowing observed at higher free Zn2+ levels and that the same site could be involved in Zn2+-induced block measured with the II-V protocol. KZn values for the low-affinity slowing were ∼150 µM and well separated from those for the low-affinity shift. Interestingly, Zn2+ and other trace metal ions have been shown to slow activation of several native HVA Ca2+ channels lacking critical histidine residues in domain I (Magistretti et al., 2001, 2003; Castelli et al., 2003), so that the site involved in the slowing could be shared with other members of the family. Because Ca2+ channel block and permeation are thought to be governed by the same principles, and Ca2+ channel gating is well known to be affected by the nature of permeating ions (for review, see Neumaier et al., 2015), the metal-induced slowing has been proposed to reflect an allosteric effect linked to occupation of the pore (Castelli et al., 2003), an idea that is reinforced by our electrophysiological and modeling results (see A model of Cav2.3 channel gating and Zn2+-induced modulation). Based on the shallow voltage dependence of low-affinity II-V current suppression, the putative Zn2+-blocking site in Cav2.3 channels could reside in or at a superficial part of the pore near the outer vestibule rather than deep within the electric field, which is consistent with a number of previous studies on VGCC block by d-block metal ions (Winegar et al., 1991; Díaz et al., 2005; Lopin et al., 2012). As such, one promising candidate site appears to be a putative EF-hand motif located external to the selectivity filter EEEE-locus and outside of the narrow pore region (Fig. 1 A), which is present in all HVA Ca2+ channels and has previously been implicated in their differential sensitivity to Zn2+ block (Sun et al., 2007). Lack of this site in low-voltage activated channels could explain why the effects of Zn2+ on these channels appear to be much less uniform, with several studies in different preparations reporting inconsistent or even contradictory findings (Cataldi et al., 2007; Traboulsie et al., 2007; Sun et al., 2007; Noh et al., 2010).

Low-affinity shift

KZn values for the low-affinity shift were >500 µM and similar for activation and inactivation voltage dependence. The concentration dependence suggested that this effect might also be related to block measured with the II-V protocol, but because it is unlikely to ever become significant under (patho)physiological conditions, we have neglected it in our modeling study.

A model of Cav2.3 channel gating and Zn2+-induced modulation

Gating models provide quantitative predictions that can be used to test hypotheses about molecular mechanisms and understand the role of voltage-gated ion channels in electrical excitability and cell signaling. Here, we developed a preliminary Markov model for Cav2.3 channel voltage-dependent gating that is consistent with the available data on channel structure and accurately reproduces most salient features of ionic and gating currents under near-physiological ionic conditions. Voltage-sensor activation in the model is probabilistic in nature and only governed by the respective steady-state and kinetic properties, with the simplifying assumption that two of the VSMs activate in a specific sequence. The latter is at odds with a VCF study on Cav1.2 channels, where fluorescent changes in all four domains occurred without a discernible lag (Pantazis et al., 2014), but it has been shown that sequential and parallel activation models may not always be resolvable from each other in electrophysiological recordings (Chanda and Bezanilla, 2002). The model also incorporates recent findings that activation of only two VSMs may be obligatory for Ca2+ channel opening (Pantazis et al., 2014), an idea that is reinforced by (1) a slow component of charge movement observed in our own and previous Ca2+ channel gating current recordings (Josephson and Varadi, 1996; Josephson, 1997), (2) evidence for multiple Ca2+ channel open states (Fass and Levitan, 1996; Schneider et al., 1994; Nakayama and Brading, 1993), and (3) the success of HH m2h-type models in describing Ca2+ channel ionic currents (Sala, 1991; Kostyuk et al., 1977; Kay and Wong, 1987; Benison et al., 2001).

In addition, our model provides insight into potential mechanisms of Zn2+-induced modulation and shows that electrostatic modification and mechanical slowing of a single VSM mediated by Zn2+ binding to a common site could quantitatively account for the high-affinity shift and slowing and also explain the observed changes in macroscopic inactivation if the process is state dependent and coupled to activation.

The low-affinity slowing was modeled as an allosteric effect that results from occupation by Zn2+ of a pore blocking site, which could well account for the experimental data, even though we made several simplifying assumptions. As such, the modeling results also confirm that slower opening of blocked channels could result in slower macroscopic currents even though only nonblocked channels contribute to these currents, which might account for the fact that many inorganic blockers also alter Ca2+ channel gating (Neumaier et al., 2015). Given that we have only circumstantial evidence for an intrapore location of the site involved in low-affinity slowing, other models could almost certainly account for these findings as well, albeit at the cost of more complicated model structures with additional binding sites. In addition, until exact VCF data on Cav2.3 channel voltage-sensor movement become available, structural interpretation of the model in terms of specific protein domains remains problematic (see also Limitations). Regardless of its physical interpretation, however, our model faithfully reproduces Cav2.3 channel gating in the absence of trace metals and most hallmarks of Zn2+-induced suppression as well as their dependence on Zn2+ concentration. It is freely available at ModelDB (accession number 261714) and can be readily integrated into existing cell models, making it a useful tool for future studies on the physiological role of Cav2.3 channels and/or the effects of synaptic Zn2+ release on electrical excitability and cell signaling.

(Patho)physiological implications

Although some have questioned that synaptic Zn2+ can exceed 1 µM (Erreger and Traynelis, 2005; Vergnano et al., 2014), most studies suggest that physiological peak cleft concentrations at Zn2+ enriched synapses could reach at least low micromolar levels, especially during intense, LTP-inducing stimulation (Aniksztejn et al., 1987; Assaf and Chung, 1984; Besser et al., 2009; Howell et al., 1984; Kodirov et al., 2006; Qian and Noebels, 2005, 2006; Vogt et al., 2000; Ueno et al., 2002; Komatsu et al., 2005; Li et al., 2001; Quinta-Ferreira et al., 2016). One of our most important findings may therefore be that low micromolar Zn2+ concentrations could inhibit or stimulate Ca2+ influx through Cav2.3 channels depending on RMP. In addition, slow reversal of the stimulation during washout at depolarized RMP could result in a paradoxical increase of Ca2+ influx above the control level that persists for some time after cessation of the Zn2+ signal. The latter is especially interesting, because rises in synaptic Zn2+ concentrations during neuronal activity have been shown or are thought to be transient in nature (Vergnano et al., 2014; Quinta-Ferreira et al., 2016). As such, it could potentially provide a link between Zn2+ signals and certain plasticity processes like presynaptic LTP at hippocampal mossy fiber synapses, which is in part mediated by Cav2.3 channels (Dietrich et al., 2003) and has been shown to depend on synaptic Zn2+ release in brain slice recordings (Pan et al., 2011). In principle, the holding potential dependence of Zn2+ effects could also be involved in the reported proictogenic role of Cav2.3 channels (Weiergräber et al., 2006a, 2007; Dibué-Adjei et al., 2017), since depolarization of the neuronal RMP due to, for example, spreading depolarization or paroxysmal depolarizing shifts might lead to a decrease in the inhibitory action or even reverse the direction of Zn2+ effects. Considering that even very small changes in ion channel function (Thomas et al., 2009) and synaptic gain (Du et al., 2019) can lead to seizure-like activity, reduced Cav2.3 channel suppression by Zn2+ could conceivably contribute to the ictogenic processes when the brain moves into a proseizure state.

Because maximum Zn2+ cleft concentrations have not been established with sufficient certainty, the potential relevance of low-affinity Zn2+-induced modulation in the brain remains ambiguous. However, the slowing effect could be important in certain tissues outside of the brain, such as in pancreatic islets of Langerhans, where local Zn2+ concentrations during cosecretion of Zn2+ and insulin have been estimated to reach several hundred micromoles (Kim et al., 2000). Animal studies have linked Cav2.3 channels to α-cell glucagon (Pereverzev et al., 2005), β-cell insulin (Jing et al., 2005; Matsuda et al., 2001; Pereverzev et al., 2002), and δ-cell somatostatin (Zhang et al., 2007) secretion and we have previously shown that they are involved in intra-islet paracrine Zn2+ signaling (Drobinskaya et al., 2015). However, further studies will clearly be required to firmly establish whether the low-affinity effects described here are physiologically relevant or simply phenomena that must be taken into account when studying the high-affinity effects. Additional studies will also be necessary to determine the kinetics, magnitude and direction of Zn2+ effects on native Cav2.3 channels in different cells under physiological conditions, as they could be influenced by a number of factors such as RMP, subunit-composition or alternative splicing. For example, Cavβ-subunits have been shown to differentially modify the time course of Cav2.3 channel recovery from inactivation at depolarized test potentials (Jeziorski et al., 2000) as well as the gating effects of Ni2+ on cloned Cav2.1 channels (Zamponi et al., 1996), suggesting that auxiliary subunits could directly or indirectly influence trace metal-induced VGCC modulation.

Limitations

There are some important limitations and inherent assumptions of our work that need to be addressed. First of all, to reduce uncertainty with regard to the KZn and Emax values we analyzed all of the concentration–response relationships using a Hill slope of unity, which assumes simple, bimolecular reactions. With regard to the high-affinity shift and slowing, this assumption seems justified based on the proposed structure of the trace metal binding site. Moreover, when the data were fitted with unconstrained Hill slopes, the values obtained for the high-affinity component were always close to 1 (i.e., 0.7–1.2). Likewise, the Hill slope obtained for the low-affinity slowing after DEPC pretreatment was 0.9 (CI, 0.7–1.0). The low-affinity shift could often be equally well described using different values for the Hill slope, possibly because full saturation of this effect was not consistently observed and/or nonspecific surface charge effects contributed to the net Zn2+ action (but see below). However, by fixing the Hill slope to 1, we still obtained visibly good fits, adjusted χ2 values close to 1, and consistent results for the Emax values, suggesting that the plateau phase was sufficiently well defined by the data.

Second, we used DEPC to probe the role of histidine residues for high-affinity Zn2+ binding, which is frequently employed for this purpose (Choi and Lipton, 1999; Bancila et al., 2005; Harvey et al., 1999) but has no perfect target specificity and can also react with other amino acid residues (Mendoza and Vachet, 2008; Limpikirati et al., 2019). Protons often compete with Zn2+ for binding to the histidine imidazole ring, so that their effects on Zn2+-induced modulation can to some extent support or oppose an action at histidine residues. For example, moderate acidification reduced the KZn and Emax values for high-affinity shift and slowing and produced effects similar to Zn2+ under control conditions, which is consistent with an effect mediated by the known loop histidines. Also, neither DEPC nor acidification altered the concentration dependence of low-affinity slowing, suggesting that histidine residues are not involved and that Zn2+ binding to the underlying site was unaffected. On the other hand, DEPC pretreatment completely prevented and partly reversed the Zn2+-induced changes in activation slope factor, while moderate acidification only slightly reduced apparent Zn2+ affinity and even increased the maximum Zn2+ effects. Likewise, DEPC and protons both reduced the voltage dependence of block/low-affinity II-V current suppression, but DEPC did so by increasing apparent Zn2+ affinity at negative test potentials, while protons reduced apparent Zn2+ affinity at positive test potential. As such, further studies will clearly be required for firm conclusions with regard to the exact identity of residues that could be directly or indirectly involved in some of the more complex Zn2+-induced effects and their modification by DEPC and protons.

We have also neglected any contribution of nonspecific surface charge screening or binding to the observed effects, which might have introduced some error, especially at the highest free Zn2+ levels examined. However, divalent cation concentrations in our recording solutions were relatively high even before addition of Zn2+, and there was no significant difference in channel voltage dependence between recordings performed with 2 versus 4 mM Ca2+ or 4 mM Ca2+ versus Mg2+, suggesting that the contribution of nonspecific surface charge effects was small.

Finally, although our Markov model for Cav2.3 channel gating and Zn2+-induced modulation describes well many qualitative and quantitative features of the experimental data, it should be considered preliminary for several reasons. First of all, our model obviously represents a considerable simplification, and the available data are insufficient for a detailed physical interpretation or full validation of the underlying assumptions. The most important limitation in its current form is that the VSMs in the model cannot be related to specific domains in the channel protein, even though its success in modeling the high-affinity Zn2+ effects makes it tempting to propose that VSM 1 in the model could correspond to the VSM in domain I. Another related shortcoming of our model is that the state dependence of inactivation had to be determined from the data using an empirical approach. While somewhat arbitrary, this approach was sufficient to demonstrate that Zn2+-induced changes in activation gating alone could bring about the observed changes in inactivation kinetics and voltage dependence if inactivation is state dependent and coupled to activation. Moreover, once exact fluorescence data on Cav2.3 channel voltage-sensor movement and activation inactivation coupling become available, it should be possible to revise and extent the model structure accordingly.

Lastly, our model in its current form does not reproduce the kinetics of recovery from inactivation or the process of ultraslow inactivation, which we have shown here to be of potential importance for the time course and direction of slow Zn2+ effects at depolarized RMPs. Despite all these limitations, we think it is useful to present our model at this time, since it may provide a basis for further investigation of trace metal effects on Cav2.3 channel function and could be extended based on future findings to ultimately help predict the intricate effects of endogenous Zn2+ on neuronal excitability.

Conclusion

The present study performed a comprehensive assessment of the modulation of Cav2.3 channel electrophysiological properties by a wide range of Zn2+ concentrations and reveals how the degree and even direction of effects could be influenced by the prevailing neuronal properties and ionic conditions. While still far from complete, the model developed provides a first quantitative framework for understanding Zn2+ effects on Cav2.3 channel function and a step toward the application of computational approaches for predicting the complex actions of Zn2+ on neuronal excitability.

Acknowledgments

Christopher J. Lingle served as editor.

We thank Renate Clemens for her excellent technical assistance.

This work was financially supported by the Köln Fortune Program/Faculty of Medicine, University of Cologne (259/2013) and the Deutsche Forschungsgemeinschaft (SCHN 387/21-1 and SCHN 387/21-2).

The authors declare no competing financial interests.

Author contributions: F. Neumaier was involved in conceptualization, formal analysis, funding acquisition, investigation, methodology, visualization, and writing (original draft, review, and editing). T. Schneider was involved in conceptualization, funding acquisition, project administration, supervision, and writing (review and editing). S. Alpdogan and J. Hescheler contributed resources.

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