INTRODUCTION

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Ca²⁺ entry through voltage-dependent calcium channels is critical for both electrical and chemical signaling. To perform such functions, calcium channels must select for Ca²⁺ over more plentiful monovalent cations. The basic mechanism for Ca²⁺ selectivity is not simple molecular sieving, because calcium channels pass large monovalent cations if divalent cations are absent (McCleskey and Almers, 1985). Selectivity involves ion-ion interactions (Almers and McCleskey, 1984; Hess and Tsien, 1984; Dang and McCleskey, 1998) and electrostatic interactions of ions with negatively charged amino acids in the channel pore (Yang et al., 1993; Nonner and Eisenberg, 1998).

Permeation mechanisms have been studied most thoroughly for L-type calcium channels. Many of the basic features are also present in T-type Ca²⁺ channels, including high permeability to monovalent cations and block by micromolar concentrations of divalent cations (Fukushima and Hagiwara, 1985; Lux et al., 1990), but there are also differences in ion selectivity among calcium channels. Notably, inward currents are ~2-fold larger with Ba²⁺ than Ca²⁺ for L-channels (Hess and Tsien, 1984), but most T-channels show comparable inward currents with Ca²⁺ or Ba²⁺ (Fukushima and Hagiwara, 1985; Bean, 1985; Carbone and Lux, 1987; Huguenard, 1996).

The recent cloning and functional expression of T-type calcium channels allows the study of their biophysical properties in isolation (Perez-Reyes et al., 1998). We recently examined the gating kinetics of the 1G channel (Serrano et al., 1999), which is highly expressed in many brain regions, including thalamic relay neurons (Talley et al., 1999), where T-channels play an important role in generation of bursting activity (Huguenard, 1996). In our initial experiments on the ion selectivity of 1G, we were surprised to find that inward currents were much larger with Ca²⁺ than with Ba²⁺ (Dashti et al., 1999). We report here that this results from preferential block by Mg²⁺ of currents carried by Ba²⁺. Without Mg²⁺, inward currents are very similar with Ca²⁺ and Ba²⁺. However, the reversal potential (V_R) is more positive, and outward monovalent currents are smaller with Ca²⁺, indicating Ca²⁺ selectivity. We conclude that 1G can distinguish Ca²⁺ from Ba²⁺ ions. Our results can be described by Eyring rate theory (a 2-site, 3-barrier model) if Ca²⁺ enters the pore more easily than Ba²⁺, but Ba²⁺ exits more rapidly. Small differences between the energetics of Ca²⁺ versus Ba²⁺ are sufficient to produce a ~7-fold difference in Mg²⁺ block, although inward currents carried by Ca²⁺ and Ba²⁺ are similar over a wide voltage range.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Electrophysiology

Whole-cell recordings were made from the Nr2+ cell line, HEK 293 cells stably transfected with rat 1G (Lee et al., 1999a), as described previously (Serrano et al., 1999). Briefly, data were recorded at room temperature using Clampex (pClamp 6.03, Axon Instruments, Foster City, CA) with an Axopatch 200A amplifier. Data were usually sampled at 20 kHz following 10 kHz analog filtering. Series resistances (initially 6.6 ± 0.4 M, n = 34) were compensated nominally by 80-90%.

The standard intracellular (pipette) solution contained 140 mM NaCl, 2 mM CaCl₂, 11 mM EGTA, 10 mM HEPES, 4 MgATP, pH 7.2 with ~25 mM NaOH. Free [Ca²⁺]_i was 40 nM, and free [Mg²⁺]_i was 0.8 mM, calculated from the program Bound and Determined (BAD) (Brooks and Storey, 1992). The extracellular solutions contained 140 mM NaCl, 2 mM CaCl₂ or BaCl₂ (as noted), 0 or 1 mM MgCl₂ (as noted), 10 mM HEPES, pH 7.2 with ~5 mM NaOH.

Extracellular solutions were exchanged by a gravity-driven flow system, remotely controlled by solenoid valves. We found it difficult to record from cells with sufficient stability to obtain fully reversible responses (requiring >10 min), resulting from slow changes in leakage currents, current amplitudes, etc. Thus, many comparisons of currents in different conditions were made between populations of cells (e.g., part B, Figs. 1-6), but key results were confirmed in cells where reversible effects were obtained (as illustrated in part A, Figs. 2-5). Some averaged I-V curves are shown in multiple figures, to make pairwise comparisons between different conditions.

Data analysis

Currents were analyzed using Clampfit v.6 and Microsoft Excel (v.5 or 97), and graphs were prepared using Microcal Origin v.5 and Micrografx Designer v.7. Unless noted, values are given as mean ± SEM. For averaged data in the figures, error bars are shown if larger than the symbols. Current records in the figures were Gaussian-filtered 2 kHz (unless noted otherwise) using Clampfit. Statistical significance levels given in the text are from unpaired 2-tailed t-tests (Excel), with p < 0.05 considered to be significant.

Our experiments require accurate voltage clamp to control the large currents observed over a wide voltage range. For analysis of instantaneous I-V relations, cells were selected based on two primary criteria, the rise time of tail currents at 100 mV, and the effect of partial inactivation on the time course of tail currents at 100 mV (protocol illustrated in Fig. 7). For selected cells, ~70% inactivation affected the time constant for channel deactivation by <20% (corresponding to 5 mV or less of series resistance error, given the voltage-dependence of channel closing; Serrano et al., 1999).

Instantaneous I-V relations were measured by fitting single exponentials to the decay of current following a brief (2-ms) step to +60 mV (see Fig. 1 A). The exponential fit began when the tail currents reached a peak (0.3-0.7 ms), and extended to the end of the 40-ms voltage steps. In some cells, the tail currents were well described by a single exponential over that entire time course, while other cells exhibited slight deviations from exponential decay during the first ~1 ms (which was not strongly weighted in the fit). The amplitude of the fitted exponential at the starting point of the fit was used for the instantaneous I-V measurements shown, as an estimate of the current at the time when accurate voltage clamp was actually achieved (extrapolating back to time 0 would overestimate the tail current amplitudes at extreme voltages). This procedure resulted from much trial-and-error, and was judged to give more consistent results than alternative approaches (e.g., measurement of the actual peak tail current, which was more sensitive to filtering and to slight deviations from exponential kinetics). However, different methods produced only subtle differences in the I-V relations, as the main results were visible "by eye" in the raw currents (see part A, Figs. 1-5).

Calculations and models

For two permeant ions A and B of any charge (z_A, z_B), each of which may be present on both sides of the membrane, the Goldman-Hodgkin-Katz permeability ratio (P_A/P_B) was calculated from the observed reversal potential (V_R) (Frazier et al., 2000):

(1)

where _A = z_AV_RF/RT and _B = z_BV_RF/RT. Permeability ratios in the Results were calculated using concentrations, not activities.

The voltage dependence of Mg²⁺ block was described by a simplified Woodhull (1973) model, assuming that Mg²⁺ binds to a single site within the pore, can enter the pore only from the outside, and cannot permeate:

(2)

where f is the fraction of current remaining unblocked in the presence of Mg²⁺, K_D,0 is the dissociation constant for Mg²⁺ at 0 mV, z = 2 is the charge on Mg²⁺, and  is the apparent electrical location of the binding site, as a fraction of the electrical field of the membrane measured from the outside.

Permeation and Mg²⁺ block were also described by a 2-site, 3-barrier model including ion-ion repulsion, based on the model of Almers and McCleskey (1984). Specifically, positions of the barriers in the electrical field ( values) were 0.05, 0.5, and 0.95, with wells at 0.33 and 0.67. Each rate constant (k) was related to barrier/well energies by:

(3)

where G is the difference in zero-voltage energies between the well and the barrier, z is the charge on the ion, and is the difference in electrical locations. For comparison to most previous models, we use kT/h (6.1 × 10¹²) as the preexponential factor (k₀) for all rate constants, including entry of ions into the pore. This has been criticized (Nonner and Eisenberg, 1998), especially for entry rates (Yue and Marban, 1990), so the height of the "energy barriers" in the model should not be interpreted literally (Andersen, 1999). When both binding sites were occupied, rate constants for exit from the pore were increased by the factor Q · z_A · z_B, where Q = 11.89 and z_A and z_B are the charges on the ions in the two sites (Almers and McCleskey, 1984). The model was implemented using the SCoP simulation package (v.3.51; Simulation Resources, Berrien Springs, MI). Whole-cell currents were scaled to typical single-channel current levels assuming 8000 channels per cell. The energy levels of the barriers and wells were varied for each ion (Ca²⁺, Ba²⁺, Mg²⁺, and Na⁺). To limit the number of free parameters, the energy profiles were assumed to be symmetrical for Ca²⁺, Ba²⁺, and Na⁺ (but not Mg²⁺), and the middle barrier was the same height (with respect to the outer well) for all ions. External barriers were constrained to be from 8 to 12 RT, and the outer well for Mg²⁺ was constrained to be at least 1 RT less than the outer barrier. The 11 resulting parameters (2 energies each for Ca²⁺, Ba²⁺, and Na⁺, and 5 for Mg²⁺) were estimated using the SCoPfit program, which uses the principal axis (Praxis) algorithm.

	RESULTS

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With Mg_o²⁺, inward currents are larger with Ca²⁺ than with Ba²⁺

To examine the ion selectivity of the 1G channel, we began with nearly normal ionic conditions, including 2 mM Ca_o²⁺, except that K_i⁺ was replaced by Na_i⁺. The recording solutions contained 1 mM Mg_o²⁺ and an estimated 0.8 mM free Mg_i²⁺ (see Materials and Methods). To examine permeation using whole-cell currents, we measured instantaneous current-voltage (I-V) relations following brief, strong depolarizations designed to activate channels while producing minimal inactivation (Fig. 1). In principle, each prepulse should activate the same number of channels, producing the same outward current at +60 mV during each 2-ms step. If so, the currents measured shortly after repolarization should reflect the voltage-dependence of current flow through a constant number of open channels (Hodgkin and Huxley, 1952). This analysis is aided by the characteristically slow deactivation of T-channels, with  > 1 ms even at 120 mV (Serrano et al., 1999).

View larger version (14K): [in this window] [in a new window]   FIGURE 1   With Mgo2+, inward currents are larger with Ca2+ than with Ba2+. (A) Sample records from the protocol used to measure instantaneous I-V relations, in Ca2+ (left) or Ba2+ (right). Note small inward currents and large outward currents with Ba2+. Channels were activated by a 2-ms step to +60 mV, immediately followed by voltage steps in 10-mV increments from 120 to +70 mV; every other voltage step is illustrated here. The decay of currents at each voltage reflects a combination of channel closing (deactivation) and inactivation (Serrano et al., 1999); cell a9n26 (Ca2+ + Mg2+); cell c9711 (Ba2+ + Mg2+). (B) Instantaneous I-V relations, measured as described in Materials and Methods, from the protocol of A, averaged from 8 cells (Ca2+ + Mg2+) or 15 cells (Ba2+ + Mg2+).

With 2 mM Ca²⁺, the reversal potential (V_R) was +26.0 ± 2.0 (n = 8), in good agreement with our previous study on gating of 1G (Serrano et al., 1999) and other reports on Ca²⁺/Na⁺ selectivity of T-channels (Fukushima and Hagiwara, 1985). V_R is less positive than commonly observed for calcium currents in native cells because most such studies use Cs⁺ (or even less permeant ions such as N-methyl-D-glucamine) to improve current isolation, and calcium channels are ~3-fold selective for Na⁺ over Cs⁺ (Fukushima and Hagiwara, 1985; Lux et al., 1990; Hess et al., 1986; Dashti et al., 1999). We found it convenient to use Na_i⁺ because outward currents and V_R were easily measurable, and the presence of a single permeant monovalent cation simplified calculation of permeability ratios (Eq. 1).

The instantaneous I-V relations in Ca²⁺ have a sigmoidal shape, indicating a relatively high conductance at strongly negative or positive voltages, and a low conductance near the reversal potential. As for L-channels (Hess et al., 1986), this presumably indicates Ca²⁺ permeation at negative voltages, permeation of monovalent cations at positive voltages, and mutual block near the reversal potential.

When Ca²⁺ was replaced by Ba²⁺, the instantaneous I-V was affected in several ways. V_R was 7 mV less positive (+18.8 ± 2.1 mV, n = 15; p = 0.03), outward currents were ~2-fold larger, and inward currents were ~3-fold smaller. The shift in V_R is consistent with the idea that the channel pore binds Ca²⁺ more tightly than Ba²⁺, as for L-channels. Weaker binding of Ba²⁺ could also explain the larger outward Na⁺ currents. However, the considerably smaller inward currents with Ba²⁺ were a surprise, as currents through L-channels are larger for Ba²⁺ than Ca²⁺ (Hess and Tsien, 1984), and most T-channels exhibit similar inward currents with Ca²⁺ and Ba²⁺ (Fukushima and Hagiwara, 1985; Carbone and Lux, 1987). Even for 1G, some other studies have found comparable currents with Ca²⁺ and Ba²⁺ (Klugbauer et al., 1999; Monteil et al., 2000). We suspected that this discrepancy resulted from some difference in recording conditions. The weak voltage-dependence of the inward currents in Ba²⁺, reminiscent of voltage-dependent block, focused our attention on Mg_o²⁺, a known blocker of calcium channels (Wilson et al., 1983; Kuo and Hess, 1993), including T-channels (Fukushima and Hagiwara, 1985; Lux et al., 1990).

Mg_o²⁺ selectively blocks inward currents carried by Ba²⁺

One millimolar Mg_o²⁺ strongly blocked inward currents carried by 2 mM Ba²⁺ (Fig. 2). Interestingly, outward currents (carried by Na⁺) were not affected. Averaging across cells, the ratio of currents with/without Mg_o²⁺ was 0.19 ± 0.04 at 120 mV (p = 1 × 10⁶), but 1.03 ± 0.22 at +60 mV (n.s.). Because Mg²⁺ blocks T-currents more potently with monovalents as charge carrier (Fukushima and Hagiwara, 1985), the preferential block of inward currents presumably reflects voltage-dependent block (analyzed further below). Note that the I-V relations measured by this protocol would not be affected by effects of Mg²⁺ on channel gating, e.g., by screening of surface charge.

View larger version (16K): [in this window] [in a new window]   FIGURE 2   One millimolar Mg2+ strongly blocks inward currents with Ba2+. (A) Sample records from one cell (a0130), recorded before (left), during (middle), and after recovery (right) from application of 1 mM Mg2+. Note that Mg2+ reversibly inhibited inward currents with no effect on outward currents. The prepulse (4 ms) was twice the duration normally used, so more inactivation occurred during the prepulse. (B) Instantaneous I-V relations, averaged from 13 cells (Ba2+) or 15 cells (Ba2+ + Mg2+).

Mg_o²⁺ also blocked currents carried by 2 mM Ca²⁺, but more weakly (Fig. 3). Current ratios (with/without 1 mM Mg_o²⁺) were 0.62 ± 0.15 at 120 mV (p = 0.04), and 1.15 ± 0.24 at +60 mV (n.s.). In an attempt to match the degree of block observed with Ba²⁺, the effect of 6 mM Mg_o²⁺ was tested on currents with 2 mM Ca²⁺ (Fig. 4). Current ratios were 0.23 ± 0.04 at 120 mV (p = 4 × 10⁶), and 0.75 ± 0.14 at +60 mV (n.s.). Mg²⁺ had no significant effect on V_R, either with Ca²⁺ or with Ba²⁺.

View larger version (18K): [in this window] [in a new window]   FIGURE 3   One millimolar Mg2+ weakly blocks inward currents with Ca2+. (A) Sample records, cell g0209. (B) Instantaneous I-V relations, averaged from 17 cells (Ca2+) or 8 cells (Ca2+ + Mg2+).

View larger version (16K): [in this window] [in a new window]   FIGURE 4   Six millimolar Mg2+ strongly blocks inward currents with Ca2+. (A) Sample records, cell x0303. (B) Instantaneous I-V relations, averaged from 17 cells (Ca2+) and 11 cells (Ca2+ + Mg2+).

In the absence of Mg_o²⁺, inward currents were very similar with Ca²⁺ or Ba²⁺ (Fig. 5). This confirms that nearly all of the difference in inward currents in Fig. 1 can be attributed to selective Mg²⁺ block of currents carried by Ba²⁺. However, two subtle but important differences remain between the I-V relations in Ca²⁺ and Ba²⁺. The outward currents are smaller in Ca²⁺ (Ca²⁺/Ba²⁺ ratio 0.47 ± 0.09 at +60 mV, p = 0.003; versus 0.90 ± 0.15 at 120 mV, n.s.), and V_R is more positive in Ca²⁺ (+28.9 ± 1.3 mV in Ca²⁺, n = 18; +23.0 ± 2.1 mV in Ba²⁺, n = 13; p = 0.02). In terms of Goldman-Hodgkin-Katz theory, these V_R values correspond to P_Ca/P_Na = 193, and P_Ba/P_Na = 115 (Eq. 1).

View larger version (16K): [in this window] [in a new window]   FIGURE 5   Without Mg2+, inward currents are comparable with Ca2+ or Ba2+. (A) Sample records, from the same cell as Fig. 3 A. (B) Instantaneous I-V relations, averaged from 17 cells (Ca2+) or 13 cells (Ba2+).

Like most T-channels, 1G passes similar inward currents with Ca²⁺ and Ba²⁺ (in the absence of Mg_o²⁺). However, that does not mean that the 1G channel cannot distinguish Ca²⁺ from Ba²⁺. Three observations indicate that the 1G pore interacts more strongly with Ca²⁺ than with Ba²⁺: the permeability ratio is larger with Ca²⁺, outward currents are smaller with Ca²⁺ (indicating stronger block of Na⁺ currents by Ca²⁺), and Ba²⁺ currents are blocked more potently by Mg²⁺.

Mg_i²⁺ does not block strongly

Our standard recording solutions included 4 mM MgATP, estimated to produce 0.8 mM free Mg_i²⁺ (see Materials and Methods). Because a comparable concentration of Mg_o²⁺ potently blocked currents with Ba²⁺, we examined the effect of removing Mg_i²⁺ by dialyzing cells without MgATP (and including 1 mM EDTA). No significant difference was observed in the instantaneous I-V relationship, although there was a suggestion of larger outward currents in the absence of Mg_i²⁺ (Fig. 6). Although we cannot exclude a weak blocking effect of Mg_i²⁺, block by Mg²⁺ is clearly stronger from the extracellular side of the channel, as reported previously for L-channels (Kuo and Hess, 1993).

View larger version (13K): [in this window] [in a new window]   FIGURE 6   Mgi2+ has little or no effect. (A) Sample records from a cell (b9728) dialyzed with an intracellular solution containing 1 mM EDTA and no MgATP. (B) Instantaneous I-V relations, averaged from 8 cells (Ba2+, no MgATP) or 13 cells (Ba2+).

Effects on channel kinetics

The description of Mg²⁺ block presented so far effectively assumes that Mg²⁺ block is instantaneous with respect to the speed of our voltage clamp. Clearly, the strong block of the peak inward tail currents in Fig. 2 A and Fig. 4 A demonstrates that Mg²⁺ can block 1G channels rapidly. However, in several cells, especially when the clamp quality was judged to be especially good, there was a fast component to the tail currents in the presence of 2 mM Ba²⁺ + 1 mM Mg²⁺ (arrow, Fig. 7 B). That component is not a residual capacity transient or a gating current, because 1) it is not seen in the absence of Mg²⁺ (Fig. 7 A), 2) it is greatly reduced by partial inactivation (Fig. 7 B), and 3) it is absent in 10 mM Mg²⁺ (Fig. 7 C), where block should be 10-fold faster. We interpret that rapid component as the partially resolved time course of Mg²⁺ block. Our method of measuring the instantaneous I-V relationship was designed to avoid including the fast component (see Materials and Methods). Thus, the measured currents should reflect the extent of block at each voltage following equilibration of Mg²⁺ with the open channel. There was no obvious fast component to tails with Ca²⁺ + Mg²⁺, probably because the extent of block was low with 1 mM Mg²⁺, and the rate of block was high with 6 mM Mg²⁺.

View larger version (14K): [in this window] [in a new window]   FIGURE 7   A fast component to inward tail currents in 2 mM Ba2+ + 1 mM Mg2+. Currents were recorded in response to 2-ms steps to +60 mV, in the absence of Mgo2+ (A), with 1 mM Mgo2+ (B), or with 10 mM Mgo2+ (C). In each condition two records are shown, one in a rested cell (the larger current), and one following partial inactivation (by a 42-ms step to +60 mV, followed by 20 ms at 120 mV to allow channels to deactivate fully). Same cell as Fig. 6 A (no intracellular MgATP). Similar fast tail current components could also be observed in cells with MgATP; 2.5 kHz Gaussian filter.

Our results suggest that the time constant for block by 1 mM Mg²⁺ is ~0.1 ms, possibly faster. That would correspond to a bimolecular blocking rate of ~10⁷ M¹ s¹. For comparison, for high voltage-activated (HVA) calcium channels, Mg²⁺ blocks currents carried by monovalent cations at ~10⁸ M¹ s¹ (Kuo and Hess, 1993; Carbone et al., 1997). With 110 mM Ba²⁺, the rate is 1.9 × 10⁵ s¹, but that increases sharply at lower Ba²⁺ (Lansman et al., 1986).

Although our experiments were designed to analyze effects on permeation, preliminary results suggest that Mg²⁺ may also affect gating. With a "standard I-V" protocol, where the cell was depolarized directly to a range of voltages without a prepulse to +60 mV, Mg²⁺ appeared to shift channel gating by ~10 mV to more depolarized voltages (data not shown). Consequently, at negative voltages, the percentage inhibition by Mg²⁺ was greater measured from the standard I-V than from the "instantaneous I-V." With Ca²⁺, addition of either 1 or 6 mM Mg²⁺ decreased the time constants for channel deactivation; the effect of Mg²⁺ on the main component of deactivation was less clear with Ba²⁺. These effects are in the direction expected for screening by Mg²⁺ of a surface charge associated with gating, but we cannot rule out additional effects (e.g., altered activation of a Mg²⁺-blocked channel, or modification of gating by binding of Mg²⁺ to a separate site outside the pore). Mg²⁺ did not affect the time constant for inactivation, but inactivation of inward currents was ~30% faster in Ba²⁺ than in Ca²⁺, as previously reported for 1G (Klugbauer et al., 1999).

For purposes of this paper, we conclude that our measurements of instantaneous I-V relations reflect the voltage-dependence of Mg²⁺ block of the open channel, with negligible interference from effects on gating, or time-dependence of Mg²⁺ block. Possible effects of Mg²⁺ and other blockers on gating of 1G (Lee et al., 1999b; Lacinová et al., 2000) will require further study.

Analysis of Mg²⁺ block

Block by Mg²⁺ is clearly voltage-dependent (Figs. 2-4). We first examined whether the voltage-dependence was consistent with a simple Woodhull model (Eq. 2), where Mg²⁺ can enter and exit the pore only from the extracellular side (Fig. 8). The data were fitted reasonably well, especially for Ca²⁺, assuming a binding site 25-30% of the distance through the electrical field of the membrane from the outside, with 7-fold lower affinity with Ca²⁺ as the charge carrier.

View larger version (20K): [in this window] [in a new window]   FIGURE 8   Analysis of Mg2+ block using a Woodhull model. (A) The current ratio (Ba2+ + Mg2+/Ba2+) calculated from the data of Fig. 2 B. The smooth curve was fitted using Eq. 2, with KD,0 = 2.7 mM and  = 0.30. (B) Current ratios calculated from three cells where 6 mM Mg2+ reversibly inhibited the currents with 2 mM Ca2+. The average of currents recorded before and after recovery from Mg2+ block was used as the control. Because the comparisons were made within each cell rather than across populations of cells, the standard errors are less in B than in A. The fit to Eq. 2 gave KD,0 = 19 mM and  = 0.25 (smooth curve).

The lower affinity for Mg²⁺ in the presence of Ca²⁺ presumably reflects ion-ion competition, not considered in a Woodhull model. We next tested Eyring rate theory models, including two binding sites within the channel pore, based on the classical models for permeation and block of L-channels (Almers and McCleskey, 1984; Hess and Tsien, 1984). The best-fit parameters reproduced many of the key features of the data, in five experimental conditions (Ca²⁺ alone, Ba²⁺ alone, Ca²⁺ or Ba²⁺ + 1 mM Mg²⁺, and Ca²⁺ + 6 mM Mg²⁺), over a 190 mV range: the overall shape of the I-V relations, similar inward currents with Ca²⁺ or Ba²⁺ (in the absence of Mg²⁺), stronger block of inward currents carried by Ba²⁺, a more positive reversal potential with Ca²⁺, and larger outward currents with Ba²⁺ (Fig. 9). The parameters produced Ca²⁺/Ba²⁺ selectivity using deeper wells for Ca²⁺ (higher affinity binding), but higher barriers for Ba²⁺ (slower entry into the pore). Both differences contribute to the more positive reversal potential with Ca²⁺, but the effects on the amplitudes of inward currents are opposite and nearly cancel. Crudely put, Ca²⁺ can get into the pore more easily than Ba²⁺, but once in, it is less likely to exit. The energy differences are quite small, so it is striking that the model reproduces the ~7-fold difference in Mg²⁺ block. Both differences between the energetics of Ca²⁺ and Ba²⁺ favor Ca²⁺ occupancy, reducing the ability of Mg²⁺ to enter and block.

View larger version (16K): [in this window] [in a new window]   FIGURE 9   Analysis of Mg2+ block using an Eyring rate theory model. (A and B) The smooth curves are the best fits to a 2-site, 3-barrier model, superimposed on the experimental data from Fig. 2 B and Fig. 3 B, respectively. The model-generated single-channel currents were scaled to match the whole-cell currents, assuming 8000 open channels. (C) The energy profiles for the different ions. The model was based on that of Almers and McCleskey (1984); see Materials and Methods for details. The energy barriers and wells (from outside to inside) were 9.62, 10.91, 1.87, 10.91, 9.62 (Ca2+); 10.17, 9.60, 3.17, 9.60, 10.17 (Ba2+); 12, 2.38, 10.39, 2.38, 12 (Na+); and 8, 7, 19.77, 9.75, 23.75 (Mg2+). In the format recommended by the Journal of General Physiology (Andersen, 1999), 10 RT corresponds to RCR = 4.3, assuming a frequency factor of 6.1 × 1012 (see Materials and Methods).

The Eyring model predicts that Na⁺ carries an appreciable fraction of the inward current, even in the presence of 2 mM Ca²⁺ or Ba²⁺. At 50 mV, Na⁺ would carry 18% of the current with Ca²⁺, and 50% with Ba²⁺; the fractional Na⁺ current would increase with hyperpolarization (calculations not shown). Because the net currents are nearly equal with 2 mM Ca²⁺ or Ba²⁺ (in the absence of Mg_o²⁺), there actually would be more Ca²⁺ entry than Ba²⁺ entry. It is not clear whether this feature of the model is realistic.

For the Eyring model, the energy profile for Mg²⁺ includes a high energy barrier on the cytoplasmic side of the channel. That explains why a Woodhull model (effectively assuming an infinitely high barrier) can describe Mg²⁺ block reasonably well. The high barrier also explains the asymmetry in Mg²⁺ block, where Mg_o²⁺ blocks potently while Mg_i²⁺ does not. For Mg²⁺, the outer site was not well defined, and in practical terms is not really a binding site.

It is interesting that the Woodhull models suggested that Mg²⁺ bound toward the outer part of the channel ( = 0.25-0.30), while the Eyring model placed the site of Mg²⁺ block toward the cytoplasmic side ( = 0.67). When the output of the Eyring model was fitted to a Woodhull model (Eq. 2), the fits were less good than in Fig. 8, with  values for Mg²⁺ of 0.23 (with Ca²⁺) and 0.29 (with Ba²⁺). This illustrates that that Woodhull parameters cannot be interpreted literally for a multi-ion pore (Hille, 1992). We have not systematically varied the position of the binding sites in the Eyring model, so the  = 0.67 value should not be taken too literally. However, if the binding sites were constrained to be in the outer part of the channel ( = 0.2 and 0.3) (see Kuo and Hess, 1993), we were not able to obtain a good fit to the data (calculations not shown).

Recently, many crucial features of L-channel permeation have been described by a different theoretical approach, Poisson-Nernst-Planck (PNP) theory (Nonner and Eisenberg, 1998). PNP can qualitatively reproduce several of our principal results if we assume that the chemical potential for Mg²⁺ varies linearly within the pore (to explain the asymmetrical block; calculations not shown). However, we have not found parameters that quantitatively describe the instantaneous I-V curves. Thus far, we have attempted to find appropriate PNP parameters "by hand" rather than by automated error-minimization routines (as used above for Eyring models), so we cannot conclude that PNP theory is unable to explain our results.

	DISCUSSION

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Although Ca²⁺ and Ba²⁺ carry comparable inward currents through the 1G T-type calcium channel, the channel is actually selective for Ca²⁺ over Ba²⁺. This difference is shown most clearly by the ~7-fold difference in the apparent affinity for block by Mg²⁺. A more positive reversal potential with Ca²⁺, and stronger block of outward currents by Ca²⁺, also imply that Ca²⁺ interacts more strongly with the 1G pore than does Ba²⁺. In terms of an Eyring rate theory model, Ca²⁺ enters the pore more easily than Ba²⁺, but exits more slowly.

Ca²⁺-Ba²⁺ selectivity

Most studies on native T-type calcium channels found similar inward currents with Ca²⁺ and Ba²⁺ (Huguenard, 1996), with the exception of thalamic reticular neurons, where Ca²⁺ currents were ~50% larger (Huguenard and Prince, 1992). However, comparison among studies can be difficult. The Ca²⁺ and Ba²⁺ concentrations have varied from the physiological range to isotonic (especially for single-channel studies), which could affect the apparent selectivity. Many studies used the current at the peak of the I-V relationship as an index, which could be affected by changes in channel gating as well as by the conductance of the channel to Ca²⁺ or Ba²⁺. The activation of L-type and other HVA channels is known to be affected by surface potentials, which can differ between Ca²⁺ and Ba²⁺ even at the same concentration; few studies have examined effects of surface potential on T-channels (Becchetti et al., 1992).

Few studies of T-currents have compared reversal potentials or outward currents for Ca²⁺ versus Ba²⁺. One important exception is Fukushima and Hagiwara (1985), who found for T-currents of B lymphocytes that the reversal potential was ~10 mV more positive and outward currents were smaller with Ca²⁺, in good agreement with our results for 1G.

One of our main conclusions is that 1G T-channels resemble L-channels in selectivity for Ca²⁺ over Ba²⁺, by traditional criteria such as permeability ratios. For L-channels, the channel conductance is higher for Ba²⁺ (opposite to the selectivity sequence), while for 1G the whole-cell Ca²⁺ and Ba²⁺ conductances are similar. In terms of an Eyring model, in L-channels the primary difference in energy profiles for Ca²⁺ and Ba²⁺ is a deeper energy well for Ca²⁺ by ~4 RT (Almers and McCleskey, 1984). For 1G, our parameters also give a deeper well for Ca²⁺, but only by 1.3 RT. We also found a lower external barrier for Ca²⁺ not present in the L-channel models. Overall, it is noteworthy that relatively modest differences in energy profiles can have significant effects on ion selectivity and block.

Calcium channels often show an anomalous mole fraction effect (AMFE) between Ca²⁺ and Ba²⁺, where the current in a mixture of Ca²⁺ and Ba²⁺ is less than with either ion alone (Almers and McCleskey, 1984; Hess and Tsien, 1984). The Eyring model predicts a very weak AMFE for 1G, maximally a 6% reduction in current amplitudes near 60 mV, and no AMFE for the reversal potential (calculations not shown).

Although the Eyring model for 1G gave a good quantitative description of our results, we emphasize the qualitative explanation that it provides for the differential sensitivity of Ca²⁺ and Ba²⁺ currents to Mg²⁺ block. First, the results presented here are limited to a single concentration (2 mM) of divalent cation as charge carrier. Preliminary results demonstrate substantial increases in current either upon removal of extracellular divalent cations (and addition of EGTA), or in isotonic Ca²⁺ or Ba²⁺, but those data are not yet suitable for quantitative modeling. Second, there is a lively debate regarding the physical plausibility of Eyring models for channel permeation (McCleskey, 1999; Nonner et al., 1999). One specific issue is that Eyring models (including ours) tend to predict significant changes in the net charge in the pore with voltage and ion concentration, while PNP models predict an essentially electroneutral pore (Nonner and Eisenberg, 1998). For the moment, we present this model as one specific and intuitive explanation of interactions among Ca²⁺, Ba²⁺, and Mg²⁺.

The molecular basis for the variations in selectivity among calcium channels remains to be explored. All known HVA channels contain four glutamates in the P region, at the corresponding site in each of the four P loops, and mutations at those sites strongly affect channel selectivity (Yang et al., 1993). The cloned T-channels contain aspartates at two of those positions, in domains III and IV (Perez-Reyes et al., 1998; Cribbs et al., 1998; Lee et al., 1999a). Those differences are an obvious candidate for the changes in selectivity (Yang et al., 1999), but are unlikely to explain all differences in selectivity and block among calcium channels. For example, the 1E channel, which has four glutamates, exhibits larger currents with Ca²⁺ than with Ba²⁺ (Bourinet et al., 1996). Also, the 1H T-channel is ~20-fold more sensitive to block by Ni²⁺ than are the other cloned T-channels (Lee et al., 1999b).

Mg²⁺ block

Although Mg²⁺ block of calcium channels is well established, we were surprised by the potency of the block, which appears to be stronger than for L-type channels (Campbell et al., 1988; Hartzell and White, 1989; Wu and Lipsius, 1990; Dichtl and Vierling, 1991; Hall and Fry, 1992; Zhang et al., 1995; Song et al., 1996), although the use of different charge carriers at different concentrations again makes direct comparisons difficult. In cardiac cells, one study also found that Mg²⁺ inhibited T-channels more effectively than L-channels (Wu and Lipsius, 1990). For N-type channels of frog sympathetic neurons, with 2 mM Ba²⁺, the effect of 3 mM Mg²⁺ on the instantaneous I-V relationship could be described by a Woodhull model with  = 0.25 and K_D,0 = 9 mM (W. Zhou and S. W. Jones, unpublished observations), ~3-fold weaker block than found here for 1G.

It has been suggested that Mg²⁺ "block" actually results from screening of surface charge, rather than true pore block (Wilson et al., 1983). Although we do not have an estimate for the surface charge associated with T-channels, it is unlikely that a surface charge-mediated effect of 1 mM Mg²⁺ (in the presence of 2 mM Ba²⁺) could be as strong and as voltage-dependent as observed (Fig. 2 B). Furthermore, there is evidence (at least for HVA channels) that little surface charge is associated with permeation, in contrast to the well-known effects of surface charge on gating (Kuo and Hess, 1993; Zhou and Jones, 1995). The observation of discrete Mg²⁺ block of single L-channels also argues against a surface charge mechanism (Lansman et al., 1986; Kuo and Hess, 1993).

It is well known that blockade of calcium channels is a competitive process that depends on the nature and concentration of permeant ion (Hagiwara et al., 1974; Hess and Tsien, 1984; Lansman et al., 1986; Yang et al., 1993). In the calcium channel of barnacle muscle, Ba²⁺ normally carries larger currents than Ca²⁺, but currents are larger with Ca²⁺ following partial blockade by Co²⁺, early evidence that ion selectivity in calcium channels involves selective binding (Hagiwara et al., 1974). Similarly, currents carried by Ba²⁺ are more sensitive to block by Mg²⁺ in cardiac L-channels (Campbell et al., 1988). For 1G, one recent study noted that block by Cd²⁺ and Ni²⁺ is more potent with Ba²⁺ than with Ca²⁺ (Lacinová et al., 2000).

Although we have emphasized mechanistic implications, Mg²⁺ block of T-current may also play a physiological or pharmacological role. Even with Ca²⁺, 1 mM Mg²⁺ produced a modest inhibition of inward current, suggesting that Mg²⁺ block occurs even under physiological conditions. The block is stronger at more negative voltages, where significant Ca²⁺ entry can occur through T-channels during the "tail current" following an action potential (Huguenard, 1996). In cardiac cells, Mg²⁺ block of T-current has been suggested to play a role in the antiarrhythmic effect of elevated Mg_o²⁺ (Wu and Lipsius, 1990).

As a practical matter, our results demonstrate that the choice of [Mg²⁺]_o can critically affect the outcome of experiments on calcium channels in vitro. Furthermore, Mg²⁺ block can be a useful tool for dissection of calcium channel selectivity.