Ca²⁺ transport properties and determinants of anomalous mole fraction effects of single voltage-gated Ca²⁺ channels in hair cells from bullfrog saccule

Abstract

We studied the permeation properties of two distinct single voltage-gated Ca²⁺ channels in bullfrog saccular hair cells to assess the roles of the channels as physiological Ca²⁺ transporters and multi-ion pores. By varying the permeant ions (Ba²⁺, Ca²⁺) and concentrations (2–70 mm), we estimated the affinity constant (K_D) of the two channels as follows (mm): L-type channel, K_D,Ba = 7.4 ± 1.0, K_D,Ca = 7.1 ± 2.2 (n = 7); non-L-type channel, K_D,Ba = 5.3 ± 3.2, K_D,Ca = 2.0 ± 1.0 (n = 8). Using ionic concentrations close to physiological conditions (2 mm Ca²⁺ and 1.0 mm Mg²⁺), the conductance of the L-type channel was ∼2 pS. We determined the mechanisms by which ions traverse the pore of these single Ca²⁺ channels, using mixtures of Ba²⁺ and Ca²⁺ at total concentrations above (70 mm) or close to (5 mm) the K_D of the channels. We found evidence for an anomalous mole fraction effect (AMFE) only when the total divalent ion concentration was 5 mm, consistent with a multi-ion pore. We show that AMFE arises from the boundaries between the pore and bulk solution in the atria of the channel, which is derived from the presence of depletion zones that become apparent at low divalent cation concentrations. The present findings provide an explanation as to why previous whole-cell Ca²⁺ currents that were recorded in quasi-physiological Ca²⁺ concentrations (∼2–5 mm) showed clear AMFE, whereas single Ca²⁺ channel currents that were recorded routinely at high Ca²⁺ concentrations (20–110 mm) did not.

Hair cells, the sensory receptors of acoustic and vestibular organs in the inner ear, like presynaptic neurones, rely on the influx of Ca²⁺ through voltage-gated Ca²⁺ channels (VGCC) to mediate neurotransmitter release (Hudspeth, 1989; Fettiplace & Fuchs, 1999). However, unlike presynaptic neurones, which utilize similar proportions of multiple Ca²⁺ channel subtypes (Wu et al. 1999), hair cells in lower vertebrates employ mostly the dihydropyridine sensitive (L-type) Ca²⁺ channels to trigger phasic release of neurotransmitters (Roberts et al. 1990; Art et al. 1993; Zidanic & Fuchs, 1996). However, recent evidence suggests that Ca²⁺ channels in hair cells consist of both L- and non-L-type channels (Martini et al. 2000; Moser & Beutner, 2000; Rodriguez-Contreras & Yamoah, 2001). Furthermore, a substantial number of these Ca²⁺ channels in hair cells are clustered to amplify the Ca²⁺ signal (Roberts et al. 1990; Tucker & Fettiplace, 1995; Martinez-Dunst et al. 1997; Rispoli et al. 2001), ensuring rapid neurotransmitter release; others are expressed as solitary channels, which may limit cross-talk between different pathways that use Ca²⁺ as a second messenger (Hall et al. 1997; Rodriguez-Contreras & Yamoah, 2001).

Despite the important role of Ca²⁺ in the function of hair cells, the underlying mechanisms of ion permeation through the Ca²⁺ channels remain most uncertain. Numerous studies of Ca²⁺ currents using hair cells as well as other preparations have examined whole-cell current properties using elevated Ba²⁺ and Na⁺ concentrations (Hess et al. 1986; Hudspeth & Lewis, 1988; Art et al. 1993; Zidanic & Fuchs, 1996). Under these conditions, there was a significant increase in current amplitude as well as changes in voltage-dependent properties of the Ca²⁺ current (Coronado & Affolter, 1986; Art et al. 1993). Studies of whole-cell Ca²⁺ currents may also present ambiguities resulting from the diversity of Ca²⁺ currents contributed by different Ca²⁺ channel subtypes and contamination by other ionic currents (Rodriguez-Contreras & Yamoah, 2001). Single-channel current measurements, on the other hand, may provide a reasonable solution to these difficulties. Nonetheless, it introduces different uncertainties, which arise from the need to perform the recordings using elevated Ba²⁺ or Ca²⁺ concentrations (Imredy & Yue, 1994; Su et al. 1995). The gating and permeation properties of Ca²⁺ channels are dependent on the permeant ion concentrations; furthermore, there is an unavoidable charge screening effect that results from the use of high Ba²⁺ or Ca²⁺ concentrations (Hille, 1992). Therefore it is difficult to compare whole-cell data measured at low concentrations of Ca²⁺ or Ba²⁺ with ensemble-averaged currents of single-channel events recorded at high concentrations of permeant ions. For example, Ca²⁺ channels are considered to be multi-ion pores based on the evidence that in a mixture of Ca²⁺ and Ba²⁺, the current at certain Ca²⁺ : Ba²⁺ ratios is unusually smaller than that carried by Ca²⁺ or Ba²⁺ alone. This phenomenon, which is termed the anomalous mole fraction effect (AMFE), has been observed using whole-cell current recordings where physiological concentrations (1–5 mm) of divalent cations were used (Almers & McCleskey, 1984; Hess & Tsien, 1984; Campbell et al. 1988; Wakamori et al. 1998). However, single-channel currents recorded in high divalent cation concentrations (20- 110 mm) did not provide evidence for AMFE in Ca²⁺ channels (Yue & Marban, 1990), although Friel & Tsien (1989) observed small AMFE using 10 mm divalent cations. To determine the functional properties of the channels as Ca²⁺ transporters, the use of Ca²⁺ concentrations close to physiological conditions is essential. Recent studies of single Ca²⁺ channel currents using low-noise quartz glass pipettes have provided information on the elementary properties of the channels at low concentrations of Ca²⁺ (Gollasch et al. 1992; Church & Stanley, 1996; Rubart et al. 1996).

Here, we determined the permeation properties of two distinct Ca²⁺ channels in bullfrog saccular hair cells using quartz electrodes. Our findings include: (1) the conductance of the channels shows a steep response to changes in divalent ion concentrations which vary from ∼2.5 to 10 mm. As such, small alterations in Ca²⁺ concentration produced a profound change in the channel conductance at low permeant ion concentrations; (2) single L-type Ca²⁺ channel conductance is ∼2 pS using 2 mm Ca²⁺ and 1.0 mm Mg²⁺, the physiologically relevant solution for the channels; (3) single Ca²⁺ channels behave as multi-ion pores. The channels exhibit AMFE only at divalent ion concentrations close to the apparent dissociation constant (K_D) of the channel (5 mm). At external Ca²⁺ concentrations in the physiological range, the effective ion-ion and ion-channel interactions play a vital role in the functions of the channel. Thus an increase in the Ca²⁺ concentration above the apparent K_D of the channels may result in a substantial alteration of the permeation properties of the channels.

METHODS

Cell isolation

Hair cells were isolated from bullfrog (Rana catesbeiana) sacculi using a combination of enzymatic and mechanical procedures (Yamoah & Gillespie, 1996). Bullfrogs were chilled to 4 °C and killed using the double pithing method (the protocol was approved by the University of California, Davis, Animal Research Services). The inner ears were isolated and kept in oxygenated low Ca²⁺ solution (LCS) containing (mm): 120 NaCl, 2 KCl, 3 d-glucose and 5 Hepes, followed by incubation in EGTA-containing LCS for 15 min. Sacculi were isolated in LCS and transferred to LCS containing 2 mg ml⁻¹ subtilisin (type VIII protease, Sigma, USA) for 20 min. Sacculi were then transferred to LCS containing 100 mg ml⁻¹ bovine serum albumin (Sigma) and 2 mg ml⁻¹ DNAse I (Worthington Biochemical Co., Lakewood, NJ, USA) for 10 min, and then transferred to fresh LCS. After removal of the otolithic membrane with an eyelash, hair cells were isolated and placed onto coverslips, which were pretreated with concanavalin-A. Isolated cells were left undisturbed for ∼15 min at 4 °C before recording at room temperature.

Solutions

The bath solution consisted of (mm): 80 KCl, 3 d-glucose, 20 tetraethylammonium chloride (TEA-Cl), 5 4-aminopyridine (4-AP) and 5 Hepes, adjusted to pH 7.4 with TEA-OH. The membrane potentials of isolated hair cells were zeroed using a high concentration of K⁺ (80 mm). The membrane potential of cells in a high K⁺ solution was 0 ± 2 mV (n = 50). The pipette solution contained (mm): 20 TEA-Cl, 5 4-AP, 5 Hepes and 2–70 chloride salts of Ba²⁺/Ca²⁺; pH 7.4 with TEA-OH. Some experiments utilized pipette solutions containing (mm): 20 TEA-Cl, 5 4-AP, 5 Hepes, 2 CaCl₂ and 0.5–1 MgCl₂ at pH 7.4 with TEA-OH. N-methyl-d-glucamine (NMG) was used to maintain the osmolarity in pipette solutions with divalent ion concentrations lower than 70 mm. To investigate the L-type channels, 5 μm Bay K 8644 (Calbiochem, La Jolla, CA, USA) was added to the external solution after baseline recordings had been established using a 100 mm stock solution of Bay K 8644 dissolved in 100 % dimethyl sulphoxide (DMSO). In other cases, nimodipine (10 μm, Calbiochem) was included in the pipette or external solution to block L-type channels and to study the non-L-type channels. All other chemicals were purchased from Sigma.

Electrophysiology

Cells were plated into typical recording chambers (∼600 μl). The low-Ca²⁺ solution was replaced with the experimental bath solution 5–10 min before each recording. Patch-clamp recordings were made in the cell-attached patch configuration (Hamill et al. 1981). Patch pipettes were pulled from borosilicate glass with an outer diameter (o.d.) of 2 mm, and an inner diameter (i.d.) of 1 mm (5–15 MΩ) and from quartz glass tubing (o.d. 1.5 mm and i.d. 1 mm; 4–12 MΩ) using horizontal pullers (P97 and P2000, respectively; Sutter Instruments, Savato, CA, USA). The quartz glass provided low-noise current traces and allowed the resolution of single-channel currents using low permeant ion concentrations. Membrane patches were held at −70 mV and stepped to different depolarizing test pulses at frequencies between 0.2 and 0.5 Hz. Current traces were amplified and filtered (Axopatch 200B, Axon Instruments, CA, USA) using an 8-pole Bessel filter at 2 kHz and digitized at 10 kHz using custom-written software. Liquid junction potentials were measured and corrected as described (Neher, 1992; Table 1).

Table 1.

Experimental liquid junction potentials (V_j)

		Vj
[Divalent ions] (mm)	[NMG] (mm)	Ca2+	Ba2+
2	68	17.0 ± 4.2	—
5	65	16.7 ± 1.4	11.6 ± 1.2
10	60	7.3 ± 1.3	11.2 ± 0.4
20	50	9.2 ± 0.6	8.1 ± 1.9
50	20	6.0 ± 1.6	8.1 ± 1.9
70	0	1.4 ± 0.2	−0.7 ± 1.4

Liquid junction potentials of the experimental bath solutions wererecorded (mV) with respect to the pipette solutions. Data arepresented as means ±s.e.m.

Data analysis

Leakage and capacitative transient currents were subtracted by fitting a smooth template to null traces. Leak-subtracted current recordings were idealized using a half-height criterion (Colquhoun & Sigworth, 1985). Transitions between closed and open levels were determined using a threshold detection algorithm, which required that two data points exist above the half mean amplitude of the single-unit opening. The computer-detected openings were confirmed by visual inspection and sweeps with excessive noise were discarded. Amplitude histograms at a given test potential were generated, and then fitted to a single Gaussian distribution using a Levenberg-Marquardt algorithm to obtain the mean and standard deviation. At least five voltage steps and their corresponding single-channel currents were used to determine the unitary conductance. Single-channel current-voltage relationships were fitted by linear least-squares regression lines, and single-channel conductances obtained from the slope of the regression lines. Curve fits and data analysis were performed using Origin software (MicroCal Inc., Northampton, MA, USA). Where appropriate, pooled data are presented as means ± s.d.

The voltage dependence of Mg²⁺ blockade of the hair cell Ca²⁺ channels was determined assuming a binding model described by Woodhull (1973). The model assumes a single site for Mg²⁺ binding whose availability, but not intrinsic affinity, changes with voltage. Mg²⁺ is assumed to be an impermeant blocker that enters and exits the pore from the same side. A linear transformation of the voltage dependence of the ratio of the control current (unitary current using 2 mm Ca²⁺) and blocked unitary current amplitude in the presence of 1.0 mm Mg²⁺, is as follows:

where I_c and and I_b are the control and blocked (Mg²⁺) unitary current amplitudes, respectively, K_A is the association constant, δ is the fractional electrical distance from the outer face of the membrane, and Z, e, K and T have their usual meanings.

Simulation

Theoretical computations to predict the AMFE were done using the Poisson-Nernst-Planck 2 (PNP2) model of Nonner & Eisenberg (1998), with extensions as needed to describe Ba²⁺ and the ‘inert’ cations used in our solutions. The PNP2 model describes ion permeation in the Ca²⁺ channel as diffusion/drift in a force field that includes the electrical field produced by the charges of the ions and of the four carboxylate groups of the EEEE locus as well as excess chemical potentials that describe local ion-pore interactions. The free parameters of the model are the diffusion coefficient and excess potential of each ionic species, which are described as spatially constant within the narrow part of the pore (selectivity filter). For Na⁺, Ca²⁺ and Cl⁻ the parameters listed in Nonner & Eisenberg (1998: their Table 1) were used, except that the diffusion coefficient for Ca²⁺ was increased 2-fold (0.3 × 10⁻⁸ cm² s⁻¹). Ba²⁺ was assigned a diffusion coefficient D_Ba = 0.9 × 10⁻⁸ cm² s⁻¹, and the excess potential ${\mu }_{\text{Ba}}^0$(x) = −40 meV. These parameters were chosen to give approximately correct Ba²⁺ and Ca²⁺ conductances in pure solutions, and an appropriate competition between Ba²⁺ and Ca²⁺ (Ba²⁺ in this case is more mobile than Ca²⁺, but is bound less strongly by the pore). The organic cations present in some solutions were assigned a large repulsive excess potential (1 eV) by which they were excluded from the narrow part of the pore.

RESULTS

Identification of two classes of Ca²⁺ channels in saccular hair cells

Figure 1 illustrates the criteria used to identify the two distinct Ca²⁺ channels in bullfrog saccular hair cells. Cell-attached patches were held at −70 mV relative to the membrane potential, with the latter clamped at ∼0 mV using 80 mm K⁺ in the bath solution (see Methods). Using 70 mm Ba²⁺ as the charge carrier, two types of single-channel currents were recorded that differed in their kinetics of opening and in their sensitivity to dihydropyridines (DHP). Whereas the DHP-sensitive single-channel current or L-type current had a unitary current magnitude of ∼2.2 pA at a step potential of −30 mV and a conductance of ∼28 pS, the DHP-resistant current or non-L-type current, under similar conditions, had a unitary current magnitude of ∼0.9 pA and a conductance of ∼21 pS (Rodriguez-Contreras & Yamoah, 2001). To increase the open time and the probability of openings (P_o) of the L-type channel, Bay K 8644 (5 μm) was added in the external solution as shown in Fig. 1A. Consistent with previous reports, Bay K 8644 shifted the activity of the channels towards long openings, but altered neither the unitary current magnitude nor the single channel conductance (Hess et al. 1984; Rodriguez-Contreras & Yamoah, 2001). In other experiments, nimodipine (10 μm) was added to the pipette solution to study the non-L-type channel (Fig. 1B and C). To rule out the possibility that the non-L-type channel conductance was derived from modal gating of the L-type channels, we analysed patches that contained the two channel subtypes (Fig. 1D).

Figure 1. Effects of dihydropyridines on unitary Ca²⁺ channel currents.

Inward Ba²⁺ currents through single Ca²⁺ channels were recorded in membrane patches from isolated hair cells. A, the membrane patch containing a single L-type channel shows characteristic long-lasting openings when (±) Bay K 8644 (5 μm) was added to the bath solution. The membrane patch was held at −70 mV and stepped to −30 mV. The arrows denote the beginning and the end of the voltage steps. B, in contrast, the activity of non-L-type channels was not affected by 5 μm (±) Bay K 8644 in the external solution, and remained unaffected after application of 10 μm nimodipine to the bath solution. C, the open probability of the non-L-type channels was not affected significantly in the presence of DHP (P > 0.05, n = 15). D, the L-type channels showed infrequent transitions to a subconductance state as shown in a patch containing a single L-type channel (upper left). The trace shown below (lower left) is an enlargement of the segment of the upper trace indicated by the dotted lines. In patches containing the two channel types, the activity of each one was independent (upper right). For comparison, an amplification of 50 ms of recording is shown below the trace. E, representative current-voltage (I-V) plots for L-, and its subconductance, and non-L-type channels. Mean values for single-channel conductance are (in pS): non-L-type channel (•), 21.27 ± 0.99 (n = 8); L-type channel (○), 27.2 ± 0.56 (n = 9); L-type channel subconductance (▵), ∼10.0 ± 1.1 pS (n = 3). The inset shows an example of the amplitude histograms used to generate the I-V plot. The test potential is indicated.

The L-type channel exhibited a nimodipine-sensitive subconductance. We identified a substate with a unitary current amplitude of ∼0.7 pA at a step potential of −30 mV from a holding potential of −70 mV. The conductance of the substate of the L-type channel was ∼10 pS, which was distinct from that of the nimodipine-resistant non-L-type channel (Fig. 1E). Because the gating of the subconductance state of the L-type channel is remarkably different from the nimodipine-insensitive openings of the non-L-type channels, it is unlikely that the non-L-type conductance represents a switch of L-type channel into different modal gating. Rather, the non-L-type channels constitute a distinct channel subtype with diverse gating and permeation properties (see also Rodriguez-Contreras & Yamoah, 2001).

Single-channel currents in high and low Ca²⁺, and Ba²⁺ concentrations

Ca²⁺ channels may be described accurately as multi-ion pores that conduct several divalent cations, and monovalent cations in the absence of Ca²⁺ (Hess & Tsien, 1984; Tsien et al. 1987; Yue & Marban, 1990). Although the studies described above have provided the framework for determining the properties of the pore of the channels, the detailed mechanisms of ion permeation through Ca²⁺ channels remain unclear. One reason for this uncertainty is because in general, the Ca²⁺ channel properties have been studied under conditions at which the substrate ion concentrations are saturating (20–110 mm), and thus are outside the sensitivity range of the channels. By using low-noise quartz electrodes, Church & Stanley (1996) resolved the single-channel conductance in chick ciliary ganglion neurones and reported the apparent dissociation constant (K_D) of divalent cations to be ∼7 mm. We reasoned that the mechanisms of ion permeation through the Ca²⁺ channels in hair cells might be made apparent by comparing the properties of the channel using permeant ion concentrations above and below the apparent K_D of the channel. First, we examined single-channel currents through the L-type channels in hair cells using Ca²⁺ and Ba²⁺ as the charge carriers. Figure 2A and C show currents through single L-type channels at two different concentrations of 50 and 5 mm, respectively, using a holding potential of −70 mV and ∼250 ms depolarizing voltage steps as indicated. The unitary current amplitude of the channel was high when 50 mm Ca²⁺ was the charge carrier (∼1 pA at a step potential of −30 mV) compared with 5 mm Ca²⁺ (∼0.5 pA at a step potential of −30 mV). The conductance (in pS) of the two divalent cations (50 mm) of the L-type channels follows the sequence Ba²⁺ (24 ± 3, n = 5) > Ca²⁺ (12 ± 1, n = 3), as shown in the plots of the current-voltage (I-V) relationship (Fig. 2B). These results are consistent with previous reports on single-channel recordings from L-type channels in ventricular myocytes (Hess et al. 1986; Lansman et al. 1986). In Fig. 2D, we show the I-V relationship of the L-type channel using 5 mm Ba²⁺, or Ca²⁺. In this case, the conductances of the channel were 11 ± 2 in Ba²⁺ (n = 3) and 6 ± 1 in Ca²⁺ (n = 5).

Figure 2. Single-channel permeation of L-type channels using divalent cations.

Hair cell membrane patches were held at −70 mV and stepped to the potentials indicated. Note that the potentials have been corrected for liquid junction potential errors. A, characteristic inward single-channel current traces using 50 mm Ca²⁺, and Ba²⁺ and 5 mm (C) as charge carriers are illustrated for the L-type channel. The continuous lines indicate the closed levels. B and D represent the corresponding current-voltage plots. The insets show examples of the amplitude histograms from current traces at the step potentials indicated, which were used to generate the I-V plot for Ba²⁺ currents. The L-type channel activity was recorded in the presence of 5 μm Bay K 8644 in order to promote long openings. Single-channel conductance values for L-type channels in 50 mm are (in pS): Ca²⁺ (•) = 12.0; Ba²⁺ (○) = 22.0; and in 5 mm: Ca²⁺ (•) = 7.1; Ba²⁺ (○) = 12.

Figure 3 shows features of ion permeation of the non-L-type channel. The experimental conditions were similar to those described for Fig. 2, but the patch pipettes contained 10 μm nimodipine to block L-type channels (Bean, 1984). The non-L-type channels differ from the L-type channels in two respects: (1) the conductance of the non-L-type channels is smaller than that of the L-type channels, with Ba²⁺ and Ca²⁺ (50 mm) exhibiting distinct conductances (Fig. 3A and C); (2) for low concentrations (5 mm), the conductances in Ca²⁺ and Ba²⁺ are similar (Fig. 3B and D). This is in sharp contrast to the L-type channels where the conductance of Ca²⁺ ions remained low compared with Ba²⁺ ions. These features further reinforce our conclusion that the two channels are distinct.

Figure 3. Single-channel permeation of non-L-type channels by divalent cations.

The format is the same as Fig. 2 except that the data were obtained in the presence of 10 μm nimodipine, which blocks the L-type channel completely. A, representative non-L-type single-channel traces recorded from patches that were held at −70 mV and stepped to the corrected voltages indicated. The two permeant cations (50 mm), Ca²⁺ and Ba²⁺, were used in the pipette solution. C, single-channel traces of the non-L type channel using 5 mm of Ca²⁺ and Ba²⁺. B and D represent the current-voltage relationship for the non-L-type channel in 50 and 5 mm, respectively. Amplitude histograms from Ca²⁺ current traces are shown beside the I-V plots. Single-channel conductance values for non-L-type channels in 50 mm are (in pS): Ca²⁺ (•) = 15; Ba²⁺ (○) = 22 (C); and in 5 mm: Ca²⁺ (•) = 11; Ba²⁺ (○) = 12 (D). Data were corrected for liquid junction potentials.

The conductance of the L-type channels saturated at ion concentrations above ∼20 mm for Ba²⁺ and Ca²⁺ and has an apparent K_D (∼2–8 mm) slightly above the physiological Ca²⁺ concentrations (Fig. 4A; Table 2). Data were fitted with a Langmuir isotherm and the estimated K_D values and maximum conductances are indicated in Table 2. Although the apparent K_D values of L-type channel for the two divalent cations are remarkably similar, the observed maximal conductance are strikingly different. The results are comparable to single-channel conductance reported for L-type channels from chick ciliary ganglion neurones (Church & Stanley, 1996). Similar data were obtained for the conductance profile curves for the non-L-type channel (Fig. 4B), with the maximum conductance of Ba²⁺ for this channel being lower (∼23 pS) than that of the L-type channel (∼30 pS). In contrast, Ca²⁺ conductance through the non-L-type channel (∼15 pS) was close to that of the L-type channel (∼14 pS: see Table 2). An important feature of the plots in Fig. 4 is that under physiological conditions, the Ca²⁺ concentration (1–2 mm) is not at the saturating portion of the curve, but rather, is at the most sensitive phase of the conductance versus concentration curve.

Figure 4. Saturation and the apparent affinity of L- and non-L-type single-channel conductance.

The conductances of the L- and non-L-type channels were determined using different concentrations of Ca²⁺ and Ba²⁺ (2.5–70 mm). The affinity of Ca²⁺ (•) and Ba²⁺ (○) for L- (A) and non-L-type (B) Ca²⁺ channels in saccular hair cells was estimated from these plots. The continuous lines represent fits with a Langmuir isotherm of the form γ = γ_max/(1 + K_D/[I]), where γ and γ_max represent the single-channel conductance and maximum conductance, respectively, and [I] is the divalent ion concentration. The estimated K_D and γ_max values for the two channel types and the two permeant ions are shown in Table 2.

Table 2.

Estimated γ_max and K_D values from Figure 4

	KD (mm)		γmax (pS)
	Ca2+	Ba2+	Ca2+	Ba2+
L-type	6.6 ± 1.9	8.0 ± 1.2	13.5 ± 1.0	29.9 ± 1.2
Non-L-type	2.3 ± 0.8	5.7 ± 2.9	14.9 ± 1.0	23.0 ± 2.8

Values are means ±s.e.m. (n > 3 for each data point).

Effects of Mg²⁺ on single-channel conductance of the L-type channels

Physiological saline contains Mg²⁺ ions and previous studies, e.g. Lansman et al. (1986), evaluated Mg²⁺ blockade of Ca²⁺ channels, although little is known about the conductance of the channels in the presence of Mg²⁺. Figure 5A shows single-channel traces recorded with 2 mm Ca²⁺ in pipette solution containing Bay K 8644 (5 μm). The single-channel conductance as derived from the linear regression was ∼4 pS (○, Fig. 5E). As shown in Fig. 5B, the open probability (P_o) of the channel decreased upon addition of 1.0 mm Mg²⁺ in a 2 mm Ca²⁺ pipette solution (P_o at −30 mV, ∼ 0.2 ± 0.1 versus 0.03 ± 0.01, n = 3, in 2 mm Ca²⁺ and in 2 mm Ca²⁺ plus 1.0 mm Mg²⁺, respectively). The unitary current amplitude was reduced and the slope conductance (•) was ∼2 pS (Fig. 5E), which represent a twofold reduction in the conductance compared with Ca²⁺ alone. The voltage dependence of Mg²⁺ blockade of the pore was determined using a single binding site model, which assumes that the availability of Mg²⁺ but not the intrinsic affinity changes with voltage (Woodhull, 1973). The estimated membrane electrical field sensed by Mg²⁺ from the linear plot in Fig. 5F was ∼0.1 from the outside. Representative amplitude histograms used to generate the I-V plots are shown in Fig. 5C and D.

Figure 5. Magnesium block of single-channel currents using 2 mm Ca²⁺ as the charge carrier.

A, traces represent single-channel currents through L-type channels using 2 mm Ca²⁺ as the charge carrier. NMG was added to the pipette solution as non-permeant cation and Bay K 8644 was added to the bath solution to increase long openings of the L-type channel. The membrane patch was stepped to the corrected potentials indicated from a holding potential of −70 mV. C and O denote the closed and open levels, respectively. B, traces were recorded in a similar fashion as in A, except that the pipette contained 0.5 mm Mg²⁺ in addition to 2 mm Ca²⁺. As shown in the current-voltage relationship in E, the conductance of the L-type channel decreased 2-fold in the presence of 1.0 mm Mg²⁺. C and D show examples of amplitude histograms used to generate the I-V plots in E. F, estimation of the binding site for Mg²⁺. The voltage dependence of Mg²⁺ blockage of the pore was determined using a binding model as described previously (Woodhull, 1973). The model assumes a single site for Mg²⁺ binding whose availability but not intrinsic affinity changes with voltage (see Methods for equation). The membrane electric field (δ) sensed by Mg²⁺ from the linear plot was ∼0.1.

Effects of Ba²⁺ and Ca²⁺ interaction on the permeation of Ca²⁺ channels in hair cells

To further examine the mechanisms by which ions traverse the pore of single Ca²⁺ channels in hair cells, we used mixtures of Ba²⁺ and Ca²⁺ with total concentrations (Ba²⁺ + Ca²⁺) above (70 mm) and close to (5 mm) the apparent dissociation constant (K_D) of the channels (see Fig. 4). Figure 6A shows a family of L-type single-channel traces recorded from a holding potential of −70 mV to the step potentials indicated using (mm): 70 Ca²⁺, 50 Ca²⁺/20 Ba²⁺, and 70 Ba²⁺. The unitary current amplitude as well as the conductance of the L-type channel increased monotonically as the Ba²⁺ concentration in the pipette was raised and Ca²⁺ concentration reduced (Fig. 6A and C). The results are at variance with data obtained using total Ba²⁺/Ca²⁺ mixtures of 5 mm (Fig. 6D, E and F). The elementary current traces and I-V relationship in various Ba²⁺ mole fractions shown in Fig. 6D, E and F at low concentrations (5 mm) of permeant divalent cations, demonstrate that unitary current of the channel exhibits a clear anomalous mole fraction effect (AMFE) at Ba²⁺ mole fractions between ∼0.1 to 0.8. We repeated the experiments described in Fig. 6 but included 10 μm nimodipine to block L-type channels in the patch. Similar to the L-type channels, the non-L-type channels failed to show AMFE using permeant divalent ion concentrations above the apparent K_D of the channel (70 mm: Fig. 7A, B and C). Moreover, when the permeant divalent cation concentration was reduced close to the apparent K_D of the channel (5 mm), the non-L-type channel displayed an obvious AMFE at a Ba²⁺ mole fraction between ∼0.1 and 0.6 (Fig. 7D, E and F). The AMFE was observed at all test voltages in which we could adequately resolve the unitary current amplitudes. The existence of an unequivocal AMFE in the conductance of hair cell Ca²⁺ channels using 5 mm Ba²⁺/Ca²⁺ mixtures but not 70 mm is shown in Fig. 8. Since minor uncorrected variations in the resting potential of the cell may have produced the appearance of AMFE in hair cells, even in high-K⁺ solutions, we used corrected voltages to assess the data. However, the uncorrected data also showed AMFE.

Figure 6. Anomalous mole fraction effects in L-type channels are favoured at low charge carrier concentrations.

Records of single-channel currents were obtained in mixtures of Ca²⁺ and Ba²⁺ in which the concentration of divalent ions was kept constant at 70 mm. A, exemplary traces of single L-type channel currents in (mm) 70/0, 50/20 and 0/70 Ca²⁺/Ba²⁺, respectively. Cell-attached patches were held at −70 mV and stepped to the corrected potential indicated. B and E show examples of amplitude histograms used to generate the plots in C and F, respectively. C, no anomalous mole fraction effect was observed in 70 mm Ca²⁺/Ba²⁺ (n = 5). L-type current increased monotonically as a function of the Ba²⁺ mole fraction. The absence of anomalous mole fraction effects was seen at all tested voltages (-40 to 20 mV). Data are shown for test potentials of −30, −10 and 0 mV. D, when the single L-type channel current records were obtained using 5 mm Ca²⁺/Ba²⁺ mixtures, the L-type currents showed minima at various mole fractions (F). The stimulus protocol was similar to that in A, and the junction potential was corrected as described in Methods. The traces shown in D were elicited from a holding potential of −70 mV and stepped to the corrected potential noted (-40 mV).

Figure 7. AMFE is revealed in the non-L-type channels at low charge carrier concentrations.

The experiment was performed in the presence of 10 μm nimodipine. A, non-L-type single channel current traces using 70/0, 50/20 and 0/70 Ca²⁺/Ba²⁺, respectively. The current traces were generated at −30 mV from a holding potential of −70 mV. B and E show examples of amplitude histograms used to generate the plots in C and F, respectively. C, plots of the unitary current at −50, −40 and −30 mV against the Ba²⁺ mole fraction, did not show AMFE (n = 5). D, non-L-type single-channel currents traces using (mm) 5/0, 4/1 and 0/5 Ca²⁺/Ba²⁺, respectively. F, an AMFE was observed using 5 mm Ca²⁺/Ba²⁺ mixtures at Ba²⁺ mole fractions between 0.1 and 0.6.

Figure 8. Conductance of L- and non-L-type channels exhibits AMFE at low concentrations of charge carriers.

We used the conductance of the single channels to determine the presence or absence of AMFE for the L- and non-L-type channels. The use of conductance eliminates the likelihood that the AMFE seen in Figs 6 and 7 at 5 mm charge carrier resulted from voltage errors due to surface charge effects and/or liquid junction potentials. A, the L-type channels did not show evidence of AMFE using 70 mm Ca²⁺/Ba²⁺ mixtures. B, by contrast, using 5 mm Ca²⁺ + Ba²⁺, the conductance of the channel showed minima at Ba²⁺ mole fractions (Ba²⁺/(Ba²⁺ + Ca²⁺)) from 0.1 to 0.7. The data represent the mean values from 4 patches. Similar results were obtained in 70 mm (C) and 5 mm (D) Ca²⁺/Ba²⁺ mixtures, respectively, when single-channel conductance was assessed in the presence of 10 μm nimodipine to block the L-type channels and to study the non-L-type channels. A clear AMFE was evident when the charge carrier concentration was 5 mm but not in 70 mm. For the non-L-type channels, AMFE was observed at Ba²⁺ mole fraction from 0.1 to ∼0.5 (n > 4).

DISCUSSION

This study is the first systematic description of the permeation/selectivity properties of Ca²⁺ channels in vertebrate hair cells, and it provides the elementary hallmarks of hair cell Ca²⁺ channels as physiological Ca²⁺ transporters. Firstly, the data confirm that hair cells in bullfrog saccule express at least two distinct Ca²⁺ channel subtypes, with diverse properties ranging from permeation to pharmacology. Secondly, the slope conductance of the two-channel types increases with increasing external Ca²⁺/Ba²⁺ concentrations and showed a clear saturation, consistent with the existence of a ‘binding’ site for the permeant ions in the channel pore. Thirdly, with the use of low-noise quartz electrodes we have determined that the conductance of Ca²⁺ channels using permeant ion concentrations close to physiological conditions (∼2 mm Ca²⁺ and 1.0 mm Mg²⁺) is ∼2 pS. Finally, we have shown that the absolute concentration of Ba²⁺ and Ca²⁺ determines the strength of the Ba²⁺/Ca²⁺ AMFE: the effect is clearly expressed at 5 mm, but not at 70 mm, total concentration of divalent salt in the mixtures. The observation of a concentration-dependent Ba²⁺/Ca²⁺ AMFE might explain why previous studies, done at different concentrations, yielded different results.

Diversity of VGCC in hair cells

Paucity of single Ca²⁺ channel data has precluded the detailed classification of Ca²⁺ channels in hair cells. However, recent reports as well as this study have shown the existence of at least two distinct channel types (Su et al. 1995; Rodriguez-Contreras & Yamoah, 2001). Apart from pharmacological differences, the nimodipine-insensitive channel has unitary conductance that makes it unlikely to be derived from either the subconductance or the distinct modal gating of the L-type channels. Moreover, recordings of whole-cell Ca²⁺ currents from hair cells of frog semicircular canals have revealed the presence of three Ca²⁺ channel subtypes (Martini et al. 2000). The notion that hair cells may express diverse Ca²⁺ channels to execute different Ca²⁺-dependent processes may not be restricted to lower vertebrates alone but may be true in the mammalian cochlear and vestibular hair cells as well (Green et al. 1996). In a recent study, a residual current, which was insensitive to Bay K 8644, was demonstrated using a transgenic mouse model with null deletion of the α_1D Ca²⁺ channels (Platzer et al. 2000). Finally, the intricate frequency selectivity of hair cells in lower vertebrates may be conferred by the expression of different Ca²⁺ channel subtypes, several splice variants of α_1D subunit (Kollmar et al. 1997a, b), as well as multiple Ca²⁺-dependent K⁺ channel proteins (Ramanathan et al. 1999).

Permeation and selectivity of L- and non-L-type Ca²⁺ channels in hair cells

The concentration dependence of the unitary conductance of the two Ca²⁺ channel subtypes saturated at divalent concentrations over ∼20 mm, and the K_D values derived from the Langmuir isotherm (see Fig. 4), was consistent with a binding site for the permeant ions in the channel pore. Although we monitored and compensated for junction potentials throughout the experiments, we examined the concentration dependence of the unitary conductance instead of using the unitary current, thereby eliminating any charge screening effect that may complicate estimation of the K_D (Yue & Marban, 1990; Kuo & Hess, 1993; Zhou & Jones, 1995; Church & Stanley, 1996). The K_D values obtained for the L- and non-L-type channels are slightly lower than those reported for L-type channels in the chick cillary ganglia (Church & Stanley, 1996), but are slightly higher than that reported for Ca²⁺ channels in other systems where the unitary current and whole-cell currents were evaluated (Table 3: Ashcroft & Stanfield, 1982; Bossu et al. 1985; Akaike et al. 1989a, b; Aibara et al. 1992; Zhou & Jones, 1995). The tendency for voltage error in the latter methods may be responsible for the apparent variance in the K_D values. Alternatively, the differences may reflect genuine biophysical properties of distinct Ca²⁺ channel subtypes. Nonetheless, these K_D values ranging from 1 to 10 mm may reflect binding at the low-affinity site of the channel, as opposed to the high-affinity binding site that is revealed using Ca²⁺ block of monovalent current through native channels or site-directed mutagenesis of amino acid residues in the expressed channel pore (K_D ∼1 μm: Coronado & Affolter, 1986; Hess et al. 1986; Yang et al. 1993; Ellinor et al. 1994).

Table 3.

Comparison of apparent K_D values of native voltage-gated calcium channels

Reference	Tissue	Channel	KD (mm)	Charge carrier
Smith et al.(1993)	Pancreatic β-cell	L	5.5	Ba2+
Hagiwara et al. (1988)	Sino-atrial node	L	3.9	Ca2+
Hess et al.(1986)	Cardiac myocytes	L	14, 28	Ca2+, Ba2+
Akaike et al. (1989a)	Hypothalamic neurones	L	10	Ca2+
Church & Stanley (1996)	Ciliary ganglion	L	5	Ca2+, Ba2+
Aibara et al. (1992)	Paratracheal ganglion	L	15	Ca2+
Hagiwara et al. (1988)	Sino-atrial node	T	0.9	Ca2+
Carbone & Lux (1987a,b)	DRG neurones	Low-threshold	3.3	Ca2+
Akaike et al. (1989b)	Smooth muscle	Low-threshold	15	Ca2+
Zhou & Jones (1995)	DRG neurones	N	∼20	Ba2+

Using saturating concentrations of the permeant ions (50–70 mm) in the L-type and non-L-type channels, substitution of Ba²⁺ for Ca²⁺ resulted in a reduction of unitary current amplitude and channel conductances (γ_Ba > γ_Ca). With the exception of the T-type Ca²⁺ channels in which Ba²⁺ and Ca²⁺ are equally permeable, the sequence of the unitary current reported is similar to that of L-, N- and R-type Ca²⁺ channels (Fox et al. 1987; Williams et al. 1994; Bourinet et al. 1996; Wakamori et al. 1998). However, the sequence in unitary current amplitudes and conductances were altered in 5 mm for both channels (L-type: γ_Ba > γ_Ca; non-L-type: γ_Ba = γ_Ca). The voltage dependence of divalent cation block has been determined previously using Cd²⁺, Mg²⁺ and Ca²⁺ block of monovalent ion currents through Ca²⁺ channels. Consistently the estimated site (s) to which divalent ions bind are located ∼10–15 % of the electric field into the pore (Chow, 1991; Rosenberg & Chen, 1991; Kuo & Hess, 1993). These results are in accordance with the estimated site for Mg²⁺ binding in the electrical field of the channel (∼10 %) reported in this study.

Using non-stationary fluctuation analysis to determine the number of Ca2+ channels in macropatches, Roberts et al. (1990) estimated the dihydropyridine-sensitive unitary Ca2+ channel conductance to be ∼2 pS using external 2.5 mm Ca2+. Although the conductance of the channel as determined using direct single-channel measurements is 2-fold higher than that reported previously, the values are comparable given that the method used by Roberts et al. (1990) has an inherent underestimation of the single-channel amplitude associated with it. The KD obtained for the Ca2+ channels in hair cells (Fig. 4 and Table 2), and the steep relationship between the conductance versus concentration curves at the critical ambient Ca2+ concentration (1–5 mm; ∼1.0 and 2.0 pS mm-1 for the L- and non-L-type channels, respectively), are consistent with the notion that the Ca2+ channel pores are highly selective, yet allow ion transfer at a very high throughput rate (Church & Stanley, 1996).

Pore occupancy

The decrease in whole-cell and single-channel Ca²⁺ currents and conductance amplitude in mixtures of Ca²⁺ and Ba²⁺, AMFE, is a hallmark of the channel as a multi-ion pore. Previous studies of single-channel Ca²⁺ currents, however, have provided contradictory results that has led to the uncertainty as to whether AMFE is required for multi-ion pores. Thus Wakamori et al. (1998) detected a clear AMFE in 5 mm mixtures, whereas other studies done at concentrations of 20–110 mm did not (Yue & Marban, 1990). Friel & Tsien (1989) observed no AMFE in 110 mm solutions, but detected a small AMFE when divalent concentration was 10 mm. On the other hand, in the marine preparation, Aplysia neuron, Chesnoy-Marchais (1985) observed an AMFE in 60 mm divalent salt. Our results demonstrating the absence of AMFE with permeation ion concentration above the apparent K_D are in accordance with the previous reports using similar conditions. The present report also agrees with whole-cell Ca²⁺ experiments where the AMFE was detected using divalent ion concentrations close to the K_D of the channel (Almers & McCleskey, 1984; Hess & Tsien, 1984; Campbell et al. 1988; Wakamori et al. 1998). The absence of AMFE may stem from the concentration of divalent cations used rather than the channel itself.

Structure-function analysis of heterologously expressed Ca²⁺ channels has provided evidence for the four glutamic acid residues (EEEE) in the pore-lining region between S5 and S6 of each repeat as the high affinity binding sites for divalent cations in Ca_V2.1 and Ca_V1.2 channels (Tang et al. 1993; Yang et al. 1993; Ellinor et al. 1994; Ertel et al. 2000). Ca²⁺ blockade of monovalent cation currents through Ca²⁺ channel experiments have revealed that the high-affinity binding site of the channel for Ca²⁺ has an apparent K_D of ∼1 μm (Almers et al. 1984; Coronado & Affolter, 1986; Hess et al. 1986). In addition, the surrounding residues close to the EEEE locus confer net negative charges and are also conserved in the pore region of Ca_V2.2 channels (Mikami et al. 1989; Wakamori et al. 1998). These negative charges may serve as a low-affinity binding site for Ca²⁺.

The apparent K_D values that describe the conductances in pure Ba²⁺ or Ca²⁺ solutions are similar to the salt concentrations in which a significant Ba²⁺/Ca²⁺ AMFE was observed. Both the saturation characteristics and the AMFE of divalent ion conductance have been interpreted to indicate a varying occupancy of a pore with multiple ionic binding sites (Almers & McCleskey, 1984; Campbell et al. 1988; Dang & McClesky, 1998; Friel & Tsien, 1989; Yue & Marban, 1990). The selectivity filter, with the four carboxylate groups of the EEEE locus, appears to form a single accumulation site with micromolar affinity for Ca²⁺ (Yang et al. 1993; Ellinor et al. 1994; Cibulsky & Sather, 2000). Since the saturation and AMFE phenomena described here arise at millimolar concentrations, they suggest that the ionic flux in Ca²⁺ channels is determined also by the presence of ions in locations outside the high-affinity EEEE locus. Such locations are expected to occur in the electrical boundary layers that arise on either side of the highly charged EEEE locus. In order to test whether a boundary layer could account for our observations, we simulated ionic flux in a drift-diffusion model of the EEEE locus (Nonner & Eisenberg, 1998). The drift-diffusion equations predict AMFE when ions in the mixture have distinct local affinities to the pore, e.g. one species binds more strongly in a particular location than the competing species (Nonner et al. 2000). Following Nonner & Eisenberg (1998), we assumed that Ca²⁺ is attracted to the EEEE locus by a negative excess chemical potential (this potential can be accounted for in terms of electrostatic and excluded-volume interactions (Nonner et al. 2000)), and that Ba²⁺ is bound less strongly (see Methods). We also assumed that Ba²⁺ has a ∼3-fold larger diffusion coefficient in the EEEE locus than Ca²⁺, in agreement with the different saturating conductances for these ions. Note that the external parameters of this model describe properties of the EEEE locus itself. No external parameters are needed to describe the boundary layers around the locus. Instead, functional effects of these boundary layers are computed as joint solutions of the PNP equation (Nonner & Eisenberg, 1998). Figure 9A plots the conductance versus concentration relationship predicted for pure Ba²⁺ or Ca²⁺ solutions. The relationships resemble first-order isotherms with apparent dissociation constants less than 10 mm, consistent with our observations. Figure 9 plots unitary current/mole fraction relationships (Fig. 9B and C) and current versus voltage relationships (Fig. 9D and E) that are predicted from the model. The predicted AMFE is smaller than that observed (e.g. Fig. 6 and Fig. 7) at 5 mm. Conforming with our experiments, the AMFE is predicted to be smaller at 70 mm than at 5 mm. Moreover, the predicted AMFE at 5 mm depends on membrane voltage in the way previously described by Friel & Tsien (1989) at 10 mm: the effect turns into a ‘normal’ mole fraction effect at sufficiently negative potentials. Thus the model gives a qualitatively correct description of these mole fraction experiments. However, the predictions of the model are preliminary and we may revisit the subject in the future.

Figure 9. Simulation of the permeation properties of Ca²⁺ channels.

A, conductance of Ba²⁺ and Ca²⁺ in pure solutions simulated using the PNP2 model. B and C, plots of the absolute current using a mixture of Ca²⁺ and Ba²⁺ to illustrate the concentration- and voltage-dependence of AMFE as predicted by the PNP2 model. The corresponding current-voltage relationships in 70 and 5 mm divalent cations are shown in D and E, respectively.

Saturation of conductance occurs as the electrical boundary layer of the EEEE locus becomes better neutralized and thus more likely to be populated with divalent cations as bath divalent concentration is raised. The AMFE arises because Ba²⁺ added to the bath displaces some Ca²⁺ from the boundary layer, but not from the interior of the EEEE locus. Consequently, for either ion there is a location in the pore where the ion is accumulated with relatively low probability from a mixed bath (because of the presence of the other ion), and thus either ion carries less current than it could carry between pure solutions (Nonner et al. 1998). With increasing salt concentration in the bath, depletion of Ca²⁺ from the boundary layer becomes less, and so becomes the reduction of Ca²⁺ current in the presence of Ba²⁺. It is clear that a quantitative model of such effects needs to consider the specific location dependence of excess chemical potentials around the EEEE locus. Differences observed between L- and non-L-type channels (Fig. 6 and Fig. 7) could reflect such details. Nevertheless, it seems clear that even a simplified description, using constant excess potential change in a stepwise fashion, gives a qualitative account for our experimental results.