Role of outer ring carboxylates of the rat skeletal muscle sodium channel pore in proton block

Abstract

Voltage-gated Na⁺ current is reduced by acid solution. Protons reduce peak Na⁺ conductance by lowering single channel conductance and shift the voltage range of gating by neutralizing surface charges. Structure-function studies identify six carboxyls and a lysine in the channel's outer vestibule. We examined the roles of the superficial ring of carboxyls in acid block of Na_v1.4 (the rat skeletal muscle Na⁺ channel isoform) by measuring the effects of their neutralization or their substitution by lysine on sensitivity to acid solutions, using the two-micropipette voltage clamp in Xenopus oocytes. Alteration of the outer ring of carboxylates had little effect on the voltage for half-activation of Na⁺ current, as if they are distant from the channels' voltage sensors. The mutations did not abolish proton block; rather, they all shifted the pK_a (-log of the dissociation constant) in the acid direction. Effects of neutralization on pK_a were not identical for different mutations, with E758Q > D1241A > D1532N > E403Q. E758K showed double the effect of E758Q, and the other lysine mutations all produced larger effects than the neutralizing mutations. Calculation of the electrostatic potential produced by these carboxylates using a pore model showed that the pK_a values of carboxylates of Glu-403, Glu-758, and Asp-1532 are shifted to values similar to the experimentally measured pK_a. Calculations also predict the experimentally observed changes in pK_a that result from mutational neutralization or introduction of a positive charge. We propose that proton block results from partial protonation of these outer ring carboxylates and that all of the carboxylates contribute to a composite Na⁺ site.

Acidosis reduces voltage-gated Na⁺ channel current and conduction velocity, affecting the current in at least two ways: (1) peak current is reduced, and (2) voltage dependence of gating is shifted in the depolarizing direction (Hille, 2001). The gating shift undoubtedly results from titration of negative surface charges of sialic acids and of carboxylates on the protein surface (Green et al. 1987; Cukierman et al. 1988; Zhang et al. 1999), altering the electric field for the channels' voltage sensors. The reduction in peak current includes reduction in the channel's unitary conductance by titration of one or more sites that are located within the channel's pore and partially into the membrane field (Woodhull, 1973; Sigworth, 1980; Daumas & Anderson, 1993), but the titrated site or sites have not been identified and the mechanism of unitary conductance reduction is uncertain.

Structure-function studies of the Na⁺ channel α-subunit have identified four segments called P loops, one in each of the four domains, that comprise the outer vestibule of the pore (Lipkind & Fozzard, 2000). This vestibule is a funnel-like structure that is lined, in part, by four-residue strands from each of the four P loops. The inner narrow ring of the funnel is formed by Asp-400, Glu-755, Lys-1237, and Ala-1529 (Na_v1.4 numbering), also called the DEKA ring, which are considered to be major components of the channel's selectivity mechanism (Terlau et al. 1991; Favre et al. 1996; Schlief et al. 1996; Sun et al. 1997). Three or four residues external to the DEKA ring at the wider outer mouth of the vestibule are four carboxyl residues (Glu-403, Glu-758, Asp-1241, and Asp-1532), one from each P loop, which also play an important role in permeation. Their replacement by neutral residues reduces unitary conductance substantially (Terlau et al. 1991; Chiamvimonvat et al. 1996b), by mechanisms not yet understood. These outer ring carboxylates, and possibly others nearby (Li et al. 2000), are all good candidates for proton titration sites. The relative locations of these four outer ring carboxylate residues are fairly well established because they all contribute to the binding sites for guanidinium toxins (Noda et al. 1989; Terlau et al. 1991; Lipkind & Fozzard, 1994; Penzotti et al. 1998) and/or μ-conotoxin (Dudley et al. 1995; Chang et al. 1998; Chahine et al. 1998). They are superficial and their side-chains appear to face the water-filled vestibule (Chiamvimonvat et al. 1996a,b; Yamagishi et al. 1997). From the dimensions of the toxins that interact with them, we know that they are all within 10–12 Å of each other on the surface of the outer pore, where they could also interact with permeating Na⁺ ions.

The carboxylates in the DEKA selectivity filter are also logical sites for current reduction in acid solution, since intimate interaction with these residues is thought to be important in permeation (Hille, 2001), and a similar selectivity region of L-type Ca²⁺ channels has been identified as the site of proton block in that channel (Chen et al. 1996). However, the pK_a for acid block of Na⁺ channels is about 6, far higher than the pK_a expected for these carboxylates, which are close to the positive electric field of the neighbouring lysine (see Results; ‘Calculation of electrostatic effects'). In other words, the Na⁺ channel is more sensitive to block by acid solution than is accounted for by only the carboxylates of the selectivity filter. Indeed, replacement of both carboxylates and the lysine in the selectivity filter with alanines (DEKA replaced by AAAA) fails to abolish the pH sensitivity of peak conductance (Sun et al. 1997), although the pK_a is shifted about 0.4 pH units in the acid direction and a residual pH-independent current is seen. It is therefore possible that proton block involves one or more of the carboxylates in the outer ring of the vestibule, either directly or through the negative electrical field that they generate. We have examined the effect of substitution of these residues with neutral, polar residues or by positively charged ones. In every case the current remained sensitive to acid solutions, although the pK_a was shifted. Reduction in pH also shifted the voltage dependency of gating, as expected for titration of charges that influence the voltage sensors. However, neutralization or charge reversal by mutation of the vestibule carboxylates had little effect on the pH-induced gating shift, as if the charged residues within the vestibule are at a distance from the activation S4 sensors.

We propose that the vestibule outer ring carboxylates produce a local negative electrostatic field, concentrating protons in the vestibule and shifting the effective pK_a of all of the vestibule carboxylates in the alkaline direction. We suggest that the proton titration curve is produced largely by partial protonation of all of the outer ring carboxylates in acid solution, which secondarily reduces unitary conductance. Consequently, the vestibule outer ring carboxylates may be functioning as a composite interacting site for Na⁺ and its permeation, in combination with the carboxylates of the selectivity filter. Some of these data have been reported in abstract form (Romantseva et al. 2001; Khan et al. 2002).

Methods

Studies were made using the rat skeletal muscle sodium channel isoform, Na_v1.4 (a gift from Dr Randall Moorman). This isoform was chosen for study because of the large amount of published data on this channel and its mutants. The details of mutation have been described in detail (Sunami et al. 2000, 2001). In summary, the cDNA flanked by the Xenopus globin 5′ and 3′ untranslated regions was subcloned into the Bluescript SK vector (Promega) for the expression of the wild-type and D1532K channels. These channels were transcribed with T7 RNA polymerase using the T7 Message Machine Kit (Ambion). E403Q, E403K, E758Q, E758K, E403Q/E758Q (double mutant) D1241A, and D1532N were subcloned in pAlter (Promega) and transcribed with SP6 Message Machine Kit (Ambion), all according to the manufacturer's protocols. Oligonucleotide-directed mutations were introduced by using the Quikchange Site-Directed Mutagenesis Kit (Stratagene), according to the manufacturer's protocols, or in a four-primer strategy. Mutagenic oligonucleotide primers included changes in silent restriction sites, as well as the desired mutations. The presence of the intended mutations and absence of unintended ones was verified by DNA sequencing of the entire polymerized regions. All PCR reagents were obtained from Perkin-Elmer (Norwalk, CT, USA) and all restriction enzymes were obtained from New England Biolabs (Beverly, MA, USA). The μ1 vector was linearized by Not I for the wild-type channel. Sal I was used to linearize E403Q, E403K, E758Q, E758K, E403Q/E758Q, D1241A, and D1532N channels. D1532K was linearized with Spe I.

Xenopus oocytes were prepared as previously described (Penzotti et al. 1998). In brief, oocytes were collected under anaesthetic (0.15 % tricaine methanesulfonate and 25 mm NaHCO₃ buffered to pH of 7.6). The frogs were humanely killed after the final collection. Experimental procedures were appoved by the institution's ethics committee. Stage V and VI oocytes were washed and the follicular layer was removed by hand. They were injected with ≈50-100 ng of cRNA and examined for current after 1–3 days incubation at 16 °C. Bath solution contained 90 mm NaCl, 1 mm CaCl₂, 1 mm MgCl₂, and 2.5 mm KCl. Hepes at 5 mm was used as buffer, with Mes substituted for solutions with pH below 6.5. pH was adjusted by addition of NaOH. Cells were exposed to control solutions at 20–22 °C with pH of 7.08 and then to test solutions at different pH for at least 4 min before study. Between exposures to solutions with different pH the oocytes were returned to pH 7.08 for control measurements to ensure that the currents were stable. After each experiment the pH of the solutions was checked. The bath flow rate was typically 500 μl min⁻¹, and exchange occurred with time constants of 15–18 s (Penzotti et al. 1998). As a check for adequacy of exchange, voltage steps were made at 5 s intervals to ensure that the full pH effect had occurred before the full data protocol was begun.

Recordings were made in a two-microelectrode voltage clamp configuration, using a Dagan CA-1 voltage clamp (Minneapolis, MN, USA), and data were collected with pCLAMP 6.3 software (Axon Instruments, Foster City, CA, USA) at 71.4 kHz after low-pass filtration at 2 kHz (8 pole Bessel, −3 dB). Electrodes were filled with 3 m KCl and had resistances of 0.3-0.6 MΩ. The holding potential was −110 mV, and depolarizing steps were made in 10 mV steps of 100 ms duration at intervals of 20 s Only oocytes with less than 0.5 μA leak currents and with initial maximal Na⁺ currents from 2–7 μA were studied. Any oocyte showing poor voltage control, indicated by a conductance-voltage maximal slope steeper than −4, was discarded. In order to determine the activation parameters, the current-voltage (I-V) relationship was fitted to a transform of the Boltzmann distribution:

where I is the peak Na⁺ current during the test pulse of voltage, V, and V_rev is the reversal potential The parameters estimated by the fitting were V_1/2 (the voltage for half-activation), k (slope factor), and G_max (the maximum slope conductance). For each experiment maximal conductance was plotted as the ratio of maximal conductances at control and alkaline pH values, and these relative data were combined and the standard error of the mean (± s.e.m.) calculated, with n = 3 or greater for all values used. The resulting data were fitted with single site binding curves, either extrapolated to zero current or allowed to include a pH-insensitive fraction.

For single channel measurements Na_v1.4 and its mutant E758Q were expressed in HEK293 cells. Single channel recordings were made with an Axopatch 200B amplifier (Axon Instruments, Union City, CA, USA). Borosilicate glass pipettes with resistances of 3–6 MΩ were coated with HIPEC R6101 (Dow Corning, Midland MI, USA) Pipette solutions contained 280 mm NaCl and 10 mm Hepes, adjusted to pH 7.4 or 6.0 with NaOH. The bath solution contained 150 mm KCl, 10 mm Hepes, and 2 mm CaCl₂, with pH adjusted with KOH. Channel openings were lengthened with addition of 10 or 20 μM fenvalerate (Benitah et al. 1997). Unitary currents were elicited by stepping from −120 mV to various potentials at 15 ms intervals, while sampling at 10 kHz with a low-pass filter of 5 kHz. A nonlinear least squares method was used to fit amplitude histograms.

Electrostatic potential surfaces were calculated for the sodium channel vestibule model of Lipkind & Fozzard (2000) using the DelPhi module of Insight II (MSI, Inc., San Diego, CA, USA), as previously described (Hui et al. 2002). The DelPhi module calculates the electrostatic potentials in and around molecules using a finite difference solution to the nonlinear Poisson-Boltzmann equation (Gilson & Honig, 1987; Sharp & Honig, 1990). The dielectric constants were set to 10 for the protein interior (for discussion, see Antosiewicz et al. 1994) and 80 for the solvent water region. This solvent water region includes the entire vestibule and pore outside the van der Waals surface of the structural model. The carboxylate groups of Glu and Asp, the amino acid lysine, and the guanidinium group of Arg were assumed to be unit charges. The difference potentials (Δψ) for mutants (E403Q, E758Q, etc.) were calculated with respect to the potential in the vestibule of the wild-type channel. Difference potentials are given in units of kT/e, where k is Boltzmann's constant, T is temperature in kelvins, and e represents the elementary positive charge. The shift in the values of pK_a of glutamates and aspartates for each mutation inside the vestibule was calculated according to the formula:

where ψ is the average of the potentials (expressed in kT/e units) at the two carboxyl oxygens.

Results

pH effects on peak conductance of Na_v1.4

Peak currents were reduced and activation was shifted in the depolarizing direction by reduction of pH. Increased pH usually produced modest changes in the opposite direction (Fig. 1A). Plot of the peak I-V relationship and voltage dependence of activation (Fig. 1B and C) illustrates the shift of activation. Peak conductance (G_max) at each pH was normalized to the maximal value obtained at physiological pH. Figure 1D shows the reduction of conductance with increased proton concentration for a series of experiments on the wild-type Na_v1.4 channel. The relation is well fitted with a single site-binding curve, yielding a half-maximal conductance (pK_a) of 5.91 ± 0.08, if the curve is constrained to reach zero current. If a pH-independent fraction is permitted, then the best-fit single site curve yields a pK_a of 6.1 ± 0.05 and a pH-independent fraction of 0.17. There was no statistical difference between the two fits. This possible small pH-independent fraction was not always apparent in mutated channels (see later), and it could not be studied in detail in these experiments because solutions with pH < 5.0 resulted in leaky oocytes and unreliable measurements.

Figure 1. Effect of acid solutions on the Na_v1.4 channel currents.

A, uncorrected currents from steps to various voltages from a Xenopus oocyte expressing Na_v1.4 wild-type channels at pH 7.08, 5.76 and 8.3. B, current-voltage plot of peak whole-cell currents from the experiments shown in A. C, conductance transforms of the data in A and B for pH 7.08 and pH 5.76. Continuous lines represent the Boltzmann fits to the data. D, dose-response curve of average values for the wild-type channel from all pH values tested. Beside each point is the number of experimental values obtained at that pH. Error bars indicate the s.e.m. Fitted to the data is a single site binding curve with zero asymptote, resulting in a pK_a of 5.91 ± 0.08.

Effects of mutations on the pH sensitivity of maximal conductance

Each of the outer ring carboxylates was replaced individually with a neutral, hydrophilic residue or with the positively charged lysine. Each mutant was systematically exposed to solutions of different pH and the maximal conductance was determined in the same fashion as illustrated for the wild-type channel that is shown in Fig. 1. The fit of the normalized maximal conductances to single-site binding curves yielded pK_a values with variable pH-independent fractions (Table 1 and Fig. 2). Again, the mid-points determined with and without a pH-independent fraction were not significantly different. Note that the standard errors for pK_a were generally smaller for curves fitted with the assumption of a zero asymptote at low pH than for curves with unrestricted minima, and for some mutants the fitted minima were negative. In order to compare all these values, the pH producing half-block (assumption of zero asymptote) has been used here for comparison with wild-type channels and with other mutants.

Table 1.

Biophysical measurements and pK_a values

	Activation V1/2* (mV)	Erev at control pH* (mV)	pKa	ΔpKa	pKa†	ΔpKa†	pH-independent fraction
Wild-type Nav1.4	−17.9 ± 1.3 (16)	39.8 ± 3.5 (16)	5.91 ± 0.08	—	6.13 ± 0.05	—	0.17
E403Q	−13.5 ± 1.7 (20)	45.3 ± 1.3 (20)	5.82 ± 0.05	0.09	5.89 ± 0.08	0.24	0.04
E403K	−13.0 ± 0.7 (10)	34.3 ± 1.9 (10)	5.05 ± 0.07	0.86	5.37 ± 0.06	0.76	0.32
E758Q	−17.4 ± 1.0 (15)	40.6 ± 1.3 (15)	5.50 ± 0.05	0.41	5.47 ± 0.10	0.66	0.02
E758K	−19.6 ± 0.7 (38)	46.2 ± 0.7 (38)	4.99 ± 0.03	0.92	5.19 ± 0.17	0.94	0.24
E403Q/E758Q	−20.0 ± 1.0 (21)	44.7 ± 0.9 (21)	5.33 ± 0.07	0.58	5.65 ± 0.22	0.48	0.29
D1241A	−20.3 ± 1.3 (15)	34.7 ± 1.0 (15)	5.62 ± 0.03	0.29	5.51 ± 0.10	0.62	−-0.13
D1532N	−15.2 ± 1.2 (13)	40.0 ± 1.3 (13)	5.72 ± 0.05	0.19	5.38 ± 0.09	0.75	−-0.54
D1532K	−18.8 ± 1.4 (8)	36.4 ± 1.4 (8)	5.26 ± 0.03	0.65	4.89 ± 0.28	1.24	−-0.80

^*n value in parentheses

^†pK_a determined with unrestricted minima.

Figure 2. Titration curves for mutant channels compared to the wild-type channel.

A, domain I mutants. E403Q pK_a = 5.82 ± 0.05; E403Q/E758Q pK_a = 5.33 ± 0.07; E403K pK_a = 5.05 ± 0.07. B, domain II mutants. E758Q pK_a = 5.50 ± 0.05; E758K pK_a = 4.99 ± 0.03. C, domain III mutant. D1241A pK_a = 5.62 ± 0.03. D, domain IV mutants D1532N pK_a = 5.72 ± 0.05; D1532K pK_a = 5.26 ± 0.03. The derived fit to the wild-type channel illustrated in Fig. 1 is shown in each panel as a dashed line(WT). Average values (with s.e.m.) are fitted to a single site binding curve with zero asymptote. The numbers of experimental values included in the average response at one pH differ. Beginning at the most alkaline pH they are for E403Q: 7, 20, 13, 10, 3, and 3; for E403K: 4, 3, 10, 4, 5, and 4; for E403Q/E758Q: 8, 21, 5, 7, 7, and 4; for E758Q: 4, 6, 5, 3, and 3; for E758K: 16, 38, 12, 11, 7, and 4; for D1241A: 3, 15, 4, 3, 5, and 3; for D1532N: 6, 13, 6, and 3; and for D1532K: 3, 8, 8, 14, 3, 3, and 3.

The residue Glu-758 was changed to glutamine or to lysine (Fig. 2B). Neutralization of Glu-758 shifted the pH of half-block to 5.50 ± 0.05 (ΔpH = 0.41) and addition of a positive charge shifted the half-block pH further to 4.99 ± 0.03 (ΔpH = 0.92). Similar changes in charge were made for Glu-403 (Fig. 2A), with half-block pH upon neutralization of 5.82 ± 0.05, but with a shift to 5.09 ± 0.07 (ΔpH = 0.86) upon addition of a positively charge residue. Asp-1532 neutralization with Asn shifted half-block pH to 5.72 ± 0.05 (ΔpH = 0.19), and addition of a positive charge shifted the half-block pH to 5.26 ± 0.03 (ΔpH = 0.65) (Fig. 2D). The effect of E403Q on pK_a was smaller than expected, compared with the effects of mutation of the other carboxylates. Therefore, the double mutant E403Q/E758Q was tested (Fig. 2A), resulting in a shift of half-block pH to 5.33 ± 0.07 (ΔpH = 0.58), greater than for the single mutation E758Q. In domain III the outer ring residue Asp-1241 does not interact with the guanidinium toxins (Terlau et al. 1991), so it may be outside the immediate vestibule, but it is close enough to interact with μ-conotoxin (Li et al. 1997; Dudley et al. 2000). The mutation D1241A did shift the half-block pH to 5.62 ± 0.03 (ΔpH = 0.29) (Fig. 2C). As noted for the wild-type channel, fits of the titration curves that allowed a pH-independent fraction yielded different pK_a values, but the general relationship was not altered and no clear relationship between the mutations and the pH-independent fraction was seen.

There are several general observations that can be made from these mutational studies. (1) Neutralization of outer ring carboxylates resulted in a shift of the pK_a, with ΔpH for Glu-758 > Asp-1241 > Asp-1532 > Glu-403. Introduction of a positive charge caused an even greater shift, as if part of the effect of change in charge was electrostatic. (2) No mutation abolished pH sensitivity of conductance.

Effects of mutations on channel gating

Acid pH dramatically shifted the V_1/2 of activation of the wild-type Na_v1.4 channel in the depolarizing direction by as much as 30 mV, to values of +10 to +20 mV, with no sign of saturation. The majority of negative surface charges shielded by high extracellular Ca²⁺ are on the protein itself (Green et al. 1987; Cukierman et al. 1988). If the vestibule outer ring carboxylates are close enough to the channel's voltage sensors, then they could themselves bias the membrane field electrostatically at the critical sensor residues and contribute to establishment of the voltage range of wild-type channel gating. Neutralization of these negative charges by mutation would then be expected to shift gating in the depolarizing direction, similar to the effects of divalent ion shielding of negative surface charge. These gating changes might complicate the interpretation of whole-cell currents in the mutated channels. At physiological pH the activation V_1/2 values of the neutralization mutants used in these studies were probably not different from that of the wild-type channel, although there was some variation (Table 1 and Fig. 3). This impression was strengthened by the results with lysine mutations, which also showed little change. In addition, with each mutation the shift of activation produced by acid solutions was not different from the shift in the wild-type channel (Fig. 3). A similar result was seen by Sun et al. (1997) for neutralization of selectivity filter carboxylates. It seems that the charged vestibule residues have little or no effect on the electric field near activation voltage sensors. Furthermore, the similar shift of V_1/2 of activation with the mutations implies that the dramatic changes in pK_a seen with the mutations were not the result of gating shifts.

Figure 3. V_1/2 of activation as a function of pH.

The V_1/2 of activation for each pH and for each mutant is plotted, with its s.e.m. n = 3 or more for each point. The line connects the points for the wild-type Na_v1.4 channel. No obvious difference was seen between the shift of the wild-type (wt) channel and those of the outer ring carboxylate mutants.

Reversal potential changes

Reversal potential for wild-type current was 39.8 ± 3.5 mV, and the mutations altered the reversal potential minimally, even when carboxylates were replaced by lysine (Table 1). This suggests that no changes in selectivity between physiological ions occurred with these mutations, in agreement with our previous studies (Penzotti et al. 1998; Chang et al. 1998).

Single channel measurements

In order to confirm that the change in pH sensitivity derived from whole-cell currents in these experiments reflected changes in single channel conductance, rather than gating changes, we determined the shift in pH sensitivity for E758Q with single channel measurements. Wild-type Na_v1.4 under these conditions showed a conductance of 33 ± 1.8 pS at pH 7.4 (n = 3), and this was reduced to 28 ± 0.5 pS at pH 6.0. E758Q showed a reduced conductance of 24.1 ± 0.6 pS at pH 7.4 (n = 5), and at pH 6.0 it was not detectably changed at 25.2 ± 1.6 pS, as expected if the mutation had shifted the half-block pH by > 0.3 pH units.

Calculation of electrostatic effects of these mutations and their predicted effects on pK_a values

The intrinsic pK_a values for aspartate and glutamate are 4.0 and 4.5, respectively (Creighton, 1993), far from the pK_a of proton block. However, the carboxylate pK_a values would be altered by a local negative field, which is inevitable for a channel vestibule composed of many carboxylates. We can calculate the field and the expected pK_a values using the Lipkind & Fozzard (2000) model. This model of the Na⁺ channel outer vestibule is based on the crystal structure of the KcsA channel (Doyle et al. 1998) and on a high affinity binding site in the pore for the guanidinium toxins (Lipkind & Fozzard, 1994; Penzotti et al. 1998). The key components of the pore lining are the outwardly directed C-end strands of the P loop α-helix-turn-strand motif in each of the four domains, which are arranged to preserve the relationships required for channel interactions with tetrodotoxin and saxitoxin that have been found experimentally. The outer vestibule is completed by docking the P loops of domains I-IV into the extracellular part of the inverted teepee structure, formed by the S5 and S6 α-helices, that are located spatially by homology modelling based on the backbone coordinates of the KcsA potassium channel (Doyle et al. 1998). The outer border of the vestibule model is ringed by four symmetrically placed residues: Glu-403, Glu-758, Met-1240 (and its adjacent Asp-1241), and Asp-1532. The bottom of the funnel-shaped vestibule is formed by the selectivity filter ring of Asp-400, Glu-755, Lys-1237, and Ala-1529, located on the inner aspect of the P loop turns and also arranged symmetrically. The calculated electrostatic potentials inside the vestibule of the wild-type channel are shown in Fig. 4.

Figure 4. Electrostatic isopotential surfaces inside a model of the Na⁺ channel outer vestibule (top view).

Electrostatic calculations were carried out using the DelPhi module of Insight II and the Lipkind & Fozzard (2000) model of the Na⁺ channel outer vestibule. Contours of isopotential surfaces are shown at the level of −2 and −6 kT and at the level of +6 kT, with yellow and black for negative potentials, respectively, and with blue for positive potentials. The backbones for the channel P loops of domains I-IV are shown by green ribbons. The S5 and S6 α-helices from each domain were included in the calculation, but for clarity they are omitted from the figure. The residues of the selectivity filter (DEKA motif) and the residues of the external charged ring are shown by ball and stick images. This image looks directly into the outer mouth of the pore. Note the arginines (R395 and R750) located on the P loop helices of domains I and II, and the selectivity filter lysine (K1237), which make the vestibule electrostatic field asymmetrical.

The model can be used to calculate the electrostatic potential at any amino acid residue in the vestibule, produced by the other charges. For the calculations of electrostatic potentials at the individual carboxylates, their own charges were set to zero. In the DelPhi method (see Methods) all other charged residues are assumed to have unit charges and no cation is resident in the vestibule. The carboxylates are initially assumed to have the intrinsic pK_a values of the respective isolated amino acid derivatives in pure water solutions (${\text{p}K}_{\text{a}}^{\text{int,water}}$, 4.0 for aspartate and 4.5 for glutamate (Creighton, 1993)). The negative electrostatic field generated by the carboxylates concentrates protons and thereby shifts the apparent pK_a values of these residues according to the equation:

However, calculations on the basis of this approximation do not always give a satisfactory agreement with experimental data (Spassov et al. 1989; Bashford & Karplus, 1990). In fact, the charged side chains are more or less buried in the low dielectric constant protein molecule. Our own estimate of the effective dielectric constant, D_eff, in proximity to the selectivity filter of the Na⁺ channel was 31 (Dudley et al. 1995), a reasonable value intermediate between the aqueous and lipid phases. Typical calculations of the intrinsic pK_a in nonpolar protein surroundings (${\text{p}K}_{\text{a}}^{\text{int,protein}}$), taking into account the accessibility of the side chains to the bulk solvent, have led to average values of 4.5 for aspartic acid and 5.1 for glutamic acid (Spassov et al. 1989; Bashford & Karplus, 1990). Therefore, we have used the approximation:

The calculated values for the electrostatic potentials and the new pK_a values for Asp-400, Glu-755, Glu-403, Glu-758, Asp-1241, and Asp-1532 are given in Table 2. The calculated apparent pK_a for the three outer ring amino acids Glu-403, Glu-758, and Asp-1532 are 5.7-5.9, very close to the experimentally observed pK_a of 5.9 for proton block of the wild-type Na_v1.4 channel. For example, our calculated pK_a value for Asp-1532 inside the vestibule is 5.9, substantially higher than the typical value of 4.5, due to the presence of the very high negative electrostatic potential (-3.2kT/e) that is created at the carboxylate of Asp-1532 by the neighbouring carboxylates Glu-403, Glu-758, Asp-1241, Asp-400, and Glu-755 (Fig. 5 and Fig. 6). The negative electrostatic potentials at Glu-403 and Glu-758 are substantially less than at Asp-1532 because of underlying Arg residues in P loop α-helices of domains I (Arg-395) and II (Arg-750). Involvement of these P loop helix Arg residues in the permeation process is supported by the observation of Terlau et al. (1991) that neutralization of the equivalent domain I Arg in Na_v1.2 reduced single channel conductance.

Table 2.

Calculated electrostatic potentials and pK_a values of aspartate and glutamate residues

Residue	ψ(kT/e)	pKa
Glu-403	−1.8	5.9
Glu-758	−1.5	5.8
Asp-1532	−3.2	5.8
Asp-1241	−1.2	5.0
Asp-400	−1.2	5.0
Glu-755	+0.2	5.0

Figure 5. Electrostatic potential at the carboxylate of Asp-1532 resulting from other charged residues around the channel vestibule (top view).

Electrostatic potential inside the Na⁺ channel vestibule calculated with zero charge on the carboxylate group of the side chain of Asp-1532. Its charge was set to zero in order to determine the electrostatic potential at the oxygens of Asp-1532 produced by the other vestibule charged residues. The red contour is −3 kT, the yellow contour is −2 kT, and the blue contour is +3 kT. Note that the two oxygens of Asp-1532 (small red balls) are located close to the −3 kT contour. In this case, the electrostatic potential is less than the one shown in Fig. 4, and the −3 kT contour has a shape and distribution similar to that of the −6 kT contour in Fig. 4. Similar calculations were made for the other carboxylates (see Table 2).

Figure 6. Electrostatic potentials around the side chain of Asp-1532 (side view).

The contours are as described in the legend of Figure 5. Note the positive potential around Lys-1237, as well as the location of Asp-1532 relative to the −3 kT electrostatic potential contour.

The fields generated by adjacent residues in the wild-type channel and the resulting shift of pK_a values in the alkaline direction allow these carboxylates to be somewhat protonated at physiological pH. Certainly, they can be substantially protonated when the pH of the external solution is reduced experimentally. In contrast, the selectivity filter carboxylates Asp-400 and Glu-755 have significantly lower calculated pK_a values (≈5.0), because of their proximity to the positively charged amine on the side chain of Lys-1237. In our model (Lipkind & Fozzard, 2000) Lys-1237 forms a hydrogen bond with the carboxylate of Glu-755 and interacts with Asp-400 through a molecule of water. Therefore, at relatively high pH (pH > pK_a for acid block) both Asp-400 and Glu-755 are hardly protonated at all, although both carboxylates could be somewhat protonated at very low pH (pH < pK_a). Finally, Asp-1241 is the most external among the residues considered, explaining its low calculated pK_a of ≈5.0. Therefore, these calculations suggest that the best candidates for protonation in the vestibule are Glu-403, Glu-758, and Asp-1532, all participating simultaneously.

Mutation of any one of these vestibule carboxylates would result in a change in the pK_a of the remaining residues. The calculation of difference potentials avoids the more problematic estimate of absolute potentials and focuses the modelling on the experimentally defined differences in pK_a among the mutants. For substitution of Glu-758 of domain II by Gln, the loss of a charge caused the electrostatic potential to be less negative in the vicinity of the carboxylates of the remaining Glu and Asp residues, relative to the potentials in the vestibule of the wild-type channel. The electrostatic difference potential surface +1kT for the mutant E758Q is shown in Fig. 7. Such change could shift the pK_a values for Glu-403 and Asp-1532 by 0.4-0.45, resulting in pK_a values for these carboxylates of 5.4-5.5. This can be compared to our experimentally measured result for the mutant E758Q channel of 5.5 (Table 1). According to these model calculations, the substitution of Glu-403 by Gln should result in the same shift of pK_a as that for neutralization of Glu-758, because in the model Glu-758 and Glu-403 have symmetrical locations relative to the pore axis. However, the experimentally measured change was smaller, as if Glu-403 carboxylate is farther outside the vestibule or has a different protein environment.

Figure 7. Electrostatic difference potential surface for the E758Q mutant.

The +1 kT difference between the electrostatic fields calculated for the wild-type channel and for the mutant E758Q (ψ_E758Q – ψ_wild-type) is shown in blue. The channel structure is as shown in Fig. 4, except that it is tilted to the side to show the relation between the difference field and the selectivity filter. With neutralization of Glu-758 the potential is altered at the other carboxylate residues located within this surface sufficient to shift their pK_a values by −0.40 to −0.45 pH units.

When Glu-403 or Glu-758 were replaced in the model by the positively charged residue Lys, the calculated changes in pK_a for both mutations were close to the experimentally measured values. Charge reversal obviously produced a larger change in the electrostatic potential of the unsubstituted residues to levels of +2.5kT. For both mutations E403K and E758K the calculated shifts in the values of pK_a were ≈0.9, compared to the experimentally measured pK_a shifts of 0.8-0.9 (Table 1), and to the observed pK_a with these mutations of ≈5. In these calculations we used the average values of ΔpK_a for three rotamers of the side chain of Lys around the bond C^α-C^β (-60 deg, 60 deg, 180 deg). The similar sensitivity to charge reversal at both positions 403 and 758 implies that their side chains do face the pore. Glu-403 and Glu-758 are reported by Terlau et al. (1991) and Chiamvimonvat et al. (1996a,b) to be very important for Na⁺ permeation (Table 3), with Asp-1241 and Asp-1532 having a somewhat smaller effect on single channel conductances, in agreement with the experimental data.

Table 3.

Published values of fractional single channel conductance with mutations of the outer ring carboxylates

Reference	Glu-403	Glu-758	Asp-1241	Asp-1532
Terlau et al. (1991)	0.2 (Gln)	0.6 (Gln)	—	0.5 (Asn)
Chiamvimonvat et al. (1996a,b)	0.5 (Cys)	0.4 (Cys)	0.75 (Cys)	0.75 (Cys)
Pusch et al. (1991)	0.2 (Gln)	—	—	—

Mutation of Glu-403, Glu-758, and/or Asp-1532 could also alter the electrostatic potential at the carboxylates Asp-400 and Glu-755 in the selectivity filter, and therefore change their pK_a values. However, the calculated ΔpK_a for these residues was always less than the pK_a changes seen experimentally for the mutations. For example, the experimental ΔpK_a shifts for the mutations E758Q and E758K were 0.39 and 0.90, but the model-based calculated changes in pK_a of Asp-400 and Glu-755 were only 0.25 (for E758Q) and 0.45 (for E758K). It is likely that the selectivity filter carboxylates remain largely unprotonated under the conditions of these experiments.

Discussion

pH dependence of peak sodium conductance

In these experiments the depression of peak Na_v1.4 sodium conductance by acid solution was fitted with a single site-binding curve, yielding a pK_a of 5.91, similar to the values reported by others for the Na_v1.4 channel. Benitah et al. (1997) found that Na_v1.4 α-subunits coexpressed in Xenopus oocytes with β1-subunit and with no outside Ca²⁺ had a single site, zero asymptote pK_a of 6.1 for peak whole-cell conductance and 5.9 for single channel conductance. Sun et al. (1997) expressed Na_v1.4 α-subunit in HEK294 cells with [Ca²⁺] of 1 mm and found a pK_a of 5.86 for peak whole-cell conductance. Their recordings were extended into the range of pH 4.0, revealing a small pH-independent fraction of about 0.1. Our pK_a value for acid block is similar to those of Sun et al. (1997) and Benitah et al. (1997), in spite of the small differences in external [Ca²⁺] and in the background cell for heterologous expression. In native frog skeletal muscle cells, Spalding (1980) measured the reduction of sodium conductance with solution change from pH 7.4 to pH 5.0 with outside [Ca²⁺] of 2 mm, and using a single site-blocking curve fitted to those two points he estimated a pK_a of 5.32. The reason for this lower pK_a in native skeletal muscle is not clear, but the measurement was made with only one acid solution and in frog muscle, which may have a different isoform.

The pK_a values obtained for Na⁺ channels in other tissues, all using the zero asymptote model, are somewhat different. Conductances of single sodium channels from cardiac myocytes showed a more acid pK_a of 5.1 (Zhang & Siegelbaum, 1991). Measurements of pH titration of frog node of Ranvier peak sodium conductance and single channel conductance yielded values of 5.2-5.6 (Hille, 1968; Woodhull, 1973; Sigworth, 1980). Rat brain sodium channels reconstituted with batrachotoxin in lipid bilayers and bathed in 1 m Na⁺ showed a pK_a of 4.6 (Daumas & Andersen, 1993), quite different from the other values but perhaps because of the high Na⁺ and high ionic strength solution used. The reasons for differences in pK_a between tissues and species are not immediately obvious. The charged vestibule residues examined here appear to be conserved in all mammalian Na⁺ channel α-subunits, although there are some differences in adjacent residues. Therefore, it seems likely that the phenomena described here are applicable to other mammalian Na⁺ channel isoforms. The sequence for the frog isoform has not yet been determined.

We have already noted that there may be a pH-independent fraction of conductance. Neither our study nor the other reported studies, except for Sun et al. (1997), are extended sufficiently far in the acid region or are sufficiently detailed to reveal this fraction. In these experiments we report the less specific value of half-block pH, but it differs little from the single site pK_a with a pH-independent fraction. It should also be noted that fit of the titration curve by a single site model does not mean that only one site exists. Several sites with similar pK_a values would yield the same curve. The interesting question of a pH-independent fraction of Na⁺ current and its relationship to the vestibule residues deserves further study.

Failure of carboxylate mutations to affect gating

Several mutations in the putative outer vestibule of the sodium channel have been shown to affect gating. W402C speeds activation and enhances slow inactivation (Tomaselli et al. 1995). Mutations of the selectivity filter residues Lys-1237 and Ala-1529 increase a very slow inactivation state (Todt et al. 1999; Hilber et al. 2001). The conservative substitutions of the outer ring charged residues Glu-403, Glu-758, Asp-1241, and Asp-1532 that we used in these experiments had no effects on the kinetics of the ionic currents, in agreement with our previous studies (Chang et al. 1998) and the reports of others (Terlau et al. 1991; Chiamvimonvat et al. 1996b). Change in net charge would be expected to alter the electric field at the voltage sensors. However, the outer vestibule residues must be sufficiently far from the S4 segments responsible for voltage dependence of activation that their field is dispersed by the surrounding ionic solution, and their electrostatic effects on the voltage dependence of gating are small. This agrees with the analysis of French et al. (1996). They found that when μ-conotoxin R13Q was bound in the outer vestibule it did produce a depolarizing shift of 6–7 mV in the voltage dependence of activation, but this mutant μ-conotoxin contains 4–5 net positive charges. They estimated from the μ-conotoxin effect that the vestibule was more than 25 Å distant from the voltage sensors. Extrapolation from their results to our experiments would suggest that the maximal change from replacement of a negative charge by a positive charge in the outer vestibule that we would expect to occur at voltage sensors 25 Å distant is a 2–4 mV shift in the depolarizing direction, too small to affect our measurements of proton titration. If there was any effect of these charge-changing mutations, it was a small hyperpolarizing shift in activation at physiological pH, opposite to the expected change for outside charges (Zhang et al. 1999; Hille, 2001). It was not possible to determine a pK_a for the shift of activation because the changes had not reached a plateau at pH = 5, the most acid pH tested. Zhang & Siegelbaum (1991) measured the acid-induced shift of both activation and inactivation, and fitted the inactivation shift to a single site curve with a pK_a of 5.1, but because their changes had also not reached a plateau, the true pK_a for surface charges could be even more acid. The failure to see any direct effect of the mutations on gating also suggests that these side chains extend into the vestibule, rather than facing into the protein.

Magnitude of the vestibule electric field

Electrostatic effects on the pK_a of enzyme active sites can be quite large, exceeding 1 pH unit (Russell et al. 1987; Sternberg et al. 1987). In the Na⁺ channel vestibule we have similar geometrical conditions to those in enzymes. Calculations of charges in a funnel-like vestibule have suggested that the generated field can be substantial (Dani, 1986; Jordan et al. 1989; Cai & Jordan, 1990). The best-studied is the acetylcholine receptor channel, which has within the pore a ring of four glutamate residues (Imoto et al. 1988). Wilson et al. (2000) have estimated the potential at this region generated by the four glutamates, based on rates of reaction with cysteine mutants of similar methanesulfonate derivatives differing only in their charge. They found values of about −250 mV, and these agreed approximately with their calculations using a cylindrical pore model with a pore diameter of 8 Å and a pore dielectric constant of 80.

Certainly the Na⁺ channel vestibule has a small volume, containing perhaps 30–40 water molecules, so water is unlikely to have dipole properties as in free solution. Our previous estimate of the apparent dielectric constant in the vestibule was 31 (Dudley et al. 1995). Cations in the vestibule would also be rare, since one cation in a vestibule volume of 30 water molecules represents a ≈2 m solution. Experimentally we found that a change of one unit charge at the outer ring resulted in a typical change in pK_a of ≈0.25-0.40. If we use the conservative figure of 0.25, then the field change estimated for this is shown by:

If we further assume that all four of the outer ring carboxylates are fully dissociated at physiological pH, then the total change might be ΔpK_a of 1.0 and this represents a field of at least −58 mV at the protonation sites. Using the experimentally determined relationship of single channel conductance to concentration of Na⁺ and very different assumptions from ours, Green et al. (1987) estimated the electrostatic potential in the Na⁺ channel outer vestibule to be −65 mV.

A suggested mechanism for pH sensitivity

It is clear that the critical site being titrated by protons is not uniquely one of the outer ring carboxyls. Neutralization of each residue individually produced a parallel shift in the proton titration curve. Because of their charge the carboxyls are most likely to be on the protein surface, and this impression is supported by their intimate interaction with the guanidinium toxins (Terlau et al. 1991; Penzotti et al. 1998). Estimates of the depth of these residues into the electrical field based on Cd²⁺ block of Cys mutants also show that they are relatively superficial (Chiamvimonvat et al. 1996b). However, their pK_a values would be displaced from the values of 4.0-4.5 expected for free amino acids in water solution (Creighton, 1993) by the lower dielectric environment and the electric field generated by the nearby carboxylates. Although they would be minimally protonated at physiological pH, during exposure to lower pH solutions they would be partially protonated, depending on their pK_a. The estimates from our model calculations indicate that Glu-403, Glu-758, and Asp-1532 would be ≈30 % protonated at 5.91, the apparent pK_a of the wild-type channel, and Asp-1241 would be ≈10 % protonated.

We know that complete neutralization of any of these outer ring carboxylates by mutation reduces single channel conductance (Table 3). It is plausible to consider that partial neutralization by acid solutions reduces single channel conductance partially. This partial protonation also would reduce the electrostatic field and thereby shift the pK_a from the values calculated for physiological pH (Table 2). To evaluate the modified electrostatic potential and resultant ΔpK_a values of the Glu and Asp residues at pH 5.91 when surrounded by other partially protonated residues, we have used an iterative procedure, where the initial step assumes that the carboxylates are half-protonated. From this we can calculate the effect on unitary conductance if the outer ring carboxylates are partially protonated. Table 3 shows the reported fractional values from the literature of unitary conductance with neutralizing mutations of these residues. If we assume that the effects of partial protonation on unitary conductance are linear with fractional charge and use the conductance measurements of Terlau et al. (1991) for mutational neutralization, then at pH 5.91 we have fractional reductions of single channel conductance for E403Q (1 – (0.3 × 0.8)) of 0.75 for E758Q (1 – (0.3 × 0.4)) of 0.88; for D1241C (1 – (0.1 × 0.25)) of 0.975; for D1532N (1 – (0.3 × 0.5)) of 0.85. Then the product of all these simultaneous changes is 0.75 × 0.88 × 0.975 × 0.85 = 0.55, which is close to 0.5, the fractional current at pK_a for the wild-type channel. Inclusion of the selectivity filter carboxylates and the single channel conductances for D400N and E755Q reported by Terlau et al. (1991) and Pusch et al. (1991) gave a similar result. The reason that inclusion of the selectivity filter carboxylates had only a small effect on the calculation is that they are predicted to be almost entirely unprotonated at a pH of 5.91. More exact calculations are probably not useful at this time because of the scarcity of single channel conductance measurements and the lack of quantitative agreement among those. In addition, it is possible that there may be additional carboxylates near the vestibule, which could contribute to the electric field and produce a calculation even closer to the experimental measurement of wild-type pK_a.

Upon mutation of an outer ring residue such as Glu-758 to glutamine, the vestibule electrostatic potential would be less negative, altering the pK_a values of the other carboxylates less than in the wild type channel. A similar iterative calculation for the mutated channels predicts a shift of the calculated pH titration curve in the acid direction by 0.3-0.4 pH units, similar to the experimentally observed change. Calculation of the effect of lysine substitution for one carboxylate predicts double the shift in pK_a.

We therefore speculate that acid solutions reduce Na⁺ conductance by partially protonating all carboxylates in the vestibule. Because all of the outer ring carboxylates participate in the pH response, as well as the selectivity filter carboxylates (Sun et al. 1998), we suggest that they all contribute to a common vestibule site for Na⁺, where the carboxylate groups can substitute for some of the waters of hydration. The effect is at least partly electrostatic, because substitution of outer ring residues with lysine has at least twice the effect of neutral mutations. In these calculations the electrostatic effect is achieved by change in the pK_a of the remaining carboxylates. This is consistent with the experimental results of Chiamvimonvat et al. (1996a) with charge alteration at residue 758. In their studies, restoration of a negative charge at residue 758 by reaction of a cysteine mutant with MTSES only partially restored conductance at physiological levels of Na⁺. The sulfate can contribute to the electrostatic field, but not to the dehydration process. This conclusion that multiple carboxylates constitute the site of proton block in the Na⁺ channel is similar to that of Chen et al. (1996) for the L-type Ca²⁺ channel. In that situation the carboxylates are spatially closer to each other and no lysine is present, so the negative electric field may be much larger, partly explaining why the pK_a for the L-type Ca²⁺ channel is ≈8.5, more alkaline than for the Na⁺ channel.

An alternative way for the negative electrostatic potential to affect Na⁺ conductance is by increasing the concentration of Na⁺ in the vestibule, in the same way that it raises the concentration of protons. However, this implies that the conductance reduction seen with neutral mutations of the outer ring carboxylates would disappear at high and saturating concentrations of Na⁺. The experiments of Chiamvimonvat et al. (1996a) showed conclusively that saturating concentrations of Na⁺ did not restore single channel conductance for the mutant channel E758C, a result confirmed by J. Satin and H. A. Fozzard (unpublished observations) for E758Q. Therefore, it is likely that the unprotonated carboxylate oxygens do interact directly with Na⁺ during permeation, contributing to its dehydration.

This explanation of the reduction in conductance by acid solution is different from the usual concept of proton block. Our interpretation does not imply that a proton physically occludes the pore, nor that a proton competes for a single site with Na⁺. Rather, we suggest that the unprotonated oxygens of the vestibule carboxylates can contribute directly to the permeation process, presumably by assisting in the dehydration of Na⁺, and indirectly by electrostatic effects on the pK_a of the vestibule carboxylates.

The Cys mutations of Glu-403, Asp-1241, and Asp-1532 have been reported to alter Na⁺ channel selectivity to Li⁺ or NH₄⁺, raising the suggestion that these residues might contribute to selectivity (Chiamvimonvat et al. 1996b). We have previously reported that the mutations do not change the reversal potential with physiological solutions (Penzotti et al. 1998), which would be expected if there is much change in the P_Na/P_K permeability ratio, and that result was confirmed again in these experiments (Table 1). Because of the expected flexibility of the outer ring carboxylate side chains, they might not be very sensitive to the radius of a cation in the vestibule, leaving selectivity to be accomplished by interaction at the DEKA ring. However, subtle changes in selectivity might result from differences in dehydration efficiency.

Effect of symmetry of the vestibule model on the vestibule electrostatic field

If the carboxylates are partially into the membrane field, then that potential would also alter their pK_a values. A frequently used method for estimating depth of a residue into the pore is to mutate the residue to cysteine and determine the voltage dependence of block by a divalent ion such as Cd²⁺ by altering the external field under voltage clamp. This method has been used by Chiamvimonvat et al. (1996a), Yamagishi et al. (1997), and Li et al. (2000) to determine the relative location of vestibule residues in the Na⁺ channel. The sequential relationship of residues in each of the P loops located in this manner agrees with the arrangement in the model of Lipkind & Fozzard (2000) that we used for our electric field calculations. However, the field fraction is sufficiently small that the effects of transmembrane potential on pK_a are negligible at voltages where the Na⁺ current is activated. The experimental estimates of membrane potential field fraction are different for each the outer ring residues that the model places on the same plane, suggesting that their symmetry in the Lipkind & Fozzard (2000) model may be an oversimplification. For example, the field fractional depths for Glu-403, Glu-758, and Asp-1532 are 0.13, 0.07, and 0.17, respectively (Chiamvimonvat et al. 1996b). The potential in the pore generated by the membrane field may not be uniform, and is likely to be altered asymmetrically by the outer ring carboxylates. The local fields predicted here would add to the membrane field, resulting in different electrostatic potentials at each residue and perhaps different levels of Cd²⁺ block at 0 mV transmembrane potential. Mutation of the outer ring carboxylates would further alter symmetry of the electrostatic field. For example, if neutralizing Glu-758 reduces pK_a at Glu-403 and Asp-1532 by 0.4 pH units, then this represents a reduction in the negative potential at those residues by ≈15 mV. The symmetry in the Lipkind & Fozzard (2000) model may indeed be an oversimplification, but alteration of the pK_a values of the outer ring carboxylates by the large negative electrical potential in the vestibule would still result.