The steady-state voltage and [Na+]o dependence of the electrogenic sodium pump was investigated in voltage-clamped internally dialyzed giant axons of the squid, Loligo pealei, under conditions that promote the backward-running mode (K+-free seawater; ATP- and Na+-free internal solution containing ADP and orthophosphate). The ratio of pump-mediated 42K+ efflux to reverse pump current, Ipump (both defined by sensitivity to dihydrodigitoxigenin, H2DTG), scaled by Faraday's constant, was −1.5 ± 0.4 (n = 5; expected ratio for 2 K+/3 Na+ stoichiometry is −2.0). Steady-state reverse pump current-voltage (Ipump-V) relationships were obtained either from the shifts in holding current after repeated exposures of an axon clamped at various Vm to H2DTG or from the difference between membrane I-V relationships obtained by imposing Vm staircases in the presence or absence of H2DTG. With the second method, we also investigated the influence of [Na+]o (up to 800 mM, for which hypertonic solutions were used) on the steady-state reverse Ipump-V relationship. The reverse Ipump-V relationship is sigmoid, Ipump saturating at large negative Vm, and each doubling of [Na+]o causes a fixed (29 mV) rightward parallel shift along the voltage axis of this Boltzmann partition function (apparent valence z = 0.80). These characteristics mirror those of steady-state 22Na+ efflux during electroneutral Na+/Na+ exchange, and follow without additional postulates from the same simple high field access channel model (Gadsby, D.C., R.F. Rakowski, and P. De Weer, 1993. Science. 260:100–103). This model predicts valence z = nλ, where n (1.33 ± 0.05) is the Hill coefficient of Na binding, and λ (0.61 ± 0.03) is the fraction of the membrane electric field traversed by Na ions reaching their binding site. More elaborate alternative models can accommodate all the steady-state features of the reverse pumping and electroneutral Na+/Na+ exchange modes only with additional assumptions that render them less likely.

Introduction

The electrogenic sodium pump or Na,K-ATPase exports three Na ions and imports two K ions for each molecule of ATP hydrolyzed. According to the generally accepted Albers-Post model (Albers 1967; Post et al. 1969; also see Fig. 8) the Na,K-ATPase undergoes a sequence of conformational changes driven by phosphorylation/dephosphorylation reactions, during which the pump's binding sites for Na+ and K+ alternately face the intracellular and extracellular sides of the cell membrane. The sodium pump molecule belongs to the superfamily of P-type ATPases (Axelsen and Palmgren 1998), so named after the phosphorylation and dephosphorylation they undergo during their enzymatic cycle. The only high resolution P-type ATPase structure published to date is that for the Ca-ATPase of the sarcoplasmic reticulum (Toyoshima et al. 2000). In the absence of a high resolution structure for the sodium pump, it is possible to formulate structural constraints from a detailed analysis of the pump's kinetics. Provided its stoichiometry remains fixed, a sensitive measure of an electrogenic transporter's steady-state turnover rate is the transmembrane current it generates.

Information on charge-translocating steps in a transporter's reaction cycle can be obtained from the voltage dependence of the turnover rate of its various modes of operation (for reviews see De Weer et al. 1988, De Weer et al. 2000; Apell 1989; Läuger 1991a,Läuger 1991b; Rakowski et al. 1997b). Transient sodium pump currents elicited by [ATP] or voltage jumps in the absence of external K+ suggest that at least one charge-moving step accompanies deocclusion/release of Na ions to the exterior. Three of the pump's modes of operation involve Na+ translocation: forward pumping, ADP-dependent Na+/Na+ exchange, and reverse pumping. The voltage and [Na+]o dependence of the former two have been examined so far. Steady-state pump current-voltage (Ipump-V) relationships have been obtained for the forward-running mode of the Na/K pump in cardiac ventricular myocytes (Gadsby et al. 1985; Gadsby and Nakao 1989; Nakao and Gadsby 1989; Peluffo and Berlin 1997), cardiac Purkinje cells (Glitsch et al. 1989; Bielen et al. 1991), Xenopus oocytes (Lafaire and Schwarz 1986; Horisberger et al. 1991; Rakowski and Paxson 1988; Rakowski et al. 1991; Sagar and Rakowski 1994), HeLa (Argüello et al. 1996) or HEK293 (Kockskämper et al. 1997) cells expressing recombinant pump molecules, and squid giant axons (Rakowski et al. 1989). In all preparations, at near-saturating intracellular sodium ([Na+]i) and extracellular potassium concentrations ([K+]o), the I-V relationship of the forward-running pump at high extracellular sodium concentration ([Na+]o) is approximately sigmoid, approaching a plateau or shallow positive slope at large positive potentials and tending towards zero at very negative potentials. In the absence of extracellular Na+, however, the pump current at saturating [K+]o is nearly voltage-independent over the accessible voltage range. In squid axons, the pump's coupling ratio in the forward transport mode is 3 Na+/2 K+ and independent of [Na+]o or membrane potential (Rakowski et al. 1989). Moreover, in both high and low [Na+]o media, membrane potential affects pump current (i.e., net transport) and radiotracer Na+ efflux (i.e., unidirectional transport) in closely parallel fashion, signifying that the marked effects of [Na+]o on the I-V relationship of the pump in the forward mode reflect selective voltage-dependent slowing, by [Na+]o, of forward pump turnover and not, for example, stimulation of reverse transport.

Much evidence shows that extracellular Na+ and K+ both interact with the Na/K pump at sites within the membrane's electric field (Läuger 1991a,Läuger 1991b). Rakowski et al. 1991, Stürmer et al. 1991, and Bielen et al. 1993 found that the apparent affinity for activation of the forward-running pump by K+ is enhanced by hyperpolarization. Although this might reflect voltage dependence of any step in the K+ translocation pathway, the observation that K+ translocation is electrically silent at saturating [K+]o (Goldshlegger et al. 1987; Bahinski et al. 1988; Stürmer et al. 1989) strongly suggests that K+ binding is voltage-dependent and, hence, that extracellular K ions might reach their binding sites through an access channel. A more direct argument for a high field access/release channel between ion binding sites in the pump and the external medium is found in our analysis, in squid giant axons, of the voltage dependence of the ADP-requiring electroneutral Na+/Na+ exchange mode in K+-free media (Gadsby et al. 1993). The rate of this Na+/Na+ exchange flux (ΦNa/Na) declines at positive potentials, but, upon membrane hyperpolarization rises along an apparently saturating sigmoid curve. Furthermore, activation of Na+/Na+ exchange by Na+o and by hyperpolarization are kinetically equivalent (Mitchell 1969) so that the flux-voltage (ΦNa/Na-V) curve is simply shifted laterally when [Na+]o is altered. Both characteristics point to a voltage sensitivity related to the external Na+ rebinding step, which therefore must be influenced by the membrane field (Gadsby et al. 1993).

A third mode of operation of the sodium pump, besides electrogenic forward Na+/K+ transport and electroneutral Na+/Na+ exchange, is electrogenic K+/Na+ transport in which the cycle runs backwards to generate both ATP (Garrahan and Glynn 1967; Chmouliovsky 1970; Lew et al. 1970) and an inward current (De Weer and Rakowski 1984; Bahinski et al. 1988; Efthymiadis and Schwarz 1991). Because all Na+-translocating modes of operation of the pump share one or more reaction steps, it is important to establish the extent to which these common steps bring about common overall kinetic behavior, in particular, voltage sensitivity. We investigate here the voltage and [Na+]o dependence of backward-running sodium pump current in voltage-clamped internally dialyzed squid giant axons. We show that, as is the case for electroneutral Na+/Na+ exchange, the voltage dependence of electrogenic backward pumping is sigmoid with the current apparently saturating at large negative potentials, and that alterations in [Na+]o cause simple parallel shifts of this curve along the voltage axis. The high field access channel model we proposed for electroneutral Na+/Na+ exchange (Gadsby et al. 1993) predicts such behavior.

Materials And Methods

Voltage Clamp and Internal Dialysis

Membrane current and unidirectional 42K+ tracer efflux were measured in voltage-clamped internally dialyzed giant axons of the squid, Loligo pealei, using methods previously described (Rakowski et al. 1989). In brief, a porous, 160-μm-diam cellulose acetate capillary was inserted through one cannulated end of the axon while a glass voltage-measuring electrode and piggyback blackened platinum wire (each ∼75 μm in diameter) were inserted through the other end. A conventional voltage clamp circuit measured membrane current, and two ancillary voltage clamp circuits prevented longitudinal stray current flow between the center pool and adjacent guard pools. The cytoplasmic composition was maintained and, in some cases, 42K+ was introduced inside the axon by perfusing the porous intracellular capillary (1.4 μl/min) with appropriate solutions. To measure 42K+ efflux, the artificial seawater superfusing (2 ml/min) the axon in the center pool was collected in scintillation counting vials. Initial experiments were carried out near 17°C; but, to increase sodium pump turnover rate and hence signal magnitude, the temperature was raised to ∼22°C in later experiments (see Fig. 4 and Fig. 7). A 30–60 min period of dialysis (to allow for equilibration) preceded data collection in all experiments.

Solutions

External solutions were K+-free artificial seawater typically containing (in mM): 400 Na isethionate, 75 Ca sulfamate, 5 Tris HEPES, pH 7.7, 1 3,4-diaminopyridine (DAP), 0.1 Tris EDTA, and 0.2 μM tetrodotoxin (TTX). In 200 mM-Na+ seawater N-methyl-d-glucamine (NMG) sulfamate replaced half of the Na isethionate. In some early experiments, chloride replaced the isethionate and sulfamate. The internal dialysis solutions were Na+-free and typically contained (in mM): ∼160 K+, 100 glycine, 50 phenylpropyltriethylammonium (PPTEA) sulfate, 2.5 BAPTA, 40 Mg HEPES, 5 dithiothreitol, 25 ADP, and 25 orthophosphate, pH ∼7.5; the principal anion was HEPES. In some early experiments, EGTA replaced BAPTA, MgSO4 or MgCl2 replaced Mg HEPES, and 20–25 mM l-arginine (a substrate for arginine kinase) sulfate or chloride, 1–2.5 mM Li5-diadenosine pentaphosphate (an inhibitor of adenylate kinase), and 50–100 μM Na atractyloside (an inhibitor of mitochondrial ATP/ADP transfer) were added to minimize ATP accumulation within the axon. The osmolality of these internal solutions was 930–940 mOsm/kg, and that of the external solutions was 920–930 mOsm/kg. To extend the experimental [Na+]o range, hypertonic (1,780–1,790 mOsm/kg) internal and external solutions were used in some cases. In hypertonic dialysis fluid, 130 mM NMG HEPES replaced glycine. One hypertonic artificial seawater matched the typical composition above except that it contained 800 mM Na isethionate, and the other contained 800 mM NMG sulfamate instead. Intermediate (200 and 400 mM) Na concentrations were obtained by mixing.

External TTX and DAP, and internal PPTEA, minimized nonpump Na and K channel currents (Rakowski et al. 1989), and internal BAPTA or EGTA kept internal [Ca2+] low to suppress Na+/Ca2+ exchange (DiPolo and Beaugé 1987). The external K+- and internal Na+- and ATP-free conditions were designed to prevent forward, and promote reverse, Na/K pump cycling. To reduce membrane conductance in the end pools, those regions were bathed in K+-free, Na+-free seawater (NMG sulfamate replaced Na isethionate) containing 100 μM dihydrodigitoxigenin (H2DTG) in addition to TTX and DAP. Na/K pump-mediated current and 42K+ efflux were defined as those components abolished by sudden introduction of 10 or 100 μM H2DTG into the center pool (100 μM was used in all experiments in which [Na+]o was varied, and in many at 400 mM [Na+]o). The pump is inhibited ∼90% by 10 μM H2DTG in 400 mM–Na+, K+-free seawater (Gadsby et al. 1993) and ∼94% by 100 μM H2DTG in Na+-free seawater (Rakowski et al. 1989). H2DTG was added from a 100-mM stock solution in DMSO whose final concentration (≤0.1% vol/vol) did not affect the membrane current under our conditions (see Fig. 5 A). Ouabain was used at 100 μM, from a 10-mM stock solution in the appropriate artificial seawater. DAP was added directly to artificial seawater, and TTX from a 1-mM aqueous stock.

Correction for Baseline Drift

In two instances the shapes of several I-V plots obtained under different conditions and/or from different axons needed to be rigorously compared (two experiments on a single axon are compared in Fig. 6 C, and numerous experiments on two dozen axons are compared in Fig. 7A and Fig. B). To that end, it was necessary to correct each individual “raw” H2DTG (or ouabain) difference I-V curve for any inadvertently included spontaneous baseline conductance drift. Baseline drift was estimated from “time only” differences (typically two before, and two after, exposure to the pump blocker) between consecutive I-V plots recorded at time intervals matching that between the I-V plots obtained just before and shortly after addition of the pump blocker (illustrated in Fig. 4). To avoid the sampling noise that would result from point-by-point correction, the “time only” difference I-V plots were individually fit with second-degree polynomials, a time-weighted average of which was then subtracted from the raw signal difference to yield the drift-corrected H2DTG-sensitive I-V plot. To obviate time weighting, the six experimental I-V records were generally (as in Fig. 4) evenly spaced. The drift correction was usually small (≤6% of Ipump at −60 mV in most axons.)

Global Least-Squares Fit of Access Channel Model to the Data of Fig. 7

Our access-channel model (see discussion) yields an S-shaped expression for the voltage and [Na+]o dependent reverse pump current of the form:

 
\begin{equation*}{\mathrm{I}}_{{\mathrm{pump}}}=\frac{{\mathrm{I}}_{{\mathrm{pump}}}^{{\mathrm{max}}}}{1+ \left \left(\displaystyle\frac{{\mathrm{K}}_{0.5}^{0}}{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{o}}}}{\cdot}{\mathrm{e}}^{{\mathrm{V}}_{{\mathrm{m}}}\displaystyle\frac{{\mathrm{{\lambda}F}}}{{\mathrm{RT}}}}\right) \right ^{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}

(where Vm is membrane potential and F, R, and T have their usual meaning), such that reverse Ipump vanishes at extreme positive potentials and reaches Imaxpumpat extreme negative potentials. This expression can be interpreted either as a Boltzmann partition equation with [Na+]o-dependent midpoint or as a Hill approximation with fixed Hill coefficient n but voltage-dependent affinity for external Na+. K00.5 is the apparent dissociation constant of a Na+-binding site at the bottom of an access channel in the absence of transmembrane field, and λ is the access channel's depth as a fraction of electrical distance across the membrane, measured from the external solution.

To combine and compare multiple data sets from different axons (see Fig. 7), the following procedure was adopted. All I-V plots, individually corrected for baseline drift as described, were simultaneously fit, in a global least-squares procedure (Simchowitz et al. 1986), with Boltzmann equations of the above form, appropriate for the temperature at which each experiment had been carried out. The global fit generated two adjustable parameters for each individual I-V plot: a scaling variable Imaxpump and any nonzero offset at large positive potentials (not shown in the above equation, but see results). In addition, the global least-squares fit estimated the following adjustable parameters: (1) an apparent access channel depth (or fraction of the field traversed) (λ) common to all experiments; (2) a Hill coefficient n common to all experiments; and (3) two values for the apparent Na affinity in the absence of membrane potential (K00.5): one value shared by all normotonic experiments (see Fig. 7 A) and another shared by all hypertonic experiments (see Fig. 7 B). All theoretical curves in Fig. 7 are drawn for 22°C (where RT/F = 25.34 mV) with these common parameters, and with normalized Imaxpump= −1 and no offset at positive voltages. The drift-corrected data were offset to zero at large positive voltages, normalized to −1 at large negative voltages, grouped by experimental protocol, and averaged. Symbols represent averages ± SEM. Lognormal statistics were used to calculate the standard error of ratios.

Results

Reverse Pump Stoichiometry: Simultaneous Measurements of H2DTG-sensitive Current and 42K+ Efflux

Fig. 1 shows representative results from one of five axons engaged in reverse pumping in which H2DTG-sensitive current and 42K+ efflux were measured simultaneously at −60 mV. Since H2DTG is a specific Na/K pump inhibitor without additional effects (but see below) the small H2DTG-induced outward shift of the holding current (ΔI = 0.055 μA cm−2 in Fig. 1 A) must reflect abolition of the inward current generated by the backward-running Na/K pump. H2DTG washout allows repetition of this type of experiment. The mean ΔI of three successive trials on the axon of Fig. 1 A was 0.056 ± 0.002 μA cm−2. Fig. 1 B shows the average of the corresponding three 42K+ efflux determinations; mean H2DTG-sensitive K efflux (−ΔΦ) was 1.04 ± 0.07 pmol cm-2 s−1 in this axon, yielding a value of 1.79 ± 0.22 for the ratio −FΔΦ/Δ (where F is Faraday's constant), which is compatible with the value of 2.0 expected for 2 K+/3 Na+ transport stoichiometry. The mean values of ΔI and ΔΦ for all five axons were 0.106 ± 0.011 μA cm−2 (n = 18) and −1.46 ± 0.19 pmol cm−2 s−1 (n = 16). The (geometric) mean of the individual −FΔΦ/ΔI ratios was 1.5 ± 0.4, not significantly (P > 0.2) different from 2.0. The correspondence of H2DTG-sensitive current and flux argues that both reflect backward cycling of the Na/K pump.

Membrane Potential Effect on Reverse Pump Current

We used two procedures to estimate the voltage dependence of reverse pump current magnitude. The first determined the magnitude of H2DTG-sensitive current at various holding potentials by repeated exposures of an axon to H2DTG with intervening periods of washout. Fig. 2 shows successive H2DTG-induced holding current shifts in a single axon. The records in the first column (at the reference holding potential of −40 mV) show a steady decline of reverse pump current magnitude with time. The ΔI measurements at other holding potentials, therefore, were corrected for this rundown by exponential interpolation (extrapolation for final measurement). The H2DTG-induced ΔI is large at negative potentials, negligible at about +10 mV, and reversed at +30 mV. Data from 14 axons (including that of Fig. 2) are summarized in Fig. 3 A, which plots the magnitude of the abolished backward-running pump current. In six of these axons, bracketed data allowed correction for rundown and normalization to the interpolated magnitude of the H2DTG-induced ΔI at −40 mV (Fig. 3 B). The results show that reverse pump current magnitude increases monotonically with hyperpolarization throughout the voltage range examined. The small outward current at +30 mV is probably caused by small variations of [K+] in the extracellular space, as will be discussed later.

Reverse Pump Current-Voltage Relationship

In the second method, illustrated in Fig. 4, we recorded entire steady-state I-V curves in the absence and presence of H2DTG (or ouabain), and obtained the reverse pump I-V relation by difference, subject to correction for any baseline drift. This method, though unsuited for simultaneous measurement of 42K+ efflux, more accurately renders the shape of the I-V relationship and (being rapid) is much less affected by rundown. Fig. 4 A shows a sequence (a–f) of six identical 48-step down-up-down membrane potential staircases (1 s per 5-mV step) imposed from a holding potential of −30 mV, before and during exposure to 100 μM H2DTG. Fig. 4 B shows the resulting changes in membrane current, as well as the outward shift upon application of H2DTG (between c and d) reflecting abolition of inwardly directed reverse pump current. The repeated I-V measurements allowed accurate assessment of any spontaneous drift in the shape of the membrane I-V curve before and/or after H2DTG addition.

Fig. 4 C shows four (of the six) corresponding steady-state membrane I-V relationships, two (b and c; circles) before and two (d and e; squares) during exposure to H2DTG, obtained by plotting the current recorded near the end of each 1-s staircase step against step voltage. The measured currents reflect a true steady state as there was negligible hysteresis in the I-V plots, the same steady-state current being obtained at a given voltage during ascending and descending limbs of the staircase. The overlapping of open and filled symbols in Fig. 4 C indicates only modest drift with time. The difference (Fig. 4 D, c and d; closed circles) between records just before (c) and shortly after (d) H2DTG addition gives a raw H2DTG-sensitive I-V plot, so qualified because it is not corrected for any unrelated, spontaneous baseline drift that occurred during the 5-min interval between c and d. Even without baseline drift correction, the voltage dependence of H2DTG-sensitive current is clearly sigmoid, with inward current apparently saturating at large negative potentials.

Four estimates of how much the baseline drifted during an equivalent time interval are given by difference I-V relationships obtained in the absence (a minus b and b minus c) and presence (d minus e and e minus f) of H2DTG; one of each is shown in Fig. 4 D. The raw H2DTG-sensitive I-V plot, if necessary (see materials and methods), can be corrected for this – here negligibly small – baseline drift. For any Vm, the drift-corrected H2DTG-sensitive current is given by the distance between the raw H2DTG-sensitive plot and the background drift plot.

Evidence that H2DTG-induced Shifts in Holding Current Represent Na/K Pump Current

We have previously established (Rakowski et al. 1989) that, in squid axons, H2DTG-sensitive current may be equated with Na/K pump current under forward-running pump conditions. Fig. 5 demonstrates the same for the reverse pumping mode. Control application (Fig. 5 A) of 0.1% DMSO, the solvent we used for H2DTG, caused no change in membrane currents in the presence of 100 μM ouabain (to inhibit the pump). DMSO also caused no change in the absence of ouabain (not shown). Application of 100 μM H2DTG plus 0.1% DMSO in the presence of ouabain (Fig. 5 B) also had no perceptible effect at any voltage. These results confirm that neither H2DTG nor DMSO has any electrophysiologically discernible effect on nonpump currents. Other tests (not shown) verified that 100 μM ouabain had no measurable effect on axons already exposed to 100 μM H2DTG.

As in the case of forward Na/K pump current (Gadsby and Nakao 1989; Rakowski et al. 1989), if H2DTG-sensitive current is to be equated with current generated directly by reverse pumping, it must be shown that any changes in K+-sensitive electrodiffusional currents are negligible. Indeed, reverse operation of the Na/K pump (in nominally K+-free seawater) is expected to establish, in the restricted-diffusion space between axolemma and Schwann cells, a finite [K+] which should fall back to zero once the pump is arrested with ouabain or H2DTG. These activity-dependent [K+]o variations, estimated to reach 1 mM in the case of forward pumping (Rakowski et al. 1989), are likely to be smaller for the slower reverse pump. Fig. 5 C shows a stringent test of the effectiveness of our block of K+-sensitive nonpump current, the mean membrane current shift (seven tests on three axons) caused by switching from K+-free solution to a 10-mM K+ solution in the presence of 100 μM ouabain and 1 mM DAP externally and of 50 mM PPTEA internally. Since this residual current is presumably carried by inward-rectifier K channels that are sensitive to extracellular K+, it will decline as [K+]o drops when reverse pumping is stopped and, thus, contribute to the measured H2DTG-sensitive current. Such nonpump, yet indirectly H2DTG-sensitive, current component likely accounts for the small outward H2DTG-sensitive current seen at positive potentials (Fig. 2, Fig. 3, and Fig. 6 B) despite the nominal absence of extracellular K+. Thus, the data in Fig. 4 and Fig. 5 show that H2DTG-sensitive current may be equated with reverse pump current under our experimental conditions. Possible inclusion of a small K+-sensitive, nonpump current (a minor fraction of that obtained with 10 mM K in Fig. 5 C) masquerading as reverse pump current, does not materially affect our conclusions.

H2DTG- and Ouabain-sensitive Currents

Current-voltage relationships of the backward-running pump obtained by H2DTG or ouabain inhibition are compared in Fig. 6. Fig. 6 A shows (closed circles) the mean raw H2DTG difference I-V relationship obtained from seven measurements on four axons. (The absolute current magnitudes were sufficiently similar to warrant simple averaging without normalization.) Open circles show the average ± SEM of the corresponding seven baseline drift estimates. Fig. 6 B shows the analogous data for ouabain, also simply averaged, obtained from four axons. There are no obvious differences between the two sets except perhaps for the small outward current at positive potentials in the case of H2DTG.

Since ouabain binds irreversibly to the Na pump of squid giant axons, measurements of ouabain-sensitive difference currents were usually performed after some other protocol(s) had been completed. At the concentration of the reversible blocker H2DTG used (100 μM), and under our experimental conditions, its difference signal should be ∼94% of that of ouabain (Rakowski et al. 1989). To test for a possible difference between the H2DTG and ouabain results, we measured H2DTG-sensitive current and then ouabain-sensitive current 1 h later on the same axon (Fig. 6 C). Corrections for baseline drift were very small in both cases (not exceeding the size of the symbols in the case of H2DTG, or half their size in the case of ouabain), and were applied to the raw difference plots to yield the drift-corrected H2DTG- or ouabain-sensitive I-V relationships plotted in Fig. 6 C. These appear entirely superimposable. It is likely that the expected minor effect of incomplete inhibition by H2DTG was approximately offset by a small degree of rundown before the test with ouabain.

Influence of Extracellular [Na+] on the Backward-running Sodium Pump I-V Curve

The saturating sigmoid shape of the reverse pump I-V relationship, tending to a constant maximal reverse pump current Imaxpumpat extreme negative potentials, is predicted by our model (see discussion) which features an external high field access/release channel. A key property of the access channel models is that alterations in membrane potential and alterations in concentration of a charged reagent (here, external Na+) are kinetically equivalent (Mitchell 1969). Because hyperpolarization enhances the probability (via a Boltzmann partition effect) of extracellular Na+ ions finding their way to the bottom of the access channel, a reduction of [Na+]o is expected to cause a simple leftward displacement of the I-V curve, whereas raising [Na+]o should cause a parallel shift toward positive potentials. Conversely, sufficient hyperpolarization (subject to experimental range limitations) should cause saturation of Na-dependent steps at any finite [Na+]o. In the absence of other major voltage sensitive steps in the reaction cycle, all inward pump I-V curves should reach the same maximum Imaxpump, regardless of [Na+]o, at extreme negative membrane potentials where the reverse transport cycle becomes rate-limited by steps independent of voltage and external Na.

These predictions were verified by our findings. First (data not shown), when repeated inward pump I-V curves were obtained on a single axon and fit with Boltzmann partition functions, the (extrapolated) maximal pump current magnitudes Imaxpumpwere indistinguishable (except for exponential rundown) whether the axon, if hypertonic, was bathed in 800, 400, or 200 mM Nao or, if normotonic, in 400 or 200 mM Nao. Second, Fig. 7 shows that, for both normal tonicity solutions (in which [Na+]o of 400 and 200 mM can be compared; Fig. 7 A) and hypertonic solutions (that permit raising [Na+]o to 800 mM; Fig. 7 B), the parallel shifts are identical (29 mV) for each twofold change of external Na+ concentration. The magnitude of this shift reflects the fraction of the membrane's electric field dropped along the postulated access channel, λ = 0.61 ± 0.03 (see discussion). The uniform apparent valence (z = nλ = 0.80) of all five Boltzmann partition curves reflects, besides the common λ already mentioned, a common molecularity (Hill coefficient) value of n = 1.33 ± 0.05. The midpoint voltages of the curves reflect values for the apparent Nao affinity in the absence of transmembrane potential (K00.5) of 715 ± 37 mM for normotonic, and 1,065 ± 80 mM for hypertonic axons.

In practice, the simultaneous global fit to all the data (normotonic and hypertonic) shown in Fig. 7 was preceded by one (not shown) in which normotonic and hypertonic data were fit separately. After verifying that the refined least-squares parameters did not differ significantly between the two groups, we proceeded with the global fit as described in materials and methods.

Discussion

Reversal of the Na/K Pump

Garrahan and Glynn 1967 demonstrated enhanced incorporation of 32Pi into ATP in resealed red cell ghosts under conditions where reversal of the Na/K pump is expected. Net ATP synthesis was later demonstrated in guinea pig red blood cells (Lew et al. 1970) as well as in rabbit nonmyelinated nerve fibers (Chmouliovsky 1970). De Weer and Rakowski 1984 showed that, under conditions designed to support reverse pumping in voltage-clamped internally dialyzed squid giant axons, the pump generates inward current. As in cardiac myocytes (Bahinski et al. 1988) and Xenopus oocytes (Efthymiadis and Schwarz 1991), the current-voltage relationship of the backward-running pump is a monotonic function with a positive slope that tends towards saturation (at least for squid axons and guinea pig myocytes) at the negative, and towards zero at the positive, extremes of the experimentally accessible voltage range. Here, we extend these findings to include the influence of external [Na+], and propose an economical model to account for the pump's steady-state voltage dependence in this and other transport modes.

Reliability of Reverse Pump Current Measurements

The technical difficulties of accurately measuring the small inward current and K+ efflux generated by the backward-running Na/K pump have been largely overcome. During reverse pumping, K ions are extruded into an extracellular restricted-diffusion space (Frankenhaeuser and Hodgkin 1956) in which they might support currents not intrinsic to the pump. The control measurements shown in Fig. 5 C set an upper limit to the magnitude of spurious current contributions caused by any changes in [K+]o that might occur upon stopping and starting the pump. An independent measure of the reliability of the current measurement is afforded by experiments like that of Fig. 1. Assuming a reverse cycle transport stoichiometry of 2 K ions per elementary charge transferred, a ratio of H2DTG- or ouabain-sensitive 42K+ efflux to current (scaled by Faraday's constant) of 2.0 is expected. We found a ratio of 1.5 ± 0.4, which is not significantly different from the theoretical value. However, the result shows the large residual variability in these difficult simultaneous measurements.

Kinetic Model of the Na/K Pump

The kinetics of the Na/K pump are well described by the Albers-Post model (Albers 1967; Post et al. 1969; Karlish et al. 1978; Heyse et al. 1994), an outline of which is shown in Fig. 8. In this model, the Na/K pump protein cycles through four major stages, with interlocking alternations of conformation (E1 versus E2), and of phosphorylation/dephosphorylation and ion binding/occlusion and deocclusion/release steps. Although these ion binding/release events in reality are composed of successive reactions involving 3 Na or 2 K ions (Fig. 8, boxed area), the steady-state kinetics of each sequence of events are adequately described by the Hill approximation with a single apparent molecularity (n) per sequence. Furthermore, in the experiments described here and in our study of Na+/Na+ exchange (Gadsby et al. 1993), the intracellular concentrations of ATP, ADP, and Pi were all held approximately constant. For the present discussion of steady-state behavior, the Albers-Post scheme of Fig. 8, therefore, can be compressed (Fig. 9 B) without loss of generality by combining several steps and states (those within the boxes of Fig. 8) into apparent single binding/occlusion and deocclusion/release reactions, with corresponding “lumped” rate constants (Fig. 8 and Fig. 9 B) that are either first-order (k−1, k2, k−3, and k4) or pseudo-first-order (k1, k−2, k3, and k-4). Models derived from steady-state experiments cannot predict presteady-state behavior; in particular, they do not assign voltage sensitivity to individual steps within a lumped group. Presteady-state voltage-jump experiments (Nakao and Gadsby 1986; Bahinski et al. 1988; Rakowski 1993; Hilgemann 1994; Wuddel and Apell 1995; Peluffo and Berlin 1997; Holmgren et al. 2000) are needed to resolve demonstrably voltage-sensitive lumped steady-state rate coefficients (such as k−2 or k3) into their component parts. Conversely, kinetic models derived from presteady-state experiments are necessarily constrained by such steady-state observations as reported here.

It is firmly established that positive charge is carried outward across the membrane during the Na+-translocating part of the forward Na/K pump cycle, predominantly in steps that occur late in the Na+ hemicycle (for reviews see De Weer et al. 1988, De Weer et al. 2000; Läuger 1991a,Läuger 1991b; Rakowski et al. 1997b). Modest voltage dependence of intracellular Na+ binding also has been shown (Goldshlegger et al. 1987; Stürmer et al. 1991; Heyse et al. 1994; Wuddel and Apell 1995) but must have contributed little in our experiments both on Na/Na exchange (Gadsby et al. 1993) with [Na+]i near-saturating and on reverse pumping, reported here, with [Na+]i nominally zero. In the case of the K+ hemicycle, the apparent affinity of the forward-running pump for K+ is voltage dependent in Xenopus oocytes (Rakowski et al. 1991; Sagar and Rakowski 1994), cardiac myocytes (Bielen et al. 1991, Bielen et al. 1993; Gadsby et al. 1992; Berlin and Peluffo 1997), and squid giant axons (Rakowski et al. 1997a), and evidence for charge transfer accompanying K+ binding/occlusion has been obtained (Stürmer et al. 1991; Berlin and Peluffo 1997; Hilgemann 1997; Peluffo and Berlin 1997), with kinetics that suggest that external K+ access to the pump occurs across a small fraction of the transmembrane electric field. Both our Na/Na experiments (Gadsby et al. 1993) and the present reverse pumping experiments were carried out in K+o-free conditions.

Two Modes: Na+/Na+ Exchange and Reverse Pumping

Because the ADP-requiring Na+/Na+ exchange mode and the reverse pumping mode likely have reaction steps in common, and because we have identified (Gadsby et al. 1993) a putative step in the steady-state model that renders the Na+/Na+ exchange mode voltage sensitive (see also Heyse et al. 1994; Hilgemann 1994; Wuddel and Apell 1995; Holmgren et al. 2000), it is instructive to compare the pseudo-4-state schemes appropriate for these two modes (Fig. 9). In the Na+/Na+ exchange mode (Fig. 9 A), the enzyme is constrained to oscillate within the Na+ hemicycle, alternately transporting labeled Na+ outward and unlabeled Na+ inward over the same pathway. Hence, of the eight rate coefficients from the full cycle Albers-Post model of Fig. 8, only four (three of them independent because of the microscopic reversibility constraint) are needed to describe the four-step Na+/Na+ exchange mode. Moreover, because only the internal solution contains labeled Na+, external release of labeled Na+ and internal release of unlabeled Na+ are effectively irreversible steps, each governed by a rate coefficient (k2 and k−1, respectively) that also affects another, reversible, step in the cycle. In the reverse pumping mode (Fig. 9 B), the enzyme traverses all four pseudosteps of the full Albers-Post cycle but, because our zero-trans (Na+- and K+-free) experimental conditions render two of the four steps irreversible, two rate coefficients of the full model (k1 and k3; Fig. 8) vanish. Comparison of Fig. 9A and Fig. B, and of the contents of our external solutions shows that when [Na+]o is the same, the two models share rate coefficients k2 and k−2 (though probably not k−1 because somewhat different ADP concentrations were used in the two types of experiment).

Voltage Dependence of Na+/Na+ exchange

In the discussion that follows, we will analyze the steady-state voltage dependence of the reverse pumping mode in light of our previous findings on the Na+/Na+ exchanging mode. We have shown (Gadsby et al. 1993) that the steady-state rate of electroneutral Na+/Na+ exchange (with [Na+]i kept high) is enhanced by hyperpolarization along a saturating sigmoid curve which, itself, undergoes identical leftward shifts (without change in shape) for each twofold reduction of [Na+]o. The observed fixed relationship among (1) the steepness of the fitted Boltzmann distribution equation, (2) the dependence of the sigmoid's midpoint voltage on [Na+]o, and (3) the Hill coefficient for exchange activation by external Na+ reflects kinetic equivalence between [Na+]o and membrane potential. These relationships compellingly point to the external Na+ rebinding/occlusion step (pseudo-first-order rate coefficient k−2 in Fig. 9 A) as the major rate-limiting voltage-sensitive reaction of the overall steady-state cycle, in the experimentally accessible voltage range. (Under the experimental conditions we used, i.e., [Na+]i ≥ 50 mM, the voltage sensitivity of Nai+ binding mentioned earlier is negligible for practical purposes). A formal interpretation of the observed behavior is that step 2 takes place over an Eyring barrier that is positioned highly asymmetrically within the membrane electrical field (our data required ≥95% asymmetry; see Gadsby et al. 1993). Models with a symmetric Eyring barrier in step 2 require additional particular relationships among the four (or three independent) rate coefficients to fit the data (see below). The most parsimonious, and physically appealing interpretation (Gadsby et al. 1993) of the observed behavior is that all rate coefficients of the simplified scheme of Fig. 9 A, including the intrinsic higher-order rate coefficient k2, are effectively voltage independent under the prevailing experimental conditions, whereas Na+ binding occurs at the bottom of a high field access channel, i.e., within the membrane electric field, so that the probability of Na ions reaching their binding site becomes an exponential function of membrane potential. (The escape rate of ions from the channel is similarly governed by Vm but, since it is expected to be orders of magnitude faster than the rate-limiting enzymatic deocclusion step(s), it should have no perceptible effect on overall steady-state cycling rate.) Consequently the expression for the pseudo-first-order rate coefficient k−2 becomes an exponential function of Vm:

 
\begin{equation*}{\mathrm{k}}_{-2}={\mathrm{k}}_{-2}^{^{\prime}} \left \left[ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{o}}}{\mathrm{exp}} \left \left(\frac{-{\mathrm{{\lambda}V}}_{{\mathrm{m}}}{\mathrm{F}}}{{\mathrm{RT}}}\right) \right \right] \right ^{{\mathrm{n}}}{\mathrm{,}}\end{equation*}
1

where k−2 is the corresponding voltage-insensitive intrinsic higher-order rate coefficient, λ is the fraction of the membrane field dropped along the access channel measured from the external solution edge, and n is the empirical Hill coefficient (apparent molecularity) of external Na+ binding. In this simple physical model, the lateral voltage shifts caused by doubling of [Na+]o are defined by ΔV = (RT/λF)ln2, and the apparent valence of the Boltzmann partition function is defined as z = nλ.

If k−2 is effectively (over the accessible voltage range) the sole voltage sensitive rate coefficient in the Na+/Na+ exchange reaction scheme of Fig. 9 A, then this pseudo-4-state scheme may be further reduced to the pseudo-2-state Na+/Na+ exchange scheme of Fig. 9 C, without loss of kinetic information with regard to steady-state dependence of exchange rate on Vm and [Na+]o. (For a general proof that any multistep unbranched reaction cycle with a single voltage-sensitive step can be reduced to a pseudo-two-state model for the purpose of describing the voltage sensitivity of steady-state currents or turnover rates see Hansen et al. 1981.) Indeed, standard derivation methods (King and Altman 1956) applied to either the pseudo-four-state or the pseudo-two-state model yield identical kinetic expressions for the exchange flux rate ΦNa/Na = f(Na+]o) K0.5 or ΦNa/Na = f(Vm):

 
\begin{equation*}{\mathrm{{\Phi}}}_{{\mathrm{NaNa}}}=\frac{{\mathrm{{\Phi}}}_{{\mathrm{NaNa}}}^{{\mathrm{max}}}}{1+ \left \left[\displaystyle\frac{{\mathrm{K}}_{0.5}^{0}{\mathrm{exp}} \left \left(\displaystyle\frac{{\mathrm{{\lambda}V}}_{{\mathrm{m}}}{\mathrm{F}}}{{\mathrm{RT}}}\right) \right }{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{o}}}}\right] \right ^{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}
2a

(a Hill equation with voltage-sensitive apparent K0.5), or

 
\begin{equation*}{\mathrm{{\Phi}}}_{{\mathrm{NaNa}}}=\frac{{\mathrm{{\Phi}}}_{{\mathrm{NaNa}}}^{{\mathrm{max}}}}{1+{\mathrm{exp}} \left \left[\displaystyle\frac{ \left \left({\mathrm{V}}_{{\mathrm{m}}}-\overline{{\mathrm{V}}}\right) \right {\mathrm{n{\lambda}F}}}{{\mathrm{RT}}}\right] \right }{\mathrm{,}}\end{equation*}
2b

(a Boltzmann equation with [Na+]o-dependent midpoint), where –V(the midpoint voltage of the Boltzmann equation) and K00.5 (the Na+ concentration for half-maximal exchange flux activation at Vm = 0) are related by

 
\begin{equation*}\overline{{\mathrm{V}}}=\frac{{\mathrm{RT}}}{{\mathrm{{\lambda}F}}}{\mathrm{ln}}\frac{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{o}}}}{{\mathrm{K}}_{0.5}^{0}}{\mathrm{.}}\end{equation*}

In terms of the models' rate coefficients, the Na+ concentration for half-maximal activation of Na+/Na+ exchange rate ΦNa/Na at Vm = 0 is given by:

 
\begin{equation*}{\mathrm{K}}_{0.5}^{0}= \left \left[\frac{{\mathrm{k}}_{2}}{{\mathrm{k}}_{-2} \left \left(1+\displaystyle\frac{{\mathrm{k}}_{-1}}{{\mathrm{k}}_{1}}\right) \right }\right] \right ^{{1}/{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}

for the pseudo-4-state model (Fig. 9 A), or

 
\begin{equation*}{\mathrm{K}}_{0.5}^{0}= \left \left[\frac{{\mathrm{k}}_{2}+{\mathrm{{\kappa}}}_{{\mathrm{E}}}}{{\mathrm{k}}_{-2}}\right] \right ^{{1}/{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}

for the pseudo-2-state model (Fig. 9 C), where κE is a lumped (apparent) rate constant governing all reaction steps of the exchange cycle except for the external Na+ binding/occlusion and deocclusion/release steps.

Voltage Dependence of Reverse Pumping

A corollary of the compelling evidence, just discussed, for voltage dependence of rate coefficient k−2 is that this same rate coefficient, since it figures in the pseudo-4-state reverse pump reaction scheme of Fig. 9 B, may contribute to the voltage dependence of the reverse pumping mode as well. Our findings reported here show that the voltage dependence of reverse pumping is well described by the simplest (i.e., high field access channel) model that accounts for the Na+/Na+ exchange kinetics, with rate expressions entirely analogous to and . In fact (data not shown), we were able to satisfactorily fit simultaneously both Na+/Na+ exchange (data of Gadsby et al. 1993) and reverse pumping data with a single set of values for λ (fraction of membrane field traversed by external Na+ ions within the access channel), apparent molecularity or Hill coefficient (n) and, hence, apparent valence (z = nλ).

If k−2 is, for practical purposes, the sole voltage-sensitive rate coefficient in the pseudo-4-state reverse pumping scheme of Fig. 9 B by virtue of a high field access channel effect (), then that scheme too can be reduced to a pseudo-2-state model (Fig. 9 D). Accordingly, the backward-running pump appears to operate in two steps (a and b). One of these is Na+- and voltage-sensitive because it includes the binding of (at least one) Na+ by a voltage-sensitive mechanism; the other reflects all remaining reactions in the reverse pump cycle. The general expression for the cycling rate, a · b/(a + b), can be cast in two forms (, a and b)

 
\begin{equation*}{\mathrm{I}}_{{\mathrm{pump}}}=\frac{{\mathrm{I}}_{{\mathrm{pump}}}^{{\mathrm{max}}}}{1+ \left \left(\displaystyle\frac{{\mathrm{K}}_{0.5}^{0}{\mathrm{exp}} \left \left(\displaystyle\frac{{\mathrm{{\lambda}V}}_{{\mathrm{m}}}{\mathrm{F}}}{{\mathrm{RT}}}\right) \right }{ \left \left[{\mathrm{Na}}^{+}\right] \right _{{\mathrm{o}}}}\right) \right ^{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}
3a

(a Hill equation with voltage-sensitive apparent K0.5), or

 
\begin{equation*}{\mathrm{I}}_{{\mathrm{pump}}}=\frac{{\mathrm{I}}_{{\mathrm{pump}}}^{{\mathrm{max}}}}{1+{\mathrm{exp}} \left \left[\displaystyle\frac{ \left \left({\mathrm{V}}_{{\mathrm{m}}}-\overline{{\mathrm{V}}}\right) \right {\mathrm{n{\lambda}F}}}{{\mathrm{RT}}}\right] \right }{\mathrm{,}}\end{equation*}
3b

(a Boltzmann equation with [Na+]o-dependent midpoint), which are identical to those given above (, a and b) for the rate of Na+/Na+ exchange ΦNa/Na except, naturally, for the components of K00.5 for Na+ (pseudo-4-state model; Fig. 9 B):

 
\begin{equation*}{\mathrm{K}}_{0.5}^{0}= \left \left[\frac{{\mathrm{k}}_{-3}{\mathrm{k}}_{-4} \left \left({\mathrm{k}}_{-1}+{\mathrm{k}}_{2}\right) \right }{{\mathrm{k}}_{-2} \left \left({\mathrm{k}}_{-1} \left \left[{\mathrm{k}}_{-3}+{\mathrm{k}}_{4}\right] \right +{\mathrm{k}}_{-4} \left \left[{\mathrm{k}}_{-1}+{\mathrm{k}}_{-3}\right] \right \right) \right }\right] \right ^{{1}/{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}

or (pseudo-2-state model; Fig. 9 D):

 
\begin{equation*}{\mathrm{K}}_{0.5}^{0}= \left \left[\frac{{\mathrm{k}}_{2}+{\mathrm{{\kappa}}}_{{\mathrm{R}}}}{{\mathrm{k}}_{-2}}\right] \right ^{{1}/{{\mathrm{n}}}}{\mathrm{,}}\end{equation*}

where κR is a lumped (apparent) rate constant governing all reaction steps of the backward pumping cycle except for the external Na+ binding/occlusion and deocclusion/release steps. As shown earlier, the characteristic sensitivity of the reverse pump to Vm and [Na+]o (data of Fig. 7) is well described by this parsimonious model. The model's merit over more complex ones is its ability to equally account for the kinetics of voltage and Na+ dependence of two modes of operation of the sodium pump (electroneutral Na+/Na+ exchange and reverse pumping) without further assumptions.

Kinetic expressions for more elaborate models of Na+/Na+ exchange also reduce to those derived for the access channel model, provided certain constraints on the individual rate coefficients are satisfied. For example, if both k2 and k−2 in the pseudo-4-state scheme of Fig. 8 were voltage-sensitive rate coefficients by virtue of a symmetric Eyring barrier in step 2 (i.e., Na+ deocclusion/release or rebinding/occlusion), the resulting kinetic expressions would be more complex, not only for pump current Ipump in the reverse mode (Fig. 9 B), but especially for the flux rate ΦNa/Na in the Na+/Na+ exchange mode (Fig. 9 A) because the reciprocating character of the latter causes rate coefficient k2 to govern two of the four steps in the cycle. Specifically, the Ipump-V and ΦNa/Na -V curves are no longer simple Boltzmann partition functions; the lateral shifts with changes in [Na+]o are not identical for Ipump -V and ΦNa/Na -V curves, nor are they uniform for each doubling of [Na+]o; the steepness of the curves is not uniform; and the ΦNa/Na-V curves at various [Na+]o do not tend to the same ΦNa/Na . Given certain constraints on the relationships between individual rate coefficients, these complex equations for the Eyring barrier model can be made to formally approximate those for the high field access model and satisfy some, but not all, of its criteria. For example, if k−1 ≪ k−2, then each doubling of [Na+]o will cause uniform parallel shifts (i.e., the curves will retain their slopes as they move sideways a fixed distance), but the magnitudes of the lateral shifts will differ between Ipump-V and ΦNa/Na-V curves, and the slope of the curves will differ for the two modes. We found no model with an Eyring barrier in step 2, whether symmetric (Läuger and Stark 1970) or with <90% asymmetry, that gave a satisfactory simultaneous fit to both Na+/Na+ exchange and reverse pumping data.

Comparison of A and B in Fig. 9 now raises the question whether the rate coefficient k−3 (Fig. 9 B) could have a characteristic voltage dependence sufficiently similar to that of k2 (which occupies an analogous position in the isotope hemicycle of Na+/Na+ exchange, see Fig. 9 A) to endow the reverse pumping cycle with a voltage sensitivity formally indistinguishable from that of the Na+/Na+ exchange mode. This possibility is remote for two reasons. First, the voltage sensitivity of the K+ hemicycle is known to be much weaker than that of the Na+ hemicycle (Bielen et al. 1991, Bielen et al. 1993; Rakowski et al. 1991; Stürmer et al. 1991; Gadsby et al. 1992; Sagar and Rakowski 1994; Bühler and Apell 1995; Berlin and Peluffo 1997; Hilgemann 1997; Peluffo and Berlin 1997; Rakowski et al. 1997a). Second, if the weak voltage dependence of step 3 (in the pseudo-4-state model of Fig. 8) is ascribed to a high field access channel mechanism (Sagar and Rakowski 1994; Bühler and Apell 1995; Berlin and Peluffo 1997; Peluffo and Berlin 1997; Rakowski et al. 1997a), then the intrinsic first-order rate coefficient k−3 will be devoid of voltage sensitivity.

The average maximum inward pump current we observed in this study was roughly one third to one half as large as the maximum forward Na+/K+ transport current we observed previously in squid giant axon (Rakowski et al. 1989). Since 22Na+ efflux in the Na+/Na+ exchange mode (Gadsby et al. 1993) represents an approximately similar fraction of the 22Na+ efflux mediated by forward pumping, we surmise that the electroneutral Na+/Na+ exchange and reverse transport modes are rate-limited by a common voltage-independent transition, perhaps within step 1 of the pseudo-4-step Albers-Post model (Fig. 8).

Influence of Hypertonic Solutions

Fig. 7 shows that hypertonic solutions do not modify the least-squares fit values of the fractional electrical distance (λ) or the apparent molecularity (Hill coefficient n) of our access channel model. However, they do reduce the apparent affinity for Na+ ∼1.5-fold: K00.5 is 715 ± 37 mM in normotonic solutions (Fig. 7 A), but 1,065 ± 80 mM in hypertonic solutions (Fig. 7 B). This causes a uniform 17-mV leftward shift of the Boltzmann partition curves of Fig. 7 B compared with those of Fig. 7 A. To examine whether this could be due to additional shielding of negative membrane surface charges by the high ionic strength seawater, we used the Grahame 1947 equation and found that no more than about 1/3 of the observed shift could be ascribed to additional shielding by the hypertonic seawater. Therefore, other mechanisms (e.g., anion effects; Suzuki and Post 1997) must (also) come into play to lower the apparent affinity for Na+ in hypertonic seawater.

Conclusion

The extracellular Na+ access channel model we proposed for the voltage dependence of the steady-state rate of electroneutral Na+/Na+ exchange (Gadsby et al. 1993) is strongly supported by our finding here that, formally, it accounts equally well and without additional postulates for the voltage dependence of the steady-state rate of reverse electrogenic pumping. Assuming structural homology between Ca-ATPase and Na,K-ATPase, it is also compatible with the structure of the sarcoplasmic reticulum calcium pump published by Toyoshima et al. 2000, which features Ca2+ binding/release sites deep inside the protein, near the cytosolic end of its transmembrane domain. More complex models that account for the steady-state voltage dependence of Na+/Na+ exchange, such as those featuring symmetric Eyring barriers, cannot be constrained to accommodate all of the features of the steady state voltage dependence of reverse pumping as well unless demonstrably implausible assumptions (e.g., strong voltage dependence in the K+ hemicycle) are included. These requirements render alternative models highly contrived and, therefore, less likely.

Acknowledgments

This research was supported by National Institutes of Health grants NS11223 (to P. De Weer), NS22979 (to D.C. Gadsby), and HL36783 (to R.F. Rakowski).

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The present address of Dr. Gadsby is Laboratory of Cardiac/Membrane Physiology, The Rockefeller University, 1230 York Avenue, New York, NY 10021. The present address of Dr. Rakowski is Department of Biological Sciences, Ohio University, Irvine Hall, Athens, OH 45701.

Abbreviation used in this paper: H2DTG, dihydrodigitoxigenin.