Na,K -ATPase containing the amino acid substitution glutamate to alanine at position 779 of the α subunit (Glu779Ala) supports a high level of Na-ATPase and electrogenic Na+–Na+ exchange activityin the absence of K +. In microsomal preparations of Glu779Ala enzyme, the Na+ concentration for half maximal activation of Na-ATPase activity was 161 ± 14 mM (n = 3). Furthermore, enzyme activity with 800 mM Na+ was found to be similar in the presence and absence of 20 mM K +. These results showed that Na+, with low affinity, could stimulate enzyme turnover as effectively as K +. To gain further insight into the mechanism of this enzyme activity, HeLa cells expressing Glu779Ala enzyme were voltage clamped with patch electrodes containing 115 mM Na+ during superfusion in K +-free solutions. Electrogenic Na+–Na+ exchange was observed as an ouabain-inhibitable outward current whose amplitude was proportional to extracellular Na+ (Na+o) concentration. At all Na+o concentrations tested (3–148 mM), exchange current was maximal at negative membrane potentials (VM), but decreased as VM became more positive. Analyzing this current at each VM with a Hill equation showed that Na+–Na+ exchange had a high-affinity, low-capacity component with an apparent Na+o affinity at 0 mV (K 00.5) of 13.4 ± 0.6 mM and a low-affinity, high-capacity component with a K 00.5 of 120 ± 13 mM (n = 17). Both high- and low-affinity exchange components were VM dependent, dissipating 30 ± 3% and 82 ± 6% (n = 17) of the membrane dielectric, respectively. The low-affinity, but not the high-affinity exchange component was inhibited with 2 mM free ADP in the patch electrode solution. These results suggest that the high-affinity component of electrogenic Na+–Na+ exchange could be explained by Na+o acting as a low-affinity K + congener; however, the low-affinity component of electrogenic exchange appeared to be due to forward enzyme cycling activated by Na+o binding at a Na+-specific site deep in the membrane dielectric. A pseudo six-state model for the Na,K -ATPase was developed to simulate these data and the results of the accompanying paper (Peluffo, R.D., J.M. Argüello, and J.R. Berlin. 2000. J. Gen. Physiol. 116:47–59). This model showed that alterations in the kinetics of extracellular ion-dependent reactions alone could explain the effects of Glu779Ala substitution on the Na,K -ATPase.

## Introduction

After making the amino acid substitution glutamate to alanine at residue 779 of the α subunit (Glu779Ala), Na,K -ATPase mediates an extracellular K + (K +o)-activated current whose amplitude is practically unchanged over a wide range of membrane potentials in the presence of high (148 mM) extracellular Na+. The inability of membrane potential (VM) to affect current amplitude is observed at widely varying K +o concentrations, including those well below the concentration for half maximal current activation (Argüello et al. 1996). This behavior contrasts sharply with that of native enzyme, which shows a pronounced VM dependence in transport rate under similar conditions (Gadsby et al. 1985; Gadsby and Nakao 1989; Bielen et al. 1991; Rakowski et al. 1991; Sagar and Rakowski 1994; Berlin and Peluffo 1997). Understanding the reason for these changes in the mutant enzyme is complicated by the presence of a high level of electrogenic Na+–Na+ exchange (Argüello et al. 1996) and Na-ATPase activity (Vilsen 1995; Argüello et al. 1996; Koster et al. 1996) that occurs in the absence of K +o.

Given the unexpected changes in current generated by Glu779Ala-containing enzyme, additional amino acid substitutions at residue 779 were investigated. One substitution, glutamate to glutamine (Glu779Gln), also resulted in K +o-activated currents mediated by the Na,K -ATPase that were VM independent over a broad range of K +o and VM in extracellular Na+ (Na+o)-containing solutions. However, unlike Glu779Ala enzyme, electrogenic Na+–Na+ exchange was not measurable (Peluffo et al. 1997). These results showed that the VM dependence of electrogenic Na+–K + exchange (i.e., Na,K -pump current) in the presence of Na+o can be quite different for wild-type enzyme and variant enzymes containing substitutions at residue 779.

Membrane potential-dependent behavior of the Na,K -ATPase is due to the electrogenicity and kinetics of reactions controlling the ion transport cycle (Hansen et al. 1981). The preceding paper (Peluffo et al. 2000) showed that the electrogenicity and kinetics of K +o-dependent reactions are not dramatically affected in enzyme containing the substitution Glu779Gln. Thus, another explanation for the lack of VM dependence for Na,K -pump current in Na+o-containing solutions is that the electrogenicity and/or kinetics of Na+o-dependent reactions are affected by Glu779Ala and Glu779Gln substitutions. In this regard, the high rate of electrogenic Na+–Na+ exchange activity by Glu779Ala enzyme becomes extremely fortuitous because Na+o interactions with the Na,K -ATPase can be studied in the absence of K +o.

This study demonstrates that Na+o-dependent reactions of Glu779Ala enzyme are highly VM dependent and suggests that Na+o activates enzyme turnover at K +o and Na+o binding sites, similar to those in wild-type Na,K -ATPase. Thus, in addition to effects on K +o binding reactions (Peluffo et al. 2000), residue 779 may play a role in the kinetics of Na+o binding and/or occlusion reactions.

Using data in this and previous studies (Argüello et al. 1996; Peluffo et al. 1997, Peluffo et al. 2000), a model is developed to explain the VM and ion-dependent properties of electrogenic Na+–K + and Na+–Na+ exchange in Glu779Ala-containing enzyme. This model shows how alterations in the kinetics of ion binding reactions can explain the observed changes in VM-dependent behavior of mutant enzymes.

Finally, the VM-dependent properties of electrogenic Na+–Na+ exchange have not been studied, owing to the slow kinetics of this exchange mechanism in native enzyme. The present results, therefore, may also provide mechanistic information about electrogenic Na+–Na+ exchange in wild-type Na,K -ATPase.

## Methods

Mutagenesis, transfection, and cell culture protocols were similar to the previous paper (Peluffo et al. 2000). Patch-clamp techniques were also similar. However, in some experiments, the intracellular electrode solution contained 11 mM ADP, as in “(Na+ salt)”, 4 mM MgATP, and 9.2 mM MgCl2, but omitted phosphocreatine and pyruvate. This solution was calculated to have a free ADP concentration of 2 mM (MaxChelator, supplied by Chris Patton, Hopkins Marine Station, Pacific Grove, CA). After establishing a whole-cell voltage clamp, the superfusion solution was switched to a K +-free solution containing various concentrations of Na+. Na+ concentration in these solutions was changed by equimolar substitution of tetramethylammonium ion (TMA) with total monovalent cation concentration ([Na+] + [TMA]) equal to 148 mM. Electrogenic Na+–Na+ exchange mediated by heterologous enzyme was calculated as the ouabain-sensitive difference current recorded in the presence of 1 μM and 10 mM ouabain. Enzyme activity assays were performed as previously outlined (Argüello et al. 1996) except that total ionic strength was maintained at 1 M with choline chloride.

## Results

### Na-ATPase Activity

Na,K -ATPase enzyme containing the substitution Glu779Ala in the α subunit has been reported to support Na-ATPase activity in the absence of K + that is 30–60% of maximal Na,K -ATPase activity, a level that is much higher than wild-type enzyme (Vilsen 1995; Argüello et al. 1996; Koster et al. 1996). However, these studies were conducted over a limited range of Na+ concentrations, up to 200 mM. To determine the Na+-dependent activation of this enzyme more completely, activity assays were performed at Na+ concentrations up to 800 mM (Fig. 1). Na,K -ATPase activity, measured in the presence of 20 mM K + and various concentrations of Na+, was activated by Na+ with a half maximal concentration (K 0.5) of 10.8 ± 2.9 mM (Hill coefficient equal to 1.0 ± 0.2), consistent with previous reports (Karlish and Stein 1985; Nakao and Gadsby 1989). At Na+ concentrations >200 mM, enzyme activity decreased slightly from a maximum, probably due to competition between Na+ and K + at K + binding sites in the enzyme (Skou 1960). In contrast, Na+-dependent activation of Na-ATPase activity showed a monotonic concentration dependence with a K 0.5 of 161 ± 14 mM (Hill coefficient fixed at 1). Maximal Na-ATPase activity was calculated to be 79 ± 3% of maximal Na,K -ATPase activity, but, at the highest Na+ concentrations, the levels of Na-ATPase and Na,K -ATPase activity were not significantly different. Thus, this mutant enzyme was stimulated by Na+ with a much lower apparent affinity than K +, as has been previously reported (Argüello et al. 1996), and, at high enough concentrations, Na+-activated enzyme turnover rates were similar to those observed in the presence of K +. These results suggest that Na+ can maximally activate enzyme activity, but at concentrations higher than K +.

### Electrogenic Na+–Na+ Exchange Current

Our previous work suggested that Na-ATPase activity can be observed as electrogenic Na+–Na+ exchange in voltage-clamped HeLa cells expressing Glu779Ala enzyme (Argüello et al. 1996). To study this exchange process in more detail, the Na+o and VM dependence of electrogenic Na+–Na+ exchange was examined.

Current activation was measured with Na+o concentrations ranging from 0 to 148 mM, while cells held at −40 mV were superfused in K +o-free solutions. Fig. 2 shows the effect of increasing ouabain concentration in the superfusion solution from 1 μM to 10 mM at the indicated Na+o concentrations. Adding 10 mM ouabain produced an inward shift in holding current, the magnitude of which depended on Na+o. The transient increase in current observed during the solution switch at intermediate Na+o concentrations reflected an artifact due to the presence of 148 mM Na+ solution in the dead space of the superfusion bath. In Na+o- and K +o-free solution, ouabain-sensitive changes in current were not observed (Fig. 2, bottom). This last result, in particular, shows that current arises from Na+–Na+ exchange rather than uncoupled Na+ efflux.

The voltage dependence of Na+–Na+ exchange current was examined by stepping the membrane potential from −100 to +60 mV in 10-mV increments during superfusion with 1 μM and 10 mM ouabain-containing solutions. Typical current–voltage relationships for two selected Na+o concentrations, 12.5 and 148 mM, show that increasing ouabain concentration resulted in an inward shift of current at all potentials (Fig. 3), as would be expected for an exchange process that moved net positive charge out of the cell. As in Fig. 2, the amplitude of the ouabain-sensitive current was larger at the higher Na+o concentration. In addition, current amplitude decreased at positive VM with both Na+o concentrations. Na+–Na+ exchange current was calculated as a difference current at each VM by subtracting current recorded in the presence of 10 mM ouabain from that recorded during superfusion with 1 μM ouabain.

Fig. 3 also shows that, as Na+o concentration was decreased, the slope conductance of the cell decreased. This change probably reflects the decreased concentration of permeant ions in the extracellular solution. The increased membrane resistance was accompanied by decreased current noise so that current densities less than 0.1 pA/pF (i.e., 3–5 pA in a typical cell) could readily be measured.

Summary results for experiments at a variety of Na+o concentrations are shown in Fig. 4 as ouabain-sensitive difference currents. Maximal Na+–Na+ exchange current at each Na+o concentration was observed at negative VM with current density decreasing as VM became more positive. The voltage dependence of ouabain-sensitive difference current in the presence of Na+o contrasts with the relative VM independence of K +o-activated current observed in 148 mM Na+o-containing solution (Argüello et al. 1996; Peluffo et al. 1997) and shows that some interactions of Na+o with the enzyme involve VM-dependent reactions.

The negative slope in the I-V relationship could be analogous to the negative slope of K +o-activated Na,K -pump current observed in Na+o-free solutions with wild-type (Nakao and Gadsby 1989; Rakowski et al. 1991; Sagar and Rakowski 1994), RD control enzyme (Peluffo et al. 2000), and Glu779 enzyme variants (Peluffo et al. 2000). This similarity might suggest that Na+o is acting as a K +o-like congener to activate Na+–Na+ exchange. If Na+o is acting as a K +o congener, maximum current levels in I-V relationships for Na+–Na+ exchange are anticipated to shift to the right as Na+o concentration is increased (Sagar and Rakowski 1994). However, the I-V relationships in Fig. 4 show little change along the VM axis as Na+o is increased from 50 to 148 mM. Thus, these data suggest that, at least at higher concentrations, Na+o does not act as a simple K +o congener.

Fig. 4 also shows a small positive slope in the I-V relationship with 9.4 mM Na+o at potentials more negative than −80 mV. At several low Na+o concentrations, such positive slopes were sometimes observed at the most negative potentials tested. Given their small size and the increased variability of current at these VM, we did not investigate this point further.

To examine the VM dependence of current more carefully, current density at selected VM was plotted as a function of Na+o concentration (Fig. 5). Viewed in this manner, it was immediately obvious that Na+o dependence of current activation was not described by Michaelis-Menten kinetics. At the most negative VM, current activation was a biphasic function of Na+o. Even at positive VM, current density showed a rapid increase below 25 mM Na+o, along with an additional component of current activation that occurred at higher Na+o concentrations. Given this complex dependence on Na+o, ouabain-sensitive current density data at each VM was fitted with a two-component Hill equation,

\begin{equation*}I=\frac{I_{{\mathrm{max,h}}}}{1+ \left \left({{\mathit{K}}_{{\mathrm{h}}}}/{ \left \left[{\mathrm{Na}}^{{\mathrm{+}}}\right] \right _{{\mathrm{o}}}}\right) \right ^{{\mathrm{{\gamma}}}_{{\mathrm{h}}}}}+\frac{I_{{\mathrm{max,l}}}}{1+ \left \left({{\mathit{K}}_{{\mathrm{l}}}}/{ \left \left[{\mathrm{Na}}^{{\mathrm{+}}}\right] \right _{{\mathrm{o}}}}\right) \right ^{{\mathrm{{\gamma}}}_{{\mathrm{l}}}}}{\mathrm{,}}\end{equation*}
1

which included exchange current activated with relatively high (h) and low (l) affinities for Na+o. Maximum overall current (i.e., Imax,h + Imax,l) was assumed to be constant. The solid curves in Fig. 5 are best-fit functions to the data at −100, 0, and +60 mV. In all cases, the Hill coefficient (γh) for the high affinity component of current was assumed to be equal to 1. This assumption was used because the limited number of low Na+o concentrations tested would not allow an accurate estimate of the Hill coefficient, and since no sigmoidicity was apparent in the data, a value of 1 for γh seemed reasonable. was fitted to the data at all VM. The resulting values of Kh and Kl, the Na+o concentrations for half-maximal activation of the high and low affinity current components, respectively, are plotted separately in Fig. 6. Both Kh and Kl tended towards larger values as VM became more positive, a result that suggests both current components are VM dependent.

The Hill coefficient for the low affinity current component (γl) was not dependent on VM. As a result, γl at all VM were averaged to yield a value of 2.2 ± 0.6 (n = 17), an indication that the activation of current at higher Na+o concentrations displayed positive cooperativity; i.e., more than one Na+ is involved. This fitting procedure also showed that Imax,h was considerably smaller than Imax,l, consistent with the high affinity current component having a lower capacity for ion transport.

Given the apparent ability of Na+o to act as a K +o-like congener, we first attempted to analyze the VM-dependent properties of Na+–Na+ exchange current based on a pseudo two-state model similar to that used to analyze Na,K -pump current in the previous paper. Thus, by analogy to in Peluffo et al. 2000, the fraction of the membrane dielectric (λx) dissipated during Na+o-dependent activation can be estimated by the following:

\begin{equation*}{\mathit{K}}_{{\mathrm{x}}}={\mathit{K}}_{{\mathrm{x}}}^{{\mathrm{0}}}{\mathrm{exp}} \left \left({\mathrm{{\lambda}}}_{{\mathrm{x}}}{\mathit{U}}\right) \right {\mathrm{,}}\end{equation*}
2

where x represents the high or low affinity component of exchange current, Kx0 is the concentration for half maximal current activation at 0 mV, and U is dimensionless VM. As pointed out in Peluffo et al. 2000, this equation (and , below) does not imply a particular reaction mechanism for Na+–Na+ exchange.

Fitting to the data for the high affinity component of exchange current (Fig. 6, ○) showed that K h0 equaled 13.4 ± 0.6 mM and λh equaled 0.30 ± 0.03. Of particular note, λh is similar to the fraction of the membrane electric field dissipated by K +o during activation of Na,K -pump current mediated by Glu779Ala enzyme in Na+o-free solutions.

We also attempted to fit to the K l values shown in Fig. 6; however, this equation did not satisfactorily describe the data regardless of the weighting procedure (not shown). The inability to fit these data with a function in the form of again suggested that the activation of Na+–Na+ exchange by Na+o was more complicated than a K +o congener-like action. For this reason, we attempted to fit the data for the low-affinity component of current with an equation analogous to in the preceding paper (Peluffo et al. 2000), in which we assume that Na+o has two actions, one to activate current and the other to inhibit forward cycling of the enzyme (see discussion). Given these assumptions, the VM dependence of K l was analyzed by:

\begin{equation*}{\mathit{K}}_{{\mathrm{l}}}^{{\mathrm{{\gamma}}}_{{\mathrm{l}}}}={\mathit{K}}_{{\mathrm{l}}}^{{\mathrm{0}}}{\mathrm{exp}} \left \left({\mathrm{{\gamma}}}_{{\mathrm{l}}}{\mathrm{{\lambda}}}_{{\mathrm{l}}}U\right) \right +B \left \left[{\mathrm{Na}}^{{\mathrm{+}}}\right] \right _{{\mathrm{o}}}^{{\mathrm{{\gamma}}}_{{\mathrm{i}}}}{\mathrm{exp}} \left \left[ \left \left({\mathrm{{\gamma}}}_{{\mathrm{l}}}{\mathrm{{\lambda}}}_{{\mathrm{l}}}-{\mathrm{{\gamma}}}_{{\mathrm{i}}}{\mathrm{{\lambda}}}_{{\mathrm{i}}}\right) \right U\right] \right {\mathrm{,}}\end{equation*}
3

where Kl0 is Kl at 0 mV, B is the product of VM-independent rate constants, and γlλl and γiλi are the products of the Hill coefficient and fractional distance for the low-affinity activating and inhibitory actions of Na+o, respectively. Using the average value of γl determined above, was fitted to the data in Fig. 6. The Kl0 for Na+o activation, 120 ± 13 mM (n = 17), was similar to the Na+ concentration for half-maximal activation of Na-ATPase activity (Fig. 1). This result is consistent with the suggestion that electrogenic Na+–Na+ exchange is the functional manifestation of Na-ATPase activity measured in vitro (Argüello et al. 1996).

As expected from the steep negative slope of the I-V relationships (Fig. 4), the low affinity reaction component dissipated over 80% of the membrane dielectric, λl = 0.82 ± 0.07 (n = 17). This high degree of electrogenicity is similar to that reported for Na+o rebinding to wild-type Na,K -ATPase (Nakao and Gadsby 1986; Rakowski 1993; Heyse et al. 1994; Hilgemann 1994; Peluffo and Berlin 1997). These data show that low affinity activation of Na+–Na+ exchange occurs by a mechanism different than K +o-dependent activation of enzyme turnover and suggests again that Na+o is not simply acting as a K + congener.

### Relationship to Electroneutral Na+–Na+ Exchange

In the absence of K +o, wild-type Na,K -ATPase also carries out Na+–Na+ exchange that has one-to-one stoichiometry (Garrahan and Glynn 1967a; Abercrombie and De Weer 1978), is highly VM-dependent (Rakowski et al. 1989; Gadsby et al. 1993), and has a strong dependence on ADP (De Weer 1970; Glynn and Hoffman 1971). Therefore, to determine the relationship between this electroneutral exchange and the electrogenic Na+–Na+ exchange measured with Glu779Ala enzyme, experiments compared the Na+o and VM dependence of Na+–Na+ exchange current with and without 2 mM free ADP in the patch electrode solution. Fig. 7 shows that, in the presence of 25 mM Na+o, a concentration chosen primarily to stimulate the high affinity component of electrogenic exchange, increasing free ADP concentration in the patch electrode from 0 to 2 mM had little effect on the amplitude or VM dependence of ouabain-sensitive current. In the presence of 148 mM Na+o, increasing ADP concentration substantially reduced membrane current at all VM. Even so, the steep negative slope in the I-V relationship remained, consistent with the presence of a highly VM-dependent reaction in the remaining current. Thus, the high affinity component of electrogenic exchange appears to be ADP insensitive, while the low affinity exchange component is ADP sensitive.

## Discussion

In this and the accompanying paper (Peluffo et al. 2000), we have examined effects of the amino acid substitution Glu779Ala on properties of membrane current mediated by the Na,K -ATPase. We have found that Na+o- and K +o-dependent reactions in this enzyme variant are VM dependent and, as will be discussed below, alterations in enzyme kinetics are sufficient to explain the VM-dependent behavior of both Na+–K + and Na+–Na+ exchange-reaction cycles.

### Na+–Na+ Exchange in Glu779Ala Enzyme

Na,K -ATPase containing Glu779Ala has the unique property that Na+ can stimulate enzyme activity in the absence of K + at rates much higher than with wild-type enzyme (Vilsen 1995; Argüello et al. 1996; Koster et al. 1996). The present results demonstrate that the rate of this Na-ATPase activity can be comparable with that of Na,K -ATPase activity, albeit at very high Na+ concentrations. Thus the principal question of this study is the mechanism by which Na+ promotes enzyme activity in this mutant enzyme.

Na+-stimulated enzyme activity is clearly electrogenic, since ouabain-sensitive currents are observed, and it does not represent uncoupled Na+ transport because Na+o is required to activate current (Fig. 2; Argüello et al. 1996). Thus, Na-ATPase activity appears to be the in vitro manifestation of electrogenic Na+–Na+ exchange.

Na+o-dependent activation of electrogenic Na+–Na+ exchange in Glu779Ala enzyme shows a biphasic dependence on Na+o concentration (Fig. 5). Biphasic steady state reaction kinetics have previously been interpreted as indicative of (a) multiple enzyme isoforms catalyzing the same reaction, (b) complex allosteric substrate interactions in a multi-site enzyme (Segel 1975), or (c) kinetic heterogeneity in the reaction sequence of an enzyme (Froehlich and Fendler 1991). We can exclude the first possibility in our expression system; however, our data do not allow us to distinguish between the latter two possibilities. Nonetheless, kinetic heterogeneity has been previously postulated for the Na,K -ATPase (Froehlich and Fendler 1991; Post and Klodos 1996), and such a postulate simplifies data analysis by allowing us to separate Na+–Na+ exchange current into high and low Na+o affinity components, as in . The high affinity component has a maximal velocity at −100 mV that is 24% of calculated maximal Na+–Na+ exchange current, and its apparent affinity is well described by an equation analogous to used to analyze Na,K -pump current in the previous paper (Peluffo et al. 2000). Using this model, our analysis suggested that Na+o-dependent reactions dissipate ∼30% of the membrane electric field during Na+–Na+ exchange. This fractional distance for Na+o is similar to that for K +o activation of Na,K -pump current (Sagar and Rakowski 1994; Berlin and Peluffo 1997).

The low-affinity component of Na+–Na+ exchange current is highly VM-dependent and accounts for 76% of calculated maximal Na+–Na+ exchange current at −100 mV. Using , which is based on a pseudo three-state scheme for the Na,K -ATPase (Sagar and Rakowski 1994), we found that Na+o-dependent activation dissipated ∼80% of the membrane electric field. It is interesting that the VM dependence of this reaction appears to be quite similar to that for Na+o rebinding in wild-type enzyme (Gadsby et al. 1993). Thus, it is tempting to postulate that activation of low-affinity electrogenic Na+–Na+ exchange in Glu779Ala enzyme occurs at a Na+-specific site.

Biphasic activation of Na-ATPase activity is not apparent in Fig. 1. However, the lowest Na+ concentration tested in these assays was still several-fold higher than the K 00.5 for Na+o of the high affinity current component. The Na+ concentration for half-maximal activation of Na-ATPase activity is similar to that of the low Na+o affinity current component. Thus, Fig. 1 probably shows activation of enzyme activity that is equivalent to the low affinity component of Na+–Na+ exchange.

### Na+–Na+ Exchange Reactions by the Na,K -ATPase

Two types of Na+–Na+ exchange reactions have been previously reported in wild-type Na,K -ATPase (Glynn 1985). Electroneutral exchange is a one-to-one Na+ counter-transport mechanism (Garrahan and Glynn 1967a; Abercrombie and De Weer 1978) that involves no net hydrolysis of ATP (Garrahan and Glynn 1967b), is stimulated by ADP (De Weer 1970; Glynn and Hoffman 1971) and high concentrations of Na+o (Garrahan and Glynn 1967a; Garay and Garrahan 1973), and includes a highly electrogenic Na+ deocclusion/release step (Bühler et al. 1991; Gadsby et al. 1993; Hilgemann 1994). The Na+o dependence of this electroneutral exchange reaction has several similarities with the Na+o dependence of the low affinity component of electrogenic exchange in Glu779Ala enzyme. However, two results suggest that electroneutral exchange and low Na+ affinity electrogenic exchange involve different reaction pathways. First, intracellular ADP inhibits low-affinity electrogenic exchange. Second, our previous data (Argüello et al. 1996) and the work of Vilsen 1995 show that high Na+ concentration promotes enzyme dephosphorylation, unlike electroneutral Na+–Na+ exchange. Thus, from our data, we conclude that the low Na+o affinity component of electrogenic exchange occurs via enzyme dephosphorylation promoted by Na+o binding at a Na+-specific site. Even so, we cannot determine whether the exchange reaction involves an E1P(Na)2- or E2P(Na)2-like conformation.

The second type of Na+–Na+ exchange reaction in wild-type enzyme uses Na+o as a low-affinity K + substitute to stimulate enzyme dephosphorylation (Lee and Blostein 1980) and moves charge across the cell membrane (Forgac and Chin 1982; Cornelius and Skou 1985; Wuddel and Apell 1995). This electrogenic exchange occurs in the absence of ADP and is generally much slower than electroneutral Na+–Na+ exchange (Lee and Blostein 1980; Cornelius and Skou 1985). As a result, previous studies have not examined the VM dependence of reactions involved in this transport mode in any detail. The present data show that the VM dependence for Na+o activation of high affinity Na+–Na+ exchange is similar to that for K +o activation of Na,K -pump current. The inability of intracellular ADP to influence this component of Na+–Na+ exchange is also expected if electrogenic exchange reactions follow a K +-like dephosphorylation reaction pathway via an E2P(Na)2 conformation. Thus, Na+o appears to be acting as an electrical as well as a biochemical congener of K +o in this sequence of exchange reactions.

The stoichiometry of Na+–Na+ exchange has previously been reported as 1:1 (Blostein 1983), 2:1 (Cornelius and Skou 1985), and varying with Na+ concentration (Forgac and Chin 1982). While we have no direct data on this point, our results are consistent with a 3:2 stoichiometry, at least for the low Na+o affinity component of electrogenic exchange. First, if we assume that the enzyme extrudes three Na+ ions, an outward exchange current necessitates the number (n) of Na+ ions being transported inward to be less than three. Second, the Hill coefficient (γl) for the high-capacity, low-affinity component of electrogenic Na+–Na+ exchange is ∼2.0. Thus, n must be >1. Taken together, these data suggest that n must be an integer such that 1 < n < 3; i.e., n = 2.

To summarize, activation of the high affinity component of Na+–Na+ exchange shares some similarities with K +o activation of Na,K -pump current, analogous to the Albers-Post scheme (Glynn 1985). Activation of the low-affinity component has several similarities to Na+o activation of electroneutral Na+–Na+ exchange, but is inhibited by intracellular ADP. These data would seem to indicate that Na+o binding at a Na+-specific site promotes enzyme cycling. Overall, Na+o-dependent activation of Glu779Ala enzyme turnover appears to occur at sites comparable with K +o and Na+o sites in wild-type enzyme. The implication of this conclusion is that reaction kinetics in the mutant enzyme are altered, but, as pointed out above, without marked changes in the VM dependence of extracellular ion-dependent reaction steps.

Other mutant enzymes showing a high rate of Na-ATPase activity have been identified recently (Argüello et al. 1999). These variant enzymes may also serve as beneficial model systems to study reactions that are otherwise difficult to examine in wild-type Na,K -ATPase.

### Apparent VM Independence of K +o-activated Currents in Na+o-containing Solutions

Aside from the high level of Na+–Na+ exchange activity, the most surprising observation with Glu779Ala enzyme is the apparent VM independence of K +o-activated currents measured in 148 mM Na+o-containing solutions, even at K +o concentrations well below that which produces half-maximal current activation (Argüello et al. 1996). Glu779Gln enzyme also mediates Na,K -pump current that appears to be VM-independent (over the entire range of VM tested; −100 to +60 mV) at nonsaturating K +o concentrations; however, this enzyme does not have measurable Na+–Na+ exchange currents (Peluffo et al. 1997). Even so, the accompanying paper (Peluffo et al. 2000) shows that K + transport remains VM dependent in Glu779Ala and Glu779Gln enzymes. Thus, one goal of this study was to find a reasonable explanation for these apparently conflicting data.

With wild-type Na,K -ATPase, a negative slope in I-V relationships of Na,K -pump current is observed at nonsaturating K +o concentrations. However, at high enough K +o, this negative slope is lost due to saturation of K + binding sites in the enzyme (Sagar and Rakowski 1994; Berlin and Peluffo 1997). A similar K +-dependent saturation of ion binding sites can be ruled out as an explanation for the behavior of Glu779Ala enzyme because current amplitude varied widely at different K +o, as pointed out in the previous paragraph.

An alternative explanation for our experimental observations with Glu779Ala enzyme may lie in data suggesting that quaternary organic amines inhibit Na,K -pump current by interacting at two sites on the enzyme, one in and the other out of the membrane electric field (Berlin and Peluffo 1998). Previous reports have shown that quaternary amines inhibit Na,K -ATPase by acting as K +o antagonists (Kropp and Sachs 1977; Forbush 1988). Together, these data lead us to postulate that one K +o binding site in the Na,K -ATPase is located in the membrane dielectric and the other out of the dielectric.

To explain the lack of a negative slope in the I-V relationships for K +o-activated current in Na+o-containing solutions, Na+o must bind at the K +o site in the membrane dielectric with high enough affinity that this site is saturated with Na+o and/or K +o at all K +o concentrations when [Na+] + [K +] = 148 mM. Data showing that the high-affinity component of Na+–Na+ exchange has a K 00.5 for Na+o of 13 mM are certainly compatible with this idea.

The implication of our postulate is that the substitutions Glu779Ala and Glu779Gln increase the relative affinity of the K + site in the membrane dielectric for Na+o as compared with wild-type enzyme. This idea is consistent with Vilsen 1995, who concluded that rat Glu781Ala enzyme, equivalent to sheep Glu779Ala enzyme, had reduced selectivity between K + and Na+ for enzyme dephosphorylation.

Another feature of Glu779Ala and Glu779Gln enzymes is the lack of positive slope in the I-V relationships for Na,K -pump current in Na+o-containing solutions (Argüello et al. 1996; Peluffo et al. 1997). Wild-type Na,K -ATPase displays similar behavior in Na+o-free solutions (Nakao and Gadsby 1989; Sagar and Rakowski 1994; Berlin and Peluffo 1997; Peluffo et al. 2000). Thus, an explanation for this lack of positive slope in the I-V relationship of variant enzymes could be that the apparent affinity for Na+o binding to E2P is greatly decreased with Glu779Ala and Glu779Gln substitutions. In fact, the Na+ binding affinity need not actually change. Instead, a decrease in apparent affinity for the inhibitory action of Na+o could just reflect the fact that Na+o can also promote forward enzyme cycling in variant enzymes.

### Effect of Glu779Ala on the VM Dependence of Extracellular Ion Binding Reactions

An alternative explanation for the apparent VM independence of Na,K -pump current observed in Na+-containing solutions is that the VM dependence of extracellular ion binding reactions are altered by mutations at Glu779. Our experimental data alone do not allow us to judge whether this explanation is reasonable. Thus, to address this point, computer simulations were developed to qualitatively reproduce our experimental observations with Glu779Ala enzyme using a reaction scheme that was as simple as possible. Previously published pseudo three-state (Sagar and Rakowski 1994) and pseudo four-state models (Wang et al. 1996) could not account for the biphasic response of Na+–Na+ exchange current to changes in Na+o concentration, nor the VM independence of K +o-activated currents discussed above (see Argüello et al. 1996; Peluffo et al. 1997). Both of these observations could be reproduced by a branched pseudo five-state reaction scheme that included (a) a reaction pathway in which enzyme turnover was promoted by Na+o binding at a Na+-specific site, and (b) a reaction pathway with two nonidentical K +o binding sites, one located in the membrane dielectric and the other out of the membrane electric field. To reproduce the steepness of the negative slope in the I-V relationships under Na+o-free conditions (see Figure 3 B in Peluffo et al. 2000), we had to assume an ordered binding scheme (Forbush 1987) with the K +o binding first at the site located outside the membrane dielectric. Furthermore, Na+ binding to K + sites also promoted enzyme turnover.

The pseudo five-state model could not reproduce the lack of Na+o-dependent shift in the I-V relationships for Na+–Na+ exchange current at higher Na+o concentrations (Fig. 4). To account for this observation, VM dependence in the Na+-specific reaction pathway was assigned to a step following Na+ loading of the enzyme. This step could represent ion occlusion, analogous to models of the Na/Ca exchanger adopted by Matsuoka and Hilgemann 1992, or enzyme interconversion between E1 and E2 conformations. Although our results cannot distinguish between these alternatives, enzyme interconversion in wild-type enzyme has been shown to display little VM dependence (Wuddel and Apell 1995). Thus, we prefer the former explanation, which would suggest that Glu779Ala mutation changes reaction kinetics associated with Na+o occlusion, rather than the latter, which would imply a major change in the identity of charge-moving reaction steps. Assignment of VM dependence to such a reaction step necessitated that we propose a branched pseudo six-state model to simulate ion transport by Glu779Ala enzyme.

The reaction steps comprising this pseudo six-state model are shown in Fig. 8 A. For the K +-sensitive clockwise reaction pathway (i.e., the Albers-Post scheme; Glynn 1985), we assume that transport stoichiometry is the same as wild-type enzyme, whether enzyme turnover is stimulated by K +o or Na+o. As discussed above, our data for the low Na+o affinity component of Na+–Na+ exchange are also consistent with a 3:2 stoichiometry. Each reaction branch is also modeled with an irreversible step that lumps together all reactions subsequent to extracellular ion binding/occlusion (Hansen et al. 1981). This assumption is consistent with our experimental conditions (i.e., high intracellular Na+ and ATP concentrations), which tend to strongly favor forward enzyme cycling. In addition, the assumption simplifies the analytical solution of the model (see  ).

Using this model, simulations were performed for: (a) wild-type and (b) Glu779Ala Na,K -pump current in the presence of Na+o, (c) Glu779Ala Na,K -pump current in the absence of Na+o, and (d) Glu779Ala Na+–Na+ exchange current in K +-free solution (see  ). The simulated I-V relationships, obtained using the rate constants listed in Table (see  ) are displayed in Fig. 8B–E. In all cases, simulated maximum current levels (Imax) were consistent with their experimental counterparts. The values and VM dependence of K 0.5 calculated from the simulated I-V relationships were similar to those found in the experiments. Even the biphasic dependence of Na+–Na+ exchange current on Na+o was reproduced (Fig. 8 E, inset).

An important conclusion derived from these simulations is that wild-type–like and Glu779Ala electrical behaviors under all ionic conditions could be modeled by modifying rate constants for ion binding reactions while keeping the fractional electrical distances for VM-dependent reactions unchanged. Thus, our simulations suggest that the unique VM dependence of ion transport by Glu779Ala enzyme can be explained by changes in reaction kinetics without the need to invoke alterations in the VM dependence of extracellular ion binding reactions.

Taken as a whole, our simulations suggest that the substitution Glu779Gln, which removes the carboxyl moiety from the side chain, has two major effects. The first effect is to change the relative Na+o and K +o affinities of a K +o binding site located in the membrane dielectric so that the site is saturated in 148 mM Na+o-containing solutions. The second effect is a decrease in the apparent affinity for Na+o to inhibit forward enzyme cycling. In addition, the substitution Glu779Ala, which also removes side chain bulk, promotes enzyme turnover after Na+o binds to the Na+-specific site and/or K +-binding sites. In wild-type enzyme, this reaction must be strongly inhibited to ensure efficient exchange of Na+ and K + across the cell membrane. The structure of the side chain at residue 779 must, therefore, contribute to the high threshold energy that normally prevents electrogenic Na+–Na+ exchange from occurring at a high rate.

## Acknowledgments

The authors thank the excellent technical assistance of Ms. Palak Raval-Nelson and Marguarita Schmid.

This work was supported by a Grant-in-Aid from the American Heart Association (J.R. Berlin), a postdoctoral fellowship from the Southeastern Pennsylvania affiliate of the American Heart Association (R.D. Peluffo), and grants HL03373 (J.M. Argüello), GM57253 and HL43712 (J.R. Berlin), and HL28573 (J.B Lingrel) from the National Institutes of Health.

Equations describing the reaction scheme in 8 A were derived for steady state conditions using the King and Altman method (Segel 1975). This derivation yielded the following expression for Na,K -ATPase-mediated current as a function of membrane potential and extracellular ion concentration:

\begin{equation*}I \left \left({\mathit{V}}_{{\mathrm{M}}}; \left \left[{\mathrm{X}}\right] \right \right) \right =Fn{\mathrm{{\alpha}}}_{{\mathrm{l}}}\frac{{\mathrm{A}}+{\mathrm{B}}-{\mathrm{C}}}{{\mathrm{D}}+{\mathrm{E}}}{\mathrm{,}}\end{equation*}

where [X] represents Na+o and/or K +o concentration, F is the Faraday constant, n is the total amount of enzyme per square centimeter of membrane area, and

\begin{equation*}{\mathrm{A}}= \left \left \left[{\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}+{\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}+{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{6}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\alpha}}}_{7}+ \left \left[{\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}+{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right \left \left({\mathrm{{\alpha}}}_{7}+{\mathrm{{\beta}}}_{6}\right) \right {\mathrm{{\beta}}}_{5} \right {\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\alpha}}}_{4}\end{equation*}

\begin{equation*}{\mathrm{B}}= \left \left[{\mathrm{{\alpha}}}_{4}+{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right \left \left \left[{\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}+{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{6}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\alpha}}}_{7}+ \left \left({\mathrm{{\alpha}}}_{7}+{\mathrm{{\beta}}}_{6}\right) \right {\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\beta}}}_{5} \right {\mathrm{{\beta}}}_{2}\end{equation*}

\begin{equation*}{\mathrm{C}}= \left \left[ \left \left({\mathrm{{\alpha}}}_{7}+{\mathrm{{\beta}}}_{6}\right) \right {\mathrm{{\beta}}}_{5}+{\mathrm{{\alpha}}}_{6}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\alpha}}}_{7}\right] \right \left \left \left[{\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right +{\mathrm{{\beta}}}_{2}\right] \right {\mathrm{{\alpha}}}_{4}+{\mathrm{{\beta}}}_{2}{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right {\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \end{equation*}

\begin{equation*}{\mathrm{D}}= \left \left \left( \left \left[{\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right +{\mathrm{{\beta}}}_{2}\right] \right {\mathrm{{\alpha}}}_{4}+{\mathrm{{\beta}}}_{2}{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right) \right \left \left( \left \left[{\mathrm{{\alpha}}}_{1}+{\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}+{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{7}+{\mathrm{{\alpha}}}_{1}{\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}\right) \right + \left \left( \left \left[{\mathrm{{\alpha}}}_{1}+{\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{4}+ \left \left[{\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right +{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{1}\right) \right {\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}{\mathrm{{\alpha}}}_{7} \right {\mathrm{{\alpha}}}_{6}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \end{equation*}

\begin{equation*}{\mathrm{E}}= \left \left({\mathrm{{\alpha}}}_{7}+{\mathrm{{\beta}}}_{6}\right) \right \left \left \left( \left \left[{\mathrm{{\alpha}}}_{1}+{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right \left \left[{\mathrm{{\alpha}}}_{4}+{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\beta}}}_{2}+ \left \left[{\mathrm{{\alpha}}}_{1}+{\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}+{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\alpha}}}_{4}+ \left \left[{\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right +{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right] \right {\mathrm{{\alpha}}}_{1}{\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}\right) \right {\mathrm{{\beta}}}_{5}+ \left \left[ \left \left({\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right {\mathrm{{\alpha}}}_{4}+{\mathrm{{\beta}}}_{2}{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right \right) \right {\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}+ \left \left({\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}{\mathrm{{\beta}}}_{2}+{\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}{\mathrm{{\beta}}}_{5}\right) \right {\mathrm{{\alpha}}}_{4}\right] \right {\mathrm{{\alpha}}}_{1} \right \end{equation*}

in which pseudo first-order and/or VM-dependent rate constants were defined as follows:

\begin{equation*}{\mathrm{{\beta}}}_{1}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right ={\mathrm{{\beta}}}_{1} \left \left[{\mathrm{Na}}\right] \right ^{{\mathrm{{\gamma}}}_{{\mathrm{{\beta}}}1}}{\mathrm{exp}} \left \left(-{\mathrm{{\gamma}}}_{{\mathrm{{\beta}}}1}{\mathrm{{\lambda}}}_{{\mathrm{{\beta}}}1}U\right) \right \end{equation*}

\begin{equation*}{\mathrm{{\alpha}}}_{2}^{{\mathrm{*}}}={\mathrm{{\alpha}}}_{2} \left \left[{\mathrm{Na}}\right] \right ^{{\mathrm{{\gamma}}}_{{\mathrm{{\alpha}}}2}}\end{equation*}

\begin{equation*}{\mathrm{{\alpha}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right ={\mathrm{{\alpha}}}_{3}{\mathrm{exp}} \left \left(-{\mathrm{{\lambda}}}_{{{\mathrm{{\alpha}}}3}/{{\mathrm{{\beta}}}3}}{U}/{2}\right) \right \end{equation*}

\begin{equation*}{\mathrm{{\beta}}}_{3}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right ={\mathrm{{\beta}}}_{3}{\mathrm{exp}} \left \left({\mathrm{{\lambda}}}_{{{\mathrm{{\alpha}}}3}/{{\mathrm{{\beta}}}3}}{U}/{2}\right) \right \end{equation*}

\begin{equation*}{\mathrm{{\alpha}}}_{5}^{{\mathrm{*}}}={\mathrm{{\alpha}}}_{5} \left \left[{\mathrm{X}}\right] \right \end{equation*}

\begin{equation*}{\mathrm{{\alpha}}}_{6}^{{\mathrm{*}}} \left \left({\mathit{V}}_{{\mathrm{M}}}\right) \right ={\mathrm{{\alpha}}}_{6} \left \left[{\mathrm{X}}\right] \right {\mathrm{exp}} \left \left(-{\mathrm{{\lambda}}}_{{\mathrm{{\alpha}}}6}U\right) \right {\mathrm{,}}\end{equation*}

where γβ1 and γα2 are the Hill coefficients for those Na+o-binding reactions of uncertain stoichiometry; λβ1, λα3/β3, and λα6 are the fractional electrical distances for the respective VM-dependent reactions; and U, the reduced membrane potential, equals F VM/RT. In the case of the rate constants describing the ion-independent VM-dependent transition, α3 and β3, the membrane potential dependence was introduced via a symmetric Eyring barrier (Läuger and Stark 1970).

Steady state ion transport rate (i.e., current) was simulated using Mathcad 8 Professional software (Mathsoft) run on a personal computer. In these simulations, explicit interactions between Na+ and K + at extracellular ion binding sites of Glu779Ala enzyme were not modeled. Instead, rate constants were varied to account for possible interactions at ion binding sites. The K +o binding site for Glu779Ala enzyme located in the membrane dielectric was assumed to bind Na+o and K +o with the same affinity, consistent with the suggestion of Vilsen 1995, so that the enzyme could effectively “see” the sum of the concentration of both ions.

In the simulations, transformation of I-V relationships from a wild-type–like (8 B) to a Glu779Ala-like (8 C) behavior in the presence of extracellular Na+ required a 100-fold decrease in the rate constant for inhibitory Na+o rebinding, β1 (see 8 A), together with a twofold increase in the dissociation constant for binding of K +o to the VM-independent site in the pump (β55), as shown in 1. Furthermore, the K +o binding site located in the membrane dielectric was assumed to have zero Na+o affinity in wild-type enzyme; however, this site was assumed to bind Na+o and K +o with equal affinity in Glu779Ala enzyme, consistent with the finding that Na+o activates the “K +-like” high-affinity, low-capacity component of electrogenic Na+–Na+ exchange with a K00.5 of ∼10 mM. With these constraints, the lack of VM dependence in the I-V relationships for Glu779Ala enzyme reported in solutions containing Na+o and nonsaturating K +o concentrations (Argüello et al. 1996) could be well reproduced (8 C).

To reproduce the VM and K +o dependence of Na+–K + exchange by Glu779Ala under Na+o-free conditions (8 D), the forward rate constant for K +o binding to the VM-independent site (α5) was increased 200-fold, as compared with the wild-type enzyme, with only minor changes in the other three rate constants involved in K +o binding/release (β5, α6, and β6, see 1).

Simulation of Na+–Na+ exchange electrical behavior by Glu779Ala variant enzyme (8 E) required a large increase in the forward rate constant for Na+o binding (α2) with respect to the wild-type enzyme, so that a significant fraction of total enzyme would cycle through the counterclockwise branch of the reaction scheme shown in 8 A. The apparent dissociation constant for Na+o binding (β22) was set to 0.4 M. To simulate the high-affinity, low-capacity Na+–Na+ exchange component (clockwise reaction pathway in 8 A), Na+o was assumed to act as a low-affinity K +o congener. Thus, values of the forward (α5, α6) and backward (β5, β6) rate constants for Na+o binding were decreased from those used to simulate K +o binding to wild-type Na,K -pump. Finally, the low-capacity characteristic of this Na+–Na+ exchange current component was obtained by reducing fivefold the value of the rate constant for the irreversible step (α7).

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Portions of this work were previously published in abstract form (Peluffo, R.D., J.M. Argüello, J.B Lingrel, and J.R. Berlin. 1998. Biophys. J. 74:A191).