Mutational analysis of Glu-327 of Na+-K+-ATPase reveals stimulation of 86Rb+ uptake by external K+

Katherine Tepperman1, Lauren A. Millette1, Carl L. Johnson2, Elizabeth A. Jewell-Motz3, Jerry B. Lingrel3, and Earl T. Wallick2

1 Department of Biological Sciences, McMicken College of Arts and Sciences, University of Cincinnati, Cincinnati 45221-0006; and 2 Department of Pharmacology and Cell Biophysics and 3 Department of Molecular Genetics, Biochemistry, and Microbiology, University of Cincinnati College of Medicine, Cincinnati, Ohio 45267-0575

    ABSTRACT
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

A competition assay of 86Rb+ uptake in HeLa cells transfected with ouabain-resistant Na+-K+-ATPase mutants revealed a stimulation of 86Rb+ uptake at low external concentrations (1 mM) of competitor (K+). Of the models that were tested, those that require that two K+ be bound before transport occurs gave the worst fits. Random and ordered binding schemes described the data equally well. General models in which both binding and transport were allowed to be cooperative yielded parameter errors larger than the parameters themselves and could not be utilized. Models that assumed noncooperative transport always showed positive cooperativity in binding. E327Q and E327L mutated forms of rat alpha 2 had lower apparent affinities for the first K+ bound than did wild-type rat alpha 2 modified to be ouabain resistant. The mutations did not affect the apparent affinity of the second K+ bound. Models that assumed noncooperativity in binding always showed positively cooperative transport, i.e., enzymes with two K+ bound had a higher flux than those with one K+ bound. Increases in external Na+ decreased the apparent affinity for K+ for all models and decreased the ratio of the apparent influx rate constants for E327L.

sodium pump; mutagenesis; transport; potassium flux; mechanistic modeling

    INTRODUCTION
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

THE ROLE OF Na+-K+-ATPase, present in most eukaryotic cells, is to maintain the ionic gradients of Na+ and K+ (14, 27, 38). It is generally agreed that the stoichiometry (i.e., the number of internal-to-external transport sites) is three internal (Na+) to two external (K+) to one phosphorylation site. Unlike the stoichiometry, which is fixed by the number of sites, the coupling ratio (i.e., the ratio of Na+ extruded to K+ taken up) can vary depending on ionic conditions (25). Under normal physiological conditions, the coupling ratio is three Na+ pumped out to two K+ pumped into the cells.

The Na+-K+-ATPase shows a high degree of homology to other P-type ATPases, which include the sarcoplasmic reticulum Ca2+-ATPase and the H+-K+-ATPase, found in stomach and colon (17). Site-directed mutagenesis studies of the sarcoplasmic reticulum Ca2+-ATPase (7) have suggested that six polar, oxygen-containing residues, predicted to reside within the transmembrane domains, appear to comprise the high-affinity binding site for Ca2+. Four of these residues are conserved in the Na+-K+-ATPase, where they correspond in the rat alpha 2-isoform to Glu-327 and Glu-778, Thr-806, and Asp-807.

Both chemical modification (15) and site-directed mutagenesis (27) have been used to elucidate the mechanism by which Na+ and K+ are transported against their concentration gradients and to identify and locate specific amino acids involved in this transport process. N, N'-dicyclohexylcarbodiimide has been used to modify the carboxyl side chains of Glu and Asp. The results of these studies suggested that the conserved Glu, corresponding to residues 953 and 327 of rat alpha 2-isoform, are sites of modification by N, N'-dicyclohexylcarbodiimide (15) and thus potential cation binding sites. Another carboxyl-modifying reagent, 4-(diazomethyl)-7-(diethylamino)coumarine, identified Glu-779 (corresponding to residue 778 in rat alpha 2) as a possible cation binding site (2).

Lingrel and co-workers (35, 40) have developed a strategy to study site-directed mutations in Na+-K+-ATPase. This consists of introducing substitutions into a cDNA for a ouabain-insensitive enzyme, followed by transfection of the cDNA into HeLa cells, which have an endogenous enzyme that is ouabain sensitive (35). Cell growth in the presence of 1 µM ouabain is then used as an indication that the transfected enzyme is capable of functioning as a pump. Using site-directed mutagenesis, Van Huysse and Lingrel (40) showed that Glu-955 and Glu-956 of the rat alpha 1-subunit (corresponding to Glu-952 and Glu-953 of rat alpha 2-subunit) are not essential for enzyme function and that substitution of Gln or Asp at these positions had very little effect on the cation dependence of ATPase activity. Substitution in rat alpha 2 modified to be ouabain resistant (rat alpha 2*; see Mutagenesis and cloning below) of Glu-778 and Asp-807 with Leu and of Asp-803 with Leu, Asn, or Glu caused inactivation of the enzyme (19). Substitution of Asp-925 with Leu or Asn yielded functional enzymes. The Leu substitution caused a twofold increase in the concentration of K+ that stimulated enzymatic activity 50% (K1/2), but the Asn substitution decreased the K1/2 for K+. Substitution of Glu 327 with Ala or Asp failed to yield functional enzymes, whereas substitution of this position with Gln or Leu yielded functional enzymes with lower apparent affinities for both Na+ and K+ (9, 19, 41). Thus Glu-327 and Glu-778 and Asp-803, Asp-807, and Asp-925 of rat alpha 2 might comprise at least a portion of the cation binding site. The purpose of the present study was to determine the effects of mutations at Glu-327 on the ability of the mutated enzyme to pump Rb+ into intact cells.

    MATERIALS AND METHODS
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

Materials. 86Rb+ was purchased from DuPont-NEN. The specific radioactivity varied from ~2 to 10 mCi/mg. Ouabain and furosemide were from Calbiochem or Sigma. Scintillation fluid (Scintiverse BD) was from Fisher. Cell culture supplies were purchased from GIBCO, Life Technologies, Sigma, and Fisher. All other reagents [NaCl, KCl, tris(hydroxymethyl)aminomethane (Tris) base, HCl, phosphoric acid, and MgCl2] were from Fisher.

Mutagenesis and cloning. The mutated rat alpha 2-isoform referred to as rat alpha 2* has been modified by the substitution of Arg for Leu at residue 111 and Asp for Asn at residue 122 (using the rat alpha 2 numbering system) at the borders of the first intracellular domain (34). This makes rat alpha 2* resistant to ouabain [concentration for 50% inhibition (IC50) is ~50 µM]. Site-directed mutagenesis was used to make further mutations at position 327 as previously described (19). E327Q signifies that Glu-327 (using the rat alpha 2 numbering system) has been replaced by Gln. E327L signifies that Glu-327 has been replaced by Leu.

Culture of HeLa cells. Wild-type HeLa cells and HeLa cells transfected with the rat alpha 2* mutants were maintained in Dulbecco's modified Eagle's medium with 10% calf serum, 100 U/ml penicillin, 0.1 mg/ml streptomycin, and 250 ng/ml amphotericin B, incubated at 37°C in a 5% CO2 atmosphere. Unless otherwise indicated, transfected cells were maintained in 1 µM ouabain.

Rb+ uptake assay and ouabain dose response. Native HeLa cells transfected with rat alpha 2* were plated at 3 × 104 cells/ml in 24-well tissue culture plates (1 ml/well). The effect of ouabain on 86Rb+ uptake by cells transfected with rat alpha 2* was determined. Cells were incubated until about 80% confluent (both in the absence and presence of 1 µM ouabain) and then rinsed with phosphate-buffered saline (PBS; in mM: 135 NaCl, 3.5 KCl, 0.5 CaCl2, 0.5 MgCl2, 5 glucose, 6.5 Na2HPO4, and 1.5 KH2PO4) and incubated with PBS containing the indicated ouabain concentrations for 30 min at 37°C. 86Rb+ was then added at ~2 µCi/ml, and cells were incubated for 10 min at 37°C. The concentration of 86Rb+ ([86Rb+]) typically ranged from 2 to 15 µM. The incubation was stopped by submerging the plate in an ice-cold solution of 0.9% NaCl and 5 mM N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (pH 7.4). The wells were then rinsed eight times in this solution. Total rinse time was <1 min. Cells were extracted with 0.5 ml of 0.2 N NaOH for 1 h and then neutralized with HCl before counting. Samples were counted in a Packard Tricarb liquid scintillation analyzer (model 2000CA), which has an efficiency for 86Rb+ of 97%. Each data point represents the average of the radioactivity present in four separate wells. Protein concentration was determined by the method of Lowry et al. (28).

Rb+ uptake competition assay. For routine experiments, all solutions contained 1 µM ouabain and 1 mM furosemide. Cells were preincubated in PBS containing ouabain and furosemide for 30 min at 37°C. The cells were rinsed with K+-free PBS (in mM: 135 NaCl, 0.5 CaCl2, 0.5 MgCl2, 5 glucose, 6.5 Na2HPO4, and 1.5 NaH2PO4) or K+-free low-Na+ PBS (in mM: 135 choline chloride, 0.5 CaCl2, 0.5 MgCl2, 5 glucose, 6.5 Na2HPO4, and 1.5 NaH2PO4). The cells were then changed to prewarmed PBS or low-Na+ PBS varying in [K+] as indicated. 86Rb+ was immediately added and incubated for various times up to 30 min. Because these rates of uptake were always linear up to 15 min for all combinations of external ion concentrations, the majority of the experiments were carried out for a single time of 10 min. Cells were rinsed and extracted as described in the previous paragraph. In some experiments, 4 mM monensin, a Na+ ionophore, was used during the K+ competition assays to stabilize the internal [Na+] during the course of the incubation.

Measurement of internal [Na+]. To determine the amount of internal Na+, cells were grown on 100-mm dishes and treated exactly as above, but without 86Rb+. After 10 min, the cells were washed with an ice-cold solution containing (in mM) 135 choline chloride, 5 glucose, 0.5 MgCl2, 0.5 CaCl2, and 15 Tris phosphate (pH 7.4). The cells were then scraped from the plates and suspended in water. The [Na+] of the lysates was measured using an International Laboratories IL353 double-beam atomic absorption spectrophotometer. The concentrations were normalized to protein levels determined by the method of Lowry et al. (28).

Data analysis. Data were plotted and curve fits obtained using KaleidaGraph by Abelbeck Software. The KaleidaGraph program uses the Levenberg-Marquardt algorithm for nonlinear curve fitting. Parameter values were constrained to be nonnegative. Starting values for the parameters were determined from examination of the plots and systematically varied. The initial estimates did not affect the parameter values obtained on convergence. Equations for the curve fits are given in the APPENDIX. Nonspecific uptake is defined as the amount of 86Rb+ associated with the cells in the presence of excess unlabeled competing ligand (100 mM KCl) and was obtained in some cases by direct measurement or, in the case in which K+ was varied over a wide range, by fits to the models. The use of "constant percent" error is well established for weighting radioligand binding data (29). The data of the present study were therefore weighted using the reciprocals of the weighting factors (w) calculated from the equation
<IT>w</IT> = (SD)<SUP>2</SUP> = <IT>C</IT> × (CPM)<SUP>2</SUP> (1)
where CPM is the mean amount of radioactivity taken up per well for quadruplicate determinations at each [K+]. Suspected outliers (<1% of total replications) among the quadruplicates were discarded on the basis of a Q-test (16). The coefficient C of Eq. 1 was determined by an error analysis of several months of experiments. From a total of 885 measurements of Rb+ uptake, each determined in quadruplicate, the square of the SD for these measurements was plotted against the square of the mean CPM bound. A fit to Eq. 1 gave the value 0.00928 for C (equivalent to a constant percent error of 9.63%). The goodness of fit was assessed by comparing the data to the curve predicted by the model. It was evaluated in terms of the size of the parameter errors, the chi 2 value, and the number of runs, where a run is the change of sign of the residual. The greater the number of runs, the better the fit. The probability that the distribution of the runs was random was determined using published tables (8). Student's t-test was used to determine that parameter values were statistically different.

    RESULTS
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Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

The experiments reported here assessed the effect of external K+ on the steady-state net uptake of 86Rb+ by HeLa cells. The term "uptake" is used to describe the radioactivity [in counts/min (cpm) of 86Rb+] accumulated by the cells in 10 min. Because the apparent affinities for activation of ATPase activity by the two ions are virtually identical (4), it has been assumed that K+ is a congener of Rb+. If it is assumed that the apparent binding constants for transport and the influx rate constants for Rb+ and K+ are also identical, one can estimate the steady-state unidirectional influx of the sum of 86Rb+ and unlabeled K+, referred to in this article as "total influx." To calculate the unidirectional influx of K+ plus 86Rb+, it is necessary to calculate the specific radioactivity at each [K+]. The assumption here is that adding K+ is equivalent to adding unlabeled Rb+. The specific radioactivity as a function of [K+] is equal to the specific radioactivity of carrier-free 86Rb+ multiplied times the factor [86Rb+]/([86Rb+]+[K]). The uptake of 86Rb+ can be converted to total influx of K+ plus 86Rb+ by dividing the uptake (units of cpm/10 min) by the specific radioactivity (units of cpm/pmol) at each [K+]. If contaminating K+, which might be present in the water and reagents (estimated to be, at the highest, 5 µM), were comparable to the [86Rb+] (2-30 µM), it could affect this calculation. We emphasize that this calculated total influx is not the net rate of K+ transport, since it does not take efflux of K+ or 86Rb+ into account. The efflux of 86Rb+ will be negligible during the assay period because of the high [K+] in the cell. There may be, however, some K+ efflux, as the result of K+-K+ exchange. Influx rate constants, used in the expressions for uptake (U), are assumed to include all steps beyond the binding of the ion to the external site, i.e., occlusion and deocclusion.


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Fig. 1.   Ouabain dose response in HeLa cells. Native HeLa cells were preincubated for 30 min at 37°C in phosphate-buffered saline (PBS) containing indicated ouabain concentration and 1 mM furosemide (bullet ) or no furosemide (black-square). After addition of 2 µCi/ml 86Rb+, cells were further incubated for 10 min at 37°C. Incubation was stopped and cells were rinsed as described in MATERIALS AND METHODS. Data are means ± SE of 4 determinations; cpm, counts/min. Data were fit to Hill equation with Hill coefficient constrained to be 1. Concentration for 50% inhibition (IC50) for ouabain was 0.140 ± 0.022 µM in absence of furosemide and 0.244 ± 0.026 µM in presence of furosemide.

The rat alpha 2*-isoform is a modified form of Na+-K+-ATPase, designed to be insensitive to ouabain so that functional activity of the endogenous HeLa enzyme (which has a high affinity for ouabain) can be eliminated by use of low concentrations of ouabain. Preliminary experiments with the parental HeLa line were carried out to determine a concentration of ouabain that would eliminate 86Rb+ uptake due to the endogenous HeLa Na+-K+-ATPase. Uptake of 86Rb+ is significantly inhibited by increasing concentrations of ouabain, with an IC50 of ~140 nM (Fig. 1). At saturating concentrations of ouabain, however, there is still significant 86Rb+ uptake. A transport system that could be responsible for this ouabain-independent 86Rb+ uptake is the Na+-K+-Cl- cotransporter (24). This cotransporter is inhibited by bumetanide or furosemide. Figure 1 shows that, in the presence of 1 mM furosemide, essentially all 86Rb+ uptake in parental HeLa cells was blocked by the addition of 1 µM ouabain (IC50 for ouabain is 244 nM). Approximately 40% of the 86Rb+ uptake is sensitive to furosemide but insensitive to ouabain. The IC50 for inhibition of 86Rb+ uptake by ouabain in these experiments, 140-240 nM, is consistent with the known sensitivity of the human alpha 1-isoform present in HeLa cells. Subsequent experiments were carried out in the presence of 1 mM furosemide plus 1 µM ouabain to eliminate (>95%) uptake by endogenous HeLa Na+-K+-ATPase.

Figure 2 shows a ouabain dose-response curve for HeLa cells transfected with the rat alpha 2* cDNA and cultured in the absence or presence of 1 µM ouabain. Uptake of 86Rb+ was followed in the presence of 1 mM furosemide and 5 mM K+. The dose-response curve for the cells grown in the absence of ouabain is clearly biphasic, with IC50 values for the two components of 70 ± 2 nM and 240 ± 60 µM. The higher affinity component is the endogenous HeLa Na+-K+-ATPase, since its IC50 is close to that for HeLa cells alone (cf. Fig. 1). For the cells grown in the presence of 1 µM ouabain, uptake by the endogenous HeLa Na+-K+-ATPase is inhibited, and therefore only one component, with an IC50 of 150 ± 30 µM, is detected, consistent with it being the transfected ouabain-insensitive rat alpha 2* Na+-K+-ATPase. The magnitudes of the components are approximately the same, suggesting that the amount, or at least the activity, of the transfected enzyme is equal to the endogenous HeLa Na+-K+-ATPase. Thus the 86Rb+ uptake observed in the presence of 1 mM furosemide and 1 µM ouabain represents uptake by the rat alpha 2* (transfected) enzyme.


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Fig. 2.   Ouabain dose response in cells transfected with rat alpha 2 modified to be ouabain resistant (rat alpha 2*). HeLa cells transfected with rat alpha 2* were grown for 2 days in presence (bullet ) or absence (black-square) of 1 µM ouabain. Incubations in various ouabain concentrations were then carried out as described in Fig. 1. All solutions contained 1 mM furosemide. Data are means ± SE of 4 determinations. Data were fit to a 1- or 2-compartment Hill inhibition equation as for Fig. 1, with Hill coefficients constrained to be 1.

The effect of varying external [Na+] and [K+] on uptake kinetics was examined over a 20-min period. Figure 3 indicates that in the presence of 15 mM external Na+ (low-Na PBS), the time course of 86Rb+ uptake into HeLa cells was linear for at least 15 min at all [K+] tested. Figure 3 shows the rate of uptake of 86Rb+ at three different external [K+]. The highest rate of uptake is observed at 0.5 mM K+, with lower rates observed both at 0.01 mM and at 4 mM. The intercepts of the plots were not different from those of nonspecific uptake determined in the presence of 100 mM K+, suggesting that there is neither a lag time nor an initial burst in the uptake. The rate of uptake in the presence of 150 mM external Na+ was also linear. The cells used in the experiments shown were transfected with E327Q; likewise, cells transfected with either rat alpha 2* or E327L (in 15 and 150 mM Na+) also showed this linear relationship at a variety of external [K+] (data not shown). Having demonstrated the linearity of the uptake over the range of external [Na+] and [K+] employed, subsequent experiments were done at a single time point of 10 min.


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Fig. 3.   Time course of 86Rb+ uptake. HeLa cells transfected with E327Q were assayed for 86Rb+ uptake in presence of PBS containing 15 mM NaCl, 1 mM furosemide, and 1 µM ouabain. [K+] were 0.01 mM (open circle ), 0.5 mM (black-square), and 4.0 mM (black-lozenge ). Data are means ± SE of 3 determinations. Data were fit to a linear equation. Slopes were as follows: 74.7, 529, and 117 cpm/min for external [K+] of 0.01, 0.5, and 4.0 mM, respectively. This corresponds to a total K+ influx of 0.598, 47.7, and 78.0 pmol/min, respectively.

Figure 4 shows uptake of trace amounts of 86Rb+ in the presence of increasing amounts of K+ (K+ competition curve). The data clearly do not fit to a conventional Hill equation, since the competition curve predicted by the Hill equation is monophasic. As K+ is increased from the lowest concentrations, the amount of 86Rb+ uptake in 10 min increases. As the concentration of competitor continues to increase, there is a decrease in 86Rb+ uptake. This is consistent with Fig. 3, which shows that, at the lowest external [K+] shown, there was a relatively low rate of 86Rb+ uptake. At 0.5 mM external K+, the peak of stimulation under the conditions of this experiment (15 mM Na+), the highest rate of 86Rb+ uptake is observed.


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Fig. 4.   Effect of external K+ on 86Rb+ uptake. HeLa cells transfected with rat alpha 2* were assayed for 86Rb+ uptake in presence of various [K+], as indicated, and PBS containing 150 mM Na+, 1 mM furosemide, and 1 µM ouabain. Data are means ± SE of 4 determinations. Data were fit to a Hill inhibition equation (dashed line). Fitted parameters (± SE) were IC50 = 4.85 ± 0.38 mM and Hill coefficient = 2.73 ± 0.33. Data were also fit to the ordered binding model (model IIA1) described in Eq. A3 (solid line). Fitted parameters for this fit were dissociation constants K1 = 2.77 ± 0.23 mM and K3 = 0.420 ± 0.112 mM.

Changing the external K+ solution to anything other than 5 mM could have caused an immediate change in membrane potential. Although the degree of change is not expected to have a significant effect on the activity of the pump (36), any change in membrane potential could, in theory, be followed by a slower increase in internal [Na+]. To test the possibility that the internal [Na+] was changing over the time course of our experiments, the effect of external K+ on internal Na+ was monitored using atomic absorption spectroscopy. The [Na+] (normalized to protein concentration) does not vary significantly over the range of [K+] in which the peak of stimulation of uptake is observed (Fig. 5). The results shown are for E327Q and are analogous to those obtained for all cell lines investigated. Thus the observed stimulation of uptake cannot be explained by changes in internal [Na+]. Further evidence for this conclusion was obtained by conducting a K+ competition experiment in the presence of 4 µM monensin (data not shown). The degree of stimulation of uptake in the presence of monensin and 15 mM external Na+ was comparable to the stimulation in the absence of monensin. This suggests that stimulation of uptake was not a result of changes in internal [Na+]. In addition, the linearity of Fig. 3 is consistent with the concept that we have maintained steady state over the 10-min time period of the experiments. If the uptake were increasing over a 10-min period, one would expect the curve to be parabolic.


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Fig. 5.   Effects of external K+ on 86Rb+ uptake and content of internal Na+. HeLa cells transfected with mutant E327Q were assayed for 86Rb+ uptake as described for Fig. 4 (black-square). In a parallel experiment, internal Na+ was monitored (by atomic absorption spectroscopy) in cells incubated with various external [K+] (open circle ). Amount of Na+ was normalized to cell protein as determined by method of Lowry et al. (28). Data are means ± SE of 4 determinations. Horizontal line indicates average [Na+] at 5 mM external K+ as a point of reference.

To determine whether the nature of the external competitor makes a difference in the apparent stimulation of Rb+ uptake, the competing K+ was replaced by unlabeled Rb+. The dissociation constants determined with unlabeled Rb+ were within 1 SD of those determined with K+ as the competitor (data not shown), suggesting that Rb+ and K+ are interacting with the binding site with similar affinities.

In all the experiments so far described, the procedure for varying the [K+] was that a K+-free PBS solution was made. Various amounts of a 1 M KCl solution were added to this to achieve the specific [K+]; thus ionic strength varied somewhat in different samples. To test whether these variations in ionic strength had any effect on the dissociation constants, an experiment was carried out in which ionic strength was maintained constant by addition of choline chloride to the incubation solutions (choline chloride + KCl = 50 mM). The values for the dissociation constants determined in this experiment were no different from those seen in the routine experimental design (data not shown).

To test whether the stimulation of 86Rb+ uptake by K+ is due to the activity of the Na+-K+-ATPase, the effect of ouabain on the system was determined (Fig. 6). When the effect of K+ on 86Rb+ uptake was determined in the presence of 1 µM ouabain, the standard conditions for these experiments, stimulation was observed. In the presence of 10 mM ouabain, the 86Rb+ uptake is reduced almost to background, indicating that the stimulating component is due to activity of the Na+-K+-ATPase.


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Fig. 6.   Effects of ouabain on Rb+ transport. HeLa cells transfected with rat alpha 2* were incubated with 1 mM furosemide and either 1 µM (bullet ) or 10 mM (black-square) ouabain. K+ effects on 86Rb+ transport were determined as described for Fig. 4. Data are means ± SE of 4 determinations. Parameter values for fit to model IIA1 in absence of ouabain were K1 = 2.09 ± 0.16 mM, K3 = 0.58 ± 0.17 mM, maximum uptake (Umax) = 1.06 ± 0.08 × 107 cpm, and nonspecific uptake constant (NS) = 1.39 ± 0.24 × 106; chi 2 = 8.7.

The degree of stimulation of 86Rb+ uptake by K+ is greater with the E327Q mutation than with rat alpha 2* (Figs. 5 and 7 vs. Figs. 4 and 6). We therefore attempted to fit the data to models that predict both stimulatory and inhibitory phases. We considered 11 models, which are described in detail in the APPENDIX. Two models (see DISCUSSION) were eliminated because they did not show stimulation of uptake. Fits to the remaining nine models were applied to data obtained from eight separate experiments with mutant E327Q (external Na+ = 150 mM) and are shown in Table 1. The chi 2 values and the number of runs are also shown in Table 1. The fact that the chi 2 values for our fits were approximately equal to the degrees of freedom (Table 1) indicates that the weighting scheme employed is appropriate (33). The data set used in Fig. 7 is experiment 6 (Table 1).


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Fig. 7.   Comparison of fits to 9 models of 86Rb+ uptake. HeLa cells transfected with mutant E327Q were assayed for 86Rb+ uptake as described for Fig. 4. A: fits to 3 models with cation dissociation constants described in terms of a single effective dissociation constant. Parameters for fit to ordered model IIC2 (solid line) were K1 = 1.35 ± 0.11 mM, Umax = 4.83 ± 0.55 × 106 cpm, and NS = 2.48 ± 0.12 × 105. For fit to random model IC2 (dashed line) parameters were K1 = 1.22 ± 0.11 mM, Umax = 2.73 ± 0.33 × 106 cpm, and NS = 2.40 ± 0.12 × 105. For simultaneous model III (dotted line) parameter values were K1 = 1.49 ± 0.11 mM, Umax = 3.84 ± 0.41 × 106 cpm, and NS = 2.64 ± 0.11 × 105. B: fits to 2 models in which both binding and transport are infinitely cooperative. Parameters for fits to ordered model IIC1 (solid line) were K1 = 13.0 ± 4.1 µM, K3 = 37.3 ± 18.4 mM, Umax = 5.31 ± 3.60 × 107 cpm, and NS = -1.06 ± 1.51 × 105. Parameters for fit to random model IC1 (dashed line) were K1 = 1.70 ± 1.08 mM, K3 = 0.963 ± 0.612 mM, Umax = 2.58 ± 0.66 × 106 cpm, and NS = 2.45 ± 1.74 × 105. Data also converged to negatively cooperative parameters as follows: K1 = 4.00 ± 2.96 µM, K3 = 41.1 ± 32.3 mM, Umax = 7.83 ± 9.88 × 107 cpm, and NS = -4.04 ± 4.67 × 105. C: fits to 2 models in which transport is noncooperative and binding is cooperative. Ordered model IIA1 (solid line) had parameter values of K1 = 17.2 ± 1.29 mM, K3 = 0.695 ± 0.140 mM, Umax = 1.01 ± 0.12 × 107 cpm, and NS = 9.10 ± 2.31 × 104. Random model IA1 (dashed line) had parameter values of K1 = K2 = 18.1 ± 1.3 mM, K3 = 0.646 ± 0.127 mM, Umax = 5.44 ± 0.67 × 106 cpm, and NS = 8.27 ± 2.45 × 104. D: fits to models in which transport is cooperative and binding is noncooperative. Ordered model IIB1 (solid line) had parameter values of K1 = 3.29 ± 0.39 mM, f (ratio of influx rate constants) = 6.54 ± 0.73, Umax = 1.36 ± 0.17 × 107 cpm, and NS = 5.69 ± 2.69 × 104. Random model IIB1 (dashed line) had parameter values of K1 = 3.219 ± 0.41 mM, f = 8.14 ± 0.86, Umax = 9.14 ± 1.33 × 106 cpm, and NS = 1.74 ± 3.27 × 104. Data are means ± SE of 4 determinations.

                              
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Table 1.   Summary of fits to models

Figure 7A shows fits to the three models in which the binding of K+ is described in terms of a single dissociation constant (K1). The K1 for E327Q usually had a value of 1-2 mM in the presence of 150 mM Na+. These three models assume either infinitely cooperative binding (model III) or infinitely cooperative transport with noncooperative binding (models IC2 and IIC2). For all three models, transport by definition occurs only when two cations (K+ or Rb+) are bound. The shapes of the fits are similar to the actual data, and the errors in the parameters are reasonable. The chi 2 values are, however, unacceptably high (>100), along with a very low number of runs (Table 1), and the models were therefore rejected on this basis.

When the possibility of infinitely cooperative transport with cooperative binding was allowed (models IC1 and IIC1), the unrestrained weighted fits indicated negative cooperativity, i.e., the binding of the second K+ (K3 = 40-70 mM) had a much lower apparent affinity than the first (K1 = 0.01-0.02 mM). The shape of the curve was very different from the data points (Fig. 7B). With the exceptions of experiments 4 and 8 (Table 1), these fits had very large chi 2 values and a low number of runs compared with the models that assume that enzyme with either one or two K+ bound can transport. With some data sets, under some conditions (e.g., nonweighted fits, exclusion of nonspecific binding from the fits), convergence could also be obtained in which the binding was positively cooperative. These fits, however, also had large chi 2 values and unacceptable errors in the parameters. These infinitely cooperative transport models were therefore rejected.

Figure 7C shows fits to random and ordered models (models IA1 and IIA1) in which transport is noncooperative. On the basis of criteria of parameter errors, chi 2, and runs, these two models clearly fit well to all the data. For these two models, the binding is always positively cooperative. Figure 7D shows fits to cooperative transport models (models IB1 and IIB1; f1 not equal  f2; f = f2/f1; where f1 is the flux constant for the singly occupied species and f2 is the flux constant for the doubly occupied species, with units of time-1, and f is the ratio of influx rate constants) in which the binding of K+ is assumed to be noncooperative (K1 = K3). The f is always >1. That is, doubly occupied enzyme transports faster than singly occupied enzyme. Table 2 summarizes the analyses of the wild type and E327 mutants in terms of binding constants or in terms of varying ratios of influx rate constants.

                              
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Table 2.   Fits of E327 mutants and wild-type alpha 2* to Rb uptake models

Of the models that we tested, whether cooperative binding or cooperative transport, the only models that fit the data were models that allow transport with one or two K+ bound (variable coupling models). In all of the variable coupling models, the numerator for the equation for transport contains both [K+] and [K+]2 terms. In all of the fixed ratio models (models that allow transport only when 2 K+ are bound), the numerator contains only [K+]2 terms. Thus, at [K+] much less than the dissociation constant the total influx is linearly dependent on [K+], whereas in the fixed ratio models the total influx is linearly dependent on [K+]2. Data from uptake experiments were therefore transformed to total influx and plotted against [K+] and [K+]2. Figure 8 shows that uptake is a linear function of K+, consistent with variable ratio models. Identical results were obtained with the other mutants.


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Fig. 8.   Relationship of transport to external [K+]. HeLa cells transfected with rat alpha 2* were monitored for uptake of 86Rb+ as described in Fig. 4. Specific radioactivity for each [K+] was determined as disintegrations · min-1 · pmol-1 [86Rb+/(Rb+ + K+)]. Total influx was calculated by dividing uptake (disintegrations · min-1 · 10 min-1) at each concentration by specific radioactivity. Values were plotted vs. [K+ + Rb+]2 (A) and vs. [K+ + Rb+] (B). Data were fit to linear regression equations: for A, y = 18.9 + 3,161x, R = 0.989; for B, y = -9.02 + 781x, R = 0.995.

The effect of external Na+ on 86Rb+ uptake was determined. Experiments were carried out at an external [Na+] of 15 mM rather than the 150 mM present in PBS. Figure 9 shows the results of lowering external [Na+] on 86Rb+ uptake by the E327Q mutant: a higher level of 86Rb+ uptake was observed at the lower [Na+]. Whether the data were fit to the cooperative binding model (model IIA1) or cooperative transport model (model IIB1), the apparent affinity for K+ was increased at the lower [Na+]. These results are consistent with the fact that external Na+ competes with external K+ for transport. Similar effects were seen with the other transfectants tested. In all cases, lowering the external Na+ decreased the apparent binding constant(s) for K+ (Table 2).


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Fig. 9.   Effect of external Na+ on 86Rb+ uptake. E327Q-transfected cells were assayed for effects of external K+ as in Fig. 4. External Na+ was held at either 150 mM (bullet ) or 15 mM (black-square). For experiments in low Na+, osmolarity was maintained by addition of choline chloride. Data were fit to ordered binding model allowing 86Rb+ transport with either 1 or 2 ions bound to enzyme. For cells incubated in 150 mM Na+, parameter values for fit to model IIA1 (solid line) were K1 = 17.5 ± 1.3 mM, K3 = 0.685 ± 0.140 mM, Umax = 4.52 ± 0.52 × 106 cpm, and NS = 4.09 ± 1.04 × 104. Parameter values for fit to model IIB1 (dashed line) were K1 = 3.29 ± 0.39 mM, f = 6.66 ± 0.77, Umax = 6.12 ± 0.77 × 106 cpm, and NS = 2.55 ± 1.21 × 104. For low-Na+ experiments, parameter values for fit to model IIA1 (solid line) were K1 = 3.14 ± 0.23 mM, K3 = 0.147 ± 0.025 mM, Umax = 4.38 ± 0.24 × 106 cpm, and NS = 8.37 ± 6.01 × 103. Parameter values for fit to model IIB1 (dashed line) were K1 = 0.537 ± 0.044 mM, f = 7.40 ± 1.07, Umax = 4.82 ± 0.28 × 106 cpm, and NS = 2.71 ± 6.36 × 103. Data are means ± SE of 4 determinations.

    DISCUSSION
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

The 86Rb+ uptake methodology used for these experiments has a very good signal-to-noise ratio; in the presence of furosemide and ouabain, 86Rb+ uptake is essentially completely inhibited to the nonspecific level (Figs. 1 and 2). In addition, the utilization of intact cells simplifies interpretation of the results, since, unlike fragmented membrane preparations, the concentrations of ions on the extracellular side can be varied independently of the concentrations on the intracellular side. This enables testing of more complex models (cf. APPENDIX) of transport than has previously been done with mutated Na+-K+-ATPase. The primary experimental result that had to be rationalized was the stimulation of 86Rb+ uptake at low concentrations of unlabeled competitor (Figs. 4-7). The peak of stimulation of 86Rb+ uptake occurs at ~1 mM external K+. The subsequent decrease of 86Rb+ taken up occurs because the two sites become occupied by nonradioactive competing ligand.

A portion of the observed stimulation of uptake of 86Rb+ might have resulted from changes in the membrane potential as a result of the variations in external K+. Such a change could have two consequences, a direct effect of the membrane potential change on the activity of the pump and/or an indirect effect on pump activity due to changes in intracellular [Na+]. The latter possibility was tested by monitoring the internal [Na+] in different external [K+]. As shown in Fig. 5, the [Na+] (normalized to protein concentration) did not vary significantly over the range of [K+] in which the peak of stimulation of uptake is observed. It has been shown that changes in resting membrane potential independent of changes in internal Na+ can affect the pump turnover number. For example, at constant external K+, depolarization of resting membrane potential caused a slight monotonic increase in steady-state pump current (3). On the basis of previous reports (1, 22), we have estimated the expected membrane potentials at various [K+] and the expected changes in current that would result. For rat alpha 2* cells, 86Rb+ uptake is relatively flat up to 0.1 mM and reaches a peak at ~1 mM. As the external K+ is changed from 0.1 to 1 mM, the change in resting membrane potential would be approximately -79.4 to -76.4 mV (3.8%). This would, by itself, directly increase the pump current by 7.6% (3). The uptake of 86Rb+ increases by 43% over this same change in [K+], and the unidirectional influx increases 16-fold. Therefore, although the change in membrane potential does directly influence the pump turnover rate, the effect is small compared with the effect of K+ on unidirectional flux. Changes in membrane potential cannot account for the majority of the stimulation of 86Rb+ uptake that we observe.

A number of models were tested to determine how well they fit the data. In general, the models that we tested describe 86Rb+ uptake in terms of binding constants and influx rate constants. It should be emphasized that the models that were tested are no doubt simplistic compared with the actual transport model. For example, occlusion and/or deocclusion steps could not be included, since the more complex models incorporating these steps contain too many parameters for fitting. The term "noncooperative transport" refers to models in which transport can occur with one or two cations bound to the extracellular site and the influx rate constants are assumed to be the same for doubly and singly occupied enzyme. In these models, the binding can be either cooperative or noncooperative. The term "cooperative transport" refers to models in which either doubly or singly occupied enzyme can transport and the influx rate constants differ; i.e., transport can occur at different rates for singly or doubly occupied enzyme. In addition, the binding can be cooperative or noncooperative. "Infinitely cooperative transport" refers to models in which the flux for singly occupied enzyme is zero. That is, transport takes place only when two K+ are bound to the extracellular side of the pump. We make the assumption that the rate of uptake of K+ is proportional to the amount of K+ bound in a rapid equilibrium manner. This will be true even if the rapid binding of K+ is followed by a slower occlusion step, as suggested by Forbush (10). It should be pointed out that the binding and flux constants of our schemes are not necessarily intrinsic binding constants and may have embedded in them other rate constants of the transport cycle. They should therefore be considered apparent constants.

Uptake is also a function of the actual rate of movement of the bound ions across the membrane, which, in turn, is determined by any rate-limiting step or steps (e.g., occlusion of K+) that follow the binding of K+. Because the influx rate constant for the singly occupied species could be different from that of the doubly occupied species, the uptake rate is a function of the two influx rate constants and the amount of singly occupied and doubly occupied enzyme (E): transport = f1[EK] + f2[KEK]. Because there is a flux term in both the denominator and numerator of the equation used for fitting, one cannot derive absolute values for the rate constants, but only ratios.

Of the 11 models tested, 2 were eliminated because they could not show stimulation of uptake. These were random and ordered models in which neither transport nor binding was cooperative. Of the remaining nine models (shown in Table 1), five can be eliminated on the basis of statistical criteria for goodness of fit, including chi 2 and the runs tested.

The simplest models that allow stimulation of 86Rb+ uptake are infinitely cooperative transport or infinitely cooperative binding models in which the binding of K+ is described by a single effective dissociation constant (Fig. 7A). For example, early studies (12) of 86Rb+ uptake were analyzed using either 1) models that assume the presence of two infinitely cooperative binding sites, sometimes called simultaneous models, or 2) cooperative transport models consisting of two identical noninteracting, noncooperative binding sites. Implicit in the three models above (models III, IC2, and IIC2; see APPENDIX) is the concept that the transport process is infinitely cooperative; i.e., only enzyme that has two K+ (or Rb+) bound to external sites can undergo the transport process. In the infinitely cooperative binding model, this is because the apparent affinity of the enzyme for a second K+ is so high that there are effectively no singly occupied enzyme molecules present. For the infinitely cooperative transport models, the singly occupied species influx rate constant equals zero, reflecting no ion movement by singly occupied enzyme. These cooperative transport models, in which the binding of K+ is described by a single effective dissociation constant, did not fit our data (Fig. 7A and Table 1), although the apparent dissociation constant obtained from these fits (0.06-0.10 mM for rat alpha 2* in the presence of 15 mM external Na+) is not very different from those obtained from previous studies (0.14-0.40 mM in the absence of external Na+) in erythrocytes (13, 31, 32, 42). More recent 86Rb+ uptake studies of rat alpha 2* reported an apparent binding constant of 0.20 mM in the presence of 10 mM external Na+ (30). Infinitely cooperative transport in which the binding is cooperative (models IC1 and IIC1) also does not fit our data very well (Fig. 7B). Thus, of the models that we tested, those that require that external sites of the enzyme be filled with two K+ (or Rb+) before transport can occur (infinitely cooperative transport) do not fit our data, whether the binding of K+ is cooperative or noncooperative.

The four remaining models that do adequately fit the data describe the stimulation of 86Rb+ uptake by external K+ either in terms of cooperativity of binding (Fig. 7C) or cooperativity of transport (Fig. 7D). For the binding models described in the APPENDIX, two different possibilities were considered, random or ordered models. In these two binding models, transport can occur whether one or two K+ are bound to the external site. In support of this concept, at limiting [K+], total influx is dependent on [K+] not [K+]2 (Fig. 8). In physical terms, the random model would describe an enzyme with two separate binding sites for K+. The ordered model would suggest a binding pocket in which the two K+ bind in sequence. The random binding model contains one more parameter (an extra binding constant for K+) than the ordered model. It was always necessary to make the simplifying assumption that the two binding constants for K+ had the same apparent affinities to obtain convergence. In this case, the equations for the two binding models are almost identical. Therefore, the random and ordered models gave fits that were almost superimposable, and we cannot distinguish between the two binding models. The remainder of the discussion is therefore limited to the less complex ordered binding model

With the ordered binding model, it is possible to get stimulation of uptake at low concentration of unlabeled competitor by either positive cooperativity of binding, positive cooperativity of transport, or a combination of both. Because we were unable to obtain satisfactory fits with the most general case (APPENDIX, scheme 2; K1 not equal  K3, f1 not equal  f2), we were forced to consider the two extreme cases: cooperative binding, noncooperative transport (K1 not equal  K3, f1 = f2) or noncooperative binding, cooperative transport (K1 = K3, f1 not equal  f2). When the results are described in terms of cooperative binding (Table 2), the only models that fit the data show positive cooperativity. This suggests that stimulation of 86Rb+ uptake by external K+ could be a result of the fact that the binding of the first K+ (or Rb+) increases the apparent affinity of the enzyme for the second ion. Enzyme with either one or two K+ can transport, and as external [K+] increases there will be more molecules capable of transport. This will cause an increase in the amount of 86Rb+ taken up. In contrast, describing the results in terms of cooperativity of transport (Table 2) suggests that the influx rate constant of the doubly occupied enzyme is greater than that of the singly occupied enzyme (f > 1). As the external [K+] increases, there are more doubly occupied enzyme molecules capable of this higher rate of transport; thus there is an increase in 86Rb+ uptake. The stimulation, of course, could also be caused by a combination of cooperativity in both transport and binding.

Data for K+ activation of ATPase activity (26) were fit best by a model that had two nonequivalent K+ sites with dissociation constants (extrapolated to 0 Na+) of 0.2 and 0.1 mM. Recent studies by Buhler and Apell (5) reject a simultaneous binding of two K+ to the extracellular face. Their data allowed a quantitative distinction between the binding of the first and second K+. Studies of K+-induced quench of fluorescein isothiocyanate-labeled enzyme (39) suggested that two K+ are bound before the conformational change can occur. The data (39) could then be fit either by an ordered model in which the binding was negatively cooperative or by a random binding model in which the two sites were independent and identical. Our data, in contrast, suggested that transport would occur with only one external site occupied and that the cooperativity was positive (K1/K3 = 4 for rat alpha 2*).

Cation transport is a complex process consisting of a series of steps such as binding, occlusion, and actual ion movement. The existence of half-occluded states, i.e., occlusion when only a single ion is bound, has been suggested by Forbush (11) in the development of his flickering gate model. Sachs (37) concluded earlier from steady-state kinetic analysis that movement of a lone 86Rb+ was possible in the absence of external Na+ when external Rb+ was limited. These findings are consistent with the concept that, unlike the stoichiometry, which is fixed by the number of sites, the coupling ratio (i.e., the actual flux of Na+ extrusion and K+ uptake) can vary depending on ionic conditions (25).

Analysis of our 86Rb+ uptake data did not allow us to distinguish between ordered or random binding. A study of inhibition by K+ of [3H]ouabain binding to purified sheep enzyme indicated, however, that an ordered binding model fit the data better than a random binding model (21). Other lines of investigation that distinguish between random and ordered binding of K+ include deocclusion experiments. Forbush (10) has suggested, on the basis of transient measurement of both 22Na+ efflux and 86Rb+ uptake within a single turnover cycle of the enzyme, that Na+-K+-ATPase has two distinct cation sites. He proposed a slow site and a fast site from which Rb+ is released. The release of the occluded ions is slow because a conformational change must occur before Rb+ can be released inside the cell. Because Rb+ in the fast site can exchange with Rb+ in the slow sites, this is consistent with a model in which the two external transport sites are located in the same region of the enzyme in a sort of "binding pocket."

A steady-state model for transport consistent with the findings of Forbush (11) is the ordered model (APPENDIX, model II). One can envision that the external cation transport site consists of a binding pocket into which two K+ (or Rb+) can fit. The first K+ binds with an apparent affinity K1. Binding of the first K+ so alters the force field in the pocket that the second K+ binds with a different apparent affinity, K3. For stimulation by external K+ to be observed in Rb+ uptake, K3 must be lower than K1, i.e., the binding must be positively cooperative. The degree of stimulation is dependent on the ratio of K1 to K3 (Table 2). Alternatively, the stimulation could be due to an increased rate of ion movement that occurs after the second K+ is bound. Finally, stimulation can be explained as some combination of cooperativity of binding and transport.

On the basis of chemical modification studies (15), it had been hypothesized that Glu-327 participates in coordinating K+. Site-directed mutagenesis studies (9, 19, 41) have shown that substitution of Glu-327 of the alpha 2-isoform with either Ala or Asp yielded enzyme that could not support cell viability (18). In contrast, substitution with either Gln or Leu yielded a mutated enzyme that was able to transport cations and maintain cell viability. From these results, it was concluded that neither the negative charge nor the carboxyl side chain at position 327 was absolutely essential for overall functioning of the enzyme. By examination of the cation activation of ATPase activity, it was shown that, under conditions of the experiments (30 mM Na+), mutant E327Q had a twofold lower apparent affinity for Na+ and a three- to sixfold lower apparent affinity for K+ (19). Mutant E327L had a fourfold lower apparent affinity for Na+ and a twofold lower apparent affinity for K+. It was suggested that the length of the side chain at position 327 might be important for enzyme function.

The effects of mutation at amino acid 327 as analyzed from 86Rb+ uptake data are consistent with those described previously. Both of the mutants (E327L and E327Q) have a reduced apparent affinity for the first K+. Table 2 provides the values for apparent binding constants that were calculated using the ordered, noncooperative transport model (model IIA1). Although all three cell lines show stimulation of 86Rb+ uptake by external K+, the two mutants show greater stimulation than the wild type, as reflected in higher ratios of K1 to K3. All three lines show positive cooperativity (K3 < K1). Table 2 provides the values of f calculated from the same data using the cooperative transport, noncooperative binding model (model IIB1). Again, compared with wild type, the mutants have a reduced apparent affinity for K+, as reflected in the increase in the average binding constant determined from the fit. In all three lines, the apparent influx rate constant for the doubly occupied enzyme, f2, is greater than that for the singly occupied enzyme, f1 (or f > 1). The reduced apparent affinity for K+ in activation of 86Rb+ uptake in mutants E327L and E327Q is in qualitative agreement with earlier studies of K+ activation of ATPase activity. In addition, our present studies, using intact cells, demonstrate altered apparent cation affinities, specifically for an external cation transport site. It should be emphasized that the binding constants and f are apparent and may have embedded in them other rate constants of the turnover cycle.

The degree of stimulation and the apparent affinity of the enzyme for K+ are functions of the specific enzyme (wild type or mutant) and of the external [Na+] (Table 2). With the assumption that Na+ is purely competitive with K+, the apparent intrinsic affinity of rat alpha 2* for K+ (extrapolated to 0 external Na+) would be 0.20 mM for the cooperative transport model. The apparent intrinsic affinity for Na+ would be 32 mM. Similar analyses for mutants E327Q and E327L yielded apparent intrinsic affinities of 0.32 and 0.4 mM for K+ and 18 and 8.4 mM for Na+, respectively. These values are not very different from each other and are consistent with previous studies in erythrocytes (13, 31, 32, 42) and fragmented enzyme preparations (26).

With the assumption that Na+ is a purely competitive inhibitor of K+ binding, there should be no effect of external Na+ on f for the two enzyme species capable of transport. Although the external [Na+] does not affect f for rat alpha 2* and E327Q, there was a threefold increase in f of E327L on lowering the [Na+] to 15 mM. This suggests that Na+ is not simply competing with K+ for the transport sites in the mutant but plays a more complex role. Cavieres and Ellory (6), as well as Sachs (37), have suggested the existence of an allosteric Na+ site that affects 86Rb+ uptake.

Although substitutions E327A and E327D expressed in HeLa cells produce nonfunctional Na+-K+-ATPase (19), the same mutants when expressed in NIH/3T3 cells are able to support [3H]ouabain binding (23), indicating that these mutations are able to insert into the membrane correctly. [3H]ouabain-binding experiments indicate that K+ interacts with the E327A mutant expressed in 3T3 cells with an affinity not very different from wild type (20, 23). K+ also interacts with the E327D mutant as probed by [3H]ouabain binding, although there is an activation rather than an inhibition. It was concluded from these studies that Glu-327 was important for stabilizing a K+-induced conformation within the catalytic cycle of the enzymatic cycle, which is normally not rate limiting. Removal of the charge alters the rate-limiting step. Interestingly, Vilsen (41) has suggested that the E327Q mutation has a large effect on the E2(K)-to-E1 transition.

Our 86Rb+ studies are consistent with these previous studies that suggest that, although Glu-327 is not essential for cation binding, it plays an important role. Although we cannot conclude that Glu-327 directly interacts with K+, it is clear that mutation to Gln or Leu alters the apparent affinity of the enzyme for the external transport site for K+. In addition, the present study has been able to test more complex models of enzyme mechanism than can be tested with isolated membrane preparations. Of the models that were tested, those that require that transport occur only when two K+ are bound gave the worst fits. Models tested that allowed transport to occur with either one or two K+ bound and that, in addition, showed positive cooperativity in either binding or transport gave reasonable fits.

    APPENDIX
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

Our data, consistent with previously published data, require models that involve two K+ (Rb+) sites per enzyme molecule. We have considered two binding schemes, random and ordered, as well as three transport schemes, cooperative, noncooperative, and infinitely cooperative. In schemes 1-3 and Eq. A1-A5 below, E represents the enzyme, Rb+ the labeled ligand, and K+ the competing unlabeled ligand. It is assumed that the dissociation constants (Kx) for Rb+ and K+ are identical (e.g., Kx for K+ is equal to Kx for Rb+). For all the models considered, it is assumed that 86Rb+ uptake is proportional to the amount of enzyme that has 86Rb+ bound.

Random Binding Models

The most general binding model, which under certain conditions allows for stimulation of uptake, is the random binding model (model I) shown in scheme 1 
<AR><R><C>RbERb </C><C>⇌</C><C> Rb<SUP>+</SUP> + </C><C>RbE + K<SUP>+</SUP> </C><C>⇌</C><C> RbEK</C></R><R><C>⥮<IT>K</IT><SUB>3</SUB></C><C></C><C></C><C>⥮<IT>K</IT><SUB>2</SUB></C><C></C><C>⥮<IT>K</IT><SUB>3</SUB></C></R><R><C>Rb<SUP>+</SUP></C><C></C><C></C><C>Rb<SUP>+</SUP></C><C></C><C>Rb<SUP>+</SUP></C></R><R><C>+</C><C><IT>K</IT><SUB>1</SUB></C><C></C><C>+</C><C><IT>K</IT><SUB>1</SUB></C><C>+</C></R><R><C>ERb </C><C>⇌</C><C> Rb<SUP>+</SUP> + </C><C>E + K<SUP>+</SUP> </C><C>⇌</C><C> EK</C></R><R><C>+</C><C></C><C></C><C>+</C><C></C><C>+</C></R><R><C>K<SUP>+</SUP></C><C></C><C></C><C>K<SUP>+</SUP></C><C></C><C>K<SUP>+</SUP></C></R><R><C>⥮<IT>K</IT><SUB>3</SUB></C><C></C><C></C><C>⥮<IT>K</IT><SUB>2</SUB></C><C></C><C>⥮<IT>K</IT><SUB>3</SUB></C></R><R><C>KERb </C><C>⇌</C><C> Rb<SUP>+</SUP> + </C><C>KE + K<SUP>+</SUP> </C><C>⇌</C><C> KEK</C></R></AR>
This model assumes that labeled Rb+ or unlabeled K+ binds randomly to two separate independent binding sites, each able to contain one K+ (or Rb+). In scheme 1, the two sites are represented by right and left designations, i.e., ERb or RbE with dissociation constants K1 and K2, respectively. Binding of the second cation to either the ERb or EK species has a dissociation constant, K3. Binding of the second cation to either the RbE or KE species would, therefore, have a dissociation constant equal to K1K3/K2.

If one assumes that all cation-containing species are capable of transport of the cation(s), then uptake of 86Rb+ radioactivity (U) is a function of all 86Rb+-containing forms. Mathematically, U = f1[ERb] + f2[RbE] + f3(2[RbERb] + [KERb] + [RbEK]), where f1, f2, and f3 are the first-order kinetic influx rate constants for transport through the membrane.

The maximal amount of uptake (Umax) is defined to be the amount of uptake that would occur if all of the enzyme present (Etotal) contained two 86Rb+. Mathematically, Umax = 2f3[Etotal]. U and Umax have the units cpm per 10 min. Nonspecific uptake is defined as the constant NS multiplied by [86Rb+]. Thus the term NS[Rb+] represents the amount of radioactivity (CPM) associated with the cells in the presence of a vast excess of specific competitor (K+). With these definitions, the general equation below (Eq. A1) represents the radioactive uptake under steady-state conditions, as described by a random binding model For model IA1, K1 = K2 not equal  K3 and f1 = f2 = f3; for model IB1, K1 = K2 = K3 and f1 = f2 not equal  f3.

Case A: noncooperative transport (f1 = f2 = f3 ). Equation. A1 contains eight parameters to be fit, which proved too many for convergence. To reduce the number of parameters, simplifying assumptions had to be made. One such assumption is that f1 = f2 = f3, in which case the influx rate constants drop out of the equation describing the uptake. Note that it is assumed transport can occur whether the enzyme has one or two cations bound. Attempts to fit the data to the general case (K1 not equal  K2) yielded parameter errors that were much larger than the parameters themselves, and convergence was obtained only if the initial estimates of K1 and K2 were similar. We therefore made a further simplification that K1 = K2. Whether one assumes that K1 = K2 or K1 not equal  K2, model I predicts stimulation of Rb+ uptake by low concentrations of unlabeled cation (K+) only if K3 is less than both K1 and K2 (i.e., positively cooperative binding). If it is assumed that K1 = K2, the amount of stimulation is dependent on the ratio of K3 to K1. The results of a fit of model IA1 to an experiment with mutant E327Q in the presence of 150 mM external Na+ is shown in Fig. 7C. Binding model I with K1 = K2 = K3 and f1 f2 = f3 cannot show stimulation, does not fit our data, and was not considered further.

Case B: cooperative transport (f1 = f2 not equal  f3 ). The assumption of this model is that transport can occur when the enzyme has either one or two cations bound. To reduce the number of parameters to be fit, it was assumed that f1 = f2 and that K1 = K2. Equation A1 is still the equation used to fit the data but unlike in case A yields a ratio of influx rate constants (f = f3/f1) as well as binding constants. Attempts to fit the data to the case K1 = K2 not equal  K3 yielded parameter errors that were much larger than the parameters themselves, and convergence was obtained only if the initial estimates of K1 and K3 were similar. With the assumption that K1 = K2 = K3, this model predicts stimulation of Rb+ uptake by low concentrations of unlabeled cation (K+) only if f is >1 (i.e., positively cooperative transport; Fig 7D).

Case C: infinitely cooperative transport (f1 = f2 = 0, f3 > 0). A version of the cooperative transport model assumes that only doubly occupied forms of the enzyme ([RbERb], [KERb], [RbEK], and [KEK]) are capable of transport (infinitely cooperative transport). This is equivalent to assuming that f1 and f2 are zero. Mathematically, U = f3(2[RbERb] + [KERb] + [RbEK]). Equation A1 can, therefore, be simplified to the equation used for the curve fitting of the uptake data. For model IC1, K1 = K2 not equal  K3; for model IC2, K1 = K2 = K3.

Stimulation of uptake occurs in this case because increasing K+ increases the concentration of the two species KERb and RbEK. Stimulation of uptake at low concentrations of competitor can occur whether or not the binding is cooperative. The degree of stimulation is determined by the relative values of K1 and K2 and the [86Rb+]; the greater the ratio K1/[Rb+], the greater the stimulation. Attempts to fit the data to the general case in which K1 not equal  K2 not equal  K3 yielded parameter errors much larger than the parameters themselves, and convergence was obtained only if the initial estimates of K1 and K2 were similar. Therefore, we have used the more restricted model K1 = K2. Stimulation of uptake at low concentrations of unlabeled cation (K+) will occur if K1 = K2 < K3 (negatively cooperative binding) or if K1 = K2 > K3 (positively cooperative binding). An example of a fit to model IC1 is shown in Fig. 7B (dashed-line). Stimulation also occurs if the binding is noncooperative (K1 = K2 = K3), as shown in Fig. 7A. Comparisons of the fits to all the models are summarized in Table 1.

Ordered Binding Models

A simplification of the random model illustrated in model I is an ordered binding model (model II) shown as scheme 2 
<AR><R><C></C><C><IT>K</IT><SUB>1</SUB></C><C></C><C><IT>K</IT><SUB>3</SUB></C></R><R><C>E + Rb<SUP>+</SUP> </C><C>⇌</C><C> ERb + Rb<SUP>+</SUP> </C><C>⇌</C><C> ERb<SUB>2</SUB></C></R><R><C>+</C><C></C><C> +</C></R><R><C>K<SUP>+</SUP></C><C></C><C> K<SUP>+</SUP></C></R><R><C>⥮<IT>K</IT><SUB>1</SUB></C><C><IT>K</IT><SUB>3</SUB></C><C> ⥮<IT>K</IT><SUB>3</SUB></C></R><R><C>EK + RB<SUP>+</SUP> </C><C>⇌</C><C> EKRb</C></R><R><C>+</C></R><R><C>K<SUP>+</SUP></C></R><R><C>⥮<IT>K</IT><SUB>3</SUB></C></R><R><C>EK<SUB>2</SUB></C></R></AR>
This model assumes that the first K+ binds with a dissociation constant K1 and the second cation binds with a dissociation constant K3. A physical interpretation of the ordered model is that the external binding site for transport consists of a single binding pocket, able to hold up to two K+ (or Rb+), rather than two widely separated sites. The two K+ (or Rb+) enter the binding pocket in sequence. Because of the prior binding of the first ion, the second ion entering the pocket could, theoretically, have either greater, the same, or less affinity for the binding pocket.

U is a function of all 86Rb+-containing forms. Mathematically, U = f1[ERb] + f2([EKRb] + 2[ERb2]) and Umax = 2f2[Etotal]. With these definitions, the radioactive uptake under steady-state conditions is represented by the general equation
U  =  <FR><NU>U<SUB>max</SUB>  <FENCE><FR><NU><IT>f</IT><SUB>1</SUB>[Rb<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB><IT>1</IT></SUB></DE></FR><IT>  +  </IT><FR><NU><IT>f</IT><SUB>2</SUB>[Rb<SUP>+</SUP>][K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR>  +  <FR><NU>2<IT>f</IT><SUB>2</SUB>[Rb<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB><IT>3</IT></SUB></DE></FR></FENCE></NU><DE><IT>2f</IT><SUB>2</SUB>  <FENCE>1  +  <FR><NU>[Rb<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB></DE></FR>  +  <FR><NU>[Rb<SUP>+</SUP>][K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR>  +  <FR><NU>[Rb<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR>  +  <FR><NU>[K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB></DE></FR>  + <FR><NU>[K<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR></FENCE></DE></FR> 
+ NS[Rb]  (A3)
For model IIA1, K1 not equal  K3 and f1 = f2; for model IIB1, K1 = K3 and f1 not equal  f2.

Case A: noncooperative transport (f1 = f2 ). Equation A3 contains six parameters to be fit, which proved too many for convergence. To reduce the number of parameters, simplifying assumptions had to be made. One such assumption is that f1 = f2, in which case, the influx rate constants drop out of the equation describing the uptake. Again, it is assumed transport can occur whether the enzyme has one or two cations bound. Stimulation of uptake at low concentrations of unlabeled cation (K+) will occur only if K3 < K1 (model IIA1). The amount of stimulation will depend on the ratio of K3 to K1. The results of fits to model IIA1 using mutant rat alpha 2* and E327Q in the presence of 150 mM external Na+ are shown in Figs. 4 and 7C, respectively. Binding model II with K1 = K3 cannot show stimulation, does not fit our data, and was not considered further.

Case B: cooperative transport (f1 not equal  f2 ). Stimulation of transport can occur when the enzyme has either one or two cations bound, if f1 is assumed to be unequal to f2. Equation A3 is still the equation used to fit the data but unlike in case A yields an f (= f2/f1) as well as binding constants. Attempts to fit the data to the general case, K1 not equal  K3, yielded parameter errors that were larger than the parameters themselves, and convergence was obtained only if the initial estimates of K1 and K3 were similar. If K1 is assumed to be equal to K3, model II predicts stimulation of Rb+ uptake by low concentrations of unlabeled cation (K+) only if f is >1 (i.e., positively cooperative transport). See Fig 7D.

Case C: infinitely cooperative transport (f1 = 0). It is assumed in this model that only doubly occupied forms of the enzyme (ERb2 and EKRb) are capable of transport (infinitely cooperative transport; f1 = 0). Mathematically, U = f2(2[ERb2] + [EKRb]) and Umax = 2f2[Etotal]. Equation A3 therefore reduces to
U  =  <FR><NU>U<SUB>max</SUB> <FENCE><FR><NU>[Rb<SUP>+</SUP>][K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR>  +  <FR><NU>2[Rb<SUP>+</SUP>]<SUP>2</SUP></NU><DE>  <IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR></FENCE></NU><DE>2  <FENCE>1  +  <FR><NU>[Rb<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB></DE></FR>  +  <FR><NU>[Rb<SUP>+</SUP>][K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR>  +  <FR><NU>[Rb<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR>  +  <FR><NU>[K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUB>1</SUB></DE></FR>  +  <FR><NU>[K<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUB>1</SUB><IT>K</IT><SUB>3</SUB></DE></FR></FENCE></DE></FR> 
+ NS[Rb]  (A4)
the equation used to fit the uptake data. For model IIC1, K1 not equal  K3; for model IIC2, K1 = K3.

In this case, stimulation can occur even though K1 = K3 (Fig. 7A and Table 1). As with the random model, stimulation of transport occurs because increasing K+ increases the concentration of the EKRb form of the enzyme. Stimulation of transport will also occur if K3 > K1 (negatively cooperative binding) or K3 < K1 (positively cooperative). An example of a fit to model IIB1 is shown in Fig. 7B.

Simultaneous or Infinitely Cooperative Binding

Finally, we considered an infinitely cooperative (or simultaneous) binding model in which the affinity of the second K+ (or Rb+) is so high that no significant amount of the EK or ERb form exists (model III). Model III describes the affinity of K+ in terms of a single effective dissociation constant, K1, as shown in scheme 3 
<AR><R><C></C><C><IT>K</IT><SUP>2</SUP><SUB>1</SUB></C><C></C><C></C><C></C><C><IT>K</IT><SUP>2</SUP><SUB>1</SUB></C></R><R><C>ERb<SUB>2</SUB></C><C> ⇌ </C><C>2Rb<SUP>+</SUP> + </C><C>E + </C><C>2K<SUP>+</SUP></C><C> ⇌ </C><C>EK<SUB>2</SUB></C></R><R><C></C><C></C><C></C><C>+</C></R><R><C></C><C></C><C></C><C>K<SUP>+</SUP></C></R><R><C></C><C></C><C></C><C>+</C></R><R><C></C><C></C><C></C><C>Rb<SUP>+</SUP></C></R><R><C></C><C></C><C></C><C>⥮<IT>K</IT><SUP>2</SUP><SUB>1</SUB></C></R><R><C></C><C></C><C></C><C>EKRb</C></R></AR>
As indicated in scheme 3, enzyme with a single K+ (or Rb+) bound does not exist. Therefore, only doubly occupied forms of the enzyme ([ERb2], [EKRb], and [EK2]) are capable of transport. Mathematically, U = f (2[ERb2] + [EKRb]) and Umax = 2f [Etotal]. Equation A5 is the equation used for the curve fitting of the uptake data for model III. Note that the influx rate constant drops out of the equation, since it appears in every term in the numerator and denominator
U = <FR><NU>U<SUB>max</SUB> <FENCE><FR><NU>[Rb<SUP>+</SUP>][K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUP>2</SUP><SUB>1</SUB></DE></FR> + <FR><NU>2[Rb<SUP>+</SUP>]<SUP>2</SUP></NU><DE> <IT>K</IT><SUP>2</SUP><SUB>1</SUB></DE></FR></FENCE></NU><DE>2 <FENCE>1 + <FR><NU>[Rb<SUP>+</SUP>][K<SUP>+</SUP>]</NU><DE><IT>K</IT><SUP>2</SUP><SUB>1</SUB></DE></FR> + <FR><NU>[Rb<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUP>2</SUP><SUB>1</SUB></DE></FR> + <FR><NU>[K<SUP>+</SUP>]<SUP>2</SUP></NU><DE><IT>K</IT><SUP>2</SUP><SUB>1</SUB></DE></FR></FENCE></DE></FR> + NS[Rb] (A5)
As with other models of cooperative transport, stimulation of uptake occurs because increasing [K+] increases the amount of EKRb. An example of a fit to the infinitely cooperative model is shown in Fig. 7A.

    ACKNOWLEDGEMENTS

We thank Dr. Theresa Kuntzweiler, Dr. Terry Kirley, and David Balshaw for helpful discussions and Dr. J. S. Lee for assisting with uptake experiments.

    FOOTNOTES

Address for reprint requests: K. Tepperman, Dept. of Biological Sciences, McMicken College of Arts and Sciences, University of Cincinnati, Cincinnati, OH 45221-0006.

Received 12 July 1995; accepted in final form 31 July 1997.

    REFERENCES
Top
Abstract
Introduction
Materials & Methods
Results
Discussion
Appendix
References

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AJP Cell Physiol 273(6):C2065-C2079
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