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J. Biol. Chem., Vol. 277, Issue 8, 5922-5928, February 22, 2002

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The Occlusion of Rb⁺ in the Na⁺/K⁺-ATPase

II. THE EFFECTS OF Rb⁺, Na⁺, Mg²⁺, OR ATP ON THE EQUILIBRIUM BETWEEN FREE AND OCCLUDED Rb^+*

Rodolfo M. González-Lebrero, Sergio B. Kaufman, Patricio J. Garrahan^§, and Rolando C. Rossi^¶

From the Instituto de Química y Fisicoquímica Biológicas and the Departamento de Química Biológica, Facultad de Farmacia y Bioquímica, Universidad de Buenos Aires, Junín 956, C1113AAD Buenos Aires, Argentina

Received for publication, June 25, 2001, and in revised form, November 7, 2001

	ABSTRACT

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS AND DISCUSSION REFERENCES

We used the direct route of occlusion to study the equilibrium between free and occluded Rb⁺ in the Na⁺/K⁺-ATPase, in media with different concentrations of ATP, Mg²⁺, or Na⁺. An empirical equation, with the restrictions imposed by the stoichiometry of ligand binding was fitted to the data. This allowed us to identify which states of the enzyme were present in each condition and to work out the schemes and equations that describe the equilibria between the ATPase, Rb⁺, and ATP, Mg²⁺, or Na⁺. These equations were fitted to the corresponding experimental data to find out the values of the equilibrium constants of the reactions connecting the different enzyme states. The three ligands decreased the apparent affinity for Rb⁺ occlusion without affecting the occlusion capacity. With [ATP] tending to infinity, enzyme species with one or two occluded Rb⁺ seem to be present and full occlusion seems to occur in enzymes saturated with the nucleotide. In contrast, when either [Mg²⁺] or [Na⁺] tended to infinity no occlusion was detectable. Both Mg²⁺ and Na⁺ are displaced by Rb⁺ through a process that seems to need the binding and occlusion of two Rb⁺, which suggests that in these conditions Rb⁺ occlusion regains the stoichiometry of the physiological operation of the Na⁺ pump.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS AND DISCUSSION REFERENCES

In media in which Rb⁺ is the only ligand of the Na⁺/K⁺-ATPase both the kinetics of direct occlusion and deocclusion and the equilibrium distribution between free and occluded Rb⁺ seem to indicate that either one or two Rb⁺ can be occluded per Na⁺/K⁺-ATPase molecule (1). This contrasts with the experimental evidence that under physiological conditions occlusion takes place only when two Rb⁺ are trapped per enzyme molecule. This contradiction may be caused because in physiological conditions other pump ligands are also present. This was analyzed in the experiments in this paper by means of a quantitative study of the effects of ATP, Mg²⁺, or Na⁺ on the equilibrium between free and occluded Rb⁺ formed by the direct route. Results show that occlusion of either one or two Rb⁺ persists in enzymes saturated with ATP but not in enzymes fully bound to Mg²⁺ or Na⁺. Although in all cases Rb⁺ was able to displace the second ligand and to reach maximal occlusion, in media with either Na⁺ or Mg²⁺ the displacement required the binding of two Rb⁺ to the enzyme suggesting that Na⁺ or Mg²⁺ have to be present to allow Rb⁺ occlusion to take place with a fixed stoichiometry of two.

	EXPERIMENTAL PROCEDURES

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS AND DISCUSSION REFERENCES

The enzyme preparation, incubation conditions, reagents, methods for the determination of occluded Rb⁺ as well as the statistical procedures applied to the data are described in the previous paper of this series (1). ATP was purchased as the disodium salt and freed of Na⁺ by passing a 100 mM solution of ATP followed by 1 ml of 200 mM imidazole-HCl (pH 7.4 at 25 °C) through a column containing 1 ml of a cation exchange resin (Bio-Rad AG MP-50). Contaminant [Na⁺] in the eluate, measured by flame photometry, was less than 0.05% of the [ATP] on a mole to mole basis. Free Mg²⁺ was taken as equal to [MgCl₂] minus [EDTA]. In all experiments, occlusion equilibrium was attained by incubating enzyme during 15 min at 25 °C in media of the desired composition.

Model Selection-- Regression procedures permitted to define the goodness of fit of a given equation to the experimental results and to choose among different models, by using the AIC criterion (2) which, as mentioned in the previous paper (1), is defined as AIC = N ln(SS) + 2 P, with N = number of data, P = number of parameters, and SS = sum of weighted square residual errors. Statistical weights were 1 in all cases. To test if a parameter included in a given equation was significantly different from 0, AIC was calculated either adjusting the parameter or fixing its value to 0 (thus decreasing P by 1), and the equation with the lower AIC value was chosen.

The Quantitative Analysis of Rb⁺ Occlusion and Ligand Binding-- Let us consider the transition from an occluded state with i occluded Rb⁺ and j bound X, E(Rb_i)X_j, to a non-occluded state, ERb_iX_j, followed by the dissociation into its constituent components.

In our experiments, X is ATP, Mg²⁺, or Na⁺. This equilibrium is governed by a deocclusion constant, T_ij, and a dissociation constant, K_ij (see Ref. 1). Note that the dissociation of ERb_iX_j in Scheme 1 could be split into its elementary reactions and that K_ij can accordingly be factored into the equilibrium constants of each step (see Scheme 2 below). According to Scheme 1, the equilibrium concentrations of every E(Rb_i)X_j and ERb_iX_j can be written as follows.

(Eq. 1)

This allows us to express the amount of occluded Rb⁺ (Rb_occ) as follows.

(Eq. 2)

In Equation 2, [E] cancels out because it appears as a factor of all the terms both in the numerator and in the denominator, and when i = j = 0 then K_ij = 1. The equation includes four stoichiometric coefficients which measure the maximal numbers of occluded Rb⁺ (p), of X bound to the enzyme holding occluded Rb⁺ (q), of bound Rb⁺, either occluded or not (r), and of bound X (s). For obvious reasons, the index i in the numerator of Equation 2 starts at one and not at zero. Notice that the numerator contains only terms that correspond to enzyme states holding occluded Rb⁺, so that p  r and q  s. In this respect, it differs from a general binding equation, in which all bound states are measurable. For this reason the factor 1 + T_ij is present in each term of the denominator of Equation 2, where both occluded and not occluded states must be taken into account, and is absent from the terms in the numerator, where only occluded states are considered.

Equation 2 can be written as,

(Eq. 3)

where

(Eq. 4)

Notice that, from Equation 4 it follows that N_ij/D_ij = i E_T/(1 + T_ij). This allows us to identify the relative distribution between states with bound Rb⁺ and states with bound and occluded Rb⁺ (which, to facilitate the reading, we hereafter shall call bound Rb⁺ and occluded Rb⁺, respectively). If the equilibrium between states with occluded and states with bound Rb⁺ is displaced toward the occluded states then T_ij 1 and the ratio will become not significantly different from i E_T. We have already discussed in detail the consequences of T_ij 1 on the apparent dissociation constant for Rb⁺ (see comments to Scheme 2 in Reference 1, where T_ij was denoted as K_deocc).

Equations 2 and 3 take into account that every E(Rb_i)X_j and ERb_iX_j states permitted by the stoichiometry of binding of Rb⁺ and of X are present. This may not be always the case and, in a given experimental situation, one or more of these states may not exist and their corresponding terms have to be eliminated from Equations 2 and 3. Although it is not possible to know beforehand which states are absent, these can be identified adjusting an "empirical" equation of the form of Equation 3 to the data, without the restrictions imposed by Equation 4. When this is done, the coefficients of terms that express the concentration of absent states will become not significantly different from zero. On this basis, when fitting this empirical equation to our data we discarded those terms whose coefficients became negligible and considered as nonexistent the enzyme states described by them, provided that this did not affect the goodness of the fit and diminished the value of the AIC criterion. We thus obtained a "reduced" empirical equation. Additionally, by evaluating the ratios N_ij/D_ij as described above, we were able to define which of the E(Rb_i)X_j and ERb_iX_j states were actually present and use this information to write down the minimal scheme that describes the equilibria among them. Once a minimal equilibrium diagram was established, an equation was derived in terms of E_T and the equilibrium constants of the scheme (for obvious reasons this equation will have the same form as the reduced empirical equation). In general, these equilibrium constants differed from the K_ij in Scheme 1 because: (i) stepwise dissociation constants like those governing the following equilibria,


were considered, so that the coefficients K_ij of Equation 2 were expressed as the product of these constants, (ii) when information was not enough as to identify them, some of the stepwise equilibrium constants were grouped together into constants that included deocclusion of Rb⁺ and dissociation of ligands. Thus, using the equation derived from the scheme, the values of the equilibrium constants were obtained by means of regression analysis.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL PROCEDURES RESULTS AND DISCUSSION REFERENCES

When Rb⁺ is the only ligand, Equation 2 can be written (for [X] = 0; p = r = 2) as,

(Eq. 5)

in which K₁ and K₂ are the equilibrium constants for the release of a single Rb⁺ from the enzyme states holding either one or two occluded Rb⁺ (see comment ii to Scheme 2 above). We have shown (1) that in the absence of other ligands, Rb_occ is a hyperbolic function of [Rb⁺]. In the case of Equation 5, hyperbolic behavior demands that K₂ = 4 K₁.

When X was present, we also looked at the effect of different fixed values of the stoichiometric coefficients, p, q, r, and s, for the binding of ligands on the goodness of the fit of Equation 3 to the experimental data. In agreement with the stoichiometric numbers observed by most workers, best results were obtained using 2 for the binding and occlusion of Rb⁺ (3-6), 1 for the binding of Mg²⁺ (Ref. 7, but see Ref. 8) or ATP (Refs. 9 and 10, and see Ref. 11 for further references), and 3 for the binding of Na⁺ (3, 8, 12, 13) expressed as moles of binding sites per mol of ADP- or ouabain-binding sites in the enzyme. Therefore, in terms of Equations 2 and 3, p = r = 2 for Rb⁺, s = 1 for Mg²⁺ and ATP, and s = 3 for Na⁺. Best values of q, the maximal stoichiometric number for the binding of Mg²⁺, ATP, or Na⁺ to the occluded states, were found to be 0, 1, or 2, respectively.

On the basis of these properties, when we adjusted an empirical equation of the form of Equation 3 to the data we reduced the number of independent parameters setting as constants the above-mentioned values for p, q, r, and s. Once an equilibrium scheme was obtained, we included the constraint that K₂ = 4 K₁ for [X] = 0 into its derived equation.

In what follows we will apply the reasoning developed in the preceding paragraphs to the studies of the effects of ATP, Mg²⁺, and Na⁺ on the equilibrium between free and occluded Rb⁺ formed through the direct route. As it will be seen, regression analysis reveals with sufficient clarity qualitative and quantitative differences as to allow to interpret with little ambiguity which of the bound species are present in each condition tested, thus making it unnecessary the replot of parameters.

The Effects of ATP on the Equilibrium Distribution between Occluded and Free Rb⁺-- The equilibrium level of occluded Rb⁺ was measured after incubating Na⁺/K⁺-ATPase preparation in media containing from 0.8 to 500 µM Rb⁺ and from 0 to 2000 µM ATP. Results are plotted in Fig. 1 as Rb_occ as a function of either [ATP] (panels A and B) or [Rb⁺] (panels C and D). It can be seen that at constant [Rb⁺], the increase in [ATP] led to a progressive decrease in Rb_occ, and that this effect was reduced markedly by high [Rb⁺] (panels A and B). Conversely, at constant [ATP], Rb_occ raised along sigmoidal and saturable functions of [Rb⁺] that were progressively shifted to the right as [ATP] increased (panels C and D).

View larger version (43K): [in this window] [in a new window]   Fig. 1.   The effects of ATP on the equilibrium distribution between free and occluded Rb+. Rbocc was measured in media containing 0.8 (), 3 (), 8 (), 24.7 (), 98.7 (), 250 (), and 500 () µM Rb+, as a function of the concentration of ATP (panel A). Panel B shows the initial part of the plot in panel A. In panel C Rbocc is plotted as a function of the concentration of Rb+ in media containing 0 (), 20 (), 60 (), 200 (), 600 (), 1200 (), or 2000 () µM ATP. Panel D is the plot of the initial part of the same curve. The continuous lines are the plot of Equation 6 with its coefficients replaced by their meaning in terms of equilibrium constants of the scheme in Fig. 2 (see Table I) with the best fitting values given in Table II.

The following empirical equation gave best fit to the experimental data of Rb_occ as a function of both [Rb⁺] and [ATP].

(Eq. 6)

Equation 6 contains all the terms predicted by the stoichiometry of binding of Rb⁺ and ATP, which suggests that all the possible states of the enzyme with bound ATP and/or bound or occluded Rb⁺ are present in equilibrium with free Rb⁺ and ATP. As none of the N_ij/D_ij ratios were significantly different from i E_T (see Equation 4 and Scheme 1 for T_ij 1), it follows that all states with bound Rb⁺ were mostly in the occluded form. These states and the equilibria among them are given in the scheme in Fig. 2. From what we have already mentioned, it is obvious that the equation derived from this scheme will have the same form as Equation 6. The dependence of its coefficients with the equilibrium dissociation constants of the scheme in Fig. 2 is given in Table I and the best fitting values of the constants are shown in Table II. These values were used to draw the continuous lines that fit the data in Fig. 1.

View larger version (12K): [in this window] [in a new window]   Fig. 2.   A minimal model for the equilibria between the ATPase, Rb+, and ATP during direct occlusion of Rb+ in the Na+/K+-ATPase. Parentheses denote an occluded Rb+.

View this table: [in this window] [in a new window]   Table II The best fitting values of the equilibrium constants of the scheme in Fig. 2 KATP and KATP were calculated as K1K'ATP/K'1, and K'2K'ATP/K2, respectively, using the thermodynamic equivalence of pathways, and propagating the error of the estimations of the fitted constants. ET was 2.844 ± 0.015 nmol (mg protein)1.

The following are relevant properties of the scheme in Fig. 2,

1) For all ATP concentrations,

(Eq. 7)

which indicates that, for the reasons discussed in comments to Scheme 1 and Equations 2-5, even for the ATP-bound enzyme, the equilibrium between bound and occluded Rb⁺ is sufficiently shifted toward occlusion as to allow complete saturation of the two occlusion sites in the ATPase. Since the K⁺-K⁺ exchange catalyzed by the pump requires but does not consume ATP (14) and probably involves direct occlusion, it is likely that during this condition ATP binds to the enzyme containing two occluded Rb⁺.

2) As [ATP] goes from zero to infinity at constant [Rb⁺], Rb_occ will fall along a rectangular hyperbola whose K_0.5 will depend on [Rb⁺] according to the following equation.

(Eq. 8)

Equation 8 indicates that the value of K_0.5 for ATP will go from K_ATP when [Rb⁺] = 0 to K when [Rb⁺] tends to infinity. At [Rb⁺] between these two limits K_0.5 for ATP will be a combination of K_ATP, K and K, that is, of the equilibrium constants for the dissociation of ATP from the enzyme having either none, one or two occluded Rb⁺, respectively. Table II shows that K > K > K_ATP indicating that increases in [Rb⁺] will increase K_0.5. It is noteworthy that the best fitting values for K_ATP and K are comparable with the equilibrium constants for the dissociation of ATP from the catalytic or regulatory sites for the nucleotide, which are usually supposed to be present in the E₁ or E₂ conformers of the ATPase, respectively (5, 15-17). A definition of E₁ and E₂ is given in Ref. 1.

3) The initial slope of the Rb_occ = ([Rb⁺]) curve,

(Eq. 9)

will go from E_T/K₁ to E_T/K'₁ as [ATP] goes from zero to infinity so that, when [ATP] tends to infinity, the initial part of the Rb_occ = ([Rb⁺]) curve will be a straight line of zero intercept and positive slope equal to E_T/K'₁.

The Effects of Mg²⁺ on the Equilibrium Distribution between Occluded and Free Rb⁺-- These were measured in media containing from 0 to 4.5 mM Mg²⁺ and from 2.4 to 250 µM Rb⁺. Results are shown in Fig. 3 as plots of Rb_occ as a function of [Mg²⁺] (panels A and B). It is apparent that as [Mg²⁺] increased Rb_occ tended to zero along curves which were shifted to the right as [Rb⁺] raised. Since the set of [Mg²⁺] was different at each of the [Rb⁺] tested (i.e. there are only two points for [Mg²⁺] 4.5 or 1.6 mM, only one point for [Mg²⁺] 4 or 1.7 mM, etc.), it was not convenient to use experimental values for the curves of Rb_occ versus [Rb⁺] in panels C and D. Instead, we plotted theoretical values (see legend to Fig. 3) whose meaning will be discussed below. Each curve in panels C and D correspond to a given [Mg²⁺].

View larger version (40K): [in this window] [in a new window]   Fig. 3.   The effects of Mg2+ on the equilibrium distribution between free and occluded Rb+. Rbocc was measured as a function of [Mg2+] in media containing 2.4 (), 5 (), 12 (), 50 (), 125 (), or 250 () µM Rb+. Panel B is a plot of the initial part of the curves in panel A. The continuous lines are the plot of Equation 10 where its coefficients were replaced by their meaning in terms of the equilibrium constants of the scheme in Fig. 4 (see Table III), using the best fitting values given in Table IV. This procedure was also used to replot the calculated values of Rbocc as a function of [Rb+] (panels C and D) for [Mg2+] (read from left to right) 0, 0.01, 0.045, 0.1, 0.45, 1, and 4.5 mM, since there were not enough experimental values for each of these curves.

Best fit to the results was obtained with the following reduced empirical equation.

(Eq. 10)

It can be seen that Equation 10 has no terms containing [Mg²⁺] in the numerator and that only a first order term in [Rb⁺] [Mg²⁺] appears in the denominator.

The states of the enzyme with Mg²⁺ and/or Rb⁺ and the equilibria among them are given in the scheme in Fig. 4. In this scheme, Rb_occ will obey an equation like Equation 10 whose coefficients will depend on the equilibrium dissociation constants as shown in Table III and whose best fitting values are given in Table IV. These values were used to draw the continuous lines in Fig. 3.

View larger version (10K): [in this window] [in a new window]   Fig. 4.   A minimal model for the equilibria between the ATPase, Rb+, and Mg2+ during direct occlusion of Rb+ in the Na+/K+-ATPase. Parentheses denote an occluded Rb+.

View this table: [in this window] [in a new window]   Table IV The best fitting values of the equilibrium constants of the scheme in Fig. 4 KMg was calculated as K1K'Mg/K'1 using the thermodynamic equivalence of pathways, and propagating the error of the estimations of the fitted constants. ET was 2.789 ± 0.019 nmol (mg protein)1.

The following considerations are relevant to the scheme in Fig. 4. 1) Since Rb⁺ competes with Mg²⁺, as [Rb⁺] tends to infinity, Rb_occ will tend to 2 E_T as in the absence of Mg²⁺. 2) At constant [Rb⁺], as [Mg²⁺] tends to infinity, Rb_occ will tend to zero along rectangular hyperbolas which will become half-maximal when,

(Eq. 11)

so that K_I will increase without bounds as [Rb⁺] increases. This is consistent with the scheme in Fig. 4 which shows that Rb⁺ fully displaces Mg²⁺ from the enzyme and necessarily means that Mg²⁺ will also fully displace Rb⁺ from the ATPase. 3) As [Mg²⁺] increases, the plots of the theoretical values of Rb_occ versus [Rb⁺] (panels C and D in Fig. 3) evinced an increasing sigmoidicity and a drop in the apparent affinity for Rb⁺. 4) The initial slope of Rb_occ = ([Rb⁺]),

(Eq. 12)

will tend to zero as [Mg²⁺] tends to infinity. 5) Although the scheme in Fig. 4 includes an enzyme state holding only one occluded Rb⁺, the concentration of this state will be negligible when [Mg²⁺] tends to infinity so that, in this condition, displacement of Mg²⁺ will need the binding of two Rb⁺. Additionally, the scheme includes a Mg²⁺-bound state where Rb⁺ is bound, but not occluded (a unique case in this paper).

The Effects of Na⁺ on the Equilibrium Distribution between Occluded and Free Rb⁺-- The equilibrium level of occluded Rb⁺ was measured after incubating Na⁺/K⁺-ATPase preparation in media containing from 0 to 10 mM Na⁺ and from 0.74 to 248 µM Rb⁺. Results in Fig. 5 are plotted as a function of [Na⁺] (panels A and B) or of [Rb⁺] (panels C and D). It can be seen that at constant [Rb⁺], Na⁺ decreased the equilibrium level of occlusion along sigmoidal curves that tended to zero as [Na⁺] raised and which were displaced to the right as [Rb⁺] increased (panel A). The initial part (0 to 0.5 mM Na⁺) of the Rb_occ versus [Na⁺] curves (panel B) shows that the slope of these curves approached zero as [Na⁺] tended to zero and [Rb⁺] tended to either zero or infinity.

View larger version (46K): [in this window] [in a new window]   Fig. 5.   The effects of Na+ on the equilibrium distribution between free and occluded Rb+. The equilibrium values of Rbocc plotted as a function of [Na+] in media containing 0.74 (), 1.86 (), 4.63 (), 12.81 (), 34.2 (), 78.7 (), 148.5 (), or 248 () µM Rb+ (panels A and B). Panel B is an enlargement of the initial part of the curves. Panels C and D are plots of the same results as a function of the concentration of Rb+ in media containing 0 (), 0.001 (), 0.01 (), 0.05 (), 0.1 (), 0.25 (), 0.5 (), 1 (), 2.5 (), 5 (), 7.5 ( ), or 10 ( ) mM Na+. Panel D is the initial part of the curves. The continuous lines are the plot of Equation 13 with its coefficients replaced by their meaning in terms of equilibrium constants of the scheme in Fig. 6 (Table V) whose best fitting values are given in Table VI.

Best fit of the experimental data of Rb_occ versus [Rb⁺] and [Na⁺] was obtained with the following reduced empirical equation.

(Eq. 13)

Equation 13 lacks those terms in which the value of the sum of the exponents of [Rb⁺] and [Na⁺] exceeds 3, which indicates that no enzyme forms exist holding more than three ions. As in the case of ATP, none of the N_ij/D_ij ratios were significantly different from i E_T, indicating that all states with bound Rb⁺ were mostly in the occluded form.

The possible states of the enzyme holding Rb⁺ and/or Na⁺ and the equilibria among them are given in the scheme in Fig. 6. In this scheme Rb_occ = ([Rb⁺], [Na⁺]) will obey an equation like Equation 13 with coefficients depending on the equilibrium dissociation constants as shown in Table V and whose best fitting values are given in Table VI. These values were used to draw the continuous lines that fit the data in Fig. 5.

View larger version (19K): [in this window] [in a new window]   Fig. 6.   A minimal model for the equilibria between the ATPase, Rb+, and Na+ during direct occlusion of Rb+ in the Na+/K+-ATPase. Parentheses denote an occluded Rb+.

View this table: [in this window] [in a new window]   Table VI The best fitting values of the equilibrium constants of the scheme in Fig. 4 K1,Na, K1,Na, and K2,Na were calculated as follows: K1,Na = K1 K'1,Na/K'1, K1,Na = K'2 K'1,Na/K2 and K2,Na = K'1 K'2,Na/K1, using the thermodynamic equivalence of pathways, and propagating the error of the estimations of the fitted constants. ET was 2.7864 ± 0.0040 nmol (mg protein)1.

The following comments seem pertinent to the scheme in Fig. 6. 1) At any Na⁺ concentration, as [Rb⁺] tends to infinity, Rb_occ will tend to 2 E_T. Therefore as in the cases of ATP and Mg²⁺, full occlusion is attainable in the presence of Na⁺. 2) The initial slope of Rb_occ = ([Na⁺]) when [Rb⁺] tends to infinity will be as follows.

(Eq. 14)

Inspection of Table V shows that D₂₀ = N₂₀ 2 E_T, and D₂₁ = N₂₁ 2 E_T so that the two terms in the numerator will be equal and Equation 14 will be zero. Hence, as [Rb⁺] tends to infinity, the initial slope of the Rb_occ versus [Na⁺] curves tends to zero. 3) The initial slope of the Rb_occ = ([Rb⁺]) is equal to,

(Eq. 15)

which will tend to zero as [Na⁺] tends to infinity. 4) Although states with a single occluded Rb⁺ are considered in the scheme in Fig. 6, their concentration will become negligible as [Na⁺] tends to infinity.

General Considerations and Conclusions-- We have shown that ATP, Mg²⁺, or Na⁺ decrease the equilibrium level of Rb_occ lowering the apparent affinity of the ATPase for Rb⁺ during occlusion by the direct route. Mg²⁺ or Na⁺ are able to draw the apparent affinity for Rb⁺ to zero. In contrast with this, as [ATP] tends to infinity the affinity for Rb⁺ tends to a lower but not zero, value. Regardless of the model used, these results indicate that the ATPase can simultaneously bind ATP and occlude Rb⁺ whereas enzymes fully occupied by Na⁺ or Mg²⁺ cannot occlude Rb⁺. The effects of ATP, Mg²⁺, or Na⁺ on Rb_occ are completely surmountable by [Rb⁺] so that, in the presence of any of these ligands, the maximal occlusion reaches 2 mol/mol of ATPase as it happens in media with Rb⁺ alone, indicating that in all conditions tested the equilibrium between bound and occluded Rb⁺ is strongly shifted toward occlusion. This conclusion is trivial for the case of Mg²⁺ because enzymes holding occluded Rb⁺ are unable to bind this cation, but not for the cases of ATP and Na⁺ since these ligands do bind to the Rb⁺-occluded states (according to our analysis in Figs. 2 and 6: 1 ATP or 1 or 2 Na⁺). For instance (and in contrast to what we observed in this paper), Shani et al. (4) obtained only 75% of the maximal occlusion measuring direct occlusion at 0 °C in media with 9.6 mM ATP. This might mean that in their conditions, the equilibrium between occluded and bound Rb⁺ is poised as to leave a considerable fraction of the bound Rb⁺ freely exchangeable with the medium. (Note also that the technique of cation-exchange resin columns they used could underestimate Rb_occ in media with high [ATP], because of the high rate of Rb⁺ loss during the measurement.) With regard to Na⁺, we found no other reports in the literature on whether this cation might affect the equilibrium between bound and occluded Rb⁺.

ATP, Mg²⁺, or Na⁺, apart from lowering the apparent affinity for Rb⁺, change from hyperbolic to sigmoid the shape of the Rb_occ = ([Rb⁺]) curve. This may happen either because these ligands induce the appearance of positive cooperativity for the occlusion of Rb⁺ or because they force Rb⁺ occlusion to take place only when two Rb⁺ are bound to the same enzyme molecule. Both processes require more than one Rb⁺ to be bound to the enzyme and therefore both will be inoperative as [Rb⁺] tends to zero, since in this condition the probability of having more than one Rb⁺ bound to the same enzyme molecule vanishes. For this reason, if interactions in affinity were the cause of sigmoidicity, the initial part of the Rb_occ = ([Rb⁺]) curve will be a straight line of positive slope corresponding to the saturation of the first site on different enzyme units and would have zero slope if sigmoidicity were due to a stoichiometric requirement for two Rb⁺. To select one of these two alternatives it is mandatory to examine the initial part of the Rb_occ = ([Rb⁺]) curve when the concentrations of the ligand that caused the sigmoidicity tends to infinity. This ensures that all enzyme molecules are equally affected by this ligand.

In the case of ATP, the criterion of the initial slopes strongly suggests that the nucleotide allows the occlusion of one or two Rb⁺ and induces sigmoidicity promoting positive interactions in this process. This view agrees with the equilibrium model discussed above and gains independent support from our observations that, with saturating ATP, the equilibrium constant for the release of Rb⁺ from the enzyme holding two occluded Rb⁺ is smaller than that holding one occluded Rb⁺ (cf. K'₂ and K'₁ in Table II), while it should have been four times larger to yield a hyperbolic response (see comments to Equation 5).

In contrast with the effects of ATP, the initial slope of the Rb_occ = ([Rb⁺]) curves becomes zero in media in which [Mg²⁺] or [Na⁺] tend to infinity, strongly suggesting that sigmoidicity caused by either of these ligands takes place because only occluded states with two Rb⁺ per ATPase will exist, as it is posited by the equilibrium schemes discussed above. Therefore, Mg²⁺ or Na⁺, but not ATP seem to be necessary for the ATPase to operate with a fixed stoichiometry of two Rb⁺ for occlusion that holds under physiological conditions (6, 17). The experiments in this paper do not allow us to know the molecular mechanism by which ATP generates cooperativity while Mg²⁺ or Na⁺ induce fixed stoichiometry for Rb⁺ occlusion.

The analysis of the value of the initial slope can also be applied to find out the mechanism that leads to the sigmoidal shape of the curves that describe the displacement of Rb_occ by Na⁺. Our results show that the initial slope of the Rb_occ = ([Na⁺]) curves tends to zero as [Rb⁺] tends to infinity. For the reasons already explained, this strongly suggests that more than one Na⁺ has to be bound for the displacement of occluded Rb⁺ to take place. In our equilibrium scheme in Fig. 6, 3 Na⁺ are necessary. This fits nicely with the number of Na⁺ ions translocated in each Na⁺/K⁺ or Na⁺/Na⁺ exchange cycle catalyzed by the Na⁺/K⁺-ATPase (12).

It is tempting to postulate that the effects of Mg²⁺ or Na⁺ on the apparent affinity for Rb⁺ and on the shape of the Rb_occ = ([Rb⁺]) curve are caused because either cation stabilizes the ATPase in a conformer (presumably E₁) which is unable to occlude Rb⁺ and that two Rb⁺ are needed to displace the system to a state (presumably E₂) in which they become occluded. In this process, Mg²⁺ or Na⁺ would be released from the enzyme. It is generally accepted that Na⁺ is an exclusive ligand of E₁, but in terms of scheme in Fig. 6, there are states containing occluded Rb⁺ (and therefore presumably in the E₂ form) that are able to bind Na⁺. In fact, only the states with no Rb⁺ occluded could correspond to the E₁ form, notably those with the higher number of Na⁺ bound. This would still fit to the results found by other authors on the differential properties of E₁ and E₂ (13, 18, 19). The case for Mg²⁺ is more difficult to sustain, as the cation is known to act on both E₁ and E₂ (5, 7, 20). However, the values of the dissociation constants for Mg²⁺ found in our results (see Table IV) are more consistent with the high affinity effects that Mg²⁺ exerts on E₁ than with the low affinity effects displayed on E₂.

The effects of ATP on the apparent affinity for Rb⁺ and on the shape of the Rb_occ = ([Rb⁺]) curve are substantially different from those of Mg²⁺ or Na⁺. A plausible cause for this can be found in the fact that, in contrast with the complexes of the enzyme with Mg²⁺ or fully saturated with Na⁺, the enzyme-ATP complex is able to occlude Rb⁺ with the same capacity as the free enzyme. Although its affinity for E₁ is much higher, ATP is known also to be a ligand of E₂. Since occlusion only takes place in the E₂ conformer, if the E₂ATP complex were able to bind and occlude Rb⁺, the occlusion that follows binding would displace the equilibrium between E₁ and E₂ completely toward E₂. ATP acting on E₂ induces a large increase in the rate of release of occluded Rb⁺ (1, 5, 17, 21, 22). Therefore, either this increase is unable to significantly poise the equilibrium between E₁ and E₂ toward E₁, or the postulate of occlusion in E₂ATP has to be accompanied by the additional proposal that ATP induces an increase in the rate of formation of occluded Rb⁺ large enough as to keep the maximal amount of Rb_occ independent of the concentration of the nucleotide. This latter possibility was proposed by Hasenauer et al. (23).

	ACKNOWLEDGEMENTS

We thank Dr. Jens G. Nørby for helpful discussion of the manuscript and Dr. Mónica R. Montes for assistance with some of the experiments and proofreading of the manuscript. Thanks are due to Angielina Damgaard and Birthe B. Jensen, Department of Biophysics, University of Aarhus, Denmark, for preparing the Na⁺/K⁺-ATPase.

	FOOTNOTES

^* This work was supported by grants from the Consejo Nacional de Investigaciones Científicas y Técnicas, Agencia Nacional de Promoción Científica y Tecnológica, and Universidad de Buenos Aires, Argentina.The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Research Fellow from the Consejo Nacional de Investigaciones Científicas y Técnicas.

^§ Established Investigator from the Consejo Nacional de Investigaciones Científicas y Técnicas.

^¶ Established Investigator from the Consejo Nacional de Investigaciones Científicas y Técnicas. To whom correspondence should be addressed. Tel.: 5411-4-964-5506; Fax: 5411-4-962-5457; E-mail: rcr@mail.retina.ar.

Published, JBC Papers in Press, December 5, 2001, DOI 10.1074/jbc.M105887200

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