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. 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. 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 (1González-Lebrero R.M. Kaufman S.B. Montes M.R. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 2002; 277: 5910-5921Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar). 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 PROCEDURESThe 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 (1González-Lebrero R.M. Kaufman S.B. Montes M.R. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 2002; 277: 5910-5921Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar). ATP was purchased as the disodium salt and freed of Na+ by passing a 100 mmsolution 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 SelectionRegression 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 (2Yamaoka K. Nakagawa T. Uno T. J. Pharmacokin. Biopharm. 1978; 6: 165-175Crossref PubMed Scopus (1938) Google Scholar) which, as mentioned in the previous paper (1González-Lebrero R.M. Kaufman S.B. Montes M.R. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 2002; 277: 5910-5921Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar), is defined asAIC = 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 BindingLet us consider the transition from an occluded state with i occluded Rb+ and j boundX, E(Rb i )X j , to a non-occluded state, ERb i X j , followed by the dissociation into its constituent components.E(Rbi)Xj⇄TijERbiXj⇄KijiRb++jX+E SCHEME1In 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. 1González-Lebrero R.M. Kaufman S.B. Montes M.R. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 2002; 277: 5910-5921Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar). Note that the dissociation ofERb i X 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 i X j can be written as follows. E(Rbi)Xj=[Rb+]i[X]j[E]KijTij,ERbiXj=[Rb+]i[X]j[E]KijEquation 1 This allows us to express the amount of occluded Rb+(Rbocc) as follows. Rbocc=nmol of occluded Rb+mg protein=ETâˆ'pi=1âˆ'qj=0i[Rb+]i[X]jKijTijâˆ'ri=0âˆ'sj=0[Rb+]i[X]j(1+Tij)KijTijEquation 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 thenK 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 andq ≤ 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, Rbocc=âˆ'pi=1âˆ'qj=0Nij[Rb+]i[X]jâˆ'ri=0âˆ'sj=0Dij[Rb+]i[X]jEquation 3 where Nij=iETKijTij,Dij=1+TijKijTij.Equation 4 Notice that, from Equation 4 it follows thatN 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 callbound Rb+ and occludedRb+, 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 ofT ij ≪ 1 on the apparent dissociation constant for Rb+ (see comments to Scheme 2 in Reference 1, whereT ij was denoted asK deocc).Equations 2 and 3 take into account that everyE(Rb i )X j andERb i X 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 theE(Rb i )X j andERb i X 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 ofE 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, ERbiXj⇄KiERb(i−1)Xj+Rb+ ERbiXj⇄KjERbiX(j−1)+X SCHEME2were 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 DISCUSSIONWhen Rb+ is the only ligand, Equation 2 can be written (for [X] = 0; p = r = 2) as, Rbocc=ET[Rb+]K1+2[Rb+]2K1K21+[Rb+]K1+[Rb+]2K1K2=ETK2[Rb+]+2[Rb+]2K1K2+K2[Rb+]+[Rb+]2Equation 5 in which K 1 and K 2are 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 (1González-Lebrero R.M. Kaufman S.B. Montes M.R. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 2002; 277: 5910-5921Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar) that in the absence of other ligands, Rbocc is a hyperbolic function of [Rb+]. In the case of Equation 5, hyperbolic behavior demands that K 2 =4 K 1.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+ (3Matsui H. Homareda H. J. Biochem. (Tokyo). 1982; 92: 193-217Crossref PubMed Scopus (46) Google Scholar, 4Shani M. Goldschleger R. Karlish S.J.D. Biochim. Biophys. Acta. 1987; 904: 13-21Crossref PubMed Scopus (48) Google Scholar, 5Forbush III, B. J. Biol. Chem. 1987; 262: 11104-11115Abstract Full Text PDF PubMed Google Scholar, 6Rossi R.C. Nørby J.G. J. Biol. Chem. 1993; 268: 12579-12590Abstract Full Text PDF PubMed Google Scholar), 1 for the binding of Mg2+ (Ref. 7Smirnova I.N. Faller L.D. Biochemistry. 1993; 32: 5967-5977Crossref PubMed Scopus (20) Google Scholar, but see Ref. 8Schneeberger H. Apell J. J. Membr. Biol. 2001; 179: 263-273Crossref PubMed Scopus (50) Google Scholar) or ATP (Refs. 9Moczydlowski E.G. Fortes P.A.G. J. Biol. Chem. 1981; 256: 2346-2356Abstract Full Text PDF PubMed Google Scholar and 10Moczydlowski E.G. Fortes P.A.G. J. Biol. Chem. 1981; 256: 2357-2366Abstract Full Text PDF PubMed Google Scholar, and see Ref. 11Nørby J.G. Curr. Top. Membr. Transp. 1983; 19: 281-314Crossref Scopus (14) Google Scholar for further references), and 3 for the binding of Na+ (3Matsui H. Homareda H. J. Biochem. (Tokyo). 1982; 92: 193-217Crossref PubMed Scopus (46) Google Scholar, 8Schneeberger H. Apell J. J. Membr. Biol. 2001; 179: 263-273Crossref PubMed Scopus (50) Google Scholar, 12Garrahan P.J. Glynn I.M. J. Physiol. (Lond.). 1967; 192: 217-235Crossref Scopus (180) Google Scholar, 13Esmann M. Biochemistry. 1994; 33: 8558-8565Crossref PubMed Scopus (21) Google Scholar) 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 ofq, 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 thatK 2 = 4 K 1 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 Rbocc 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 Rbocc, and that this effect was reduced markedly by high [Rb+] (panels Aand B). Conversely, at constant [ATP], Rboccraised along sigmoidal and saturable functions of [Rb+] that were progressively shifted to the right as [ATP] increased (panels C and D).The following empirical equation gave best fit to the experimental data of Rbocc as a function of both [Rb+] and [ATP]. Rbocc=N10[Rb+]+N20[Rb+]2+N11[Rb+][ATP]+N21[Rb+]2[ATP]D00+D10[Rb+]+D20[Rb+]2+D01[ATP]+D11[Rb+][ATP]+D21[Rb+]2[ATP]Equation 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 theN ij /D ij ratios were significantly different from i E T (see Equation 4and 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 TableII. These values were used to draw the continuous lines that fit the data in Fig. 1.Figure 2A 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 Large Image Figure ViewerDownload Hi-res image Download (PPT)Table IThe meaning of the coefficients of Equation 6 in terms of the equilibrium constants of the scheme in Fig. 2CoefficientMeaningN 10/E TK 2 K′2 K′ATPN 20/E T2K′2 K′ATPN 11/E TK 2 K′2N 21/E T2K 2D 00K 1 K 2 K′2 K′ATPD 10K 2 K′2 K′ATPD 20K′2 K′ATPD 01K 2 K′1 K′2D 11K 2 K′2D 21K 2All K i values are dissociation constants. Note that, due to the different pathways connecting any two states, several equivalent combinations of these constants exist but only one is shown. Open table in a new tab Table IIThe best fitting values of the equilibrium constants of the scheme in Fig. 2ConstantBest fitting valueμm ± S.E.K 12.091 ± 0.083K 28.36 ± 0.33K′1256 ± 30K′2117 ± 15K ATP0.551 ± 0.046K′ATP67.5 ± 8.9K″ATP946 ± 89K ATP and K″ATP were calculated asK 1 K′ATP/K′1, andK′2 K′ATP/K 2, respectively, using the thermodynamic equivalence of pathways, and propagating the error of the estimations of the fitted constants.E T was 2.844 ± 0.015 nmol (mg protein)−1. Open table in a new tab The following are relevant properties of the scheme in Fig. 2,1) For all ATP concentrations, limRbocc[Rb+]→∞=2ETEquation 7 which indicates that, for the reasons discussed in comments to Scheme 1 and Equations Equation 2, Equation 3, Equation 4, Equation 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 (14Karlish S.J.D. Stein W.D. J. Physiol. 1982; 328: 295-316Crossref PubMed Scopus (55) Google Scholar) 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+], Rbocc will fall along a rectangular hyperbola whose K 0.5 will depend on [Rb+] according to the following equation. K0.5=K″ATPK1K2+K2[Rb+]+[Rb+]2K1′K2′+K2′[Rb+]+[Rb+]2Equation 8 Equation 8 indicates that the value of K 0.5for ATP will go from K ATP when [Rb+] = 0 toK ATP“ when [Rb+] tends to infinity. At [Rb+] between these two limits K 0.5 for ATP will be a combination of K ATP,K ATP′ andK ATP“, 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 thatK ATP“ >K ATP′ >K ATP indicating that increases in [Rb+] will increase K 0.5. It is noteworthy that the best fitting values for K ATPand K ATP“ 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 E 1 orE 2 conformers of the ATPase, respectively (5Forbush III, B. J. Biol. Chem. 1987; 262: 11104-11115Abstract Full Text PDF PubMed Google Scholar,15Nørby J.G. Jensen J. Biochim. Biophys. Acta. 1971; 233: 104-116Crossref PubMed Scopus (207) Google Scholar, 16Hegyvary C. Post R.L. J. Biol. Chem. 1971; 246: 5234-5240Abstract Full Text PDF PubMed Google Scholar, 17Kaufman S.B. González-Lebrero R.M. Schwarzbaum P.J. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 1999; 274: 20779-20790Abstract Full Text Full Text PDF PubMed Scopus (14) Google Scholar). A definition of E 1 andE 2 is given in Ref. 1González-Lebrero R.M. Kaufman S.B. Montes M.R. Nørby J.G. Garrahan P.J. Rossi R.C. J. Biol. Chem. 2002; 277: 5910-5921Abstract Full Text Full Text PDF PubMed Scopus (24) Google Scholar.3) The initial slope of the Rbocc =ƒ([Rb+]) curve, ET1+[ATP]KATP′K1+K1′[ATP]KATP′Equation 9 will go from E T /K 1 toE T /K′1 as [ATP] goes from zero to infinity so that, when [ATP] tends to infinity, the initial part of the Rbocc = ƒ([Rb+]) curve will be a straight line of zero intercept and positive slope equal toE 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 Rbocc as a function of [Mg2+] (panels A andB). It is apparent that as [Mg2+] increased Rbocc 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 Rbocc 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 inpanels C and D correspond to a given [Mg2+].Figure 3The 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 inpanel 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 TableIII), 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.View Large Image Figure ViewerDownload Hi-res image Download (PPT)Best fit to the results was obtained with the following reduced empirical equation. Rbocc=N10[Rb+]+N20[Rb+]2D00+D10[Rb+]+D20[Rb+]2+D01[Mg2+]+D11[Rb+][Mg2+]Equation 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, Rbocc will obey an equation like Equation 10 whose coefficients will depend on the equilibrium dissociation constants as shown in TableIII and whose best fitting values are given in Table IV. These values were used to draw the continuous lines in Fig. 3.Figure 4A minimal model for the equilibria between the ATPase, Rb+, and Mg2+ during direct occlusion of Rb+ in the Na+/K+-ATPase. Parenthesesdenote an occluded Rb+.View Large Image Figure ViewerDownload Hi-res image Download (PPT)Table IIIThe meaning of the coefficients of Equation 10 in terms of the equilibrium constants of the scheme in Fig. 4CoefficientMeaningN 10/E TK′2 K MgN 20/E T2K MgD 00K 1 K 2 K′MgD 10K 2 K′MgD 20K′MgD 01K′1 K 2D 11K 2All K i values are dissociation constants. Only one of the several equivalent combination of these constants that defines the coefficient is given. Open table in a new tab Table IVThe best fitting values of the equilibrium constants of the scheme in Fig. 4ConstantBest fitting valueμm ± S.E.K 12.733 ± 0.095K 210.93 ± 0.38K′1253 ± 25K Mg7.82 ± 0.58K′Mg724 ± 58K Mg was calculated asK 1 K′Mg/K′1using the thermodynamic equivalence of pathways, and propagating the error of the estimations of the fitted constants. E T was 2.789 ± 0.019 nmol (mg protein)−1. Open table in a new tab The following considerations are relevant to the scheme in Fig.4. 1) Since Rb+ competes with Mg2+, as [Rb+] tends to infinity, Rbocc will tend to 2E T as in the absence of Mg2+. 2) At constant [Rb+], as [Mg2+] tends to infinity, Rbocc will tend to zero along rectangular hyperbolas which will become half-maximal when, KI=KMg′K1K2+K2[Rb+]+[Rb+]2K1′K2+K2[Rb+]Equation 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 Rbocc 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 Rbocc =ƒ([Rb+]), ETKMg′K1KMg′+K1′[Mg2+]Equation 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 Rbocc 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.Figure 5The effects of Na+ on the equilibrium distribution between free and occluded Rb+. The equilibrium values of Rboccplotted 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 andD 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 Equation13 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.View Large Image Figure ViewerDownload Hi-res image Download (PPT)Best fit of the experimental data of Rbocc versus [Rb+] and [Na+] was obtained with the following reduced empirical equation. Rbocc=N10[Rb+]+N20[Rb+]2+N11[Rb+][Na+]+N21[Rb+]2[Na+]+N12[Rb+][Na+]2D00+D10[Rb+]+D20[Rb+]2+D01[Na+]+D11[Rb+][Na+]+D21[Rb+]2[Na+]++D02[Na+]2+D12[Rb+][Na+]2+D03[Na+]3Equation 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 theN 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 Rbocc = ƒ([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.Figure 6A minimal model for the equilibria between the ATPase, Rb+, and Na+ during direct occlusion of Rb+ in the Na+/K+-ATPase. Parenthesesdenote an occluded Rb+.View Large Image Figure ViewerDownload Hi-res image Download (PPT)Table VThe meaning of the coefficients of Equation 13 in terms of the equilibrium constants of the scheme in Fig. 6CoefficientMeaningN 10/E TK 2 K′2 K′1,Na K′2,Na K 3,NaN 20/E T2K′2 K′1,Na K′2,Na K 3,NaN 11/E TK 2 K′2 K′2,Na K 3,NaN 21/E T2K 2 K′2,Na K 3,NaN 12/E TK 2 K′2 K 3,NaD 00K 1 K 2 K′2 K′1,Na K′2,Na K 3,NaD 10K 2 K′2 K′1,Na K′2,Na K 3,NaD 20K′2 K′1,Na K′2,Na K 3,NaD 01K 2 K′1 K′2 K′2,Na K 3,NaD 11K 2 K′2 K′2,Na K 3,NaD 21K 2 K′2,Na K 3,NaD 02K 2 K′2 K″1 K 3,NaD 12K 2
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A bstract : In steady‐state conditions and for concentrations of the K + ‐congener Rb + less than 2.5 mM, Rb + ‐dependent ATPase activity is significantly higher than the steady‐state rate of breakdown of Rb + ‐occluded states, a discrepancy that disappears at sufficiently high [Rb + ]. Direct experimental evidence is provided that supports the explanation that the binding of a single Rb + to the phosphoenzyme conformer E 2 P accelerates dephosphorylation without leading to the occlusion of the cation.
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