Kinetics of (Na+ + K+)-ATPase: analysis of the influence of Na+ and K+ by steady-state kinetics

Steady-state analysis of enzymes with non-Michaelis-Menten kinetics: The transport mechanism of Na+/K+-ATPase

Procedures to define kinetic mechanisms from catalytic activity measurements that obey the Michaelis-Menten equation are well established. In contrast, analytical tools for enzymes displaying non-Michaelis-Menten kinetics are underdeveloped, and transient-state measurements, when feasible, are therefore preferred in kinetic studies. Of note, transient-state determinations evaluate only partial reactions, and these might not participate in the reaction cycle. Here, we provide a general procedure to characterize kinetic mechanisms from steady-state determinations. We described non-Michaelis-Menten kinetics with equations containing parameters equivalent to k_cat and K_m and modeled the underlying mechanism by an approach similar to that used under Michaelis-Menten kinetics. The procedure enabled us to evaluate whether Na⁺/K⁺-ATPase uses the same sites to alternatively transport Na⁺ and K⁺ This ping-pong mechanism is supported by transient-state studies but contradicted to date by steady-state analyses claiming that the release of one cationic species as product requires the binding of the other (ternary-complex mechanism). To derive robust conclusions about the Na⁺/K⁺-ATPase transport mechanism, we did not rely on ATPase activity measurements alone. During the catalytic cycle, the transported cations become transitorily occluded (i.e. trapped within the enzyme). We employed radioactive isotopes to quantify occluded cations under steady-state conditions. We replaced K⁺ with Rb⁺ because ⁴²K⁺ has a short half-life, and previous studies showed that K⁺- and Rb⁺-occluded reaction intermediates are similar. We derived conclusions regarding the rate of Rb⁺ deocclusion that were verified by direct measurements. Our results validated the ping-pong mechanism and proved that Rb⁺ deocclusion is accelerated when Na⁺ binds to an allosteric, nonspecific site, leading to a 2-fold increase in ATPase activity.

Alternative cycling modes of the Na(+)/K(+)-ATPase in the presence of either Na(+) or Rb(+)

A comprehensive study of the interaction between Na(+) and K(+) with the Na(+)/K(+)-ATPase requires dissecting the incidence of alternative cycling modes on activity measurements in which one or both of these cations are absent. With this aim, we used membrane fragments containing pig-kidney Na(+)/K(+)-ATPase to perform measurements, at 25°C and pH=7.4, of ATPase activity and steady-state levels of (i) intermediates containing occluded Rb(+) at different [Rb(+)] in media lacking Na(+), and (ii) phosphorylated intermediates at different [Na(+)] in media lacking Rb(+). Most relevant results are: (1) Rb(+) can be occluded through an ATPasic cycling mode that takes place in the absence of Na(+) ions, (2) the kinetic behavior of the phosphoenzyme formed by ATP in the absence of Na(+) is different from the one that is formed with Na(+), and (3) binding of Na(+) to transport sites during catalysis is not at random unless rapid equilibrium holds.

Steady-state kinetic analysis of the Na+/K+-ATPase. The activation of ATP hydrolysis by cations

We studied the interactions between pairs of cations during activation of the steady-state hydrolysis of ATP of the Na+/K+-ATPase. Non-linear regression was used to obtain empirical equations that describe quantitatively the behaviour of the system. The curve relating activity to Na+ concentration was describable by a Hill equation with nH = 2 and not by the more frequently used expression based on rapid-equilibrium binding of Na+ to three identical and non-interacting sites. At non-limiting concentrations of the other ligands, changes in the concentration of Na+ or of Mg2+ modified in the same proportion the maximum effects and the apparent affinities of K+, revealing the operation of either ping-pong or of ordered sequential mechanisms with irreversible steps separating the additions of each ligand. In contrast with this, changes in the concentration of Mg2+ altered only the maximum effect of Na+, indicating that a ternary complex between the cations and the enzyme has to be formed and that certain particular relations have to hold among the rate constants of the system. The interactions described in this paper, together with those previously reported, allowed us to derive a general equation that adequately predicted the response of the Na+/K+-ATPase to the concentration of any pair of ligands at non-limiting concentrations of the rest. Confrontation of this equation with computer simulations of the behaviour of the Albers-Post model shows that this model predicts the interactions in which K+ participates and perhaps also the interaction between Mg2+ and Na+, but seems unable to predict the interactions between pairs of ligands that do not include K+.

Kinetics behaviors of Na,K-ATPase: comparison of solubilized and DPPC:DPPE-liposome reconstituted enzyme

We describe and compare the main kinetic characteristics of rabbit kidney Na,K-ATPase incorporated inside-out in DPPC:DPPE-liposomes with the C(12)E(8) solubilized and purified form. In proteoliposomes, we observed that the ATP hydrolysis of the enzyme is favored and also its affinity for Na(+)-binding sites increases, keeping the negative cooperativity with two classes of hydrolysis sites: one of high affinity (K(0.5)=6 microM and 4 microM for reconstituted enzyme and purified form, respectively) and another of low affinity (K(0.5)=0.4 mM and 1.4 mM for reconstituted enzyme and purified form, respectively). Our data showed a biphasic curve for ATP hydrolysis, suggesting the presence of (alphabeta)(2) oligomer in reconstituted Na,K-ATPase similar to the solubilized enzyme. The Mg(2+) concentration dependence in the proteoliposomes stimulated the Na,K-ATPase activity up to 476 U/mg with a K(0.5) value of 0.4 mM. The Na(+) ions also presented a single saturation curve with V(M)=551 U/mg and K(0.5)=0.2 mM with cooperative effects. The activity was also stimulated by K(+) ions through a single curve of saturation sites (K(0.5)=2.8 mM), with cooperative effects and V(M)=641 U/mg. The lipid microenvironment close to the proteic structure and the K(+) internal to the liposome has a key role in enzyme regulation, affecting its kinetic parameters while it can also modulate the enzyme's affinity for substrate and ions.

Functional coupling of phosphorylation and nucleotide binding sites in the proteolytic fragments of Na+/K(+)-ATPase

Cleavage of the alpha-subunit of Na+/K(+)-ATPase by trypsin at Arg438-Ala439 causes enzyme inhibition which has been suggested to be due to altered alignment of phosphorylation site on the 48-kDa N-terminal fragment with nucleotide binding site on the 64-kDa C-terminal fragment. Our aims were to test this hypothesis and to assess the effect of the cleavage on the enzyme's two ATP sites. Na(+)-dependent phosphorylation of the partially cleaved enzyme by ATP showed that K0.5 values of ATP for phosphorylations of intact alpha and 48-kDa peptide were the same (0.4 microM). Unchanged interactions among the residues across the cleavage site were also indicated by data showing that reaction of fluorescein isothiocyanate with the 64-kDa peptide blocked phosphorylation of the 48-kDa peptide by ATP. ATP is known to block the reaction of fluorescein isothiocyanate with the enzyme. Experiments on the partially cleaved enzyme showed that K0.5 of ATP for protection of alpha was 30-60 microM, and the value for the protection of interacting 48-kDa and 64-kDa peptides was 1-3 mM. Evidently, while the cleavage does not affect the high affinity catalytic site, it disrupts the allosteric low affinity ATP site. Experiments on reconstituted preparations showed that the cleavage abolished ATP-dependent Na+/K+ exchange, Pi+ATP-dependent Rb+/Rb+ exchange, ATP-dependent Na+/Na+ exchange, and ADP+ATP-dependent Na+/Na+ exchange activities. Selective disruption of the low affinity ATP site accounts for the inhibitions of all functions involving K+(Rb+), based on the established role of this site in the control of K+ access channels. Cleavage-induced inhibitions of other activities, however, suggest additional roles of the low affinity ATP site in the reaction cycle.

Ethanol and (Na+,K+)-ATPase: alteration of Na(+)-K+ selectivity

Relative internal concentrations of Na+ and K+ are important in regulating (Na+,K+)-ATPase in situ. Ethanol is known to inhibit (Na+,K+)-ATPase and to reduce K+ affinity, but the concentrations required for these effects in vitro are large compared with those probably attainable in vivo. Yet, there is evidence suggesting that ethanol has physiologically relevant effects on (Na+,K+)-ATPase. We have investigated the effects of ethanol on selectivity for Na+ versus K+. At 150 mM, ethanol had little effect on (Na+,K+)-ATPase activity under the usual assay conditions, slightly (but nonsignificantly) reduced K+ affinity, and had no effect on extrapolated Na+ affinity in the absence of K+. However, ethanol had marked effects on cation selectivity, doubling the Ki for K+ on Na+ affinity and halving the Ki for Na+ on K+ affinity. These data show that ethanol, at concentrations too small for effects on (Na+,K+)-ATPase activity under optimal assay conditions, can alter its responses to changes in Na+ or K+.

[32P]ATP synthesis in steady state from [32P]Pi and ADP by Na+/K(+)-ATPase from ox brain and pig kidney. Activation by K+

The ouabain-sensitive synthesis of [32P]ATP from [32P]Pi and ADP (vsyn) was measured in parallel with the ouabain-sensitive hydrolysis of [32P]ATP (vhy) at steady state, at varying concentrations of sodium, potassium, magnesium, inorganic phosphate, ADP, ATP and oligomycin, and at varying pH. Na+ was necessary for ATP synthesis, but vsyn was decreased by high sodium concentrations. Oligomycin, depending on the Na+ concentration, either decreased or did not affect vsyn. Potassium, at low concentrations (1-5 mM) increased vsyn at all magnesium and sodium concentrations tested, lower potassium concentrations being needed to activate vsyn at lower sodium concentrations. vsyn was optimal below pH 6.7, decreasing abruptly at higher values of pH. At pH 6.7, vsyn was a hyperbolic function of the concentration of inorganic phosphate. In the presence of potassium, half-maximal rate was obtained at [Pi] congruent to 40 mM, whereas a higher concentration was needed to obtain half-maximal rate in the absence of K+. In contrast, increasing the concentration of ADP caused a nonhyperbolic activation of vsyn, the pattern obtained in the presence of potassium being different from that obtained in its absence. Increasing the ATP concentration above 0.5 mM decreased vsyn. The data are used to elucidate (1) which reaction steps are involved in the ATP-synthesis catalysed by the Na+/K(+)-ATPase at steady state in the absence of ionic gradients and (2) the mechanism by which K+ ions stimulate the reaction.

Distinction between the intermediates in Na+-ATPase and Na+,K+-ATPase reactions. II. Exchange and hydrolysis kinetics at micromolar nucleotide concentrations

The ATP hydrolysis rate and the ADP-ATP exchange rate of (Na+ + K+)-ATPase from ox brain were measured at 10 microM Mg2+free and at micromolar concentrations of free ATP and ADP. (1) In the absence of K+, substrate inhibition of the hydrolysis rate was observed. It disappeared at low Na+ and diminished at increasing concentrations of ADP. This was interpreted in terms of free ATP binding to E1P. In support of this interpretation, free ATP was found to competitively inhibit ADP-ATP exchange. (2) In the presence of K+, substrate activation of the hydrolysis rate was observed. Increasing (microM) concentrations of ADP did not give rise to competitive inhibition in contrast to the situation in the absence of K+ (cf. 1, above). This was interpreted to show that at micromolar substrate, some low-affinity, high-turnover Na+ + K+ activity is possible, provided the Mg2+ concentration is low. (3) While small concentrations of K+ increased the hydrolysis rate (cf. 2) they decreased the rate of ADP-ATP exchange. To elucidate this phenomenon, parallel measurements of exchange and hydrolysis rates were performed over a wide range of ATP and ADP concentrations, with and without K+. If, in the presence and absence of K+, ADP (and ATP competing) are binding to the same phosphorylated intermediate for the backward reaction, it places quantitative restrictions on the ratio of rate constants with and without K+. The results did not conform to these restrictions, and the discrepancy is taken as evidence for the necessity for a bicyclic scheme for the action of the (Na+ + K+)-ATPase. (4) An earlier statement concerning the nature of the phosphoenzyme obtained in the presence of Na+ and K+ is amended.

Distinction between the intermediates in Na+-ATPase and Na+,K+-ATPase reactions. I. Exchange and hydrolysis kinetics at millimolar nucleotide concentrations

Parallel measurements in steady-state of ATP hydrolysis rate (vhydr) and the simultaneous reverse reaction, i.e., the ADP-ATP exchange rate (vexch), allowed the determination of a kinetic parameter, KE, containing only the four rate constants needed to characterize the enzyme intermediates involved in the sequence (Formula: see text). In order to compare the properties of these enzyme intermediates under different sets of conditions, KE was measured at varying K+ and Na+ concentrations in the presence of millimolar concentrations of ATP, ADP and MgATP, using an enzyme preparation that was partially purified from bovine brain. (1) In the presence of Na+ (150 mM), K+ (20-150 mM) was found to increase the exchange rate and decrease the ATP hydrolysis rate at steady-state. As a result, KE increased at increasing K+. However, the value of KE found by extrapolation to K+ = 0 was 7-times lower than the value actually measured in the absence of K+. This finding indicates that one of the intermediates, EATP or EP, or both, when formed in the presence of Na+ alone, are different from the corresponding intermediate(s) formed in the presence of Na+ + K+ (at millimolar substrate concentration). (2) In the presence of 150 mM K+, Na+ (5-30 mM) was found to increase the ADP/ATP exchange as well as the ATP hydrolysis rate at steady-state. The ratio of the two rates was constant. This finding, when interpreted in terms of KE, indicates that Na+ does not have to leave the enzyme for ATP release to be accelerated by K+ in the backward reaction. This also is in opposition to the usual versions of the Albers-Post model, which does not have simultaneous presence of Na+ and K+.

Oligomycin inhibition of Na,K,ATPase. Analysis of half-of-sites moderator interaction with a dimeric enzyme

It is shown that the incomplete, uncompetitive inhibition pattern exhibited by oligomycin toward Na,K,ATPase cannot be explained by a single-cycle enzyme model. In contrast, the experimental data are easily explained in terms of a dimeric enzyme, only one subunit of which can bind oligomycin at a time, and that subunit is then rendered inactive. In a brief analysis of the model thus obtained by way of numerical examples it is shown that it may show activation at small concentrations of moderator, which disappears at higher concentrations, a property observed for the hydrolysis of p-nitro-phenylphosphate, which is also catalyzed by Na,K,ATPase.

Application of the theory of enzyme subunit interactions to ATP-hydrolyzing enzymes. The case of Na,K-ATPase

The theory developed by T. L. Hill (1977, Proc. Natl. Acad. Sci. USA, 74:3632-3636) for enzyme interactions is applied to a dimeric enzyme, the subunits of which may each exist in three distinct states (as in a uni-bi kinetic mechanism). It is shown that when simultaneous binding of substrate to both subunits is excluded, the complex kinetic mechanism of the dimer reduces to a simpler scheme with two distinct, but analogous, cycles that are in principle separately observable in kinetic experiments. Because of the intersubunit interactions, which are explicitly taken into account, the two cycles have different Michaelis constants and maximal velocities. The model exhibits negative cooperativity and enhanced reactivity, relative to a monomeric enzyme. The theory is applied to Na,K-ATPase for which a complete, bicyclic, kinetic mechanism and rate constants are available. When taken together with other evidence, structural as well as functional, the striking similarity of the observed kinetics with that developed for a dimeric enzyme strongly suggests that the functional unit of Na,K-ATPase is a dimer. The free energy differences (calculated from the known rate constants) between intermediates are 6-16 kJ/mol, comparable, for example, to the free energy associated with the formation of a base pair in a nucleic acid double helix. The possible relevance of these results for other ATPases is briefly discussed.

The apparent Km is a misleading kinetic indicator

When information concerning whether or not a ligand interacts with the same enzyme species as do the substrates, the variation of the Michaelis constant Km (for each substrate) with ligand concentration is sometimes used as a diagnostic. It is shown that the Michaelis constant is of no particular value in this respect and may be misleading. Thus, depending on the mechanism, Km may vary with ligand concentration even though the ligand interacts with species far removed in the mechanism from the substrate-binding steps, and it may stay constant in cases where the ligand competes directly for the free enzyme. In contrast, the slope of a double-reciprocal plot of the kinetic data (= Km/Vmax.) (or, equivalently, the ordinate intercept of a Hanes plot A/v versus A, where A is the substrate concentration) independently of the particular mechanism involved uniquely signifies whether or not such interaction occurs. The results clearly indicate that, for purposes other than communicating the substrate concentration yielding control of the enzymic activity, usage of Km and its variation with ligand concentration should be avoided and interest instead focused on the slope, in accordance with the long-established rules of Cleland [Biochim. Biophys. Acta (1963) 67, 188-196], for which the present analysis provides the formal framework.

Reaction sequences for (Na+ + K+)-dependent ATPase hydrolytic activities: new quantitative kinetic models

To delineate better the reaction sequence of the (Na+ + K+)-ATPase and illuminate properties of the active site, kinetic data were fitted to specific quantitative models. For the (Na+ + K+)-ATPase reaction, double-reciprocal plots of velocity against ATP (in the millimolar range), with a series of fixed KCl concentrations, are nearly parallel, in accord with the ping pong kinetics of ATP binding at the low-affinity sites only after Pi release. However, contrary to requirements of usual formulations, Pi is not a competitor toward ATP. A new steady-state kinetic model accommodates these data quantitatively, requiring that under usual assay conditions most of the enzyme activity follows a sequence in which ATP adds after Pi release, but also requiring a minor alternative pathway with ATP adding after K+ binds but before Pi release. The fit to the data also reveals that Pi binds nearly as rapidly to E2 X K X ATP as to E2 X K, whereas ATP binds quite slowly to E2 X P X K: the site resembles a cul-de-sac with distal ATP and proximal Pi sites. For the K+-nitrophenyl phosphatase reaction also catalyzed by this enzyme, the apparent affinities for both substrate and Pi (as inhibitor) decrease with higher KCl concentrations, and both Pi and TNP-ATP appear to be competitive inhibitors toward substrate with 10 mM KCl but noncompetitive inhibitors with 1 mM KCl. These data are accommodated quantitatively by a steady-state model allowing cyclic hydrolytic activity without obligatory release of K+, and with exclusive binding of substrate vs. either Pi or TNP-ATP. The greater sensitivity of the phosphatase reaction to both Pi and arsenate is attributable to the weaker binding by the occluded-K+ enzyme form occurring in the (Na+ + K+)-ATPase reaction sequence. The steady-state models are consistent with cyclical interconversion of high- and low-affinity substrate sites accompanying E1/E2 transitions, with distortion to low-affinity sites altering not only affinity and route of access but also separating the adenine- and phosphate-binding regions, the latter serving in the E2 conformation as the active site for the phosphatase reaction.

Kinetics of Na+-ATPase: influence of Na+ and K+ on substrate binding and hydrolysis

An analysis of the influence of Na+ and K+ on the kinetics of Na+-ATPase in broken membrane preparations from bovine brain is presented with particular emphasis on the effect of the cations on the binding and splitting of the substrate MgATP and on the derivation of a detailed kinetic model for that interaction. It was found that the enzyme in the absence of Na+ and K+, but in the presence of 7 mM free Mg2+, at pH 7.4 (37 degrees C) exhibits an ouabain-sensitive ATPase activity. The simplest model quantitatively compatible with all the data involves two different, interconvertible (conformational) forms of the enzyme, E1 and E'1, with the following properties: The E1 form does not bind K+ but has three independent and equivalent high-affinity sites (Kd = 5.6 mM) for Na+. It binds and hydrolyzes substrate only when two or three sodium ions are bound to it. The E'1 form binds and hydrolyzes the substrate only in the absence of monovalent cations. It is competitively inhibited by K+ (Kd = 0.23 mM), and this inhibition is further enhanced by binding of Na+ to the K+-bound form at two equivalent, independent sites (Kd = 12 mM). It is suggested that the E'1 form is the Mg2+-induced conformational state of the enzyme observed by others, which differs from the usually encountered E1 and E2 forms. The model allows the calculation of ATP-binding and ADP-releasing rate constants for the E1-form for later comparison with corresponding rate constants for the (na+ + K+)-ATPase (following paper).