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

The interaction of Na+, K+, and phosphate with the gastric H,K-ATPase. Kinetics of E1-E2 conformational changes assessed by eosin fluorescence measurements

H,K-ATPase and Na,K-ATPase show the highest degree of sequence similarity among all other members of the P-type ATPases family. To explore their common features in terms of ligand binding, we evaluated conformational transitions due to the binding of Na⁺, K⁺ and Pi in the H,K-ATPase, and compared the results with those obtained for the Na,K-ATPase. This work shows that eosin fluorescence time courses provide a reasonably precise method to study the kinetics of the E1-E2 conformational changes in the H,K-ATPase. We found that, although Na⁺ shifts the equilibrium toward the E1 conformation and seems to compete with H⁺ in ATPase activity assays, it was neither possible to isolate a Na⁺-occluded state, nor to reveal an influx of Na⁺ related to H,K-ATPase activity. The high rate of the E2K → E1 transition found for the H,K-ATPase, which is not compatible with the presence of a K⁺-occluded form, agrees with the negligible level of occluded Rb⁺ (used as a K⁺ congener) found in the absence of added ligands. The use of vanadate and fluorinated metals to induce E2P-like states increased the level of occluded Rb⁺ and suggests that-during dephosphorylation-the probability of K⁺ to remain occluded increases from the E2P-ground to the E2P-product state. From kinetic experiments we found an unexpected increase in the values of k_obs for E2P formation with [Pi]; consequently, to obey the Albers-Post model, the binding of Pi to the E2 state cannot be a rapid-equilibrium reaction.

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.

The crustacean gill (Na+,K+)-ATPase: allosteric modulation of high- and low-affinity ATP-binding sites by sodium and potassium

The blue crab, Callinectes danae, tolerates exposure to a wide salinity range employing mechanisms of compensatory ion uptake when in dilute media. Although the gill (Na+,K+)-ATPase is vital to hyperosmoregulatory ability, the interactions occurring at the sites of ATP binding on the molecule itself are unknown. Here, we investigate the modulation by Na+ and K+ of homotropic interactions between the ATP-binding sites, and of phosphoenzyme formation of the (Na+,K+)-ATPase from the posterior gills of this euryhaline crab. The contribution of the high- and low-affinity ATP-binding sites to maximum velocity was similar for both Na+ and K+. However, in contrast to Na+, a threshold K+ concentration triggers the appearance of the high-affinity binding sites, displacing the saturation curve to lower ATP concentrations.Further, a low-affinity site for phosphorylation is present on the enzyme. These findings reveal notable differences in the catalytic mechanism of the crustacean (Na+,K+)-ATPase compared to the vertebrate enzyme.

Cis-allosteric effects of cytoplasmic Na+/K+ discrimination at varying pH. Low-affinity multisite inhibition of cytoplasmic K+ in reconstituted Na+/K(+)-ATPase engaged in uncoupled Na(+)-efflux

In liposomes with reconstituted shark Na+/K(+)-ATPase the effect of cytoplasmic K+ was investigated in the absence of extracellular alkali ions. During such conditions the Na+/K(+)-ATPase is engaged in the so called uncoupled Na+ efflux mode in which cytoplasmic Na+ activates and binds to the enzyme and becomes translocated without countertransport of K+ as in the physiological Na+/K+ exchange mode. In this uncoupled flux mode only low-affinity inhibition by K+cyt is found to be present. The inhibition pattern is consistent with a model in which cytoplasmic K+ exhibit mixed inhibition of Na+ activation, probably by binding at the three cytoplasmic loading sites on E1ATP (E1A). With determined intrinsic binding constants for cytoplasmic Na+ to this form of KS1, KS2, KS3 = 40 mM, 2 mM, 2 mM the inhibition pattern can be simulated assuming three K+cyt sites with equal affinity for Ki = 40 mM, similar to KS1 for the first Na+cyt site. The discrimination between cytoplasmic Na+ and K+ is therefore enhanced by allosteric interaction initiated from the cis-side due to binding of the first Na+, as opposed to K+, which induces the positive cooperatively in the successive Na+ bindings. pH is found to influence the pattern of K+cyt inhibition: A lowering of the pH potentiates the K+cyt inhibition, whereas at increased pH the inhibition is decreased and transformed into a pure competitive competition.

[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.

Interaction of magnesium with the sodium pump of the human red cell

1. In broken red cell membranes, Mg2+ inhibition of Na+,K+-adenosine-5'-triphosphatase (Na+,K+-ATPase) activity was partially competitive with MgATP. Mg2+ inhibition of Na+,K+-ATPase activity was uncompetitive with K+ in broken red cell membranes, and Mg2+ inhibition of ouabain-sensitive K+ influx in K+-free resealed ghosts was uncompetitive with external K+. 2. When Na+,K+-ATPase activity was measured at relatively high K+ concentration, Mg2+ inhibition was partially competitive with Na+. Mg2+ inhibition of ouabain-sensitive K+ influx in K+-free resealed ghosts was competitive with cell Na+. Magnesium was a more effective inhibitor of the uncoupled Na+ efflux in low-Na+ ghosts than in high-Na+ ghosts. 3. These findings indicate that Mg2+ inhibition results from combination of the ion with the enzyme form E2K at high intracellular Na+ and K+, and from combination with the form E1 at low intracellular Na+ and K+. 4. In ghosts containing high concentrations of MgPO4, inhibition of the K+-K+ exchange by Mg2+ was more effective at high than at low nucleotide concentrations. At high MgPO4 and low Mg2+ concentration the activity of the exchange increased monotonically with nucleotide concentration, but at a higher Mg2+ concentration, nucleotide activation of the exchange was biphasic: the K+-K+ exchange rate increased, reached a maximum, and then decreased with increasing nucleotide concentration.

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.

(Na+ + K+)-ATPase: confirmation of the three-pool model for the phosphointermediates of Na+-ATPase activity. Estimation of the enzyme-ATP dissociation rate constant

The dephosphorylation kinetics of acid-stable phosphointermediates of (Na+ + K+)-ATPase from ox brain, ox kidney and pig kidney was studied at 0 degree C. Experiments performed on brain enzyme phosphorylated at 0 degree C in the presence of 20-600 mM Na+, 1 mM Mg2+ and 25 microM [gamma-32P]ATP show that irrespectively of the EP-pool composition, which is determined by Na+ concentration, all phosphoenzyme is either ADP- or K+-sensitive. After phosphorylation of kidney enzymes at 0 degree C with 1 mM Mg2+, 25 microM [gamma-32P]ATP and 150-1000 mM Na+ the amounts of ADP- and K+-sensitive phosphoenzymes were determined by addition of 1 mM ATP + 2.5 mM ADP or 1 mM ATP + 20 mM K+. Similarly to the previously reported results on brain enzyme, both types of dephosphorylation curves have a fast and a slow phase, so that also for kidney enzymes a slow decay of a part of the phosphoenzyme, up to 80% at 1000 mM Na+, after addition of 1 mM ATP + 20 mM K+ is observed. The results obtained with the kidney enzymes seem therefore to reinforce previous doubts about the role played by E1 approximately P(Na3) as intermediate of (Na+ + K+)-ATPase activity. Furthermore, for both kidney enzymes the sum of ADP- and K+-sensitive phosphoenzymes is greater than E tot. In experiments on brain enzyme an estimate of dissociation rate constant for the enzyme-ATP complex, k-1, is obtained. k-1 varies between 1 and 4 s-1 and seems to depend on the ligands present during formation of the complex. The highest values are found for enzyme-ATP complex formed in the presence of Na+ or Tris+. The results confirm the validity of the three-pool model in describing dephosphorylation kinetics of phosphointermediates of Na+-ATPase activity.

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.

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

The influence of Na+ and K+ on the steady-state kinetics at 37 degrees C of (Na+ + K+)-ATPase was investigated. From an analysis of the dependence of slopes and intercepts (from double-reciprocal plots or from Hanes plots) of the primary data on Na+ and K+ concentrations a detailed model for the interaction of the cations with the individual steps in the mechanism may be inferred and a set of intrinsic (i.e. cation independent) rate constants and cation dissociation constants are obtained. A comparison of the rate constants with those obtained from an analogous analysis of Na+-ATPase kinetics (preceding paper) provides evidence that the ATP hydrolysis proceeds through a series of intermediates, all of which are kinetically different from those responsible for the Na+-ATPase activity. The complete model for the enzyme thus involves two distinct, but doubly connected, hydrolysis cycles. The model derived for (Na+ + K+)-ATPase has the following properties: The empty, substrate free, enzyme form is the K+-bound form E2K. Na+ (Kd = 9 mM) and MgATP (Kd = 0.48 mM), in that order, must be bound to it in order to effect K+ release. Thus Na+ and K+ are simultaneously present on the enzyme in part of the reaction cycle. Each enzyme unit has three equivalent and independent Na+ sites. K+ binding to high-affinity sites (Kd = 1.4 mM) on the presumed phosphorylated intermediate is preceded by release of Na+ from low-affinity sites (Kd = 430 mM). The stoichiometry is variable, and may be Na:K:ATP = 3:2:1. To the extent that the transport properties of the enzyme are reflected in the kinetic ATPase model, these properties are in accord with one of the models shown by Sachs ((1980) J. Physiol. 302, 219-240) to give a quantitative fit of transport data for red blood cells.