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 kcat and Km 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.

E2→E1 transition and Rb(+) release induced by Na(+) in the Na(+)/K(+)-ATPase. Vanadate as a tool to investigate the interaction between Rb(+) and E2.

This work presents a detailed kinetic study that shows the coupling between the E2→E1 transition and Rb(+) deocclusion stimulated by Na(+) in pig-kidney purified Na,K-ATPase. Using rapid mixing techniques, we measured in parallel experiments the decrease in concentration of occluded Rb(+) and the increase in eosin fluorescence (the formation of E1) as a function of time. The E2→E1 transition and Rb(+) deocclusion are described by the sum of two exponential functions with equal amplitudes, whose rate coefficients decreased with increasing [Rb(+)]. The rate coefficient values of the E2→E1 transition were very similar to those of Rb(+)-deocclusion, indicating that both processes are simultaneous. Our results suggest that, when ATP is absent, the mechanism of Na(+)-stimulated Rb(+) deocclusion would require the release of at least one Rb(+) ion through the extracellular access prior to the E2→E1 transition. Using vanadate to stabilize E2, we measured occluded Rb(+) in equilibrium conditions. Results show that, while Mg(2+) decreases the affinity for Rb(+), addition of vanadate offsets this effect, increasing the affinity for Rb(+). In transient experiments, we investigated the exchange of Rb(+) between the E2-vanadate complex and the medium. Results show that, in the absence of ATP, vanadate prevents the E2→E1 transition caused by Na(+) without significantly affecting the rate of Rb(+) deocclusion. On the other hand, we found the first evidence of a very low rate of Rb(+) occlusion in the enzyme-vanadate complex, suggesting that this complex would require a change to an open conformation in order to bind and occlude Rb(+).

Rb(+) occlusion stabilized by vanadate in gastric H(+)/K(+)-ATPase at 25°C.

Despite its similarity with the Na(+)/K(+)-ATPase, it has not been possible so far to isolate a K(+)-occluded state in the H(+)/K(+)-ATPase at room temperature. We report here results on the time course of formation of a state containing occluded Rb(+) (as surrogate for K(+)) in H(+)/K(+)-ATPase from gastric vesicles at 25°C. Alamethicin (a pore-forming peptide) showed to be a suitable agent to open vesicles, allowing a more efficient removal of Rb(+) ions from the intravesicular medium than C(12)E(8) (a non-ionic detergent). In the presence of vanadate and Mg(2+), the time course of [(86)Rb]Rb(+) uptake displayed a fast phase due to Rb(+) occlusion. The specific inhibitor of the H(+)/K(+)-ATPase SCH28080 significantly reduces the amount of Rb(+) occluded in the vanadate-H(+)/K(+)-ATPase complex. Occluded Rb(+) varies with [Rb(+)] according to a hyperbolic function with K(0.5)=0.29±0.06mM. The complex between the Rb(+)-occluded state and vanadate proved to be very stable even after removal of free Mg(2+) with EDTA. Our results yield a stoichiometry lower than one occluded Rb(+) per phosphorylation site, which might be explained assuming that, unlike for the Na(+)/K(+)-ATPase, Mg(2+)-vanadate is unable to recruit all the Rb(+)-bound to the Rb(+)-occluded form of the Rb(+)-vanadate-H(+)/K(+)-ATPase complex.