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

Abstract

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 transportNa+ andK+. 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 Na+/K+- ATPase transport mechanism, we did not rely onATPase 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+ since 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, unspecific site, leading to a two-fold increase in ATPase activity.