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+.