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