The steady-state kinetic mechanism of ATP hydrolysis catalyzed by membrane-bound (Na+ + K+)-ATPase from ox brain IV. Rate constant determination

The expressions for the kinetic constants corresponding to the steady state model for hydrolysis of ATP catalyzed by (Na⁺ + K⁺)-ATPase proposed recently are analyzed with the object of determining the rate constants. The theoretical background for the necessary procedures is described. The results of this analysis are: (1) A small class (four) of rate constants are determined directly by the previously published values of the kinetic constants. (2) For a somewhat larger class of rate constants upper and lower bounds may be established. For several rate constants the upper and lower bounds differ by less than a factor 1.6 (for the ‘(Na⁺ + K⁺)-enzyme’, i.e. the enzyme activity with K⁺ and millimolar substrate concentration) and 1.2 (for the ‘Na⁺-enzyme’, i.e. the activity at micromolar substrate concentrations). (3) Experiments on inhibition by K⁺ of the Na⁺-enzyme at various Mg²⁺ concentrations are reported and analyzed. With the additional assumption that the rate constants governing the addition to ATP of Mg²⁺ is independent of whether or not ATP is bound to an enzyme molecule, a set of consistent values for all the 23 rate constants in the mechanism may be obtained. (4) The values of some rate constants lend further support to the contention discussed in a previous paper that the enzyme hydrolyzes ATP along two kinetically distinct pathways, depending on the presence of K⁺ and on the concentration of substrate, without the necessity of having more than one active substrate site per enzyme unit at any time. (5) The results show that while the two enzyme forms, the ‘Na⁺-enzyme’ E₁ and the “K⁺-enzyme” E₂K, add substrate with (second order) rate constants of the same order of magnitude (differing only by a factor of four in favor of the former), the rate constants for the reverse processes differ by a factor of 100, being largest for the K⁺-enzyme. This is the main reason for the large difference in the Michaelis constants for the two forms reported previously. (6) Compatibility of the model with the well-known rapid dephosphorylation of the phosphorylated enzyme in the presence of K⁺ requires the presence, at non-zero steady state concentration, of an enzyme-potassium-phosphate intermediate, which is acid labile and is therefore not detected as a phosphorylated enzyme using conventional methods.