Mathematical modelling of ATP, K and Na interactions with (Na + K)-ATPase occurring under equilibrium conditions

The controlling effect of ATP, K⁺ and Na⁺ on the rate of (Na⁺ + K⁺)-ATPase inactivation by 7-chloro-4-nitrobenzo-2-oxa-1,3-diazole (NBD-Cl) is used for the mathematical modelling of the interaction of the effectors with the enzyme under equilibrium conditions.

1. 1. Of a series of conceivable interaction models, designed without conceptual restrictions to describe the effector control of inactivation kinetics, only one fits the experimental data described in a preceding paper.

2. 2. The model is characterized by the coexistence of two binding sites for ATP and the coexistence of two separate binding sites for K⁺ and Na⁺ on the enzyme-ATP complex. On the basis of this model, the effector parameters fitting the experimental data most closely are estimated by means of nonlinear least-squares fits.

3. 3. The apparent dissociation constants for ATP of the enzyme-ATP complex or of the enzyme-(ATP)₂ complex are computed to lie near 0.0024 mM and 0.34 mM, respectively, irrespective of whether K⁺ and Na⁺ were absent or K⁺ and K⁺ plus Na⁺, respectively, were present in the experiments.

4. 4. The origin of the high and the low affinity site for binding of ATP to the (Na⁺ + K⁺)-ATPase molecule is traced back to the coexistence of two catalytic centres which, although primarily equivalent as to the reactivity of their thiol groups with NBD-Cl, are induced into anticooperative communication by ATP binding and thus show an induced geometric asymmetry.

Keywords: (Na⁺ + K⁺)-ATPase; SH-group alkylation; Inactivation kinetics; Mathematical modelling; Substrate affinity