A kinetic description for sodium and potassium effects on (Na++K+)‐adenosine triphosphatase: a model for a two‐nonequivalent site potassium activation and an analysis of multiequivalent site models for sodium activation
Authors: Lindenmayer George E. , Schwartz Arnold , Thompson Howard K. 
Published: December 2014

1. Dissociation constants for sodium and potassium of a site that modulates the rate of ouabain‐(Na++K+)‐ATPase interaction were applied to models for potassium activation of (Na++K+)‐ATPase. The constants for potassium (0·213 m
M) and for sodium (13·7 m
M) were defined, respectively, as activation constant, Ka and inhibitory constant, Ki.

2. Tests of the one‐ and the two‐equivalent site models, that describe sodium and potassium competition, revealed that neither model adequately predicts the activation effects of potassium in the presence of 100 or 200 m
M sodium.

3. The potassium‐activation data, obtained at low potassium and high sodium, were explained by a two‐nonequivalent site model where the dissociation constants of the first site are 0·213 m
M for potassium and 13·7 m
M for sodium. The second site was characterized by dissociation constants of 0·091 m
M for potassium and 74·1 m
M for sodium.

4. The two‐nonequivalent site model adequately predicted the responses to concentrations of potassium between 0·25 and 5 m
M in the presence of 100–500 m
M sodium. At lower sodium concentrations the predicted responses formed an upper limit for the function of observed activities. This limit was reached at lower concentrations of potassium and higher concentrations of sodium, which inferred saturation of the sodium‐activation sites with sodium.

5. Sodium‐activation data were corrected for sodium interaction with potassium‐activation sites by use of the two‐nonequivalent site model for potassium activation. Tests of equivalent site models suggested that the corrected data for sodium activation may be most consistent with a model that has three‐equivalent sites. Other multiequivalent site models (n = 2, 4, 5 or 6), however, cannot be statistically eliminated as possibilities. The three‐equivalent site activation model was characterized by dissociation constants of 1·39 m
M for sodium and 11·7 m
M for potassium. The system theoretically would be half‐maximally activated by 5·35 m
M sodium in the absence of potassium.

6. Derivation of the model for sodium activation assumed that the affinities of these sites for sodium and potassium are independent of cation interactions with the potassium‐activation sites. Therefore, the kinetic descriptions for sodium and potassium effects form a composite model that is consistent with simultaneous transport of sodium and potassium.

7. Predictions of the composite equation are in reasonable agreement with data obtained by variation of sodium (potassium = 10 m
M), variation of potassium (sodium = 100 m
M) and by simultaneous variation of sodium and potassium (sodium:potassium = 10). Sodium‐activation data (2·5–20 m
M sodium) also agree with predictions of the model in the presence of potassium concentrations which are thought to be present at the sodium‐activation sites in vivo.

8. The kinetic description for sodium (three‐equivalent sites) and potassium (two‐nonequivalent sites) activation of the transport‐ATPase is in accord with the probable stoichiometric requirements of the sodium pump. The model is also in general agreement with other studies on intact transporting systems and (Na++K+)‐ATPase in fragmented membrane preparations with respect to potassium activation, although there is a quantitative disagreement. The model for sodium activation, though consistent with data obtained by other studies on fragmented (Na++K+)‐ATPase preparations, is in apparent variance with much of the data obtained for intact transporting systems. The description for potassium activation suggests that the rates of ouabain binding to (Na++K+)‐ATPase are modulated by competition between sodium and potassium for one of the two potassium‐activation sites.