Effects of ATP on the Steady-State Level of the Phosphoenzyme of Pig Kidney Na⁺/K⁺-ATPase

Abstract

The Albers-Post model for the hydrolysis of ATP by the Na⁺/K⁺-ATPase postulates that the release of Pi from ATP is preceded by the formation of at least two conformers of a phosphoenzyme as shown in Scheme I During steady-state, the rate of ATP hydrolysis (v_i) will be equal to the net rate of any of the elementary steps of the reaction. Hence in the absence of Pi:

$$v_i = k_{\textit{31}} \times E_\textit{2}P = K_{\textit{23}} \times E_\textit{1}P - K_{\textit{32}} \times E_\textit{2}P$$

$$\textup{Since} EP_T = E_\textit{1}P + E_\textit{2}P, \textup{it follows that}: EP_T =\frac{E_\textit{2}P \times (K_{\textit{31}} + k_{\textit{32}} +k_{\textit{23}})}{k_{\textit{23}}} \\ \textup{and therefore} \frac{v_i}{EP_T} = \frac{k_{\textit{31}} \times k_{\textit{23}}}{k_{\textit{31}} + k_{\textit{32}} + k_{\textit{23}}}$$

Equations essentially similar to Eqn (2), will apply for reaction schemes including any amount of additional phosphoenzymes. Eqn (2) evinces one of the fundamental features of the class of models shown in Scheme 1, i.e., that the ratio between steady-state activity and steady-state level of total phosphoenzyme will be independent of the rate of phosphorylation and of the transitions among the different dephosphoforms of the ATPase.