The Sodium-Potassium Exchange Pump: Relation of Metabolism to Electrical Properties of the Cell: I. Theory

The Na-K exchange pump is represented as a net stoichiometrically coupled reaction, r, involving ATP, Na⁺, and K⁺, and is located in the active region of the cell membrane. The reaction rate is J_r = L_rr (-ΔF_r), where ΔF_r is the free energy change of the reaction. ΔF_r includes membrane potential ø₂ in the absence of 1:1 coupling between Na⁺ and K⁺, and the reaction rate is potential dependent under these conditions. At the same time the pump will produce a potential H which is the difference between membrane potential and the diffusion potential as calculated with constant field assumptions. In the absence of 1:1 coupling, the pump is electrogenic. The feedback relation between reaction rate and membrane potential makes the membrane resistance in the presence of the pump less than or equal to the resistance in its absence, at the same membrane potential. H depends on stoichiometry, reaction rate, and passive ionic conductances. Experimental verification of the model will depend on the accuracy of permeability determinations. Dissipation and efficiency of transport can be calculated also.