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In order to evaluate the utilization of variable ATP concentration produced by an oscillatory reaction (as in anaerobic glycolysis), we analyze the thermodynamic efficiency of power output of a cyclic, ATP-driven proton pump found in the plasma membrane of plant cells. The model used includes the coupling of potassium and calcium ion transport. Oscillations in the concentration of ATP can lead to either increases or decreases in efficiency compared to that at constant ATP concentration, with corresponding decreases and increases in dissipation in the irreversible processes of the proton pump, depending on the frequency of the oscillations. Variations of imposed frequencies induce, in the periodic response, variations of phase shifts between the components of the total membrane current, which consist of the pump's proton current and the currents of potassium and calcium ions. Increases in efficiency are attained when the phase shifts are such that maxima (or minima) in the proton pump current and membrane potential occur simultaneously.

Dependence of thermodynamic efficiency of proton pumps on frequency of oscillatory concentration of ATP.