The thermodynamic efficiency of the Ca2+-Mg2+-ATPase is one hundred percent

The thermodynamic efficiency of the Ca²⁺-Mg²⁺-ATPase of skeletal sarcoplasmic reticulum has been evaluated by comparing the Ca²⁺ gradient established with the ATP/(ADP*P_i) ratio. The evaluation was made at an external Ca²⁺ level (4.7 × 10^–8 M) which is below theK _m value of 7 × 10^–8 M. The Mg-ATP and phosphate concentrations were held constant (0.1 mM) and the ADP concentration was varied. Maximal uptake to an internal free Ca²⁺ concentration of 17 mM was observed at infinite ATP/(ADP*P_i) ratio (absence of ADP). This corresponds to a Ca²⁺]_i/Ca²⁺]₀ gradient of 3.6 × 10⁵. A Ca²⁺ gradient one-half as large was observed at an ATP/(ADP*P_i) ratio of 3.5 × 10³ M^–1. The square of the Ca²⁺ gradient is shown to be proportional to the ATP/(ADP*P_i) ratio, for finite values of the latter. The proportionality constant is identical to the equilibrium constant for hydrolysis of ATP (9.02 × 10⁶ M) under these conditions (0.1 mM Mg²⁺, 30°C). The intrinsic thermodynamic efficiency of the pump is shown to be 100%, with a maximal uncertainty of 3%. The efficiency is lower under less optimal conditions, when the pump is inhibited and passive leak processes compete.Dedicated to Prof. Philip George, University of Pennsylvania, whose instruction, research, and example made this contribution possible.