Simple mechanism whereby the F<inf>1</inf>-ATPase motor rotates with near-perfect chemomechanical energy conversion

F<inf>1</inf>-ATPase is a motor enzyme in which a central shaft γ subunit rotates 120° per ATP in the cylinder made of α<inf>3</inf>β<inf>3</inf> subunits. During rotation, the chemical energy of ATP hydrolysis (ΔG<inf>ATP</inf>) is converted almost entirely into mechanical work by an elusive mechanism. We measured the force for rotation (torque) under various ΔG<inf>ATP</inf> conditions as a function of rotation angles of the γ subunit with quasistatic, single-molecule manipulation and estimated mechanical work (torque × traveled angle) from the area of the function. The torque functions show three sawtooth-like repeats of a steep jump and linear descent in one catalytic turnover, indicating a simple physical model in which the motor is driven by three springs aligned along a 120° rotation angle. Although the second spring is unaffected by ΔG<inf>ATP</inf>, activation of the first spring (timing of the torque jump) delays at low [ATP] (or high [ADP]) and activation of the third spring delays at high [P<inf>i</inf>]. These shifts decrease the size and area of the sawtooth (magnitude of the work). Thus, F<inf>1</inf>-ATPase responds to the change of ΔG<inf>ATP</inf> by shifting the torque jump timing and uses ΔG<inf>ATP</inf> for the mechanical work with near-perfect efficiency.