Rotation of F₁-ATPase: How an ATP-driven molecular machine may work

F₁-ATPase is a rotary motor made of a single protein molecule. Its rotation is driven by free energy obtained by ATP hydrolysis. In vivo, another motor, F₀, presumably rotates the F₁ motor in the reverse direction, reversing also the chemical reaction in F₁ to let it synthesize ATP. Here we attempt to answer two related questions, How is free energy obtained by ATP hydrolysis converted to the mechanical work of rotation, and how is mechanical work done on F₁ converted to free energy to produce ATP? After summarizing single-molecule observations of F₁ rotation, we introduce a toy model and discuss its free-energy diagrams to possibly answer the above questions. We also discuss the efficiency of molecular motors in general.