F1 rotary motor of ATP synthase is driven by the torsionally-asymmetric drive shaft

F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F-0 and F-1, which compete for control of their shared gamma-shaft. We present a self-consistent physical model of F-1 motor as a simplified two-state Brownian ratchet using the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical concepts of linear and rotary motors, and explains the stepped unidirectional rotary motion. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the 'no-load' angular velocity is ca. 400 rad/s anticlockwise at 4 mM ATP. Increasing the pmf torque exerted by F-0 can slow, stop and overcome the torque generated by F-1, switching from ATP hydrolysis to synthesis at a very low value of 'stall torque'. We discuss the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the 'useful outcome' is measured in the number of H+ pushed against the chemical gradient.