Torque generation mechanism in F motor of ATP synthase elucidated by free-energy and Coulomb-energy landscapes along the c-ring rotation.

F portion of ATP synthase is a proton-motive rotary motor. The Coulombic attraction between the conserved acidic residues in the c-ring and the arginine in the a-subunit (aR) was early proposed to drive the c-ring rotation relative to the a-subunit, and has been actually observed in our previous molecular dynamics simulation with full atomistic description of F embedded in the membrane. In this study, to quantify the driving force, we conducted the umbrella sampling (US) and obtained the free-energy landscape for the c-ring rotation. We first show that the free-energy gradient toward the ATP-synthesis direction appears in the deprotonated state of cE. Using the sampled snapshots that cover a wide range of the rotational angle, we further analyzed the rotational-angle dependence of the hydration and the protonation states and obtained the Coulomb-energy landscapes with a focus on the cE-aR interaction. The results indicate that both the Coulombic solvation energy of cE and the interaction energy between cE and aR contribute to the torque generation for the c-ring rotation.