The F-ATP synthase, consisting of F-1 and F-O motors connected by a central rotor and the stators, is the enzyme responsible for synthesizing the majority of ATP in all organisms. The F-1 (alpha beta)(3) ring stator contains three catalytic sites. Single-molecule F-1 rotation studies revealed that ATP hydrolysis at each catalytic site (0 degrees) precedes a power-stroke that rotates subunit-gamma 120 degrees with angular velocities that vary with rotational position. Catalytic site conformations vary relative to subunit-gamma position (beta(E), empty; beta(D), ADP bound; beta(T), ATP-bound). During a power stroke, beta(E) binds ATP (0 degrees-60 degrees) and beta(D) releases ADP (60 degrees-120 degrees). angstrom rrhenius analysis of the power stroke revealed that elastic energy powers rotation via unwinding the gamma-subunit coiled-coil. Energy from ATP binding at 34 degrees closes beta(E) upon subunit-gamma to drive rotation to 120 degrees and forcing the subunit-gamma to exchange its tether from beta(E) to beta(D), which changes catalytic site conformations. In F1FO, the membrane-bound F-O complex contains a ring of c-subunits that is attached to subunit-gamma. This c-ring rotates relative to the subunit-a stator in response to transmembrane proton flow driven by a pH gradient, which drives subunit-gamma rotation in the opposite direction to force ATP synthesis in F-1. Single-molecule studies of F1FO embedded in lipid bilayer nanodisks showed that the c-ring transiently stopped F-1-ATPase-driven rotation every 36 degrees (at each c-subunit in the c(10)-ring of E. coli F1FO) and was able to rotate 11 degrees in the direction of ATP synthesis. Protonation and deprotonation of the conserved carboxyl group on each c-subunit is facilitated by separate groups of subunit-a residues, which were determined to have different pKa's. Mutations of any of any residue from either group changed both pKa values, which changed the occurrence of the 11 degrees rotation proportionately. This supports a Grotthuss mechanism for proton translocation and indicates that proton translocation occurs during the 11 degrees steps. This is consistent with a mechanism in which each 36 degrees of rotation the c-ring during ATP synthesis involves a proton translocation-dependent 11 degrees rotation of the c-ring, followed by a 25 degrees rotation driven by electrostatic interaction of the negatively charged unprotonated carboxyl group to the positively charged essential arginine in subunit-a.