Torsional elasticity and energetics of F1-ATPase.

F(o)F(1)-ATPase is a rotary motor protein synthesizing ATP from ADP driven by a cross-membrane proton gradient. The proton flow through the membrane-embedded F(o) generates the rotary torque that drives the rotation of the asymmetric shaft of F(1). Mechanical energy of the rotating shaft is used by the F(1) catalytic subunit to synthesize ATP. It was suggested that elastic power transmission with transient storage of energy in some compliant part of the shaft is required for the observed high turnover rate. We used atomistic simulations to study the spatial distribution and structural determinants of the F(1) torsional elasticity at the molecular level and to comprehensively characterize the elastic properties of F(1)-ATPase. Our fluctuation analysis revealed an unexpected heterogeneity of the F(1) shaft elasticity. Further, we found that the measured overall torsional moduli of the shaft arise from two distinct contributions, the intrinsic elasticity and the effective potential imposed on the shaft by the catalytic subunit. Separation of these two contributions provided a quantitative description of the coupling between the rotor and the catalytic subunit. This description enabled us to propose a minimal quantitative model of the F(1) energetics along the rotary degrees of freedom near the resting state observed in the crystal structures. As opposed to the usually employed models where the motor mechanical progression is described by a single angular variable, our multidimensional treatment incorporates the spatially inhomogeneous nature of the shaft and its interactions with the stator and offers new insight into the mechanoenzymatics of F(1)-ATPase.