Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: angular torque profile of the enzyme

ATP synthase (F(O)F(1)) operates as two rotary motor/generators coupled by a common shaft. Both portions, F(1) and F(O), are rotary steppers. Their symmetries are mismatched (C(3) versus C(10-14)). We used the curvature of fluorescent actin filaments, attached to the rotating c-ring, as a spring balance (flexural rigidity of 8. 10(-26) Nm(2)) to gauge the angular profile of the output torque at F(O) during ATP hydrolysis by F(1) (see theoretical companion article (. Biophys. J. 81:1234-1244.)). The large average output torque (50 +/- 6 pN. nm) proved the absence of any slip. Variations of the torque were small, and the output free energy of the loaded enzyme decayed almost linearly over the angular reaction coordinate. Considering the threefold stepping and high activation barrier of the driving motor proper, the rather constant output torque implied a soft elastic power transmission between F(1) and F(O). It is considered as essential, not only for the robust operation of this ubiquitous enzyme under symmetry mismatch, but also for a high turnover rate of the two counteracting and stepping motor/generators.