Viscoelastic dynamics of actin filaments coupled to rotary F-ATPase: Curvature as an indicator of the torque

ATP synthase (F-ATPase) operates as an electrochemical-to-mechanical-to-che mical energy transducer with an astounding 360 degrees rotary motion of sub units epsilon gammac(10-14) (rotor) against delta(alpha beta)(3)ab(2) (stat or). The enzyme's torque as a function of the angular reaction coordinate i n relation to ATP-synthesis/hydrolysis, internal elasticity, and external l oad has remained an important issue. Fluorescent actin filaments of microme ter length have been used to detect the rotation as driven by ATP hydrolysi s. We evaluated the viscoelastic dynamics of actin filaments under the infl uence of enzyme-generated torque, stochastic Langevin force, and viscous dr ag. Modeling with realistic parameters revealed the dominance of the lowest normal mode. Because of its slow relaxation (similar to 100 ms), power str okes of the enzyme were expected to appear strongly damped in recordings of the angular velocity of the filament. This article describes the theoretic al background for the alternative use of the filament as a spring balance. The enzyme's angular torque profile under load can be gauged by measuring t he average curvature and the stochastic fluctuations of actin filaments. Pe rtinent experiments were analyzed in the companion paper.