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-chemical energy transducer with an astounding 360 degrees rotary motion of subunits epsilongammac(10-14) (rotor) against delta(alphabeta)(3)ab(2) (stator). The enzyme's torque as a function of the angular reaction coordinate in relation to ATP-synthesis/hydrolysis, internal elasticity, and external load has remained an important issue. Fluorescent actin filaments of micrometer length have been used to detect the rotation as driven by ATP hydrolysis. We evaluated the viscoelastic dynamics of actin filaments under the influence of enzyme-generated torque, stochastic Langevin force, and viscous drag. Modeling with realistic parameters revealed the dominance of the lowest normal mode. Because of its slow relaxation (approximately 100 ms), power strokes of the enzyme were expected to appear strongly damped in recordings of the angular velocity of the filament. This article describes the theoretical 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 the average curvature and the stochastic fluctuations of actin filaments. Pertinent experiments were analyzed in the companion paper.