Abstract
The torque required for the rotation of the rotor of a bacterial flagellar motor (BFM) can be generated from an impulsive force resulting from the collision between the stator and the rotor. The asymmetry in the fluctuations of the tilting angle of the rotor determines the direction of rotation. The expressions of the torque and the step size can be derived from a Langevin equation of motion. The drag coefficient of BFM derived from the Langevin equation and the measured torque–speed (τ-ω) relation is notably high; the viscous force from the environment cannot account for it. The drag force may be caused by the frictional interaction between the bearing-like L- and P-rings of BFM and the cell membrane. Order-of-magnitude estimations of the torque and the step size are consistent with previous experimental observations. The slope of the linear dependence of the rotational frequency on the temperature was estimated and was consistent with the observed value. A simulation device having the structural characteristics of BFM was designed to demonstrate the applicability of the proposed mechanism. Many observations for the actual BFM, such as the bidirectional rotation and the τ-ω relations of the clockwise and counterclockwise rotations, were reproduced in the simulation experiments.
Importance The concept that the torque required for the rotation of the rotor of a bacterial flagellar motor (BFM) can be generated from an impulsive force resulting from the collision between the stator and the rotor is new and effective. The magnitude of the torque and the size of the step derived from the proposed mechanism are consistent with the observed values. The torque-speed (τ-ω) relation might be explained by the frequency-dependent drag force caused by the frictional interaction between the bearing-like L- and P-rings of BFM and the cell membrane. The slope of the linear dependence of the rotational frequency on the temperature is consistent with the observed value, which has not been achieved previously.
