Torque generation through the random movement of an asymmetric rotor: A potential rotational mechanism of the γ subunit of F(1)-ATPase

Rotations of F-ATPase and V-ATPase analyzed by a torque approach

F-type ATP synthase (F-ATPase) and vacuolar ATP hydrolase (V-ATPase) are well-known biomolecular motors, which play significant catalytic roles in ATP synthesis and ATP hydrolysis reactions. Their rotational torques are important factors involved in their rotational behavior that can be measured experimentally but with considerable difficulty. To overcome this difficulty and thereby provide an in-depth understanding of their operation mechanism, we herein carry out simple and fast computer modelling to study the two proteins, using our torque approach that relies on interatomic forces and coordinates of unequilibrated configurations taken from brief molecular dynamics (MD) simulations. As predicted by the torque approach, F-ATPase is demonstrated to be a random rotor, but it prefers to rotate in clockwise direction (as seen from the membrane toward the protein) for ATP synthesis, owing to the predominantly negative angle-averaged torques. By contrast, V-ATPase tends to rotate only in counterclockwise direction for ATP hydrolysis, due to the almost uniform averaged positive torques generated by the unidirectional rotation near the three catalytic sites. The rotational behaviors of both proteins are also affected by the surrounding solvent which can promote or hinder the internal rotation. By combining the torque approach with classic force-field MD simulations, the torques of two biomolecular motors can be calculated economically, and are found to agree with previous experiments and theoretical calculations. This work demonstrates that our torque approach can be extended to the field of biology and can help gain a deeper insight into the mechanistic rotation of biomolecular motors with modest computation time.Communicated by Ramaswamy H. Sarma.

Surface-Mounted Dipolar Molecular Rotors Driven by External Electric Field, As Revealed by Torque Analyses

Driven by a high-speed rotating electric field (E-field), molecular motors with polar groups may perform a unidirectional, repetitive, and GHz frequency rotation and thus offer potential applications as nanostirrers. To drive the unidirectional rotation of molecular motors, it is crucial to consider factors of internal charge flow, thermal noise, molecular flexibility, and so forth before selecting an appropriate frequency of a rotating E-field. Herein, we studied two surface-mounted dipolar rotors of a "caltrop-like" molecule and a "sandwich" molecule by using quantum-mechanical computations in combination with torque analyses. We find that the rotational trend as indicated by the magnitude and the direction of torque vectors can sensitively change with the lag angle (α) between the dipolar arm and the E-field. The atomic charges timely flow within the molecule as the E-field rotates, so the lag angle α must be kept in particular intervals to maintain the rotor's unidirectional rotation. The thermal effect can substantially slow down the rotation of the dipolar rotor in the E-field. The flexible dipolar arm shows a more rigid geometry in the E-field with higher rotation speed. Our work would be useful for designing E-driven molecular rotors and for guiding their practical applications in future.

A physical mechanism underlying the torque generation of the bacterial flagellar motor

This study proposes a physical mechanism underlying the torque generation of a bacterial flagellar motor (BFM), in which the torque for the rotation of the rotor can be generated from impulsive forces resulting from collisions between the randomly moving stator and rotor. The torque required for the rotation of the rotor may be generated through two coexisting mechanisms: mechanism (A), in which the stator collides with the rotor, whose rotation axis fluctuates asymmetrically, generating a torque in the direction of the rod, and mechanism (B), in which physical collisions between the stator and the asymmetric [Formula: see text]and [Formula: see text] generate the torque in the direction of the rod. Mechanism (A) might be related the bidirectional rotation and the tumbling of the motion of the cell. Mechanism (B) might be related to occurrence of the steps in the time traces of the rotational angle, backward stepping or switching of the rotational direction, and the knee-shaped [Formula: see text]-[Formula: see text] relation. The above-mentioned characteristics of the rotation of BFM are reproduced in a model device designed to confirm the applicability of the proposed concept to real BFM. Moreover, a prediction of the disappearance of the knee-shaped [Formula: see text]-[Formula: see text] relation of the actual BFM at a high temperature is proposed.