Geometric somersaults of a polymer chain through cyclic twisting motions

摘要

This study explores the significance of geometric angle shifts, which we call geometric somersaults, arisingfrom cyclic twisting motions of a polymer chain. A five-bead polymer chain serves as a concise and minimalmodel of a molecular shaft throughout this study.We first show that this polymer chain can change its orientationabout its longitudinal axis largely, e.g., 120◦, under conditions of zero total angular momentum by changingthe two dihedral angles in a cyclic manner. This phenomenon is an example of the so-called “falling cat”phenomenon, where a falling cat undergoes a geometric somersault by changing its body shape under conditionsof zero total angular momentum. We then extend the geometric somersault of the polymer chain to a noisy andviscous environment, where the polymer chain is steered by external driving forces. This extension shows thatthe polymer chain can achieve an orientation change keeping its total angular momentum and total externaltorque fluctuating around zero in a noisy and viscous environment. As an application, we argue that the geometricsomersault of the polymer chain by 120◦ may serve as a prototypical and coarse-grained model for the rotarymotion of the central shaft of ATP synthase (FOF1-ATPase). This geometric somersault is in clear contrast to thestandard picture for the rotary motion of the central shaft as a rigid body, which generally incurs nonzero totalangular momentum and nonzero total external torque. The power profile of the geometric somersault implies apreliminary mechanism for elastic power transmission. The results of this study may be of fundamental interestin twisting and rotary motions of biomolecules.