Department of Mathematics, Chung-Ang University, Dongjakgu, Heukseokdong, Seoul 156-756, Republic of Korea.
Department of Mathematical Sciences, University of Cincinnati, 4199 French Hall West, Cincinnati, Ohio 45221, USA.
Phys Rev E. 2017 Feb;95(2-1):022410. doi: 10.1103/PhysRevE.95.022410. Epub 2017 Feb 21.
Bacteria such as Vibrio alginolyticus swim through a fluid by utilizing the rotational motion of their helical flagellum driven by a rotary motor. The flagellar motor is embedded in the cell body and turns either clockwise (CW) or counterclockwise (CCW), which may lead to straight forward or backward swimming, or reorientation of the cell. In this paper we investigate the dynamics of the helical flagellum by adopting the Kirchhoff rod theory in which the flagellum is described as a space curve associated with orthonormal triads that measure the degree of bending and twisting of the rod. The hydrodynamic interaction with the flagellum is described by the regularized Stokes formulation. We focus on two different types of instabilities: (1) whirling instability of a rotating helical filament in the absence of a hook and (2) buckling instability of a flagellum in the presence of a compliant hook that links the flagellar filament to the rotary motor. Our simulation results show that the helical filament without a hook displays three regimes of dynamical motions: stable twirling, unstable whirling, and stable overwhirling motions depending on the physical parameters, such as rotational frequency and elastic properties of the flagellum. The helical filament with a hook experiences buckling instability when the motor switches the direction of rotation and the elastic properties of the hook change. Variations of physical parameter values of the hook such as the bending modulus and the length make an impact on the buckling angle, which may subsequently affect the reorientation of the cell.
细菌，如 Alg 溶血性弧菌，通过利用其螺旋鞭毛的旋转运动在液体中游动，该旋转运动由旋转马达驱动。鞭毛马达嵌入在细胞主体中，并顺时针（CW）或逆时针（CCW）旋转，这可能导致细胞向前或向后直线游动，或重新定向。在本文中，我们通过采用 Kirchhoff 杆理论来研究螺旋鞭毛的动力学，其中鞭毛被描述为与正交三体相关的空间曲线，该三体测量杆的弯曲和扭曲程度。鞭毛与流体的水动力相互作用通过正则化 Stokes 公式来描述。我们关注两种不同类型的不稳定性：（1）在没有钩的情况下旋转螺旋丝的旋转涡动不稳定性，以及（2）在存在连接鞭毛丝和旋转马达的顺应性钩的情况下鞭毛的屈曲不稳定性。我们的模拟结果表明，没有钩的螺旋丝显示出三种动力学运动状态：稳定的旋转、不稳定的涡动和稳定的过旋转运动，这取决于物理参数，如旋转频率和鞭毛的弹性特性。当马达改变旋转方向并且钩的弹性特性发生变化时，带有钩的螺旋丝会经历屈曲不稳定性。钩的物理参数值的变化，如弯曲模量和长度，会影响屈曲角，从而可能影响细胞的重新定向。
