Wolgemuth C W, Powers T R, Goldstein R E
Department of Physics, University of Arizona, Tucson, Arizona 85721, USA.
Phys Rev Lett. 2000 Feb 14;84(7):1623-6. doi: 10.1103/PhysRevLett.84.1623.
Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.
受细胞生物物理学中多种现象的启发，包括细菌鞭毛运动以及DNA转录和复制，我们研究了具有扭转和弯曲弹性的旋转驱动细丝的过阻尼非线性动力学。扭转注入、扭转扩散和缠绕不稳定性之间的竞争由用于扭转和弯曲演化的耦合偏微分方程描述。分析和数值方法阐明了扭转/弯曲耦合，并揭示了由霍普夫分岔分隔的两种状态：(i) 扩散主导的轴向旋转，即旋转，以及 (ii) 稳态曲轴运动，即回旋。研究了这些现象对自推进的影响，并提出了实验测试。
