Hines M, Blum J J
Biophys J. 1978 Jul;23(1):41-57. doi: 10.1016/S0006-3495(78)85431-9.
A set of nonlinear differential equations describing flagellar motion in an external viscous medium is derived. Because of the local nature of these equations and the use of a Crank-Nicolson-type forward time step, which is stable for large deltat, numerical solution of these equations on a digital computer is relatively fast. Stable bend initiation and propagation, without internal viscous resistance, is demonstrated for a flagellum containing a linear elastic bending resistance and an elastic shear resistance that depends on sliding. The elastic shear resistance is derived from a plausible structural model of the radial link system. The active shear force for the dynein system is specified by a history-dependent functional of curvature characterized by the parameters m0, a proportionality constant between the maximum active shear moment and curvature, and tau, a relaxation time which essentially determines the delay between curvature and active moment.
推导了一组描述外部粘性介质中鞭毛运动的非线性微分方程。由于这些方程的局部性质以及使用了对大时间步长稳定的克兰克-尼科尔森型向前时间步长，在数字计算机上对这些方程进行数值求解相对较快。对于包含线性弹性弯曲阻力和依赖于滑动的弹性剪切阻力的鞭毛，证明了在没有内部粘性阻力的情况下，弯曲起始和传播是稳定的。弹性剪切阻力源自径向连接系统的一个合理结构模型。动力蛋白系统的主动剪切力由一个依赖于曲率历史的函数指定，该函数由参数m0（最大主动剪切力矩与曲率之间的比例常数）和tau（一个松弛时间，它本质上决定了曲率与主动力矩之间的延迟）表征。
