Hines M, Blum J J
Biophys J. 1979 Mar;25(3):421-41. doi: 10.1016/S0006-3495(79)85313-8.
The cross-bridge formalism of T. Hill has been incorporated into the nonlinear differential equations describing planar flagellar motion in an external viscous medium. A stable numerical procedure for solution of these equations is presented. A self-consistent two-state diagram with curvature-dependent rate functions is sufficient to generate stable propagating waves with frequencies and amplitudes typical of sperm flagella. For a particular choice of attachment and detachment rate functions, reasonable variation of frequency and wave speed with increasing viscosity is also obtained. The method can easily be extended to study more realistic state diagrams.
T. 希尔的横桥形式主义已被纳入描述外部粘性介质中平面鞭毛运动的非线性微分方程。本文提出了一种求解这些方程的稳定数值方法。具有曲率相关速率函数的自洽双态图足以产生具有精子鞭毛典型频率和振幅的稳定传播波。对于附着和脱离速率函数的特定选择，还可以得到频率和波速随粘度增加的合理变化。该方法可以很容易地扩展到研究更实际的状态图。
