Centre for Mathematical Biology, Mathematical Institute, University of Oxford, UK.
J R Soc Interface. 2010 Dec 6;7(53):1689-97. doi: 10.1098/rsif.2010.0136. Epub 2010 May 12.
Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.
在整个生物学领域，细胞和生物体利用鞭毛和纤毛来推动流体并实现运动。这些细胞器的运动，以及对这种运动的感知、响应和调节的相应能力，是健康和疾病许多过程的核心。虽然鞭毛-流体相互作用的力学已经成为广泛数学研究的主题，但这些模型一直局限于几何线性或弱非线性，尽管在生理上观察到了高曲率。我们研究了几何非线性的影响，重点研究了精子鞭毛。对于广泛的生理相关参数，非线性模型预测鞭毛的内部力压缩会引发有效的屈曲行为，导致对称破缺分岔，从而导致波形和游动轨迹发生深刻而复杂的变化，并打破线性理论。出现的波形也会在原本对称的系统中诱导弯曲游动，游动轨迹对头部形状敏感——不需要信号或不对称力。我们得出结论，非线性模型对于理解迁徙人类精子的鞭毛波形至关重要；这些模型对于理解其他系统中运动的鞭毛和纤毛也将非常有价值。
