Nonlinear dynamics of cilia and flagella
Nonlinear dynamics of cilia and flagella
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DOI：
10.1103/physreve.79.051918
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发表时间：
2009-05-01
影响因子：
2.4
通讯作者：
Juelicher, Frank
中科院分区：
文献类型：
--
作者：
Hilfinger, Andreas;Chattopadhyay, Amit K.;Juelicher, Frank
纤毛和鞭毛是真核细胞的毛发状延伸，它们产生振荡的节拍模式，可以推动微生物并在细胞表面附近产生流体流动。纤毛和鞭毛的进化高度保守的核心由一个圆柱形排列的九个微管对组成，称为轴丝。轴丝是一种主动弯曲的结构，其运动性是动力蛋白马达蛋白交联微管偶联并产生诱导弯曲变形的应力的作用的结果。周期性的节拍模式是机械反馈的结果，机械反馈导致沿着轴丝沿着自组织弯曲波。使用一个理论框架来描述平面跳动运动，我们推导出一个非线性波动方程，描述轴丝跳动的基本傅立叶模式。我们研究的非线性的作用，并探讨如何振荡的振幅增加附近的振荡不稳定性。此外，我们提出了不同边界条件下的非线性波动方程的数值解。我们发现，非线性波很好地近似的线性不稳定模式的振幅拍模式类似于实验观察到的。
Cilia and flagella are hairlike extensions of eukaryotic cells which generate oscillatory beat patterns that can propel micro-organisms and create fluid flows near cellular surfaces. The evolutionary highly conserved core of cilia and flagella consists of a cylindrical arrangement of nine microtubule doublets, called the axoneme. The axoneme is an actively bending structure whose motility results from the action of dynein motor proteins cross-linking microtubule doublets and generating stresses that induce bending deformations. The periodic beat patterns are the result of a mechanical feedback that leads to self-organized bending waves along the axoneme. Using a theoretical framework to describe planar beating motion, we derive a nonlinear wave equation that describes the fundamental Fourier mode of the axonemal beat. We study the role of nonlinearities and investigate how the amplitude of oscillations increases in the vicinity of an oscillatory instability. We furthermore present numerical solutions of the nonlinear wave equation for different boundary conditions. We find that the nonlinear waves are well approximated by the linearly unstable modes for amplitudes of beat patterns similar to those observed experimentally.