Nonlinear amplitude dynamics in flagellar beating

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynei...鞭毛与纤毛摆动的物理基础是生物学领域至今尚未完全阐明的重大科学问题。纤毛与鞭毛的核心细胞骨架结构为轴丝（axoneme），即由被动交联蛋白与动力蛋白马达蛋白（dynein motor proteins）连接形成的微管二联体圆柱阵列。上述组分的复杂相互作用可催生自组织弯曲波。尽管学界已提出诸多数学模型以解析该过程，但针对动力蛋白对轴丝非线性特性的调控作用的相关研究仍较为匮乏。本文基于动力蛋白活性的轴丝滑动控制机制，探究鞭毛的非线性动力学行为。该方法揭示了振荡振幅的非线性选择机制——此类机制在既往数学模型中往往被忽略或直接预设。本文推导得到显式非线性方程组并完成数值求解。本研究的分析结果揭示了动力蛋白的时空动力学行为……