Data from: 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 dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.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（cytoskeleton）结构为轴丝（axoneme），它是由被动交联蛋白与动力蛋白马达蛋白（dynein motor proteins）连接而成的微管二联体（microtubule doublets）圆柱阵列。这些组分间的复杂相互作用可催生自组织弯曲波。尽管已有诸多数学模型试图阐释这一过程，但针对动力蛋白在轴丝非线性特性中所扮演角色的研究仍寥寥无几。本文通过引入适配动力蛋白活性的轴丝滑动调控机制，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——这类机制在过往数学模型中往往被忽略或预设。我们推导得到了显式非线性方程组并完成数值求解。分析结果展现了不同马达活性、介质黏度及鞭毛弹性参数下，动力蛋白群体的时空动力学特征与鞭毛形态演化规律。不稳定模态可通过动力蛋白动力学与鞭毛形态的耦合作用实现饱和，无需引入非线性轴丝响应机制。因此，本研究揭示了轴丝摆动中不稳定模态饱和的全新机制。