Collective nonlinear dynamics of cilia and flagella: from n=2 to n>>2 interacting cilia

纤毛和鞭毛的集体非线性动力学：从 n=2 到 n>>2 相互作用的纤毛

• 批准号: 254867216
• 负责人: Professor Dr. Benjamin M. Friedrich
• 金额: --
• 依托单位: Exzellenzcluster Physics of Life (PoL)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/254867216?language=en
• 关键词: Collective; nonlinear; dynamics; cilia; flagella

Self-organized metachronal waves in cilia carpets represent a model system for the spontaneous emergence of spatio-temporal order in active matter. Each beating cilium represents a nonlinear, biological oscillator. The dynamics of several of these oscillators is coupled by the surrounding fluid, which facilitates collective dynamics. Cilia carpets are found on the surface of biological microswimmers, such as Volvox or Paramecium, as well as in the airways, oviducts and brain ventricles of higher animals. Furthermore, cilia carpets represent a minimal system for the study of collective synchronization as observed in collections of biological microswimmers with a single cilium (such as sperm cells), which are characterized by additional translation and rotation degrees of freedom. In this project, we propose a new theoretical description of collective nonlinear dynamics in cilia carpets, with special emphasis on the relationship between alignment of cilia orientation and the emergence of metachronal waves. Thereby, we will understand the interplay between spatial order (cilia alignment) and temporal order (collective synchronization) in an important model system. To achieve this aim, we propose a novel theoretical framework, titled: "Lagrangian mechanics of active systems (LAMAS)", to describe fluid-structure-interactions for active, elastic structures, such as cilia. This formalism generalizes classical Lagrangian mechanics for conservative and dissipative systems to active systems. Key elements of this formalism have been already developed in the first project phase for the case of n=2 cilia, and will now be extended to the case of n>>2 cilia. The results obtained so far include a theory of active fluctuations of the cilia beat, a characterization of the load-response of an individual cilium, as well as a theory of hydrodynamic synchronization for n=2 cilia. By developing the proposed formalism for the model system of cilia carpets, with special emphasis on rotational degrees of freedom of cilia orientation, we expect novel physics of collective nonlinear dynamics of biological microswimmers. We employ innovative methods, such as fast multipole boundary element methods for numerical solution of the Stokes equation, which governs the hydrodynamics of this system. Hydrodynamic interactions between cilia are treated using a generalized Faxen's law. The waveform compliance of the cilia beat is accounted for by incorporating principal deformation modes with dynamic amplitude. Our novel theoretical approach combines different methodologies currently in use in the SPP, including minimal theoretical descriptions with minimal number of degrees of freedom, and fine-grained, yet expensive simulations that allow quantitative predictions on collective dynamics. This project will also contribute to the rational design of artificial arrays of active cilia, drawing inspiration from biological microswimmers.

纤毛地毯中的自组织超时波代表了活性物质中时空有序自发出现的模型系统。每一个跳动的纤毛代表一个非线性的生物振荡器。其中几个振荡器的动力学与周围的流体相耦合，这有利于集体动力学。纤毛地毯存在于生物微泳者的表面，如Volvox或草履虫，以及高等动物的呼吸道、输卵管和脑室。此外，纤毛地毯是研究具有单一纤毛(如精子细胞)的生物微泳者集合中观察到的集体同步的最小系统，其特征是额外的平移和旋转自由度。在这个项目中，我们提出了一种新的理论描述纤毛地毯中的集体非线性动力学，特别强调了纤毛取向与超时波的出现之间的关系。因此，我们将理解在一个重要的模型系统中空间顺序(纤毛排列)和时间顺序(集体同步)之间的相互作用。为了实现这一目标，我们提出了一个新的理论框架，名为“主动系统的拉格朗日力学(LAMAS)”，用于描述活动的弹性结构(如纤毛)的流体-结构-相互作用。这种形式将守恒和耗散系统的经典拉格朗日力学推广到主动系统。这种形式主义的关键要素已经在第一个项目阶段针对n=2纤毛的情况进行了开发，现在将扩展到n&gt；&gt；2纤毛的情况。到目前为止，所获得的结果包括纤毛节拍的主动波动理论、单个纤毛的负载-响应特性以及n=2纤毛的流体动力学同步理论。通过发展提出的纤毛地毯模型系统的形式，特别强调纤毛取向的旋转自由度，我们期待着生物微泳者集体非线性动力学的新物理。我们使用了创新的方法，如快速多极边界元方法来数值求解Stokes方程，该方程控制了该系统的流体动力学。纤毛之间的水动力相互作用用广义的法克森定律来处理。纤毛搏动的波形顺应性通过将主要变形模式与动态幅度相结合来解释。我们新颖的理论方法结合了SPP中目前使用的不同方法，包括具有最小自由度的最小理论描述，以及允许对集体动力学进行定量预测的细粒度但昂贵的模拟。该项目还将从生物微泳者那里获得灵感，为人工活动纤毛阵列的合理设计做出贡献。