Characterizing Dynamic Transitions and Bifurcations to Understand How Flagella Beat

纤毛和鞭毛是薄的、活跃的、梁状的结构，从细胞延伸出来，有节奏地跳动以移动液体或推动细胞。“纤毛和鞭毛如何跳动”仍然是科学界最重要的悬而未决的问题之一。纤毛存在于人体内，位于排列在呼吸道和大脑中充满液体的通道的细胞上。鞭毛与纤毛具有相同的结构，存在于游动的细胞中，如精子。从工程学的角度来看，纤毛和鞭毛是独立和自动产生波浪状运动的微小机器。这些机器的部件此前已经确定，但这些部件如何在没有外部控制的情况下协同工作产生海浪仍然是个谜。该奖项支持对在微观尺度上产生有节奏运动的机制的基础研究。来自工程学、生物学和成像学的研究人员将共同努力，识别和描述行为的关键变化，如开始跳动，或从前向游泳到后向游泳的转变。这个跨学科项目将利用一个针对代表不足群体的学生的暑期研究计划，为来自不同背景的研究生和本科生提供生物和工程交叉领域的培训和研究经验。从动力系统和非线性力学的方法可以阐明鞭毛跳动的机制。鞭毛的数学模型是对机械论假说的明确的定量表述。给定的模型预测特定的行为分叉和转变，以响应内部或环境参数的变化。PIS计划使用模式生物莱茵衣藻实现三个实验目标。在每种情况下，观测结果都将与模型预测进行比较：(1)描述从静态平衡(鞭毛瘫痪)到振荡运动的分叉；(2)描述从不对称波形(前向游泳)到对称波形(后向游泳)的转变；(3)测量与这些响应相关的内部机械变形。PI将用一维偏微分方程组(1D-PDE)对鞭毛进行建模，并使用在先前NSF支持下开发的高效和强大的方法来分析这些PDE的稳定性。将使用高速视频显微镜和图像分析来表征鞭毛的运动，并利用光学和声学捕捉来测量机械性能。我们将探索聚焦离子束扫描电子显微镜(FIB-SEM)显示鞭毛“骨架”(轴丝)变形的能力。聚焦于分叉和转变，PI可以严格检验假设，并牢固地建立鞭毛振荡的基础。

Cilia and flagella are thin, active, beam-like structures that extend from cells and beat rhythmically to move fluid or propel the cell. "How do cilia and flagella beat" remains one of the most important unsolved questions in science. Cilia are found in the human body, on cells that line the airways and fluid-filled passages in the brain. Flagella share the same structure as cilia, and are found on swimming cells, such as sperm. From an engineering perspective, cilia and flagella are tiny machines that independently and automatically produce wave-like motion. The components of these machines have previously been identified, but how these components work together to produce waves, without external control, remains mysterious. This award supports fundamental research into mechanisms that produce rhythmic motions at the microscopic scale. Researchers from engineering, biology, and imaging will work together to identify and characterize key changes in behavior, such as the initiation of beating, or the transition from forward swimming to backward swimming. Leveraging a summer research program for students from under-represented groups, this interdisciplinary project will provide training and research experience at the intersection of biology and engineering, for graduate and undergraduate students from diverse backgrounds.Methods from dynamical systems and nonlinear mechanics can elucidate the mechanism of flagellar beating. Mathematical models of flagella are explicit quantitative statements of mechanistic hypotheses. A given model predicts specific bifurcations and transitions in behavior in response to changes in internal or environmental parameters. The PIs plan to pursue three experimental aims using the model organism Chlamydomonas reinhardtii. In each case observations will be compared to model predictions: (1) Characterize bifurcations from static equilibrium (paralyzed flagella) to oscillatory motion; (2) Characterize transitions from asymmetric waveform (forward swimming) to symmetric waveforms (backward swimming); (3) Measure internal mechanical deformations associated with these responses. The PIs will model flagella with one-dimensional partial differential equations (1D-PDEs), and analyze the stability of these PDEs using efficient and powerful methods developed with prior NSF support. High-speed video microscopy and image analysis will be used to characterize flagella motion, and optical and acoustic trapping will be exploited to measure mechanical properties. The ability of focused ion beam scanning electron microscopy (FIB-SEM) to visualize the deformation of the flagellar "skeleton" (the axoneme) will be explored. Focusing on bifurcations and transitions, the PIs can rigorously test the hypotheses, and firmly establish the basis of flagellar oscillations.