Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
Proc Natl Acad Sci U S A. 2018 Apr 24;115(17):4417-4422. doi: 10.1073/pnas.1712042115. Epub 2018 Apr 9.
The exact mechanism to orchestrate the action of hundreds of dynein motor proteins to generate wave-like ciliary beating remains puzzling and has fascinated many scientists. We present a 3D model of a cilium and the simulation of its beating in a fluid environment. The model cilium obeys a simple geometric constraint that arises naturally from the microscopic structure of a real cilium. This constraint allows us to determine the whole 3D structure at any instant in terms of the configuration of a single space curve. The tensions of active links, which model the dynein motor proteins, follow a postulated dynamical law, and together with the passive elasticity of microtubules, this dynamical law is responsible for the ciliary motions. In particular, our postulated tension dynamics lead to the instability of a symmetrical steady state, in which the cilium is straight and its active links are under equal tensions. The result of this instability is a stable, wave-like, limit cycle oscillation. We have also investigated the fluid-structure interaction of cilia using the immersed boundary (IB) method. In this setting, we see not only coordination within a single cilium but also, coordinated motion, in which multiple cilia in an array organize their beating to pump fluid, in particular by breaking phase synchronization.
精确的机制来协调数以百计的动力蛋白的运动以产生波状的纤毛运动仍然令人费解，并吸引了许多科学家。我们提出了一个纤毛的 3D 模型及其在流体环境中的拍打模拟。模型纤毛遵守一个简单的几何约束，这个约束自然地来自于真实纤毛的微观结构。这个约束允许我们根据单个空间曲线的配置来确定任何瞬间的整个 3D 结构。主动链接的张力，模拟动力蛋白，遵循一个假设的动力学定律，再加上微管的被动弹性，这个动力学定律负责纤毛的运动。特别是，我们假设的张力动力学导致了对称稳态的不稳定性，在这种稳态中，纤毛是直的，其主动链接受到相等的张力。这种不稳定性的结果是一种稳定的、波状的、极限循环的振荡。我们还使用浸入边界（IB）方法研究了纤毛的流固相互作用。在这种情况下，我们不仅看到了单个纤毛内的协调，而且还看到了多个纤毛在阵列中的协调运动，它们通过打破相位同步来组织拍打以泵送流体。
