How Cilia or Eukaryotic Flagella Beat

Abstract

Cilia or eukaryotic flagella are slender minute organelles responsible for moving the immersing fluid relative to a cell and sensing the environment. When motile these 200-nm-diameter “hairs” are driven by thousands of tiny motors along their length to facilitate traveling waves of bending. These motors overcome the energy dissipation of moving the surrounding fluid. Their core structure is nine doublet microtubules arranged around a central-pair. In planar beating, motors walk toward where the cilium is attached to the cell body. In so doing, they bend the elastic cilium; then motors on the other side bend it in the opposite direction. Existing models lack consistency with the data; hence there is no consensus on how cilia beat. However, this self-organized mechanical oscillator can be explained by the collective properties of the ATP-fed motors and the compliant viscoelastic elements of the longitudinal and bending springs of the longitudinally differentiated cilium in interaction with the dissipative environment. For the uniform diameter Ciona sperm cilium whatever the [ATP] or external viscosity each wave formed and propagated has close to the same energy. The motors switch side dominance at zero ciliary curvature when the bend reaches maximum mechanical potential energy and bend instability. The flexure rigidity and spring constants have been determined along the length. Ciliary beating frequency, wavelength, amplitude and wave energy are explained. Our model fits the data well. It will be interesting to see what modifications cilia with different beat patterns and tapering have made in terms of mechanism. Also interesting will be how temporal control of the described physical and chemical parameters of beating enables their diverse behavior as in phototaxis, chemotaxis and avoidance of obstacles.