Energetic Considerations of Ciliary Beating
The internal mechanism of cilia which is responsible for their beating is among the most ancient biological motors on an evolutionary scale. Ciliary beat cycles consist of two phases: the effective stroke, where the cilium moves approximately as a straight rod, and the recovery stroke, where it bends and rolls close to the surface in a mostly tangential motion.
It is commonly agreed that for efficient functioning, the effective stroke is designed to encounter strong viscous resistance and to generate thrust, whereas the recovery stroke is designed to return to starting position while avoiding viscous resistance as much as possible. Metachronal coordination between cilia, which occurs when many of them beat close to each other, is believed to be an autonomous result of the hydrodynamical interactions in the multiciliary system. Qualitatively, metachronism is understood as a way for minimizing the energy expenditure required for beating.
This paper presents a quantitative investigation of the energetic advantages of metachronism. Using a new method for computing the work by a model cilium beating in a viscous fluid we demonstrate that the energy expenditure during the effective stroke for a single cilium is approximately five times the amount of work done during the recovery stroke. Investigation of multicilia configurations shows that having neighboring cilia beat metachronally is energetically advantageous and perhaps crucial for multiciliary functioning. Finally, the model is used to approximate the number of dynein arm attachments that are likely to occur during the effective and recovery strokes of a beat cycle.
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