The wavelength of the ciliary beat in Chlamydomonas saturates at long ciliary lengths

Cilia and flagella support bending waves that propagate along their lengths. In short cilia, such as those of the motile biflagellate green alga Chlamydomonas reinhardtii, the wavelength of the ciliary beat is approximately proportional to the length of the cilium. On the other hand, for the longer cilia of other organisms, such as sea urchin and mammalian sperm, the wavelength is shorter than the length, so that each cilium supports multiple wavelengths. These different wavelength/length ratios could be due to genetic or biochemical differences between species or due to length-dependent differences in the underlying physics of motility. To distinguish between these possibilities, we measured the beat wavelength in isolated, reactivated cilia from Chlamydomonas mutants in which ciliary length is mis-regulated, leading to cilia that are shorter or longer than the wild-type. This allowed us to probe the transition between short- and long-length behavior in a single organism rather than comparing different organisms. To test quantitatively the relationship between ciliary length and wavelength, we developed a Fourier-based estimator for the beat wavelength, accurate in the regime where the length is greater than half the wavelength. We confirmed that for shorter cilia, up to 15 μm, the wavelength of the dynamic beat increased in proportion to ciliary length, as previously found. By contrast, in lf4 mutants whose cilia are up to 25 μm in length, the wavelength saturated at 15 μm. Similar saturation was observed at both high and low ATP concentrations. These findings likely suggest that the physics of motility is important for determining the wavelength. We propose that the saturating wavelength is a trade-off between maximizing swimming speed (by making the wavelength as short as possible) and minimizing power consumption (by making the wavelength as long as possible).