Waveform of free, hinged and clamped axonemes isolated from C. reinhardtii: influence of calcium

The beating of cilia and flagella is essential to perform many important biological functions, including generating fluid flows on the cell surface or propulsion of micro-organisms. In this work, we analyze the motion of isolated and demembranated flagella from green algae Chlamydomonas reinhardtii, which act as ATP-driven micro-swimmers. The beating flagella of Chlamydomonas exhibit an asymmetric waveform that is known to involve the superposition of a static component, corresponding to a fixed, intrinsic curvature, and a dynamic wave component traveling from base-to-tip at the fundamental beat frequency, plus higher harmonics. Here, we analyse free, hinged and clamped axonemes using principal component analysis. The axonemal motion is described with a high degree of accuracy, taking into account only the first four dominant eigenmodes. Our analysis suggests that the wave motion can be alternatively described with Fourier modes, with a wavelength λ, larger than the length of the filament L (λ/L ≈ 1.3). Within this representation, we demonstrate that the main base-to-tip traveling wave component coexists with standing waves. Finally, we report the effect of calcium on the constituting wave components and find that the static mode is the most sensitive component to the calcium ion concentration.