Twist - torsion coupling in beating axonemes

Motile cilia and flagella are ubiquitous cell appendages whose regular bending waves pump fluids across tissue surfaces and enable single-cell navigation. Key to these functions are their non-planar waveforms with characteristic torsion. It is not known how torsion, a purely geometric property of the shape, is related to mechanical deformations of the axoneme, the conserved cytoskeletal core of cilia and flagella. Here, we assess torsion and twist in reactivated axonemes isolated from the green alga Chlamydomonas reinhardtii . Using defocused darkfield microscopy and beat-cycle averaging, we resolve the 3D shapes of the axonemal waveform with nanometer precision at millisecond timescales. Our measurements reveal regular hetero-chiral torsion waves propagating base to tip with a peak-to-peak amplitude of 22 º/µm. To investigate if the observed torsion results from axonemal twist, we attach gold nanoparticles to axonemes to measure its cross-section rotation during beating. We find that locally, the axonemal cross-section co-rotates with the bending plane. This co-rotation presents the first experimental evidence for twist-torsion coupling and indicates that twist waves propagate along the axoneme during beating. Our work thus links shape to mechanical deformation of beating axonemes, informing models of motor regulation that shape the beat of motile cilia.