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Cilia and flagella are hairlike organelles that propel cells through fluid.The active motion of the axoneme, the motile structure inside cilia andflagella, is powered by molecular motors of the dynein family. These motorsgenerate forces and torques that slide and bend the microtubule doublets withinthe axoneme. To create regular waveforms the activities of the dyneins must becoordinated. It is thought that coordination is mediated by stresses due toradial, transverse, or sliding deformations, that build up within the movingaxoneme. However, which particular component of the stress regulates the motorsto produce the observed flagellar waveforms remains an open question. Toaddress this question, we describe the axoneme as a three-dimensional bundle offilaments and characterize its mechanics. We show that regulation of the motorsby radial and transverse stresses can lead to a coordinated flagellar motiononly in the presence of twist. By comparison, regulation by shear stress ispossible without twist. We calculate emergent beating patterns in twistedaxonemes resulting from regulation by transverse stresses. The waveforms aresimilar to those observed in flagella of Chlamydomonas and sperm. Due to thetwist, the waveform has non-planar components, which result in swimmingtrajectories such as twisted ribbons and helices that agree with observations.

Beat regulation in twisted axonemes