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