  Axonemal dyneins are the molecular motors responsible for the beating of
cilia and flagella. These motors generate sliding forces between adjacent
microtubule doublets within the axoneme, the motile cytoskeletal structure
inside the flagellum. To create regular, oscillatory beating patterns, the
activities of the axonemal dyneins must be coordinated both spatially and
temporally. It is thought that coordination is mediated by stresses or strains
that build up within the moving axoneme, but it is not known which components
of stress or strain are involved, nor how they feed back on the dyneins. To
answer this question, we used isolated, reactivate axonemes of the unicellular
alga Chlamydomonas as a model system. We derived a theory for beat regulation
in a two-dimensional model of the axoneme. We then tested the theory by
measuring the beat waveforms of wild type axonemes, which have asymmetric
beats, and mutant axonemes, in which the beat is nearly symmetric, using
high-precision spatial and temporal imaging. We found that regulation by
sliding forces fails to account for the measured beat, due to the short lengths
of Chlamydomonas cilia. We found that regulation by normal forces (which tend
to separate adjacent doublets) cannot satisfactorily account for the symmetric
waveforms of the mbo2 mutants. This is due to the model's failure to produce
reciprocal inhibition across the axes of the symmetrically beating axonemes.
Finally, we show that regulation by curvature accords with the measurements.
Unexpectedly, we found that the phase of the curvature feedback indicates that
the dyneins are regulated by the dynamic (i.e. time-varying) component of
axonemal curvature, but not by the static one. We conclude that a high-pass
filtered curvature signal is a good candidate for the signal that feeds back to
coordinate motor activity in the axoneme.
