Ciliary beating patterns map onto a low-dimensional behavioural space

Biological systems are robust to perturbations at both the genetic and
environmental levels, although these same perturbations can elicit
variation in behaviour. The interplay between functional robustness and
behavioural variability is exemplified at the organellar level by the
beating of cilia and flagella. Cilia are motile despite wide genetic
diversity between and within species, differences in intracellular
concentrations of ATP and calcium, and considerable environment
fluctuations in temperature and viscosity. At the same time, these
perturbations result in a variety of spatio-temporal patterns that span a
rich behavioural space. To investigate this behavioural space we analysed
the dynamics of isolated cilia from the unicellular algae Chlamydomonas
reinhardtii under many different environmental and genetic conditions. We
found that, despite large changes in beat frequency and amplitude, the
space of waveform shapes is low-dimensional in the sense that two features
account for 80% of the observed variation. The geometry of this
behavioural space accords with the predictions of a simple mechanochemical
model in the low-viscosity regime. This allowed us to associate waveform
shape variability with changes in only the curvature response coefficients
of the dynein motors.