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 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.