Ciliary beating patterns map onto a low-dimensional behavioral space that accords with a simple mechanochemical model

Abstract

Biological systems are robust to perturbations at both the genetic and environmental levels. Yet, these same perturbations can elicit variation in behavior. The interplay between functional robustness and behavioral variability is exemplified at the organellar level by the beating of cilia and flagella. The complex bending patterns of cilia emerge from the coordinated activities of hundreds of different proteins. Cilia are motile despite wide genetic diversity between and within species, large 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, and as of yet uncharted, behavioral space. To investigate this behavioral space we analyzed the dynamics of isolated cilia from the unicellular algae Chlamydomonas reinhardtii in thirty four different environmental and genetic conditions. We found that, despite large changes in beat frequency and amplitude, the space of waveform shapes is low-dimensional. Two features, parabolicity and asymmetry of the tangent angle, account for eighty per cent of the observed variation. Remarkably, the geometry of this behavioral 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. Our work demonstrates that, despite the molecular complexity of the cilium, the space of beat variations is low dimensional and can be attributed to variation in mechanochemical regulation of the dynein motors.