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.

The attached dataset contains 498 digitized waveforms of axonemes, isolated from Chlamydomonas Reinhardtii cells and reactivated in various conditions.

Preparation and reactivation of axonemes. 
Axonemes from Chlamydomonas reinhardtii cells (received from chlamy.org) were purified and reactivated. The procedures described in the following are detailed in [1].
Chemicals were purchased from Sigma Aldrich, MO if not stated otherwise. In brief, cells were grown in TAP+P medium (TAP medium with extra phosphate) under conditions of continious illumination (2x75 W, fluorescent bulb) and air bubbling at 24◦C over the course of 2 days, to a final density of 106cells/ml. Cilia were isolated using dibucaine, then purified on a 25% sucrose cushion and demembranated in HMDEK (30mM HEPES-KOH, 5mM MgSO4, 1mM DTT, 1mM EGTA, 50mM potassium acetate, pH 7.4) augmented with 1% (v/v) IGEPAL and 0.2mM Pefabloc SC protease inhibitor. The membrane-free axonemes were resuspended in HDMEKP (HMDEK plus 1% (w/v) polyethylene glycol (molecular weight 20kDa)), 30% sucrose, 0.2mM Pefabloc and stored at -80◦C. Prior to reactivation, axonemes were thawed at room temperature, then kept on ice. Thawed axonemes were used for up to 2hr. 

Reactivation was performed in flow chambers with a depth of 100μm, built from easy-cleaned glass and double-sided sticky tape. Thawed axonemes were diluted in HMDEKP reactivation buffer. If not stated otherwise a standard reactivation buffer, containing 1mM ATP and an ATP-regeneration system (5 units/ml creatine kinase, 6mM creatine phosphate) was used to maintain a constant ATP concentration. The axoneme dilution was infused into a glass chamber, which was blocked using casein solution (from bovine milk, 2 mg/mL) for 10 min and then sealed with vacuum grease. Prior to imaging, the sample was equilibrated on the microscope for 5 min and data was collected for a maximum time of 20 min. 

Specific reactivation conditions. 
Temperature series: The temperature was controlled using an objective heater from (Bioptech). If not stated otherwise, the sample temperature was kept constant at 24◦C. Temperature series were acquired by increasing the temperature in 2◦C steps and letting the system equilibrate for 10 min. After equilibration, the target temperature was checked using an inbuilt reference Thermistor.
ATP series: The standard buffer (without ATP) was augmented with different amounts of ATP (50, 66, 100, 240, 370, 500, 750, 1000μM).
Viscosity: The standard buffer was augmented with Ficol 400 (1%, 5%, 10% (w/v)), then axonemes were added to this solution.
Calcium: We used a Ca2+ buffered reac- tivation solution with a concentration of free Ca2+ of 100μM (calculated with the program Maxchelator: https://somapp.ucdmc.ucdavis.edu/pharmacology/bers/ maxchelator). This concentration was chosen as it converts the asymmetric beat into a symmetric one [2].
Taxol: The standard buffer was augmented with 10 μM Taxol, a concentration that stabilizes polymerized microtubules [3], then axonemes were added to this solution. 

Imaging of axonemes. 
The reactivated axonemes were imaged by phase constrast microscopy, set up on an in- verted Zeiss Axiovert S100-TV or Zeiss Observer Z1 mi- croscope using a Zeiss 63 Plan-Apochromat NA 1.4 or a 40x Plan Neofluar NA 1.3 Phase3 oil lens in combination with a 1.6 tube lens and a Zeiss oil condenser (NA 1.4). Movies were acquired using a EoSens 3CL CMOS high- speed camera. The effective pixel size was 139 or 219 nm/pixel. Movies of up to 3000 frames were recorded at a frame rate of 1000 fps. 

High precision tracking of isolated axonemes. 
To track the shape of the axoneme in each movie frame with nm precision, the Matlab-based software tool FIESTA (Ver 1.03) was used [4]. Prior to tracking, movies were background subtracted to remove static inhomogeneities arising from uneven illumination and dirt particles. The background image contained the mean intensity in each pixel calculated over the entire movie. This procedure increased the signal-to-noise ratio by a factor of 3 [1]. Phase-contrast images were inverted. For tracking, a segment size of 733 nm (approximately 5x5 pixels) was used, corresponding to the following program settings: a full width at half maximum of 750nm, and a “reduced box size for tracking especially curved filaments” of 30%. FIESTA fits these segments using two-dimensional Gaussian functions and outputs a spline-interpolated curve.
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[1] J. Alper, V. Geyer, V. Mukundan, and J. Howard, Methods in enzymology (Elsevier, 2013), vol. 524, pp. 343–369.
[2]  K.-i. Wakabayashi, T. Yagi, and R. Kamiya, Cell motility and the cytoskeleton 38, 22 (1997). 
[3] P. B. Schiff, J. Fant, and S. B. Horwitz, Nature 277, 665 (1979). 
[4] F. Ruhnow, D. Zwicker, and S. Diez, Biophysical journal 100, 2820 (2011).