Analysis of three-dimensional ciliary beating by means of high-speed stereomicroscopy

Results are presented on the analysis of three-dimensional motion of compound cilia or cirri in voltage-clamped specimens of the protozoan Stylonychia mytilus. Time series of three-dimensional data were obtained by using the anaxial illumination method for simultaneous recording of stereoscopic video images. Data processing involved the following steps: determination of a reference coordinate system based solely on features present in each stereo-pair; tracing of cirral axes in digitized images, conversion to parameter curves by means of least-squares polynomial approximation, conversion of pairs of two-dimensional data to a series of three-dimensional data; correction for distortion due to projective shortening and conversion to a series of polynomial triplets, and analysis of the periodical components of the motion pattern in the frequency domain. Reconstructed beating cycles show typical differences between hyperpolarization-induced ciliary activity and depolarization-induced ciliary activity. Reconstructions of the motion of the basal segment of a cirrus are in agreement with existing data. Analysis of the curvature and torsion of a cirral axis during beating does not reveal any simple pattern of propagated activity within the axoneme. The return stroke may be subdivided into two phases. First, a curvature peak develops proximally. Secondly, a region with increased torsion arises more distally and spreads out in proximal direction. Both curvature and torsion return to minimal values by the beginning of the power stroke.