Efficient spatiotemporal analysis of the flagellar waveform of Chlamydomonas reinhardtii

Abstract

The 9 + 2 axoneme is a microtubule-based machine that powers the oscillatory beating of cilia and flagella. Its highly regulated movement is essential for the normal function of many organs; ciliopathies cause congenital defects, chronic respiratory tract infections and infertility. We present an efficient method to obtain a quantitative description of flagellar motion, with high spatial and temporal resolution, from high speed video recording of bright field images. This highly automated technique provides the shape, shear angle, curvature, and bend propagation speeds along the length of the flagellum, with ∼200 temporal samples per beat. We compared the waveforms of uniflagellated wild-type and ida3 mutant cells, which lack the I1 inner dynein complex. Video images were captured at 350 fps. Rigid-body motion was eliminated by fast Fourier transform (FFT)-based registration, and the Cartesian (x–y) coordinates of points on the flagellum were identified. These x–y “point clouds” were embedded in two data dimensions using Isomap, a nonlinear dimension reduction method, and sorted by phase in the flagellar cycle. A smooth surface was fitted to the sorted point clouds, which provides high-resolution estimates of shear angle and curvature. Wild-type and ida3 cells exhibit large differences in shear amplitude, but similar maximum and minimum curvature values. In ida3 cells, the reverse bend begins earlier and travels more slowly relative to the principal bend, than in wild-type cells. The regulation of flagellar movement must involve I1 dynein in a manner consistent with these results.

Anomalies in the motion dynamics of long-flagella mutants of Chlamydomonas reinhardtii

“…The first and last image slices of each cell type depict the same flagellar position; the time gap between two successive slices of a montage was kept constant. As expected, wild-type cells exhibited typical waveforms [16] where both moving flagella were in the same plane and the angle of motion remained unchanged. Also, the origin and propagation of the flagellar bends were as expected (Fig.…”

“…To gain insights into the 'breast-stroke' motility [1,[9][10][11], mutants in the radial spokes [10], the central pair microtubules [12], dynein arms [8,[13][14][15][16], striated fibers [17], basal bodies [18][19][20], and a battery of these [21] have been useful. Two types of dynein arm mutants have been used to show that the outer dynein arms provide power to the flagellar beat while the inner arm dyneins are essential for normal motility [13,14].…”

Evaluating efficiency and robustness in cilia design

“…Concise mathematical descriptions date back to G. I. Taylor's swimming sheet [24], albeit for modeling symmetric beating motion. Asymmetric beating patterns were later described using various approaches, including the "biased baseline" mechanisms [25], the Taylor and Fourier series expansions [2] employed above, and more recently, efficient polynomial expansions [26] and curvature-based Fourier series expansions [27]. These methods can reconstruct the beating patterns from given experimental data, but often require sophisticated machinery and large number of parameters.…”

Human airway ciliary dynamics

“…As Bayly et al show (2,3), these data can be combined with hydrodynamic analyses to assess propulsive forces.…”

“…Recently Bayly et al (2,3) have developed a system for the semiautomated extraction of Chlamydomonas reinhardtii flagellar dynamics from videos. These organelles have two types of waveform, one of which is similar to the mammalian ciliary waveform.…”