Human airway ciliary dynamics

Abstract

Airway cilia depend on precise changes in shape to transport the mucus gel overlying mucosal surfaces. The ciliary motion can be recorded in several planes using video microscopy. However, cilia are densely packed, and automated computerized systems are not available to convert these ciliary shape changes into forms that are useful for testing theoretical models of ciliary function. We developed a system for converting planar ciliary motions recorded by video microscopy into an empirical quantitative model, which is easy to use in validating mathematical models, or in examining ciliary function, e.g., in primary ciliary dyskinesia (PCD). The system we developed allows the manipulation of a model cilium superimposed over a video of beating cilia. Data were analyzed to determine shear angles and velocity vectors of points along the cilium. Extracted waveforms were used to construct a composite waveform, which could be used as a standard. Variability was measured as the mean difference in position of points on individual waveforms and the standard. The shapes analyzed were the end-recovery, end-effective, and fastest moving effective and recovery with mean (± SE) differences of 0.31(0.04), 0.25(0.06), 0.50(0.12), 0.50(0.10), μm, respectively. In contrast, the same measures for three different PCD waveforms had values far outside this range.

Figures

Fig. 1.

Orientation axes used for the empirical model with end-recovery cilium (gray). The 3 views depicted in 3D (left) and singly (right) were defined as 1, the profile view (x,z); 2, the frontal view (y,z); and 3, the top view (x,y). The cilium beats in the x,z plane. The direction of average flow is in the x direction. The z-axis is normal to the cell surface. The y-axis is chosen to make the system right-handed orthonormal.

Fig. 2.

Doublet geometry used for displacement calculations. The cross section of the cilium is shown in the nonstandard tip-to-cell view to place the x and y axes (see Fig. 1) with their conventional orientation. The doublet numbering scheme was chosen for easy comparison with other organisms in which structures in the axoneme allow easy orientation relative to the effective stroke and in which doublet 1 has been placed at the trailing (-x) edge (24, 11). A: doublets were placed at a constant distance from the center of the axoneme starting with doublet A1 at the angle αi (185°) from the x-axis. B: effective separation between doublets used in calculations of doublet displacement was the component along the x-axis of segment (bi, ai) for that particular doublet. The values used for placing the segment were as follows: radial position of doublet A-tubule center, 74 nm; tubule radius, 10 nm; separation between A and B tubules, 14 nm; β, 8°; γ, 127°.

Fig. 3.

Reconstructed waveform. The video image (A) of a ciliated cell was viewed with a superimposed model cilium (here in red at the end-recovery position). Left: image when the fit has been completed. The original image without the superimposed model. The waveform was extracted by looking at the video with the superimposed model and adjusting the parameters to match a 2-Gaussian-based model to the original waveform. The result of the waveform reconstruction was a set of curvature parameters for each time point. The ciliary shapes (B) were then calculated from the curvature data (plotted in C as curvature functions of ciliary length). The recovery, effective, and rest phases are drawn in gray, black, and green, respectively. The graphs corresponding to the end-effective and end-recovery times are drawn in red and blue, respectively. D: composite waveform is plotted. It was generated by averaging the shapes from 11 separate empirical waveforms. Scale bars represent 1 μm (x or z in B, C horizontal) and a 1 μm−1 (c in C vertical). The arrow heads in C designate the level with 0 curvature.

Fig. 4.

Paths of cilia intersecting the optical plane traced from a video showing cilia in frontal view. For each cilium, the place on the video at which it crossed the optical section was recorded for each frame, and the paths were constructed from the time series for each cilium. Unlike for top-down or profile views, it was easy to identify single cilia in frontal view. Most cilia stayed within 1 degree of their mean plane, whereas few cilia had paths that deviated more than 5 degrees.

Fig. 5.

Empirical models describing normal ciliary dynamics. The choice of the model used to describe ciliary or flagellar dynamics will depend first on the ability of the model to represent the dynamics and second on the conceptual usefulness of the model to the person doing the fitting. The columns show 3 of the models developed for the fitting software. Top: effective phase (forward). Bottom: recovery phase. Left: 2-Gaussian model used in this paper (Gaussian). Middle: 6-parameter model that describes the waveform as 2 circular arcs each with a constant curvature for a particular shape, a start position, and an end position (arc). Right: (disc. arc), a similar model is shown in which the parameters are allowed to have discontinuities over time. This allows an arc to be propagated distally and then jumped back to the proximal end for “reuse” during a later cycle. The same cycle and position on the video was fitted in each case so that the variability seen comes from the combination of differences in the models and the differences in user action during fitting. None of the differences could be attributed to differences in the models.

Fig. 6.

Waveform as defined by the 2-Gaussian parameters. A and B: curvature is graphed as a function of length along the cilium for 2 different shapes. Inset: corresponding shape. The proximal (blue) and distal (green) Gaussian curves are defined by the parameters in Eq. 1. The scale bars are 1 μm (horizontal) and 1 μm−1 (vertical). C: most important parameters, curvature amplitudes (ai) during the effective and recovery strokes, are plotted over 1 cycle. The graph starts at the end-recovery position when a parameters had large magnitudes and opposite signs. For this waveform, the a2 parameter never became negative, which was the case with most extracted waveforms.

Fig. 7.

Eleven cultures were used to create the composite waveform. In addition, the cultures were refitted after imaging in different places and conditions. Also, some cycles were fitted twice, keeping the model cilium in the same position but starting from a constant vertical cilium. Each waveform is shown in a bordered panel with the effective phase on the left and the recovery phase on the right. The cultures are numbered sequentially in the panels with all the nasal cultures presented first and separated from the bronchial cultures with a double panel border. Two panels with identical culture labels refer to 2 fittings from different videos of the culture done at different times. In addition, some panels have a culture number followed by -d, -D, or -P and refer to a change to be compared with the waveform in the adjacent panel to the left. Duplicate fits (-d) done on the same video but using a different cycle show the variability due inherent in the cycle and in having to reposition the cilium (Cultures 4−7). Sometimes no useful change in the waveform was found. Duplicate fits (-D) done on the exact same cycle but starting from a constant vertical cilium describe the variability that comes purely from the user attempting to fit the cilium to a particular motion seen in the video (Cultures 2, 8, and 10). Duplicate fits (-P) that were done on a culture after it was exposed to polyethylene glycol (PEG, MW 8 × 103) have videos in the Supplemental Videos that show how PEG tends to increase coordination of cilia, making an accurate fitting of PEG-exposed cilia easier than for cilia beating in plain buffer. Each of the videos shows the culture before PEG exposure and then after. Culture 1-P (Supplemental Video 7) shows the cilia during the washout of 40% PEG, which completely stopped motion. Culture 2-P (Supplemental Video 8) shows cilia exposed to 15% PEG. They are very easy to track, but the PEG has caused excessive clumping of cilia. Culture 9-P (Supplemental Video 9) shows cilia exposed to 30%. This was an almost ideal exposure; the ciliary coordination was greatly improved without the clumping seen in Culture 2-P even though the PEG concentration was higher. Other culture-specific factors may have been responsible for the differences seen.

Fig. 8.

Amplitude of ciliary waveform (A) and average speed of cilia (B). In each case the individual datum points are shown on the left. Human bronchial epithelial cells (HBE) and human nasal epithelial (HNE) appeared similar.

Fig. 9.

Maximal speed attained during the effective and recovery phases (A) and the location in space at which that speed was attained (B). The difference between the bronchial and nasal maximum speed was not statistically significant, but the trend was for nasal cells to have a marginally lower maximum speed (A). There was no difference in the position at which this speed was attained (B). In both cases, the maximum speed was reached within 1 micrometer of the center position on the downstream side of mucus flow.

Fig. 10.

Bronchial cultures, maximum speed (A) and takeoff speed (B) of the 2 phases at 25 and 37°C for the effective and recovery phases. The maximum speed increased with temperature as expected (A). The takeoff speed was defined as the speed in the first 0.4 ms of the phase. The takeoff speeds were much higher for the effective phase and increase much more in absolute terms in response to the increase in temperature.

Fig. 11.

Waveforms with parameters outside the normal range of variability. A: waveform obtained from culture exposed to 20% dextran (MW = 2 × 106) and most similar to the normal beat. Unlike the simple timing changes due to temperature changes, this waveform had a greatly decreased end-recovery proximal curvature. B–D: dyskinetic waveforms from 3 different donors. The structural defects associated with the altered waveforms were not known although the waveform in C was suspected to be an inner dynein arm defect. In B, the waveform only develops a single low-amplitude curvature. In C, there are phases analogous to the effective and recovery phases of normal waveforms, but the negative curvatures never fully develop on the proximal portion of the cilium. In D, a full amplitude waveform can be seen, but there is no recognizably distinct effective or recovery phase.

Fig. 12.

Ciliary velocity profiles for the effective (A and B) and recovery (C and D) strokes. The speed of ciliary segments are plotted against their position along the cilium for evenly spaced times throughout the cycle. Each trace shows the speed profile at 1 point in time. The traces are plotted separately for increasing and decreasing speeds, as the cilium approached mid-phase and end-phase respectively. The left-most ends of the traces do not move, as they represent the proximal cilium, whereas the right-most ends map the ciliary tip velocities.

Fig. 13.

Shear angles for end-effective (dashed) and end-recovery (solid) positions for the 11 waveforms used in constructing the standard model, shear angles for the standard model itself (after 11B), and microtubule doublet displacements for all doublets for the standard model (bottom). Given the cross-sectional tracks that the doublets follow, the relative positions of the doublets were calculated according to the geometry shown in Fig. 2. The displacements are for an outer arm dynein base anchor position relative to a probable B-link binding site on the adjacent doublet. The displacement graphs are labeled with the corresponding doublet numbers. With the effective stroke generally moving the cilium in the +x direction (Fig. 1), the cross-bridges with the largest negative and positive displacements would be the lateral ones respectively closest to the -y (stem anchored to doublet 3) and +y (doublet 7) axes. Because dynein is a minus-end directed microtubule motor, a forward-bending motion would require dynein activity on the -y-axis side of the axoneme at some time.

Fig. 14.

Profile sweep area shear angle and doublet sliding rates. For each position (x,z) on the graph, the corresponding time and length along the cilium were used to determine the relative speed of doublets 3 and 4. These speeds were then plotted according to the color scale to the right with the marks denoting sliding speeds in μm/s. The geometric model used to calculate the speeds linearly relates a particular doublet displacement to shear angle. The shear angle rates corresponding to sliding speeds for doublet 3 are provided on the left side of the scale (radians/s).