Spatial Intra- and Intercellular Alignment of Respiratory Cilia and its Relation to Function

Ciliary alignment is considered necessary to establish respiratory tract mucociliary clearance, and disorientation is often associated with primary ciliary dyskinesia. Therefore, there is an urgent need for a detailed analysis of ciliary orientation (CO). We used volume electron microscopy to examine CO relative to the tracheal long axis (TLA) by measuring the inter- and intracellular basal body orientation (BBO) and axonemal orientation (AO), which are considered to coincide, both equivalently indicating the effective stroke direction. Our results, however, reveal that only the mean BBO is aligned with the TLA, whereas the AO determines the effective stroke direction as well as the mucociliary transport direction. Furthermore, we show that even if the mean CO is conserved across cell boundaries, a considerable gradient in CO exists within individual cells, which we suspect to be crucial for the emergence of coordinated ciliary activity. Our findings provide new quantitative insight into CO and correlate this new structural information with mucociliary function.


C.I. for Differences of Intracellular Means [°]
Figure 4: e graph shows 99%-Welch's t-con dence intervals for the di erence between intracellular means. Light gray and dark gray intervals correspond to AO and BBO values, respectively. e dots and triangles indicate the di erence between intracellular means in AO and BBO, respectively. e x-tick labels specify which pair of cells are being compared: for instance, the label 'A1LA2C23' denotes the di erence of intracellular means between cell 2 and cell 3 ('C23') determined on the second image stack, which was derived from ligamentum annulare ('LA2') from animal 1 ('A1').
contradiction from the last point gets resolved by the fact that our sampling was not ran-206 dom (biased representation of the population), which is caused by spatially non-isotropically 207 distributed data being subject to spatial correlations.

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In order to complement the pairwise comparisons between intracellular means, we used where BBO, AO indicates that the sets were constructed with respect to both orientational  In consideration of Tobler's rst law of geography Tobler (1970): 'everything is related to every-232 thing else, but near things are more related than distant things', we used geostatistical methods 233 in order to investigate the spatial dependence of our spatially irregularly distributed data. In order to measure spatial similarity (or rather dissimilarity in our case) we made use of the so-237 called empirical madogram, which is a rst order version of the empirical variogram Legendre 238 and Legendre (1998); Mathur (2015). We used a radial (one-dimensional) version, denoted in 239 the following as |∆α | (r ± δ r ), which provides a measure of how much the orientation of two 240 cilia (α i and α j ) separated by a certain distance deviate from each other and which is de ned 241 as: To put it simply, |∆α | (r ± δ r ) denotes the average angular deviation between pairs of cilia 243 located at ì r i , ì r j , which fall into a certain distance class r ± δ r , i.e. r − δ r ≤ ||ì r i − ì r j || ≤ r + δ r .

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N (r ± δ r ) denotes the number of all pairs of cilia located in respective distance classes. In 245 practice, |∆α | (r ± δ r ) is constructed as follows: for N cilia all N 2 possible pairs are built and 246 subsequently, the associated distances as well as the angular deviations are determined. A er 247 choosing a certain distance class width (2δ ), the average angular deviation in each distance 248 class is calculated. Note that the distance between two cilia located at ì ing two-dimensional variograms, denoted as |∆α | (∆x ± δ x , ∆ ± δ ), which was calculated 254 according to: (5) e directional, or two-dimensional, variogram was applied in its unsigned version (accord-256 ing to the formulation in Eq.5), as well as in its signed version, i.e. ∆α c (∆x ± δ x , ∆ ± δ ). 257 e horizontal and vertical distances between two cilia located at ì r i and ì r j , i.e. ∆x ij and ∆ ij , 258 were determined a er geodesically projecting the coordinates of the respective cilia. In simple 259 terms, the three-dimensional curved cellular surface was a ened by an approximate geodesic 260 mapping on a two-dimensional plane. Subsequently, the spacing between the projected coor-261 dinates, denoted by ∆x and ∆ , were determined.

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In order to determine the direction of clockwise de ection between two cilia located at ì r i and 264 ì r j , respectively, we introduced the angle β, which is de ned as: In Eq.6, sgn(x) denotes the sign function. ∆α represents the angular di erence between cilium 266 i and cilium j: ∆α = α i (ì r i )−α j (ì r j ). Finally, ∆ and ∆x are given by the projection of the relative 267 distance vector (ì r i − ì r j ) on the -and x-axis, respectively.     a 'morphological wave-like pa ern' (see Fig.6B). Unfortunately, the available data sets can 307 neither prove nor disprove such a pluricellular pa ern. is would require to examine larger 308 elds of view providing spatially isotropically distributed data.

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As can be seen in Fig.6C, the signed intracellular variograms show evidence of an intra-

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In approximately 90% of cells, for which we were able to measure at least 30 values for the AO or the BBO, cilia orientation gradually shi ed in a clockwise direction when seen from the 321 right to the le perpendicularly to the TLA, as shown in Fig.6D.

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Discussion and Conclusions 323 e use of a scanning electron microscope equipped with a 3view module allowed the two-fold 324 measurement of the CO in terms of the axonemal orientation (AO), which was unambiguously 325 derived from the central pair orientation (Fig.7), and in terms of the basal body orientation 326 (BBO), which was determined by the direction indicated by the tip of the basal foot (Fig.8).  We used spatial analysis methods in order to detect possible spatial regularities in CO. In  (Fig.7D). 501 We found a considerable axonemal twist along the ciliary long axis (as illustrated in Fig-502 ure 7 - Figure Supplement 1). Its e ect on our orientational measurements was minimized 503 by pursuing each single cilium along its longitudinal axis (z-axis), in order to determine the 504 axonemal as well as the basal body orientation as close as possible to the apical cell surface.

Basal Body Orientation (BBO)
Due to the lack of a quantitative study proving the equivalence of the two orientational ob-507 servables, we decided to measure the orientation of each cilium two-fold (whenever possible), e direction γ c of the mean resultant vector ì R , nally represents the mean direction: and corresponds to the standard deviation of the wrapped normal distribution.
Experimental Procedure and Imaging Setup for the Functional Analy- . e (quasi) three-dimensional graph at the top illustrates the (right-handed) ciliary twist along the ciliary long axis. e lower graph presents the angular measurements of cilium 1-9 illustrated at the top (triangles correspond to BBO-inferred values and circles to AO-inferred values). e abscissa indicates the vertical distance from the cu ing plane in which the basal foot orientation was measured. e grey line results from interpolating and slightly smoothing the data sets. As it can be seen, the e ective stroke direction as inferred from the axonemal orientation varies considerably along the ciliary long axis. erefore, great care was especially taken in order to measure the axonemal orientation as close as possible to the apical cell surface. 37