Three-Dimensional Structure of the Trypanosome Flagellum Suggests that the Paraflagellar Rod Functions as a Biomechanical Spring

Flagellum motility is critical for normal human development and for transmission of pathogenic protozoa that cause tremendous human suffering worldwide. Biophysical principles underlying motility of eukaryotic flagella are conserved from protists to vertebrates. However, individual cells exhibit diverse waveforms that depend on cell-specific elaborations on basic flagellum architecture. Trypanosoma brucei is a uniflagellated protozoan parasite that causes African sleeping sickness. The T. brucei flagellum is comprised of a 9+2 axoneme and an extra-axonemal paraflagellar rod (PFR), but the three-dimensional (3D) arrangement of the underlying structural units is poorly defined. Here, we use dual-axis electron tomography to determine the 3D architecture of the T. brucei flagellum. We define the T. brucei axonemal repeating unit. We observe direct connections between the PFR and axonemal dyneins, suggesting a mechanism by which mechanochemical signals may be transmitted from the PFR to axonemal dyneins. We find that the PFR itself is comprised of overlapping laths organized into distinct zones that are connected through twisting elements at the zonal interfaces. The overall structure has an underlying 57nm repeating unit. Biomechanical properties inferred from PFR structure lead us to propose that the PFR functions as a biomechanical spring that may store and transmit energy derived from axonemal beating. These findings provide insight into the structural foundations that underlie the distinctive flagellar waveform that is a hallmark of T. brucei cell motility.


Introduction
The eukaryotic flagellum (synonymous with motile cilium) is a biological machine that drives fluid movement across epithelial surfaces and propulsion of single cells. Biophysical principles underlying flagellar motility, namely dynein-dependent sliding and bending of adjacent microtubules in the axoneme, are universally conserved, as are the basic arrangements of axonemal substructures [1,2,3]. Flagellum motility is critical for normal human development and physiology, defects in motile and non-motile cilia cause a broad spectrum of human diseases, collectively referred to as ''ciliopathies'' [4,5]. Clinical manifestations of defective cilium motility include infertility, respiratory malfunction and left-right axis defects [4,5]. Flagella are also required for the motility of several important human pathogens that infect approximately 0.5 billion people worldwide [6,7]. Movement of these microbial pathogens through heterogeneous media, e.g. host blood and tissues, imposes particular demands on cell motility mechanisms [7,8] and their flagella exhibit characteristic, cell-specific beat forms [5,9,10]. Because the fundamental principles of axonemal motility are conserved, differences in beat form from one cell to another depend on cell-specific elaborations on flagellum architecture. Understanding structural foundations of flagellar motility has the potential to impact efforts to control and treat heritable and infectious disease in humans.
Trypanosoma brucei is a uniflagellated protozoan parasite that causes significant human mortality and limits economic development across sub-Saharan Africa. Without treatment, the human disease, known as African sleeping sickness, is fatal [11]. Flagellum-dependent trypanosome motility is central to transmission and disease pathogenesis [7,8,12]. Motility of the flagellum drives cell propulsion in the vertebrate host and insect vector, influences cell division, and has been implicated in immune evasion in the mammalian bloodstream [13,14,15,16,17]. Besides its canonical role in motility, the T. brucei flagellum functions in cell morphogenesis and host-parasite interactions [18,19,20].
The T. brucei flagellum exhibits an unusual, bihelical beat, in which helical waves of alternating handedness propagate from flagellum tip to base and drive cell movement with the flagellum tip leading [10]. One of the most striking features of T. brucei cell architecture is lateral connection of the flagellum to the cell [20] (Fig. 1A), which allows the flagellar waveform to be directly transmitted to the cell body, causing the cell to move in a distinctive auger-like fashion that provided the basis for naming of the genus [21]. There are several additional distinctive features of T. brucei flagellum architecture that impact flagellum waveform. Most notably the T. brucei flagellum contains a structure known as the paraflagellar rod (PFR) that is attached along the length of the axoneme [22,23] and is required for trypanosome motility [24], though its precise function is unclear. The PFR is unique to trypanosomes and a few related organisms, but extra-axonemal structures are frequently observed in a number of different organisms, such as the outer dense fibers of human sperm flagella [25]. Despite the central importance of the flagellum and flagellar motility to T. brucei biology and disease, the three-dimensional (3D) structural organization of the axoneme and PFR, particularly their relationships to one another, has not been defined.
Studies of flagellar ultrastructure in trypanosomes have traditionally used TEM techniques and freeze-fracture techniques that rely on interpreting 3D structure from 2D projection images [22,23,26,27,28,29,30]. 3D models put forward in these studies propose a lattice-like arrangement in the proximal and distal zones, with an alternate arrangement of filaments in the intermediate zone. In the present study we take advantage of the emerging technology of electron tomography (ET) [31,32] to define the 3D organization of the axoneme and PFR in T. brucei. Our studies provide the first quantitative description of the T. brucei axonemal repeating unit and provide insight into flagellum assembly and function. Given the importance of the flagellum to T. brucei biology and infection, our findings are relevant to understanding the mechanism of disease pathogenesis and development of novel therapeutics.

Results
We collected and analyzed a total of 439 tomographic datasets containing flagella (Video S1) from both frozen, hydrated flagellar skeletons (217 tilt series) (Video S2) and samples prepared using traditional chemical fixation and embedding techniques (222 tilt series) (Fig. 1B-F and Videos S1, S2 and S3). Frozen, hydrated samples offer imaging of native structures in the absence of stain, while stained samples offer high contrast and specimen stability, permitting visualization of fine heterogeneous structural features ( Figure S1). The presence of PFR posed a limitation for frozenhydrated samples, as the PFR and axoneme lie side by side on the grid, restricting possible specimen orientations (Fig 1C). Chemical fixation and resin embedding, on the other hand, provided multiple flagellum orientations in each section (Fig. 1B). Multiple orientations in stained samples facilitated compensation for missing wedge artifacts that otherwise reduce resolution in the z plane of any individual tomogram. The missing wedge was further minimized by employing dual-axis tomography.
Ultrastructure was well-preserved in all specimens, as indicated by the presence of all major axonemal structures, including the 9+2 axoneme, outer and inner arm dyneins, nexin links, radial spokes and central pair complex; together with axoneme-PFR connectors and the proximal, intermediate and distal zones of the PFR (Fig. 1D-F). Asymmetry of the axoneme-PFR interface and orientation of dynein arms allowed unambiguous identification of outer doublets, which are numbered 1-9 according to convention [33,34] (Fig. 1D). No significant differences in the fundamental dimensions of major structural landmarks were observed between stained and frozen-hydrated samples (Fig. 2), indicating that both provide faithful preservation of native flagellar substructures.

The repeating unit of T. brucei axoneme and PFR
Composition and arrangement of the trypanosome axonemal repeating unit has not previously been defined. Digital slices of tomograms were used to define the trypanosome axonemal repeat unit and determine architectural spacing of core substructures (Fig. 3). These numbers were independently confirmed by calculating the spatial frequencies in the horizontal direction (along the long axis of the flagellum) of the first order spots, which are visible in the Fourier transforms (FFT) of PFR and axoneme images ( Fig. 2C-D). A group of three radial spokes was repeated approximately every 100 nm along axoneme (Fig. 2) and defined the repeat unit of the axoneme. Spoke triplets were observed along every outer doublet connected to the A tubule. The distance between spoke heads 1 and 2, numbering from base to tip of the flagellum, was 33 nm (61.5nm, n = 164) and the distance between spoke heads 2 and 3 was 24 nm (61.5nm, n = 154). Each triplet set of spoke heads contacted a network of fibrils projecting from central pair microtubules (Fig 1E-F, 3E-I). Six fibrillar projections were generally observed per triplet group of spoke heads. Spoke heads exhibited a bi-helical arrangement around the central pair apparatus, forming two hemi-helices of alternate handedness (Fig.  S2). Outer arm dyneins were clearly resolved and structures resembling ring-shaped motor domains [35] were resolved in some samples (Fig. 3D). Outer arm dyneins were arrayed along the Atubule with a periodicity of approx. 24nm (63nm, n = 42), thus giving 4 outer arm dyneins per axoneme repeat. Two large clusters of mass density per repeat were apparent on the inner face of each A tubule, beneath the 4 outer arm dyneins, and overlapped with the sites of spoke attachment. Based on their positions relative to other structures, we interpreted these densities to encompass the inner arm dyneins and nexin-dynein regulatory complex [36].
Longitudinal views of the PFR-axoneme interface revealed mass densities that repeat every 57.2 nm (61nm, n = 109 stained; n = 82, frozen) along the length of the PFR (Fig. 1E-F, 2). Digital slices that bisected the radial spokes and the PFR showed that there were approximately two of these densities per axonemal repeat ( Fig. 1E-F). A similar longitudinal periodicity (57.9 nm61nm, n = 299, stained; n = 34, frozen; n = 6, FFT) was observed for bands of density running through the PFR distal domain ( Fig. 1E-F, 2).
The paraflagellar rod is directly connected to outer arm dyneins Electron dense filaments provide a physical connection between the PFR and axoneme in the region between outer doublets (OD) 4, 5, 6 and 7 [26,27]. We found that the axoneme-PFR connectors (Fig. 4) exhibited a defined radial organization, as revealed in transverse views, as well as a longitudinal repeating pattern, as revealed in sagittal and coronal views. We provide here a general description that encompasses the main structural elements (summarized in Fig. 4E, F).
Transverse views of the OD-PFR interface showed a radial organization of connectors to OD4, 5 and 6. In most cases one connector appeared to be (4.1, 5.1 and 6.1) attached directly to the outer arm dynein and the others attached to the A tubule, near the A tubule-B tubule (At-Bt) interface (4.2, 5.2, 6.2), and the B tubule (5.3 and 6.3) (Fig. 4C-F). Because all three connectors were not coplanar they were not always visible at the same time in the thin (3 nm) transverse slices. The OD7-PFR interface was uniquely characterized by a single thick connector (7.3) attached to the B tubule.
Axoneme-PFR connectors were examined in further detail using sagittal and coronal views of digital slices from tomograms of stained samples and sagittal view of digital slices from frozen samples. (Fig. 4C, D). These analyses confirmed the sites of connector attachment to outer arm dyneins and outer doublet microtubules. Additionally, these views revealed complexity of axoneme-PFR connections in the longitudinal axis, showing that several filamentous connectors emanated from each of the mass densities, described above, that occur at 57.2nm intervals along the axoneme-PFR interface (Fig. 4C). Connectors varied in length (7-28nm), depending on the distance between the axoneme and PFR. In longitudinal views, the OD7-PFR interface was again distinguished from the other connections and was comprised of a triplet of connectors. Two of the OD7-PFR connectors formed a Y-shaped structure, while the third remained singular (Fig. 4C-E), which correlates with connectors described previously [26,27,37].
The paraflagellar rod is composed of overlapping laths that are contiguous through the proximal, intermediate and distal domains Thin (1nm) transverse digital slices (Fig. 5A) showed that lines of density that are hallmarks of the intermediate zone in thicker (70 nm) slices (Fig. 1D, Fig. S3A) were segments of longer lines extending from the proximal through the distal zone. A series of 1nm thick slices encompassing a total sample thickness of 20 nm showed that continuity of each line was generally retained through the Z axis, but that the X,Y position of the proximal and distal segments varied considerably from one Z-section to the next (  Coronal digital slices through 3 nm of sample thickness revealed distinctive patterns of density in the proximal, intermediate and distal zones (Fig 5C). Slices through the proximal zone gave a lattice-like appearance, with two intersecting arrays of parallel lines, oriented at approximately 246u and +46u degrees relative to the flagellum's long axis. The 246u lines were slightly more distinct. Lines within each array were separated by 40 to 50nm and intersected the other array at 57 nm intervals along the flagellum's long axis (Fig. 5B, C). Digital slices through the intermediate zone showed parallel linear densities, spaced 31nm (61nm, n = 134) apart, running along the flagellum's long axis. Occasionally, amorphous densities between lines were observed. Each linear density in the intermediate zone was aligned with intersection points of the proximal zone lattice. Digital slices through the distal zone gave an appearance similar to that seen in the proximal zone, but with lattice intersection points shifted 28-29 nm along the flagellum's long axis. A single TEM image encompassing the entire 200-nm thick sample gave a composite view that correlated with the overlap of individual digital slices obtained from tomograms (Fig. S5).
Perspective views of tomograms (Fig. 5B) indicated that diagonal lines of density in the proximal and distal zones were derived from twisting segments of the straight lines in the intermediate zone. This result supports the view from transverse digital slabs that each linear density prominent in the intermediate zone is part of a continuous line of density extending from the proximal through the distal zone. Thin (3nm) sagittal views cutting through all PFR zones revealed stacked filaments parallel to the flagellum's long axis (Fig. 5D, red arrow) and obliquely orientated filaments extending from the proximal through the distal zone (Fig. 5D, blue arrow).
Surface renderings of segmented tomogram volumes provided 3D views of PFR structure, including conformational changes that mark the interface between PFR zones (Fig. 5E-F and Video S4). The proximal zone lattice consisted of two distinct structural elements. The dominant elements, corresponding to the 246u lines of the lattice, were wall-like structures, which we term proximal laths. Adjacent laths were connected by rod-like elements, which we term struts, that correspond to the +46u lines of the lattice. The intermediate zone was also comprised of parallel wall-like structures, termed intermediate laths, which run the length of the flagellum. Proximal and intermediate laths were connected by twisting structural elements at the interface between zones. Similar twisting motifs formed the intermediate-distal zone interface. The distal lattice was comprised of the same structural elements observed in the proximal lattice, namely laths corresponding to the 246u diagonal array, that were interconnected by struts, corresponding to the +46u array. The twisting motifs at the interface between zones, were spaced at 57 nm intervals, with a 28-29-nm offset between the proximal-intermediate and intermediate-distal interface. The combined 3D imaging data indicated a PFR structure composed of a repeating unit that has a longitudinal periodicity of 57-nm and a lateral periodicity of 31 nm (Fig. 5C). Laterally adjacent repeat units were offset by 28-29 nm along the flagellum's long axis.

Discussion
We define the axoneme and PFR repeat units of the T. brucei flagellum and identify connections from the PFR to dynein motors that drive axonemal motility using dual-axis ET and cryo ET. Robustness of the data is evidenced by identical dimensions of major structural landmarks in frozen-hydrated samples and stained, embedded samples. Our findings provide a structural foundation for considering molecular mechanisms of PFR assembly and flagellar motility in trypanosomes.
The number of spokes per axoneme repeat can be either be two, as in Chlamydomonas [38], or three, as in mammalian sperm and sea urchins [39,40]. T. brucei has three spokes per repeat ( Fig. 1 and 3) and spoke spacing (Fig. 2) agrees well with published dimensions for spoke triplets in other organisms [39,40,41]. T. brucei spoke heads exhibit a bi-helical arrangement around the central pair apparatus, with two hemi-helices of alternate handedness ( Figure S2). This arrangement is similar to that reported for sea urchin sperm [39] and different from the uniform helical arrangement of spoke heads in Chlamydomonas and Tetrahymena axonemes [39]. The bi-helical arrangement of spoke heads likely imposes structural constraints on the central pair apparatus and might explain the restricted range of central pair microtubule rotation relative to outer doublet microtubules in T. brucei and sea urchins [13,17,42,43].
We observed structural diversity among filamentous connectors that link the axoneme to the PFR. Axonemal dynein motors on OD4, 5 and 6 are directly connected to the PFR. To our knowledge, this link and details of the OD4-6 connectors have not been described previously. Morphology of the OD7 connectors reported here indicate they correspond to the axoneme-PFR connectors described in freeze-fracture and TEM studies [26,28,44]. PFR-dynein connectors have not been described previously, but are observed upon careful re-examination of published TEM data, for example Figure 4a of [26] and Figure 5 of [44]. The PFR imposes structural restrictions on axonemal beating [24,45] and is a scaffold for assembly of enzymatic and regulatory activities [46,47,48]. These observations have fuelled the hypothesis that the PFR plays an active role in directing axonemal motility [49], although the mechanisms are unclear. We propose that the physical connections between the PFR and outer arm dyneins provide a mechanism by which chemical and/or mechanical regulatory signals originating in the PFR can be directly transmitted to the axonemal dynein motors. Loss of outer arm dyneins causes backward cell locomotion and reversal of the tip-to-base waveform that is a hallmark of trypanosome flagellar motility [13,50,51]. Thus, PFR connection to outer arm motors may have particular relevance to the distinctive flagellar beating of trypanosomatids.
The PFR is a distinctive feature of the kinetoplastid flagellum, is required for normal flagellar motility and is essential for parasite viability [14,24,52], raising interest in the PFR as a potential drug target [49]. However, despite being described almost fifty years ago [22], PFR structure has remained enigmatic. Here we describe a PFR architecture in which individual structural elements of each PFR zone are interconnected to form a single superstructure. In the intermediate zone, parallel wall-like laths run the length of the flagellum. These laths are connected by twisting structural elements to obliquely oriented laths in the proximal and distal zones, where rod-like struts connect adjacent laths, giving rise to the lattice-like appearance of coronal sections.
The specific architecture described here was revealed using 3D imaging and is, to our knowledge, not described elsewhere. Previous 3D models for PFR structure are based on serial section TEM and freeze-fracture approaches [26,27,30,53]. The most relevant comparisons are with the pioneering works of Fuge [27] on T. brucei and Farina [26] on Herpetomonas and Phytomonas. Recent 2D freeze fracture studies [30] build on earlier work by comparing bent and straight fragments of the structure. Models put forward in these earlier studies [26,27]   observed in our raw tomogram analyses (Fig. 5D). We thus propose that intermediate zone laths (Fig. 5E, F) correspond to closely-stacked longitudinal filaments of the Fuge model, enmeshed with angled filaments of the Farina model. Proximal and distal zone laths correspond to stacks of thin (7 nm) filaments observed by Fuge and Farina. Rod-like struts that connect adjacent laths in the proximal and distal zones of our model correspond to structures reported as ''oblique bands of density'' [27], or ''thick'' (,25 nm) filaments [26]. Twisting structural elements at the interface between zones are unique features of our model. These features are deep within the structure itself and, therefore, not likely to be revealed in the earlier studies, owing to the inherent limitations of 2D projection images to reveal internal features of 3D objects. A scaled graphical model incorporating our data in the context of earlier models is shown in Figure 4G and Video S5.
Beating of the T. brucei flagellum [10] (Video S6) requires that the PFR withstand biomechanical stresses, including shear, torsion, compression and extension. Interconnection of alternating structural motifs, presented by proximal/intermediate/distal PFR zones, each with distinct biomechanical properties, provides an architecture that can withstand extensive structural deformation and recovery. Pivotal to this architecture is the interface between alternating structural motifs, which we observe to be twisted elements connecting laths at the transition between proximal-intermediate and intermediate-distal zones. We suggest that the twisting elements buffer displacements between zones caused by deformation of structure in response to stress. The entire structure can thus accommodate a wide range of movements and further, has the capacity to store potential energy as the flagellum twists. This energy would be released as the structure returns to its relaxed state. Taken as a whole, we propose the PFR superstructure acts as a biomechanical spring, which disperses and transmits energy derived from axonemal beating. Such activity would be particularly useful for facilitating the bihelical waveform that drives T. brucei motility [10].
Our model also offers insights into mechanisms of PFR assembly. The twisting interface between zones suggests models for molecular assembly of the PFR. The major PFR protein components are two repetitive proteins, PFR1 and PFR2. The PFR also includes substoichiometric amounts of other proteins containing variations on the repeating amino acid domain in PFR1 and 2 [49]. In our model, lath structures in each zone are composed of stacked filaments. We suggest that these filaments represent polymers of PFR1 and 2, which are located throughout the PFR structure [44]. Incorporation of substoichiometric isoforms of PFR1/2-repeat containing proteins into laths could induce deformation of underlying structure, giving rise to the twists that characterize the interface between zones. This hypothesis could now be tested by employing specific antibodies to determine the location of each isoform.
During the course of review, a separate group reported structural analysis of the T. brucei flagellum using CryoET [54]. In that elegant work, the authors focused on characterizing the repeating unit of the PFR in the straight and bent states. Through subtomographic averaging, based on a 56-nm periodicity, the structures of the distal domain of the PFR in both states were obtained, leading to a ''jackscrew'' model. The periodicity of the distal domain and portions of the proximal domain in a straight state correlate with our measurements of these regions. This work complements the detailed architectural organization including PFR, axoneme and connectors reported in the current study.

Materials and Methods
Procyclic 29-13 T. brucei parasites [55] were cultivated as described [17]. Asynchronous mid-log-phase cell cultures were collected by centrifugation at 2,000xg and washed three times with 1X PBS. Flagellar skeletons were prepared using a modified version of [56], as detailed in [57]. Briefly, cells were re-suspended to 2610 8 cells/ml in PMN buffer, containing 1%NP40 (1% NP40, 10 mM NaPO4 pH 7.4, 150 mM NaCl, 1 mM MgCl2, 25 mg/ml aprotinin, 25 mg/ml leupeptin, and protease inhibitor cocktail). DNase I (Worthington) was added at 0.25 mg/ml to remove mitochondrial DNA. Following a 10 minute incubation at room temperature, samples were incubated on ice for 30 minutes, and flagellar skeletons were collected by centrifugation at 16,000xg for 10 minutes. Flagellar skeleton pellets were subsequently transferred to a fresh tube and washed twice with PMN buffer. This procedure allowed for one-step fractionation to obtain flagellar skeletons and improved sample preservation [57].

Sample preparation for Transmission electron microscopy
For stained and embedded samples, flagellar skeletons were fixed in 1% glutaraldehyde and 1% paraformaldehyde in 0.1M sodium cacodylate buffer containing 1% tannic acid at pH 7.2, post-fixed in 1% osmium tetroxide with 1.5% potassium ferrocyanide. Samples were dehydrated using an ascending acetone series, followed by infiltration and embedding in Eponate 12 (Ted Pella, Co) as described in [58]. To prepare frozen samples for cryoET, freshly prepared flagellar skeletons in PMN buffer at a concentration of 1610 10 cell equivalents/ml were mixed with protein-A gold (10nm) purchased from Cell Microscopy Center of University Medical Center Utrecht at a 70:1 v/v mixing rate. A 3 ml droplet of the goldcontaining flagellar skeleton sample was applied onto 200 mesh Quantifoil 3:1 mm holey-carbon coated grids, blotted by filter paper, and plunge-frozen in ethane cooled by liquid nitrogen.

Electron tomography
Electron tomography was performed in an FEI Technai G 2 TF20, operated at 200kV as previously described [59]. Briefly, the images were recorded using a TVIPS F415MP 16 megapixel CCD camera at an original magnification of 29,000x and 50,000x. Stained sections were imaged using dual-axis tilt tomography with Batchtomography software from FEI. Each series was taken with a defocus of 23 mm from 270u to +70u tilt along alpha and beta tilt axes, with 2u increments at the lower tilt angles (range640u) and 1u increments above +40u and below 240u. Dual axis data sets were achieved by taking single tilt data sets at several points of the grid before manually rotating the grid by 90u and taking the second tilt series at the same locations.
CryoET data sets were taken using low dose imaging protocols using FEI Technai G 2 TF20, operated at 200kV, and FEI Titan Krios, operated at 300kV using a Gatan energy filter 2002 and 2kx2k CCD camera. Focus and tracking positions were located along the holder tilt axis 5-7 mm away from the exposure area, to prevent exposing the region of interest during focus and tracking. Single tilt data sets from 70u to +70u were taken at a 2u intervals. The defocus used was 25 mm. The dosage of cryo-samples was adjusted so that the total accumulated electron dose for each entire tilt series is between 70-100 e/A 2 .

Data processing
Images in each tomography tilt series were aligned and combined to generate 3D tomograms using eTomo (IMOD, Boulder, CO) [60,61]. CryoET data were aligned using standard gold bead tracking using a minimum of 5 fiducials. Fiducialless alignment was initially used for stained sample data alignment followed by patch tracking with patches set to 400x400 pixel size. The two tomograms generated for each area of interest were aligned by matching distinctive features in both tomograms and combined also using eTomo to create a single final tomogram. To reduce image noise, the tomograms were first filtered using the median function of the clip IMOD program and subsequently lowpass filtered to 40 Å resolution. Z-axis adjustment was made on the stained samples to correct for shrinkage according to IMOD protocols (3Dmod users guide). Segmentation and image processing were conducted using Amira 5.2.0 (Visage Imaging).
Segmentation is based upon distinct characteristics of the data, the density of stain and structural morphology. Regions of interest (ROI) were selected (using the ''brush'' tool), and data within the ROI displayed using automatic functions (''thresholding'' and ''smoothing''). Different colors in the volumes were the result of displaying several ROI (''materials'') together. Videos were generated using the demo-maker and movie-maker functions on Amira. Videos of tilt series and tomograms were generated using 3Dmod (IMOD, Boulder, CO) and VideoMach (Version 5.4.8, Gromada) was used to combine images into a video.
Measurements to quantify dimensions in the flagellum were made using the Amira measuring tool of frozen and stained samples. Measurements were confirmed by independently applying Fourier transform to axoneme and PFR images from frozen flagellar skeletons (generated using EMAN, National Center for Macromolecular Imaging, TX). Spatial frequencies were calculated along the horizontal plane (along the long axis of the flagellum) of the power spectrum using the bright spots as markers. Images used for the diffraction data were taken with the TF20 and Titan Krios microscopes and boxed to contain only axoneme or PFR structures (Fig. 2B). All analyses were conducted with relatively straight segments of flagellar skeletons, so as to minimize the influence of sample curvature on arrangement of structural elements. Measurements using Amira were made between edges of structures to capitalize on the high contrast.