Structure of the trypanosome paraflagellar rod and insights into non-planar motility of eukaryotic cells

Eukaryotic flagella (synonymous with cilia) rely on a microtubule-based axoneme, together with accessory filaments to carryout motility and signaling functions. While axoneme structures are well characterized, 3D ultrastructure of accessory filaments and their axoneme interface are mostly unknown, presenting a critical gap in understanding structural foundations of eukaryotic flagella. In the flagellum of the protozoan parasite Trypanosoma brucei (T. brucei), the axoneme is accompanied by a paraflagellar rod (PFR) that supports non-planar motility and signaling necessary for disease transmission and pathogenesis. Here, we employed cryogenic electron tomography (cryoET) with sub-tomographic averaging, to obtain structures of the PFR, PFR-axoneme connectors (PACs), and the axonemal central pair complex (CPC). The structures resolve how the 8 nm repeat of the axonemal tubulin dimer interfaces with the 54 nm repeat of the PFR, which consist of proximal, intermediate, and distal zones. In the distal zone, stacked “density scissors” connect with one another to form a “scissors stack network (SSN)” plane oriented 45° to the axoneme axis; and ~370 parallel SSN planes are connected by helix-rich wires into a paracrystalline array with ~90% empty space. Connections from these wires to the intermediate zone, then to overlapping layers of the proximal zone and to the PACs, and ultimately to the CPC, point to a contiguous pathway for signal transmission. Together, our findings provide insights into flagellum-driven, non-planar helical motility of T. brucei and have broad implications ranging from cell motility and tensegrity in biology, to engineering principles in bionics.


Introduction
Eukaryotic cells depend on flagella (synonymous with cilia 1 ) to move through and respond to their external environment. In humans, flagellum motility and signaling are essential for normal development, physiology, and reproduction [2][3][4] . In protists and fungi, flagella enable navigation through diverse environments 1,5-8 , direct movement and interaction of gametes for reproduction 9,10 , and contribute to transmission and pathogenesis of microbial pathogens [11][12][13][14] . The structural foundation of the flagellum is the axoneme, a microtubule-based molecular machine that drives motility and provides a platform for assembly of signaling machinery 15 . In addition to the axoneme, flagella of many organisms contain accessory structures, such as outer dense fibers and fibrous sheath of human sperm 16 , mastigonemes of algae 17 , and the paraflagellar rod (PFR) of euglenoids and kinetoplastids 18,19 . Biochemical and genetic analyses have demonstrated that these extra-axonemal structures contribute to flagellum motility and signaling functions, but the structural foundation for how they achieve this is unclear 17,[20][21][22] . Recent studies have resolved structures of the axoneme and axoneme subcomplexes in great detail, providing important insights into mechanisms and structural foundations of flagellum function [23][24][25][26][27][28] . However, much less is known about 3D ultrastructures of extraaxonemal filaments, and this presents a gap in understanding structural foundations of flagellum function in eukaryotes.
Among the most enigmatic of extra-axonemal structures is the PFR of euglenoids and kinetoplastids, a taxonomic group that includes several human and animal pathogens, such as T. brucei (Fig. 1a) and related kinetoplastid parasites, as well as free-living Euglena and related species 18,19 . T. brucei causes fatal sleeping sickness in humans and related diseases in livestock throughout sub-Saharan Africa, while other kinetoplastid parasites cause Chagas disease in the Americas and Leishmaniasis in tropical and subtropical regions globally 29 . The T. brucei PFR is a massive paracrystalline filament that runs parallel to the axoneme along most of its length and is connected to axoneme doublet microtubules (DMTs) 4-7 19,30,31 . The exact function of the PFR is not known, but it is required for cell motility, and studies of mutants lacking major portions of the PFR suggest it provides elastic resistance to axoneme bending 20,21,32 . Such internal resistance would be required for efficient movement in viscous environments where an organism must push against high external resistance, e.g., blood and other tissues encountered by T. brucei 5,33 . T. brucei motility is characterized by a vigorous, non-planar helical motion that must accommodate frequent flagellum beat reversals and collisions with external structures 5,[34][35][36] . Therefore, the PFR must have flexibility while maintaining structural integrity. The PFR also provides a platform for cAMP and Ca ++ signaling systems that control motility and host-pathogen interactions 13,[37][38][39][40][41][42] , and for metabolic activities that may participate in energy transfer within the flagellum 42,43 . Trypanosome motility and PFR-dependent cAMP signaling are required for transmission and pathogenesis of these deadly pathogens [11][12][13]39 . Therefore, the PFR presents both a model for understanding functions of extra-axonemal structures of eukaryotic flagella, and an attractive drug target in a group of organisms that pose a substantial global public health burden.
Proteomic and biochemical analyses have provided information on PFR composition 40,[44][45][46] and conventional electron microscopy and early tomography studies have provided a low resolution model for PFR structure 30,31,[47][48][49][50] . However, high-resolution 3D structures of the PFR and the PFR-axoneme interface are not available. Consequently, how the PFR and axoneme combine to direct and regulate the hallmark non-planar helical movement of T. brucei 5,35,36 remains a mystery.
Here, we have employed a combination of cryoET with Volta phase plate (VPP), energy filtering, and direct electron-counting imaging, together with subtomographic averaging 51 , to determine the structure of the entire T. brucei axoneme with PFR. The subtomographic averaged structure of the PFR distal zone reveals a largely hollow architecture comprised of planar networks of stacked "scissors densities" placed each 54 nm along and oriented at 45°to the axoneme axis and connected by thin "wire densities". Such an architecture suggests tensegrity 52 , rather than space-filling observed in other cellular structures 53 , as the means to achieve competing needs of integrity and flexibility. Structural features of wire densities are reminiscent of bundled helices, consistent with secondary structure predictions of major PFR proteins. Based on the sub-tomographic averaged structure of the PFR-axoneme interface and interconnections within the PFR, our work also provides details on interconnections within and between the PFR and axoneme that may provide a means for signaling within these complexes suggested previously 24,27,45,54 . Together, our results provide insights into flagellar motility of T. brucei and have broad implications regarding functions of extra-axonemal filaments that are a common, yet enigmatic feature of eukaryotic flagella.

Resolving T. brucei flagellum components with different periodicities
Presence of the PFR in T. brucei flagellum poses two major challenges for structural studies: possible structure distortion due to increased sample thickness and restricted flagellum orientation on the cryoEM grid due to deviation from circularity. To cope with these challenges, we developed a procedure to evaluate the width of the axoneme prior to recording 26 and relied on sub-tomographic averaging with wedge-mask differences 55 . We also used a machine learning-assisted method to compensate for the missing wedge problem (Materials and Methods). Tilt-series of T. brucei detergent-extracted flagellum samples from bloodstream form parasites were recorded in a Titan Krios electron microscope equipped with a VPP, an energy filter and a direct electron detector in electron-counting mode. Tomograms (Fig. 1b, c) were assembled as described in methods. The structure was well-preserved as indicated by presence of all major flagellum components, including the "9 + 2" axoneme, extra-axonemal PFR, and PFR-axoneme connectors (PACs) (Fig. 1b, c; Supplementary Fig. S1 and Supplementary Movie S1). Asymmetry of the PFR-axoneme interface, local arrangement of A and B tubules of DMTs, and orientation of axonemal dyneins, allowed unambiguous identification of the nine DMTs, numbered according to established convention 56 (Fig. 1c).
Based on cross-sectional views in traditional transmission electron microscopy (TEM) studies, the PFR consists of three structurally distinct zones: proximal, intermediate, and distal 30 , and these are evident in tomograms (Fig. 1b, c; Supplementary Movie S1). One can readily identify repeating densities in the PFR distal zone that have the appearance of "comb teeth" in longitudinal sectional views (Fig. 1b, d; cyan arrows). Periodicities of major axoneme substructures, e.g., radial spokes (RS), outer arm dyneins (OADs) or inner arm dyneins (IADs), CPC and microtubule inner proteins (MIPs), vary but all are integer multiples of the underlying tubulin dimer repeat of 8 nm 26,57 . By contrast, we determined the periodicity of PFR distal zone repeating units to be 54 nm along the axoneme axis (Materials and methods). A 54 nm repeat interval is consistent with earlier measurements of 54−57 nm 44,48-50 . Since 54 is not a multiple of 8, resolving the details of axoneme and PFR structures simultaneously by sub-tomographic averaging is not possible. We therefore had to design a stepwise workflow incorporating both interactive and automatic particle-picking strategies (Materials and methods) to obtain sub-tomographic averaged structures for individual flagellum components, and then fitted them into a montage (Fig. 1d, e; Supplementary Movie S2) (Materials and methods). Visualizing the RS, tubulin dimer, OAD, CPC, PACs, and different zones of PFR in this way allows us to decipher interactions among these components, as detailed below.
The PFR distal zone consists of a series of parallel SSN planes, aligned at 45°to the axoneme axis and interconnected by coiled-coil wires Previous electron tomography studies have provided important insights into building blocks of the PFR 48-50 , but were unable to fully resolve the PFR organization. Using our newly developed script called Propagate (Materials and methods), together with the PEET program 55,58 , we were able to iteratively identify and refine the paracrystalline lattice parameters of the distal zone, first in one dimension along the axoneme axis and then in all three dimensions (see details in Materials and methods) (Fig. 2). Sub-tomographic averaging of the distal zone using 1362 sub-tomograms from 12 tomograms yielded an averaged 3D structure of the distal zone at~28.5 Å resolution based on Fourier shell correlation (FSC) analysis at the 0.143 coefficient criterion ( Supplementary Fig. S4a). b-d, f Shaded surface views of the boxed region in a after rotating as indicated. The "comb teeth" densities in Fig. 1b are resolved in greater detail in b and pointed out by cyan arrows in both. b is the side view; c is looking perpendicular to an SSN plane; d is looking parallel to the SSN planes; f is looking from the axoneme to the PFR distal zone. e Same view as d, showing density slice (5 nm thick). In d and e, wires 1-5 joining four consecutive SSN planes form a shape of a smiling face. The viewing directions of b-e are indicated within panel f, with letters corresponding to each panel and viewing directions indicated by an arrow next to the eye symbol. Scale bar for panels b-f is shown between panels c and f. g Schematics depicting arrangement of SSN planes (purple) and wires (orange) at the interface of the PFR distal and intermediate zones. The viewing direction of g 1 is the same as that of f except that the horizontal direction is now along the axoneme axis. Decreased intensity of orange wires indicates further away from the viewer. h Geometry schematic illustrating the three vectors of the triclinic crystalline lattice discovered in the distal zone. The semi-transparent gray densities in the background of h 2 is the same as that in f, and rotations for h 3 and h 4 are indicated.
The refined paracrystalline lattice is triclinic (i.e., none of the three lattice angels is orthogonal) with the unit lengths of vectors a * ; b * ; c * of 18.0 nm, 47.0 nm, and 41.5 nm and angles of α, β, γ at 76°, 78°, and 79°, respectively (Fig. 2h). The dimension a * is along the vertical direction in Fig. 2a-e and 2h 1,3,4 ; that is, a * is perpendicular to the axoneme axis. Surprisingly, the other two axes of the unit cell are neither along the axoneme axis (dashed cyan line, Fig. 2h 2 ) nor orthogonal to dimension a * . Thus, the unit cell is neither orthorhombic 48 , nor helical 44 . Rather, when examining from the top of the axoneme down to the PFR (Fig. 2f, h 2 ), dimension b * is oriented approximately 45°from the axoneme axis, which may account for the~45°angle previously observed in negative-stained samples 44,49 . Dimension c * is oblique The main building block of this plane is what we call density scissors (delineated by the tan surface rendering in Fig. 2c), which is visible when viewing the face of the plane from the perpendicular perspective. This scissors-like building block differs from a previously proposed "jackscrew" model, which was based on viewing the distal zone from the axoneme side of the PFR 50 . Density scissors stack vertically upon one another along dimension a * (Fig. 2c, h 3 ), with 4−6 scissors per stack. Each stack in turn connects horizontally with adjacent scissors stacks, forming a planar network of stacks, which we term a "scissors stack network" plane (SSN plane), that is oriented 45°to the axoneme axis. Each SSN plane encompasses 5 stacks, 1 with 5 pairs of scissors, 3 with 6 pairs of scissors, and one near the boundary of the PFR on DMT4 side with 4 pairs of scissors but with densities exhibiting differences from the other 4 stacks. Thus, a 20 µm long PFR would include~370 SSN planes with~27 pairs of scissors per plane. Extending between SSN planes are thin densities, which we call wires. When viewed parallel to SSN planes (Fig. 2d, e; Supplementary Movie S3), wires from adjacent planes appear to extend contiguously to form a smile-like arc (0.8 radians) that spans four SSN planes, with two end segments (wires 1 and 5) and three middle segments (wires 2-4). When viewed from above ( Fig. 2f), the end segments of each arc deviate slightly from a straight line formed by the three middle segments. Wire 1 from one arc abuts wire 5 of an adjacent arc and their structures appear distinct (Fig. 2f). When the density threshold is lowered, wires 1 and 5 appear to interact ( ). Therefore, in the structure examined, the distal zone is a remarkable and intricate 3D nanoscale crystal consisting of many SSN planes aligned 45°to the axoneme axis and joined together by density wires, with~90% empty space when calculated using a threshold as in Fig. 2f.
To interpret structures constituting the unit cell of the distal zone, we examined elements that make up each SSN plane (same color in Fig. 3a) and connect with neighboring SSN planes (different colors in Fig. 3a). We segmented these elements in such a way that each scissors density and its connecting wires remain together (Fig. 3b, c). These structural elements can be brought together within a single unit cell by translation of one unit length along the vectors of the triclinic unit cell (Fig. 3d−f). Figure 3b is the view looking perpendicularly at the SSN plane and highlights one scissors stack in blue, with a single pair of scissors density colored tan. The handles of the scissors are at the bottom with curved blades projecting toward the top (Fig. 3b, e). Rotating this view 90 degrees (Fig. 3c) reveals the wire densities that extend between adjacent SSN planes described above. Current resolution of the PFR structure precludes identification of molecules that make up the scissors densities and wires, but the extended rod-shape of wires is consistent with structures exhibited by coiled-coil helices. Biochemical analyses indicate that major structural components of the PFR are two proteins, PFR1 and PFR2 59,60 . Deletion mutants of either PFR1 or PFR2 failed to assemble a complete PFR structure 21,32,61,62 , demonstrating that, despite sharing highpercentage amino acid identity, PFR1 and PFR2 are essential and non-redundant components of the PFR. In some cases, a rudimentary proximal domain is retained 21,32,62 . Secondary structure predictions of PFR1 and PFR2 from T. brucei and homologs from other kinetoplastids showed that more than 80% of the protein is predicted to form helices ( Fig. 3g) 60 . The N-terminal half contains helices of short lengths, followed by unusually long helices. The longest predicted helices of PFR1 and PFR2 contain 258 amino acids and 222 amino acids, respectively, which correspond to a length of 41.3 nm and 35.5 nm, respectively (~1.6 Å/amino acid in an alpha helix). In our sub-tomographic averaged structure, the lengths of individual rod-shaped density wires range from 40 nm to 45 nm. The diameter of the wire, 4 nm, would accommodate a coiled coil of 3−4 helices ( Fig. 3h−j), suggesting that multiple subunits of PFR1 and PFR2 molecules could contribute to each arm of the wire. The shorter helices and coiled-coil sequences predicted could contribute to the formation of the globular region of the scissors densities. Additional PFR components have been identified 42 , including PFC3 and PAR1 that are predicted to assemble into extended coiled-coil structures, and we expect these may also contribute to wires or other PFR structures. However, unlike PFR1 and 2, RNAi knockdown of PFC3 or PAR1 does not noticeably affect PFR ultrastructure 63 , indicating they are not required for assembly of the main PFR structural elements.

Contiguous overlapping layers in the proximal zone and flexible linkages in the intermediate zone
The organizations of the PFR proximal and intermediate zones remain a mystery, likely due to difficulties in sub-tomographic averaging caused by lack of knowledge about the periodicity, flexible nature of the structure, and the large volume to resolve. In 3D reconstructed tomograms after missing-wedge compensation, one can readily discern  (Fig. 4a, b). These densities connect to wires 1 and 5 of the distal zone (Fig. 4b, orange arrows), providing a direct link between structurally distinct PFR zones. Sub-tomographic averaging did not improve resolution of these densities (Fig. 4c), suggesting that they might be flexible or present polymorphic features.
In the sub-tomographic average of the proximal zone, the overall cross-section contour approximates a right-angle trapezoid with the right-angle side corresponding to the DMT7 side of the axoneme (Fig. 4d). The approximate dimensions of this trapezoid are base lengths of 210 nm and 70 nm, and height of 87 nm. Unlike the clearly resolved density elements in the distal zone described above, proximal zone density elements are convoluted and hard to distinguish from one another. Nonetheless, we were able to segment these densities into four layers when viewed in cross section, by following the gaps visible as shown in Fig. 4d. Three of these layers are readily visible in longitudinal views from outside the PFR (pink, blue, and light purple in Fig. 4e; Supplementary Movie S5). When viewed from the axoneme looking toward the PFR, the light purple layer is dominated by an elongated density extending perpendicular to the PFR axis and spanning from DMT7 to DMT4 of the axoneme. This density measures~210 nm long and~40 nm wide, with thickness up to 30 nm on the DMT4 side. This density repeats along the axoneme axis every 54 nm (Fig. 4f, g), which is the same interval observed for the distal zone repeat. The other proximal zone layers (pink, blue, green) are best visualized when viewed from the PFR distal zone looking toward the axoneme, which allows the visualization of all four layers of the PFR proximal zone (Fig. 4g). Diagonal densities join adjacent repeats within each layer and form interconnections between layers (Fig. 4h, i; Supplementary Movie S5). These densities form latticelike networks, when examined from the axoneme interface looking toward the PFR (Fig. 4h, i; Supplementary Movie S5). Though different from one another, these networks and that in the distal zone (Fig. 4j) appear to be congruent with the rectangular, 36 nm by 40 nm repeating units, observed in the green layer of proximal zone (Fig. 4j). This congruence suggests presence of organizational linkages extending from the distal zone into the intermediate and proximal zones, and a mechanism for mediating continuity between the linear repeat of the axoneme with the diagonal repeat of the PFR distal zone.

PAC structures bridge different repeats of the PFR and axoneme
A central question about T. brucei flagellum biology concerns the mechanism of PFR attachment to the axoneme at DMT4-7. Our finding that the PFR and DMT repeating unit dimensions are mismatched, 54 vs 8 nm, makes this a particularly challenging problem. Filaments connecting the PFR to DMT7 have been described 47,49,64 , but the 3D arrangement and structural details were limited and connections to DMT4, 5, and 6 are almost completely uncharacterized. We therefore performed subtomographic averaging of local volumes at the PFRaxoneme interface to resolve individual structures of connections at DMT4-7, which we term PFR-axoneme connectors (PACs) (Fig. 5a).
Prior studies describe PAC7 as filamentous connections between the PFR and DMT7 47,65 . Our structure reveals PAC7 is actually comprised of four components (Fig. 5b2-b5): a PFR-proximal baseplate (~30 nm in diameter), a periaxonemal plate (PAP, approximately 42 by 20 by 12 nm in size), filaments (~35 nm in length) connecting the baseplate and PAP, and small globular densities that connect the PAP to the microtubule lattice of the DMT7 B-tubule at protofilaments B2-4 ( Supplementary Fig. S3). There are typically three connecting filaments per baseplate, with two parallel filaments connecting to one PAP and the third extending from the baseplate to contact the PAP of an adjacent PAC7. Positioning of connecting filaments along the PFR-axoneme interface is not entirely uniform (Fig. 5b2, b6) and structural details of these filaments become smeared in the subtomographic average of PAC7 (Fig. 5b3, b4). The PAC7 baseplate exhibits a periodicity of 54 nm, consistent with the PFR repeating unit. However, the PAP does not repeat in an entirely regular fashion (Fig. 5b2, b6), likely reflecting the need to interface the different repeats of the PFR (54 nm) and axoneme (96 nm). Thus, our cryoET structure resolves the structural basis for bridging the distinct repeating unit dimensions of two megastructures, the PFR and axoneme, which must act together to support unique motility of the trypanosome cell.
PAC4, when viewed in cross-section, is a large globular density that forms a U-like structure at the axoneme, making separate contacts with the A and B-tubules of DMT4 at protofilaments A9, 10 and B1, 3 ( Fig. 5d1; Supplementary Fig. S3). PAC4 has a periodicity of 54 nm along the flagellum (Fig. 5d2), consistent with the repeating unit of the PFR. Because 216 is the least common multiple of 8, 24, and 54, a structural unit encompassing the PFR and its contact points on the axoneme, α/ β-tubulin dimer, and OAD, would repeat each 216 nm (Fig. 5d3), while a unit that also includes the 96 nm repeat of RS-IAD-NDRC would repeat each 864 nm.

Structure of the T. brucei central pair complex
The CPC (Fig. 6a) is an essential regulator of axoneme motility, functioning with the RS to transmit mechanochemical signals across the axoneme 27,54,66 . Importance of CPC function is evidenced by several human diseases associated with CPC abnormalities 67 and a requirement of CPC proteins for T. brucei motility 34,68 . We therefore determined the 3D structure of the T. brucei CPC in situ. The CPC is visible in individual tomograms (Figs. 1b, 6b; Supplementary Fig. S2). Sub-tomographic averaging at 96 nm periodicity shows densities protruding outward from the central pair microtubules (Fig. 6c) and diagonally arranged densities of the tripartite bridge 69 between C1 and C2 microtubules (Fig. 6d). Major densities repeated at an interval of 16 nm (Fig. 6c, d). We therefore did subtomographic averaging at 16 nm, yielding a 25 Å resolution sub-tomographic average structure ( Fig. 6e; Supplementary Fig. S4b and Supplementary Movie S6), in which we resolved the C1 and C2 microtubules, as well as densities corresponding to 11 projections and tripartite bridge between C1 and C2 described for the Chlamydomonas and Strongylocentrotus CPC 69 (Fig. 6e). Interfacing with RS is critical for CPC function 24,25,27 and extensive contacts between RS and CPC projections are observed in the T. brucei structure (Fig. 6b, f-h; Supplementary Fig.  S2). These extensive contacts may contribute to restricted orientations of the CPC relative to the DMTs in T. brucei 34,68,70 . Our results provide the first 3D structure for the CPC in trypanosomes, revealing overall conserved features and extensive direct contacts with the RS.

Discussion
In this study, we have used a combination of cryoET, machine learning-based missing wedge compensation, and sub-tomographic averaging to resolve the previously unknown molecular structures of the PFR, CPC, and PACs in T. brucei. The structures reported here provide insights into flagellar motility and mechanical bionics.
To date, studies of structural mechanisms underpinning flagellum beating have focused almost exclusively on organisms with planar axoneme beating, and have mostly ignored extra-axonemal filaments 23 . However, helical waves are common among microbes, including important pathogens 5,8,36,71 , and even occur in human sperm 72 . Non-planar helical motion may contribute to microbial pathogenesis 12 , as it is recognized to facilitate propulsion through viscous environments 73 , such as host tissues. Meanwhile, extraaxonemal filaments are common features of eukaryotic flagella 16,17,19 . Therefore, a full understanding of biomechanics of cell propulsion requires structural analysis of flagella from organisms that support helical motion, such as T. brucei, and requires analysis of extraaxonemal structures, such as the PFR.
For the sake of illustration, helical waves can be decomposed into x and y oscillations each described by a sinusoidal function HðtÞ ¼ A Á sin ωt ð Þ Áĩ þ A Á cos ωt ð Þ Á j þ v Á t Ák where A,ω, v are amplitude, rotational speed and forward speed, respectively, andĩ;j;k are orthogonal unit vectors in the x, y, and z axis, respectively (Fig. 7a). In addition, since points along the axoneme filament are connected, we must also consider twist introduced by helical waves (i.e., the situation for A > 0 in Fig. 7a). Therefore, the PFR of T. brucei must provide elastic bending resistance 21 while being flexible enough to support the axoneme as it executes complex helical motion 5,36,74,75 . SSN planes placed along the axoneme at about 45°to the axoneme axis offers an excellent solution to these competing needs (Fig. 7b). We propose that the two-dimensional SSN planes provide a rigid component for support and resistance, while connection of these planes in the third dimension by coiled-coil helix bundles (i.e., wires in Fig. 3) provides elasticity. Such organization imparts integrity to the axoneme, yet still allows sinusoidal oscillation in both x and y directions and the 45°o rientation of SSN planes also provides elastic resistance and support both across and along axoneme DMTs. By contrast, placing SSN planes at 0°or 90°with respect to the axis of axoneme would prohibit oscillation in the y direction (Fig. 7c), or lend less support along axoneme DMTs (Fig. 7d), respectively. A 45°orientation may also contribute to the helical bending of the axoneme.
A distal zone comprised of SSN planes interconnected by wire-like densities differs from a previously proposed "jackscrew" model for the PFR distal zone 50 . The jackscrew model was based on viewing the distal zone from the axoneme toward the PFR, which revealed two sets of linear densities intersecting diagonally to form a lattice of diamond shapes (Fig. 3b, d, f in 48 ). Viewing from this perspective, we also observe a lattice-like arrangement of diagonally intersecting densities (Fig. 4j). However, as noted previously 48 , there is no density connecting opposing vertices of each diamond shape, i.e., no screw for a jackscrew (Fig. 4j). Moreover, the earlier work did not resolve the structural units that comprise each diagonal density in the lattice, i.e., stacked scissors of SSN planes and wire densities that connect them as described here.
For the PFR to fulfill motility functions in unison with the axoneme, these two massive structures must be interconnected in a way that enables mechanochemical signals to be transmitted to all participating components. Such signals may go both ways, either from axoneme to PFR or vice versa, as the PFR is a platform for Ca++ and cAMP signaling systems 40,42 . The observed structural organization of connections within and between the axoneme and PFR is consistent with such needs. Within the axoneme, signaling between DMTs is supported by nexin links that connect adjacent DMTs 76 . Our prior studies 26 demonstrate capacity for DMT-DMT signaling in T. brucei, by confirming the presence of nexin links, and identifying novel, lineage-specific connections between adjacent DMTs 26 . In the present study, our observation of direct interaction between RS and CPC (Fig. 6b, f, g; Supplementary Fig. S2), is likewise consistent with the role of the RS in transmitting signals through the CPC to DMTs across the axoneme reported in other organisms 27,54,66 . Extensive contact between RS and CPC may also contribute to limited rotation observed for the T. brucei CPC relative to DMTs 34,68,70 . Signals from the axoneme may in turn be transmitted directly to the PFR proximal zone through the PACs. Contiguous structural connections extending through the proximal,  Fig. 6g; Supplementary Fig. S2).
intermediate, and distal zones (Fig. 4b, c, h−j; Supplementary Movies S2, S4, S5) allow these signals to be propagated all the way to the distal zone, which provides a highly organized spring-like structure that can store and release mechanical energy.
Structural details of PFR connections to the axoneme provide insight into how the PFR may influence axoneme beating. The mismatch in periodicity of the axoneme (8 nm) and the PFR (54 nm) is reminiscent of symmetry mismatch often observed in structures involved in dynamic biological processes, such as those of the DNA translocation portals in viruses 77,78 . Dynamic interaction is also supported by the observed heterogeneity in spacing of the PAC7-DMT7 interface (Fig. 5b), as this heterogeneity in spacing suggests capacity for sliding of PAC7 on this side of the axoneme. In addition, PAC4 and 5 appear to have more regular longitudinal spacing, and such an arrangement could support or even amplify helical bending, as it would present more resistance to bending on the DMT4 versus DMT7 side of the axoneme. A mismatch in periodicity also suggests that, although PFR assembly is coordinated with and dependent on axoneme assembly 79,80 , PFR assembly is not templated by the axoneme. This interpretation is consistent with RNAi knockdown studies showing proteins that are not part of the PFR are nonetheless required for proper PFR assembly [81][82][83] , indicating that PFR assembly is a multistep, well-controlled process with assembly steps in the cytoplasm as well as flagellum. Finally, direct connection of PAC5-1 to dynein motors on DMT5 (Fig. 5c1, c2) 49 will exert substantial influence on dynein orientation. Because reorientation of axonemal dynein during the beat cycle is a major mechanism of axonemal beat regulation 23,24,84 , PAC5-1 provides a mechanism for the PFR to directly control axonemal beating. In summary, our studies provide a high-resolution 3D description of an extra-axonemal structure, giving insight into how these common yet enigmatic components of eukaryotic flagella contribute to axonemal beating. From the standpoint of bionics, with less than 10% space filled, the PFR of trypanosomes may provide an example of cellular tensegrity-biological entities that embody a fine balance between strength and flexibility, owing to opposing forces of compression or tension-and should inform future bioengineering and mechanical design of nanomachines and microswimmers 85,86 .

Sample preparation and cryoET
T. brucei bloodstream form single marker (BSSM) cells 87 were used, and details for culturing, flagella isolation, and cryoET were described previously 26 . Briefly, demembraned flagella were isolated and vitrified on quantifoil grids with 5 nm gold particles. With Seri-alEM 88 , tilt series were collected from straight segments near the center part of full-length flagella, spanning the middle third between the basal body and tip, in a Titan Krios instrument equipped with a VPP, a Gatan imaging filter (GIF) and a post-GIF K2 direct electron detector in electron-counting mode. Frames in each movie of the raw tilt series were aligned, drift-corrected, and averaged with Motioncorr 89 . The tilt series micrographs were aligned and reconstructed into 3D tomograms by either weighted back projections (WBP, for sub-tomographic averaging) or simultaneous iterative reconstruction technique (SIRT, for visualization and particle picking) using the IMOD software package 90 . The contrast transfer function (CTF) was determined by ctffind4 91 and corrected with the ctfphaseflip program 92 of IMOD. With phase plate, the CTF is insensitive to the sign of the defocus value being negative (under-focus) or positive (over-focus) 93 so CTF of micrographs obtained with phase plate were approximated when CTF rings were not readily detected.

Missing-wedge compensation
Demembranated T. brucei flagella samples typically lie on the cryoEM grids with a preferred orientation due to the presence of the PFR. To alleviate the missing-wedge problem associated with preferred orientation, we used a novel deep learning-based method developed to compensate for missing-wedge problem (Liu et al., unpublished program). Using tilt geometry and resulting tomograms as inputs, the program iteratively learns how to fill in missing information.

Sub-tomographic averaging
In our sub-tomographic averaging scheme performed using PEET, each particle is a 3D sub-volume of the tomogram corresponding to the repeating unit of the component of interest, i.e., PFR distal zone, PFR proximal zones, PACs, or CPC.

PFR distal zone
For the PFR distal zone, sub-tomographic averaging required first defining the repeating unit through multiple rounds of PEET trials, and then using this defined repeating unit to re-pick particles automatically for the final round of PEET refinement, leading to a final subtomographic average at the best possible resolution.
To define the repeating unit a priori, we first performed crude sub-tomographic averaging with 4x binned (resulting a pixel size of 10.2 Å) SIRT tomograms. Initially, we manually picked particles (190 × 190 × 190 pixels) by taking advantage of the repeating comb teeth visible in the PFR distal zone in the raw tomograms (e.g., Figs. 1b and 2b, cyan arrows). For each particle, this process records the x, y, z coordinates of two points in the tomogram, one at each end of a tooth. The coordinates for all picked particles in each tomogram were saved into a coordinates model.mod file. With this model file as the input, we then ran stalkInit of the PEET package to generate three output files-motive list.csv file (translation and rotation parameters), coordinates model.mod file (central coordinates of particles) and rotation axes.csv file (vectors representing rotation axes for all particles)-for each tomogram. All these picked particles were summed together to generate a featureless volume, which was used as the initial reference of the first cycle of PEET. We then ran PEET iteratively by gradually decreasing the search range for both angular and distance parameters. For the angular search range, the parameters decreased from "180°max with 60°step in Phi (y axis), and 9°max with 3°s tep in both Theta (z axis) and Psi (x axis)", to "3°max with 1°step in all Phi (y axis), Theta (z axis), and Psi (x axis)". For the distance search range, the parameters decreased from 10 pixels to 2 pixels along all three axes. In addition to decreasing the search ranges, the reference was also updated by using the result of the previous round of PEET sub-tomographic averaging. This process was iterated until the averaged structure converged, and no improvement in the averaged structure could be observed. In this converged average, repeating densities, characteristic of those ultimately resolved in the lattice in Fig. 4j, were observed.
The repeating unit parameters defined above were utilized to re-pick particles following the 3D lattice. To do this for many tomograms automatically, we developed a bash script, propagate.sh, and used it to pick particles encompassing all repeating units within each tomogram, taking advantage of the unit cell dimensions of the aboveobserved lattice in all three orthogonal directions. At this stage, the sub-tomographic average volume resulting from the above initial PEET process contains more than one repeating unit. Though our script allows multiple repeating units in three dimensions, in the current case, we only needed to pick up all repeating units in the two dimensions, i.e., within an SSN plane, because the above manually picked particles cover only one unit-cell length along axoneme axis. Using the 3D visualization tools of IMOD, we identified 22 repeating units within each SSN plane. We carefully measured the x, y, and z distances between the center position of the current average volume and the center of each of the 22 repeating units and list each set of x, y, z distances in separate lines in a propagation list file. The script propagate.sh takes as inputs the follwoing: the propagation list file, and a set of three alignment files-including a motive list file (translation and rotation parameters), a coordinates model file (central coordinates of particles), and a rotation axes file (vectors representing rotation axes for all particles) for each tomogram-generated from the above PEET round. The output includes a single prm file (file pathway information) for the entire project and a new set of three alignment files for each tomogram to be used as the input files for the next round of PEET. This re-picking process ended up with 22 times as many particles as in the initial manual picking process.
With these re-picked particles, one round of iterative PEET refinement was performed by loading the new alignment and prm files to generate the final subtomographic average for the PFR distal zone. As before, the search ranges were gradually decreased and the average result from each prior refinement cycle was used as the updated reference for the subsequent cycle of refinement. The refinement was terminated when the averaged structure converged, and no further improvement could be seen. From the unMasked averaged density map file automatically generated by PEET during the refinement, the repeating length along the axoneme axis was measured to be 54 nm. Unit cell dimensions were also measured as reported as the final parameters in Fig. 2h.

PFR proximal and intermediate zones, and PACs
For sub-tomographic averaging of PFR proximal and intermediate zones, and PACs, the method is the same as that of the PFR distal zone, except that there was no need to run propagate because the repeating unit is only one dimensional. Instead, we identified prominent repeated densities from raw tomograms to be used for manual particle picking. For example, we used the baseplate density attached with 3 filaments (Fig. 5b) for manual picking PAC7. After iterative sub-tomographic averaging for the component of interest, the unMasked averaged density map file automatically generated by PEET was used to measure the dimension of a repeating unit.

CPC
To identify the periodicity of CPC, we first evaluated the tomograms and did a trial of sub-tomographic averaging using 96 nm periodicity (Fig. 6c, d). One could readily recognize 16 nm repeated features including the different projection densities. Therefore, we next utilized the 16 nm periodicity to box particles of the CPC along the axoneme axis. These sub-volumes centered on the CPC were then aligned to each other, and averaged together with PEET, with the procedures described above.
We used the following numbers of particles to generate sub-tomographic averages of various flagellar components: 763 particles from 10 tomograms for DMT, 3001 particles from 52 tomograms for the 16 nm CPC, 558 particles from 52 tomograms for 96 nm CPC, 246 particles from 17 tomograms for each of the PAC4, PAC5, PAC6, and PAC7, 246 particles from 17 tomograms for the PFR proximal zone, 1362 particles from 12 tomograms for the PFR distal zone.
The resolution of each sub-tomographic average was calculated by calcFSC in PEET based on the 0.143 FSC criterion ( Supplementary Fig. S4).

Sequence alignment and secondary structure prediction of major PFR proteins
For PFR protein sequence alignments, we used PFR1 (NCBI# XP_844025.1) and PFR2 (NCBI# XP_847331.1) from T. brucei 59 , PFR-like protein of Leishmania braziliensis (NCBI# XP_001565953) 94 , PFR1 (NCBI #AAV53924) of Angomonas deanei 95 from the Strigomonadinae family, and PFR 1D (NCBI XP_003872382.1) 96 of Leishmania mexicana from the Leishmaniinae subfamily. Sequences were aligned with multiple sequence alignment function in Clustal Omega (1.2.4) 97 . For each of the four proteins, secondary structures were predicted using PSIPRED 98 . Predicted secondary structures of proteins were combined with protein alignment results to compare the PFR protein structure between different species.

3D visualization
IMOD 90 and UCSF ChimeraX 99 were used to visualize reconstructed tomograms and sub-tomographic averages. Segmentation of densities maps was performed by the volume tracer and segger tools of UCSF Chimera 100 . For surface rendering with UCSF ChimeraX, maps were first low-pass filtered to either 30 Å or 50 Å. Montage was done in UCSF ChimeraX by fitting averaged structures (i.e., 96 nm averaged axoneme, 16 nm averaged CPC, 54 nm averaged PACs, 54 nm averaged PFR proximal zone, etc.) into an unaveraged tomogram after missing-wedge compensation. Fitting of existing model of coiled-coil helix bundle was done with the molmap and fit functions in UCSF ChimeraX 99 . Schematics were drawn by Adobe Illustrator. The built-in denoising program in Warp 101 was used to enhance visualization. Tilt series were separated into two sets and reconstructed independently, and the noise will be filtered out to improve the SNR given that the signal is consistent in both maps, but the noise is random.