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Structure of Trypanosoma brucei flagellum accounts for its bihelical motion Alexey Y. Koyfman a , Michael F. Schmid a , Ladan Gheiratmand b , Caroline J. Fu a , Htet A. Khant a , Dandan Huang b , Cynthia Y. He b , and Wah Chiu a,1 a National Center for Macromolecular Imaging, Verna and Marrs McLean Department of Biochemistry and Molecular Biology, Baylor College of Medicine, Houston, TX 77030; and b Department of Biological Science and Centre for BioImaging Sciences, National University of Singapore, Singapore 117543 Edited by Wolfgang P. Baumeister, Max-Planck-Institute of Biochemistry, Martinsried, Germany, and approved May 18, 2011 (received for review March 8, 2011) Trypanosoma brucei is a parasitic protozoan that causes African sleeping sickness. It contains a flagellum required for locomotion and viability. In addition to a microtubular axoneme, the flagellum contains a crystalline paraflagellar rod (PFR) and connecting pro- teins. We show here, by cryoelectron tomography, the structure of the flagellum in three bending states. The PFR lattice in straight flagella repeats every 56 nm along the length of the axoneme, matching the spacing of the connecting proteins. During flagellar bending, the PFR crystallographic unit cell lengths remain constant while the interaxial angles vary, similar to a jackscrew. The axo- neme drives the expansion and compression of the PFR lattice. We propose that the PFR modifies the in-plane axoneme motion to produce the characteristic trypanosome bihelical motility as captured by high-speed light microscope videography. T rypanosoma brucei has devastated the African continent for centuries by infecting humans and domestic animals and has hindered economic development in sub-Saharan Africa (1). Current sleeping sickness treatments are inadequate and the drugs used are highly toxic (2). In recent years, the motility of the T. brucei flagellum has been found to be essential for para- site survival, infection, and disease pathogenesis (3), and has emerged as a promising drug target (4). Flagella with similar structural organization and protein composition have also been found in euglenoids (5) and other kinetoplastid parasites includ- ing Leishmania spp. and Trypanosoma cruzi, which cause Leish- maniasis and Chagas disease, respectively (6). The trypanosome flagellum is more complex than most other eukaryotic microtubule-based flagella (79) and is completely different from rotary-motor based bacterial flagella (10). Each T. brucei cell contains one flagellum that moves the cell body in an alternating right and left-handed twist resulting in bihelical motion (11) (Movie S1). The membrane-enclosed flagellum, composed of an axoneme, a paraflagellar rod (PFR) (12), and connecting proteins, is attached to the cell body (Fig. 1). PFR was identified as a lattice-like ultrastructure in T. brucei flagellum (13). This periodic and crystalline nature of the PFR was con- firmed in T. brucei (14) and related species (15, 16). Monoclonal antibody screens (17) and proteomics studies (1820) have iden- tified at least 40 PFR proteins. Among them, PFR1 (73 kDa) and PFR2 (69 kDa), containing coiled-coil regions (21), are major structural components of the PFR (22). Depletion of these pro- teins results in failure of PFR assembly and cell motility defects (17, 23) (Fig. S1 and Movie S2). In the T. brucei pathogenic blood- stream form, ablation of PFR2 causes death of the parasite (18). These results demonstrate a critical role of the PFR in T. brucei motility and viability. We have employed cryoelectron tomogra- phy (cryo-ET) to determine the structure of a biochemically isolated T. brucei flagella (18). We describe here a model that explains how the structure and arrangement of the flagellar components produces the bihelical motion of the flagellum. Fig. 1B is a projection through 30 slices (33 nm) of a tomogram of the T. brucei flagellum showing three components of a straight flagellum: the crystalline PFR, the axoneme, and the proteins connecting the PFR to the axoneme. The crystallinity of the PFR is demonstrated by the computed diffraction pattern of a single image (Fig. S2), which shows diffraction spots expected for a crystal. In other tomograms, we have observed flagella in bent conformations, similar to those observed during flagellar motion. Because these three flagellar components (PFR, axo- neme, and connecting proteins) exhibit different periodicity and symmetry, we had to use different strategies to align and average each of them separately (Materials and Methods). The PFR has been found to contain multiple regions (24). We observe these distinct regions of the PFR in unaveraged, raw tomogram cross- sections (Fig. S3C and Movie S3). However, in our method of alignment, the crystallinity of the largest and most well-ordered portion of the PFR (the distal portion) strongly influences the overall PFR average. The proximal PFR region was not observed after the averaging because it does not possess such crystallinity. The final averaged structure of the entire flagellum (Fig. 2A and Movie S3) was reconstituted from the averaged components of straight flagella. The averaged PFR density was derived from five different tomograms (Fig. 2 A and B). The PFR is a three-dimensional pro- tein lattice that has crisscrossing densities and a large proportion of empty volume, both of which are reminiscent of the crystal structure of tropomyosin (25, 26). The linear densities are paral- lel to the crystallographic unit cell axes and may correspond to one or more parallel coiled-coil bundles of the major PFR pro- teins. The diagonal of the crystallographic PFR unit cell repeats at 56-nm intervals in the direction parallel to the axoneme (Fig. 2B). We used a skeletonization algorithm (27) to provide a simplified representation of the densities in the PFR lattice Fig. 1. Trypanosoma brucei flagellum. (A) Diagram of a trypanosome cell (blue) with attached flagellum (yellow). (B) Slice of a tomographic reconstruc- tion of an isolated straight flagellum. The flagellum, composed of an axo- neme, a PFR (12), and connecting proteins, is attached to the cell body. Author contributions: A.Y.K., M.F.S., L.G., C.J.F., H.A.K., D.H., C.Y.H., and W.C. designed research; A.Y.K., L.G., C.J.F., H.A.K., and D.H. performed research; A.Y.K., M.F.S., C.Y.H., and W.C. analyzed data; and A.Y.K., M.F.S., C.Y.H., and W.C. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. Freely available online through the PNAS open access option. Data deposition: The 3D cryoelectron tomographic averages have been deposited in the Electron Microscopy Data Bank, www.emdatabank.org (accession nos. EMDB-5302, 5303, 5304, 5305, and 5306). 1 To whom correspondence should be addressed. E-mail: [email protected]. This article contains supporting information online at www.pnas.org/lookup/suppl/ doi:10.1073/pnas.1103634108/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1103634108 PNAS July 5, 2011 vol. 108 no. 27 1110511108 BIOPHYSICS AND COMPUTATIONAL BIOLOGY Downloaded by guest on February 28, 2021

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Page 1: Structure of Trypanosoma bruceiflagellum accounts for its ... · Trypanosoma brucei is a parasitic protozoan that causes African sleeping sickness. It contains a flagellum required

Structure of Trypanosoma brucei flagellumaccounts for its bihelical motionAlexey Y. Koyfmana, Michael F. Schmida, Ladan Gheiratmandb, Caroline J. Fua, Htet A. Khanta,Dandan Huangb, Cynthia Y. Heb, and Wah Chiua,1

aNational Center for Macromolecular Imaging, Verna and Marrs McLean Department of Biochemistry and Molecular Biology, Baylor College of Medicine,Houston, TX 77030; and bDepartment of Biological Science and Centre for BioImaging Sciences, National University of Singapore, Singapore 117543

Edited byWolfgang P. Baumeister, Max-Planck-Institute of Biochemistry, Martinsried, Germany, and approvedMay 18, 2011 (received for reviewMarch 8, 2011)

Trypanosoma brucei is a parasitic protozoan that causes Africansleeping sickness. It contains a flagellum required for locomotionand viability. In addition to a microtubular axoneme, the flagellumcontains a crystalline paraflagellar rod (PFR) and connecting pro-teins. We show here, by cryoelectron tomography, the structureof the flagellum in three bending states. The PFR lattice in straightflagella repeats every 56 nm along the length of the axoneme,matching the spacing of the connecting proteins. During flagellarbending, the PFR crystallographic unit cell lengths remain constantwhile the interaxial angles vary, similar to a jackscrew. The axo-neme drives the expansion and compression of the PFR lattice.We propose that the PFR modifies the in-plane axoneme motionto produce the characteristic trypanosome bihelical motility ascaptured by high-speed light microscope videography.

Trypanosoma brucei has devastated the African continent forcenturies by infecting humans and domestic animals and

has hindered economic development in sub-Saharan Africa(1). Current sleeping sickness treatments are inadequate andthe drugs used are highly toxic (2). In recent years, the motilityof the T. brucei flagellum has been found to be essential for para-site survival, infection, and disease pathogenesis (3), and hasemerged as a promising drug target (4). Flagella with similarstructural organization and protein composition have also beenfound in euglenoids (5) and other kinetoplastid parasites includ-ing Leishmania spp. and Trypanosoma cruzi, which cause Leish-maniasis and Chagas disease, respectively (6).

The trypanosome flagellum is more complex than most othereukaryotic microtubule-based flagella (7–9) and is completelydifferent from rotary-motor based bacterial flagella (10). EachT. brucei cell contains one flagellum that moves the cell bodyin an alternating right and left-handed twist resulting in bihelicalmotion (11) (Movie S1). The membrane-enclosed flagellum,composed of an axoneme, a paraflagellar rod (PFR) (12), andconnecting proteins, is attached to the cell body (Fig. 1). PFRwas identified as a lattice-like ultrastructure in T. brucei flagellum(13). This periodic and crystalline nature of the PFR was con-firmed in T. brucei (14) and related species (15, 16). Monoclonalantibody screens (17) and proteomics studies (18–20) have iden-tified at least 40 PFR proteins. Among them, PFR1 (73 kDa) andPFR2 (69 kDa), containing coiled-coil regions (21), are majorstructural components of the PFR (22). Depletion of these pro-teins results in failure of PFR assembly and cell motility defects(17, 23) (Fig. S1 andMovie S2). In the T. brucei pathogenic blood-stream form, ablation of PFR2 causes death of the parasite (18).These results demonstrate a critical role of the PFR in T. bruceimotility and viability. We have employed cryoelectron tomogra-phy (cryo-ET) to determine the structure of a biochemicallyisolated T. brucei flagella (18). We describe here a model thatexplains how the structure and arrangement of the flagellarcomponents produces the bihelical motion of the flagellum.

Fig. 1B is a projection through 30 slices (33 nm) of a tomogramof the T. brucei flagellum showing three components of a straightflagellum: the crystalline PFR, the axoneme, and the proteinsconnecting the PFR to the axoneme. The crystallinity of the

PFR is demonstrated by the computed diffraction pattern of asingle image (Fig. S2), which shows diffraction spots expectedfor a crystal. In other tomograms, we have observed flagella inbent conformations, similar to those observed during flagellarmotion. Because these three flagellar components (PFR, axo-neme, and connecting proteins) exhibit different periodicity andsymmetry, we had to use different strategies to align and averageeach of them separately (Materials and Methods). The PFR hasbeen found to contain multiple regions (24). We observe thesedistinct regions of the PFR in unaveraged, raw tomogram cross-sections (Fig. S3C and Movie S3). However, in our method ofalignment, the crystallinity of the largest and most well-orderedportion of the PFR (the distal portion) strongly influences theoverall PFR average. The proximal PFR region was not observedafter the averaging because it does not possess such crystallinity.

The final averaged structure of the entire flagellum (Fig. 2Aand Movie S3) was reconstituted from the averaged componentsof straight flagella.

The averaged PFR density was derived from five differenttomograms (Fig. 2 A and B). The PFR is a three-dimensional pro-tein lattice that has crisscrossing densities and a large proportionof empty volume, both of which are reminiscent of the crystalstructure of tropomyosin (25, 26). The linear densities are paral-lel to the crystallographic unit cell axes and may correspond toone or more parallel coiled-coil bundles of the major PFR pro-teins. The diagonal of the crystallographic PFR unit cell repeatsat 56-nm intervals in the direction parallel to the axoneme(Fig. 2B). We used a skeletonization algorithm (27) to providea simplified representation of the densities in the PFR lattice

Fig. 1. Trypanosoma brucei flagellum. (A) Diagram of a trypanosome cell(blue) with attached flagellum (yellow). (B) Slice of a tomographic reconstruc-tion of an isolated straight flagellum. The flagellum, composed of an axo-neme, a PFR (12), and connecting proteins, is attached to the cell body.

Author contributions: A.Y.K., M.F.S., L.G., C.J.F., H.A.K., D.H., C.Y.H., and W.C. designedresearch; A.Y.K., L.G., C.J.F., H.A.K., and D.H. performed research; A.Y.K., M.F.S., C.Y.H.,and W.C. analyzed data; and A.Y.K., M.F.S., C.Y.H., and W.C. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Freely available online through the PNAS open access option.

Data deposition: The 3D cryoelectron tomographic averages have been deposited inthe Electron Microscopy Data Bank, www.emdatabank.org (accession nos. EMDB-5302,5303, 5304, 5305, and 5306).1To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1103634108/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1103634108 PNAS ∣ July 5, 2011 ∣ vol. 108 ∣ no. 27 ∣ 11105–11108

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(Fig. 2C). A green parallelogram, passing through the highestPFRdensities, represents four crystallographic unit cells in a plane(Fig. S4). Fig. 2C shows the layered nature of the PFR and itsspatial relationship to the axoneme (Movie S3). The distance be-tween adjacent layers corresponds to the c crystallographic unitcell spacing (22 nm). Note that none of the crystallographicaxes is parallel or perpendicular to the axoneme axis.

The axoneme average (Fig. 2D and Movie S3) was derivedfrom a single tomogram that had the best-preserved structure.It contains the characteristic nine outer microtubule doublets(28–30) (blue) arranged around the central microtubule pair(yellow) similar to those found in sea urchin sperm (8). All ninemicrotubule doublets, with their associated structures, werealigned and averaged assuming that they were structurally equiva-lent, thereby compensating for the distortions caused by thelimited range of tilt angles (Materials and Methods). In our anno-tation, microtubule doublet 1 (Fig. 2A and Movie S3) is distalto the PFR (31) and radial spokes (light green) connect outermicrotubule doublets to the central pair. Typically, axonemesbend in a plane bisecting the two microtubules of the central pair(32) with a frequency of 10–20 Hz (33). Here, cryo-ET provides adirect observation, in the same frozen specimen, of this orthogo-nal relationship between the central pair and the bending plane(Fig. S3 A and B). In our tomograms, the plane bisecting the twomicrotubules of the central pair (Fig. 2A, red dashed line) and theplane through the connecting proteins (Fig. 2A, purple dashedline) intersect at an angle consistent with previous measurements(34–36). To statistically validate our observation, we measuredthe angle that the PFR makes with the perpendicular bisector ofthe central pair for a total of eight different flagella (Fig. S3 B–H,in addition to the tomogram for Fig. 2). We found it to be 20� 7°.Some features of the axoneme (Fig. 2D), such as the nine doub-lets, the radial spokes, and the central microtubule pair, appear

similar to axonemes from other organisms (7, 8, 37–40). How-ever, structures such as the outer dynein arms could have beenpartially removed during the extraction with 1 M KCl.

Two rows of connecting proteins (red and pink in Fig. 2 A–C)between the PFR and the axoneme were identified. We observesubstantial connections to doublets 5 and 6, but not to 4 and 7 aspreviously visualized and reported (3, 41). The connections todoublets 4 and 7 are not as bulky as those to doublets 5 and6. They are longer and perhaps more flexible, and thereforenot readily visible in the raw tomograms. Indeed it was shownthat connections to doublets 4 and 7 are thin linear structures(13, 14, 16, 24, 42). Due to the difficulty in visualizing the con-nectors to doublets 4 and 7, they were not chosen for averagingfrom our reconstructions. The connecting proteins which we doobserve (to doublets 5 and 6) repeat every 56 nm in straightflagella, a distance corresponding to seven tubulin dimers alongthe axoneme (Fig. 2B). This distance is the same as the PFRrepeat along the axoneme and also similar to periodic attach-ments seen in the Euglena axoneme (5). Each of the two rowsof connecting proteins was averaged along the length of theflagella. The averages of the connecting proteins in the two rowsare similar in size (Fig. 2B and Movie S3) and are schematicallyrepresented by spheres in Fig. 2C. It is likely that each connectingdensity is a complex of several proteins.

Whereas straight flagella were used to determine the averagestructure, bent flagella can suggest amodel for their motion. Fig. 3A–F show top and side views of tomogram slices of the PFR fromthree differently bent flagella. The PFR averages are shown indifferent colors. The crystallographic unit cell lengths of bentand straight PFR agree within 5%: a ¼ 52� 2, b ¼ 46� 2, andc ¼ 22� 1 nm (a total of 7,000 unit cells went into theseaverages) (Fig. 3G, Fig. S5, and Movie S3). Because the linearPFR protein densities are parallel to the crystallographic unit cellaxes rather than to the axoneme axis, the PFR proteins are notcompressed or bent (Fig. 3) when the axoneme bends. Rather, thePFR densities pivot as if on hinges at the corners of the crystal-lographic unit cell with a scissor-like motion, resulting in interax-ial angular variations from 85° to 112° (Fig. 3 G and H).

The organization and structural flexibility of the individualflagellar components and their relationship to each other suggesta mechanism for the movement of the trypanosome powered bythe beating axoneme. It is well accepted that the axoneme powersflagellar movement (32, 43, 44). Bending of the axoneme makesthe connecting proteins bend along with it, causing their spacingto shorten or lengthen from the 56-nm spacing in straight flagella(Figs. 3H and 4A). This change in spacing of the connecting pro-teins in turn compresses or stretches the PFR along the axonemedirection (Fig. 3). Our observations suggest that each crystallo-graphic PFR unit cell is analogous to an automobile jackscrew(Fig. 3H and Movie S4). The crystallographic unit cell axes, cor-responding to the rigid arms of the jackscrew and composed of thecoiled-coil structural proteins, remain constant in length, whereasthe interaxial angles vary. The connecting proteins stretch andcompress the PFR hinges and thus correspond to the screw ina jackscrew (Figs. 3H and 4, and Movie S4). The change in thecrystallographic unit cell angles is analogous to the results ofthe action of the screw in a jackscrew. The coordinated actionof the unit cells, illustrated by the parallelograms in Fig. 3G, pro-duce an overall stretching and contraction of the PFR in amanneranalogous to an expansion gate (Fig. S6). Interestingly, using aflexible protein crystal as a part of a cellular mechanical devicehas been observed before (45). The actin-based acrosomal bun-dle, proposed as a biological spring (46), is another example of anintracellular 3D protein crystal serving a biomechanical function.

The preferred bending plane of the axoneme (34) makes anapproximately 20° angle with the PFR (the angle between thedashed lines in Fig. 2A and Movie S3). A constraint on the bend-ing of the axoneme, like that imposed by the PFR having this 20°

Fig. 2. T. brucei flagellum components. (A) Flagellum cross-section. The ax-oneme is radially colored: central pair complex (yellow), radial spokes (lightgreen), microtubule doublets (blue). The dashed red line (bisecting the cen-tral pair) represents the plane of bending of an axoneme. The PFR is offsetfrom that plane (dashed purple line through the middle of the PFR). (B) Thediagonal (shown by a horizontal white arrow) of the crystallographic unit cellof the PFR (green) repeats with the same spacing (56 nm) as that of theconnecting proteins (red and pink) along the axoneme axis. (C) The layerednature of the PFR. Skeletonized (27) PFR density is shown in gray, the crystal-lographic unit cells are shown as green parallelograms, the connectingproteins are represented as spheres, and the microtubules are cylinders.(D) T. brucei axoneme internal components.

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offset, would induce a rotation, twisting the flagellum into a right-or left-handed helix (Fig. 4B and Movie S5). Fig. S7 shows thistwist measured geometrically along a slightly bent flagellum in asingle projection image. Fig. S8 shows the twist measured in 3Dalong the axoneme axis from a tomogram. Both methods give atwist of about 15° per 800 nm in slightly bent flagella. It is possiblethat flagella were bent passively during freezing. However, nomatter what caused these flagella to bend, we observe a consistentrelationship of bend to twist (Figs. S7 and S8). It is thus likely thatthe isolated flagella are constrained to bend in the same way theywould in the motile trypanosome. We have observed long,straight flagella over a distance of up to 15 μm. On the otherhand, bent flagella occur only over short distances (less than1 μm) on the grid, possibly because the combination of bendand twist would eventually cause them to come out of the planeof the thin ice layer. Movies S1 and S5 include high-speed lightmicroscopy showing the bihelical motion of the T. brucei flagellawith a frequency of 19� 3 Hz (11). In contrast, the sea urchinsperm axoneme bends up and down with a simple sinusoidal mo-tion with a similar frequency (32, 33) (Movie S5). At the end ofeach half-cycle of the T. brucei axoneme beat, the direction of thetwist reverses, generating a helix of the opposite hand (Fig. 4Band Movies S1 and S5) (11). Thus, the normal planar motionof an axoneme is transformed into the observed bihelical wavemovement characteristic of T. brucei. Depletion of the PFRassembly (Fig. S1) of the T. brucei flagella by RNAi (17, 23)changes the bihelical motion into sinusoidal planar motion witha frequency of 18� 1 Hz (Movie S2). The RNAi experiments re-inforce the critical role of the PFR for the bihelical wave motionof the organism. Whereas other structures, including the cellbody, may influence the bihelical motion, the relative orientationof the PFR to the axoneme was observed to be consistent, unlikethe relationship of flagellum to the cell body (34).

The trypanosome flagellum is the most complex microtubule-based nanomachine that has been studied by cryo-ET. Our obser-vations support a molecular mechanism by which the propertiesof the paraaxonemal structures shape the motion of T. brucei. Wepropose a straightforward model for energy transduction, fromthe beating axoneme through the connecting proteins to thedeformable PFR crystal, resulting in efficient cell propulsion ofthis trypanosome.

Materials and MethodsIsolation of T. brucei flagella was performed as previously described (18, 47).Approximately 2 × 109 procyclic 29.13 cells (48) were extracted sequentiallywith buffers containing 1% Nonidet P-40 and 1 M KCl. Isolated flagellawere stored at 4 °C. Quantifoil Copper 200 mesh R 2∕2 grids were washedovernight with ethyl acetate. Grids were pretreated with 15-nm gold nano-particles for tomogram alignment. To prepare a frozen, hydrated grid, 2.5 μLof flagella sample was applied to the grid, blotted, and plunged intoliquid ethane using a Vitrobot (FEI). The optimal ice thickness is around300–400 nm, slightly larger than the diameter of the flagellum, as observedin our tomograms. Imaging was performed on 200-kV microscopesJEM2200FS and JEM2100 equipped with Gatan 4;096 × 4;096 pixel CCD cam-eras. The JEM2200FS has a field emission gun and an in-column energy filter,whereas the JEM2100 has a LaB6 gun. Depending on themicroscope and ima-ging conditions, the effective magnifications varied between 11,100× and16,500×. Tilt series were collected using SerialEM (49) targeted at 6–10 μmunderfocus. Each 120° tilt series contained 60 images. Electron dose pertomogram ranged from 60 to 74 electrons∕Å2 as typically used for cryo-ET(50). Tomograms were reconstructed using IMOD (51). Subvolumes enclosingsegments of the PFR, the connecting proteins, and the axoneme wereextracted from the reconstructed tomograms. Initial models for the PFRand for the connecting proteins were created by aligning and averagingtwo adjacent subvolumes (52). More distal segments were then aligned toand averaged with the initial model iteratively. A final realignment of eachsubvolume to the model was performed to create a final average. The PFRfrom bent flagella, recognized by visual inspection, were similarly aligned toeach other. For the axoneme, 288-nm segments, representing three 96-nmrepeat lengths, were extracted along each microtubule doublet. The seg-ments overlapped each other by 96 nm. These segments were first alignedalong their length by cross-correlation. The aligned segments were then aver-aged, after which the nine averaged doublets were then rotationally andtranslationally aligned and averaged with each other, mitigating the effectof the missing wedge. Finally, the original axoneme was reassembled byproperly rotating and translating the microtubule doublet average back intothe original volume in the nine original orientations. The separately aver-aged subtomograms of the PFR, of the connecting proteins, and of theaxoneme were fitted back into an original tomogram density map. Densityvisualization was performed using Chimera (53).

ACKNOWLEDGMENTS. We thank Matthew Dougherty for help in preparingthe movies, and Xiangan Liu and Ryan Rochat for help with illustrations. Thisresearch has been supported by National Institutes of Health through theNational Center for Research Resources (P41RR002250) and the PostdoctoralTraining Grant of National Institute of Allergy and Infectious Diseases(T32 AI07471 to A.Y.K.), and C.Y.H. is a research fellow of Singapore NationalResearch Foundation.

Fig. 4. Transformation of the normal axoneme (purple) planar motion intothe observed bihelical wave motion of T. brucei. (A) The relative sliding mo-tion of the microtubule doublets will tend to compress and expand the con-necting proteins (pink) (X1 > X2 > X3). (B) The presence of the PFR (green)that is offset 20° resists this tendency, leading to a bihelical twist of theattached flagellum and T. brucei cell.

Fig. 3. The T. brucei flagellum acts like a biological jackscrew. Side views (A, C, and E) and top views (B, D, and F) of a tomogram of a PFR which is bent inward(A and B), straight (C and D), and bent outward (E and F). Tomogram slices are shown in gray. Aligned and averaged subtomograms are shown in color. (Scalebars: 100 nm.) (G) Top view of the crystallographic unit cell axes. While the axial distances stay constant, the γ angle changes as the PFR bends. (H) Jackscrewmodels of the PFR representing the 85° angle of the inwardly bent (expanded) crystallographic unit cell; 106° angle of the straight crystallographic unit cell;112° angle of the crystallographic unit cell bent outward (compressed). Connecting proteins are represented by pink spheres.

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