Active beating of a reconstituted synthetic minimal axoneme
Isabella Guido, Andrej Vilfan, Kenta Ishibashi, Hitoshi Sakakibara, Misaki Shiraga, Eberhard Bodenschatz, Ramin Golestanian, Kazuhiro Oiwa
AActive beating of a reconstituted synthetic minimal axoneme
Isabella Guido, ∗ Andrej Vilfan,
1, 2
Kenta Ishibashi,
3, 4
Hitoshi Sakakibara, MisakiShiraga, Eberhard Bodenschatz,
1, 7, 8
Ramin Golestanian,
1, 9, † and Kazuhiro Oiwa
5, 6 Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 G¨ottingen, Germany Joˇzef Stefan Institute, 1000 Ljubljana, Slovenia Graduate School of Frontier Biosciences, Osaka University, Osaka 5650871, Japan Center for Information and Neural Networks (CiNet),National Institute of Information and Communications Technology, Osaka 565-0871, Japan Advanced ICT Research Institute, National Institute of Information and Communications Technology, Kobe 651-2492, Japan Graduate School of Life Science, University of Hyogo, Hyogo 678-1297, Japan Institute for Dynamics of Complex Systems, Georg-August-University G¨ottingen, 37073 G¨ottingen, Germany Laboratory of Atomic and Solid-State Physics, Cornell University, Ithaca, NY 14853, United States Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
Propelling microorganisms through fluids and moving fluids along cellular surfaces are essential biologicalfunctions accomplished by long, thin structures called motile cilia and flagella, whose regular, oscillatory beatingbreaks the time-reversal symmetry required for transport. Although top-down experimental approaches andtheoretical models have allowed us to broadly characterize such organelles and propose mechanisms underlyingtheir complex dynamics, constructing minimal systems capable of mimicking ciliary beating and identifying therole of each component remains a challenge. Here we report the bottom-up assembly of a minimal syntheticaxoneme, which we call a synthoneme, using biological building blocks from natural organisms, namely pairsof microtubules and cooperatively associated axonemal dynein motors. We show that upon provision of energyby ATP, microtubules undergo rhythmic bending by cyclic association-dissociation of dyneins. Our simple andunique beating minimal synthoneme represents a self-organized nanoscale biomolecular machine that can alsohelp understand the mechanisms underlying ciliary beating.
INTRODUCTION
Eukaryotic cilia and flagella accomplish vital physiologicaltasks [1, 2], ranging from the swimming and feeding of mi-croorganisms to the clearance of mucous in airways [3], estab-lishment of left-right body asymmetry and transport of cere-brospinal fluid in brain ventricles [4] and the spinal cord. De-fects in ciliary assembly or in their function are responsible fordiseases that affect millions of patients worldwide [5]. Eachcilium’s structural framework is the axoneme, which consistsof nine microtubule doublets and several hundred other pro-teins that maintain its structure, drive and control the beat,and transport the materials [6]. The beating is powered by ax-onemal dyneins that form two arrays (outer and inner dyneinarms) along the side wall of the doublet microtubules. Theygenerate interdoublet shear that causes the bending of micro-tubule doublets [7].The analysis of
Chlamydomonas flagellar mutants [8], bio-chemical and biophysical [9] identification and structuralstudies [10], especially using cryoelectron tomography [7],have progressed our understanding on the molecular organi-zation and function of each axonemal component [11]. Re-cently, axonemal dyneins have been reported to have mechani-cal and structural properties so distinct from other protein mo-tors to be suitable for the fabrication of biomolecular nanoma-chine [12, 13].How this complex structure drives the beating patterns isnot yet well understood [11, 14–18]. A controlled assemblyof minimal systems that reproduce certain aspects of ciliarydynamics with far less cellular feedback mechanisms can bean important step towards solving the puzzle of ciliary beat- ing dynamics. To address this issue we use the bottom-upapproach and reconstitute in-vitro a minimal axoneme madeof the main axonemal constituents, outer dynein arms (ODA)and microtubules, and we reproduce the bending oscillationof the natural cilia (flagella). We call this structure a “syn-thoneme” in analogy to the the well described axoneme.The modularity of the reconstituted structure of this syn-thoneme, its defined geometry and the nature of the buildingblocks allow the system to go beyond the minimal beating sys-tems reported in the past. Namely, two microtubule doubletsextended from frayed and disintegrated axonemes that exhibitrepetitive buckling [19, 20]; mixtures of microtubule bundlesand kinesin-1 clusters, which self-assemble in cilia-like beat-ing structures [21, 22]. The controlled assembly of our syn-thoneme has the potential for the development of controllablebeating structures that can serve as a tool for the understand-ing of the flagellar/ciliary beating and for eventual technolog-ical advance in the field of bio-inspired systems.
RESULTS
The reconstituted minimal bending system is made of taxol-stabilized microtubules and ODA extracted from flagella ofthe green algae
Chlamydomonas reinhardtii (See Supplemen-tary Fig. S1). We chose to use ODA for its ability to self-organize in arrays on microtubules [23], the high yield inpreparation, and its robust motility in vitro [8, 24, 25].Microtubules are polymerized in an experimental chamberby flowing porcine brain tubulin over fragmented
Chlamy-domonas axonemes (hereafter named seeds). The seeds repre- a r X i v : . [ c ond - m a t . s o f t ] F e b sent the joint basal end of the microtubule pair and are spon-taneously attached to the coverslip. This heterologous seed-ing procedure provides microtubule pairs with the same po-larity in which the filaments grow at a distance on axonemescale. With the seeds the relative movement of microtubulesis blocked at the basal end of the pair, but free at the distalend.These properties allow the repetitive buckling of the mi-crotubules driven by dynein. The distance between two poly-merized microtubule singlets at the basal end probably rangesfrom the minimal distance between two A-tubules of adjacentdoublets (approx. 30 nm) and the maximum corresponding tothe diameter of the axoneme (approx. 200 nm) (see Supple-mentary Fig. S2). Since the length of microtubules is longerthan 10 µ m, the tips of the filaments thermally fluctuated un-less ODAs formed cross-bridges between them. Therefore, aprecise determination of the inter-microtubule distance in in-dividual cases is not applicable in our observations.The ODA is provided to the system by perfusion of extractfrom axonemes containing ODAs and ODA-docking complex(ODA-DC) into the flow chamber. Due to the presence ofthe docking complex, ODAs are associated with the micro-tubule with high cooperativity in an end-to-end fashion andthereby align unidirectionally along one protofilament [23].We confirm the reconstitution of ODAs on microtubules withnegative staining electron microscopy (Fig. 1A and Supple-mentary Fig. S3) and the longitudinal 24-nm periodicity ofODA/ODA-DC aligned along the filament is identified byFourier analysis (Fig. 1B). This periodicity is characteristicfor ODAs in native axonemes [7] and reconstituted ODAs sys-tems shown in previous studies [26].The EM images and subsequent analysis also provide infor-mation about the occupancy of dynein arrays on microtubules(see SI text and Figs. S3 and S4 for more details). At highmixing ratios ODA arrays occupy most of microtubules andthe length of the arrays are probably underestimated due tothe limited size of the observation field. However, the lengthdistribution of contiguous dynein arrays shows that the aver-age length of about ∼
200 nm (corresponding to approx. eightODAs) is largely independent of the mixing ratio (Fig. 1C).We concluded that the ODA alignment is a highly cooperativeassembly process.After adding 1mM Mg–ATP to the system we observemany microtubule pairs with a joint basal end bending persis-tently We explain the functional mechanism behind the obser-vation in the following way. Free microtubule ends fluctuatein the bulk. Dynein motors assembled on one microtubule at-tach to the adjacent microtubule, then Brownian fluctuationsare suppressed. By using energy from ATP hydrolysis, themotors cooperatively produce shearing forces between thesetwo microtubules (see Fig. 2A). When they reach the buck-ling instability, the filaments separate.In more detail, one microtubule slides towards the seed.When the crossing angle between the microtubules increases,the forces on the motors increase and thus an increasing num-ber of motors detaches without the possibility to rebind. The other microtubule bends only weakly. The motion is stalledwhen the force produced by the remaining motors reaches theforce of the buckled microtubules. After that, stochastic fluc-tuations can tip the motors into cooperative detachment, akinto a catastrophic failure, which leads to a fast straighteningof the microtubules and a return to the original state. Thestraight microtubules again allow the attachment of a largernumber of motors. We observed that this process could repeatitself periodically. This cycle and the functional mechanismare illustrated in the schematic representation in Fig. 2B.The long lag phase and subsequent rapid sliding leading torapid buckling indicate that the attachment and movement ofmotors take place in a cooperative manner, too. The simplestpossible explanation is that the attachment rate of the first mo-tor between unconnected microtubules is low because of ther-mal fluctuations. The first motor capturing the adjacent mi-crotubule then suppresses the fluctuations and largely accel-erates the attachment of subsequent motors. The mechanismin which microtubule buckling accelerates the detachment ofmotors is also at the core of the geometric clutch hypothesisfor ciliary beating [15]. On the other hand, the release of themotors under load is reminiscent of models that propose a dy-namic instability in the sliding motion between microtubuledoublets [27].We quantify the oscillations by measuring the maximal dis-tance H between the buckled microtubules. A typical time se-ries representing the bending cycle is shown in Fig. 3A. Thiscycle can be divided into four phases consisting of an activebent state and a relaxed state with variable duration and thetwo transitions between them, namely a rapid bending fromthe relaxed to the active state and a rapid unbending from theactive to the relaxed state. The four phases are influenced alsoby the stochastic nature of dynein motors. Both rapid bendingand unbending phases completed within a few hundred mil-liseconds. The swiftness of the transitions is a likely clue onthe cooperativity of the motors as the motor recruitment actscollectively to transition between states.By analyzing the histogram of distances H in Fig. 3B wecan observe a bimodal distribution. Therefore, the above de-scription of the bending cycle as a process with two statesis a suitable one. We will call them open and close , andconsider stochastic transitions between them. We denote therates of the closed-open and open-closed transition with k + and k − , respectively. The discretized variable H then hasthe character of a telegraph noise process. A robust way todetermine the two rate constants is from the occupancy ra-tio ( P open / P closed = k + / k − ) and from the autocovariance func-tion of H , which for the telegraph process has the depen-dence ∼ exp ( − ( k + + k − ) τ ) . The autocovariance functions areshown in Fig. 3C. They have a bi-exponential form – besidesthe slow component, related to the open/closed transitions, afast one resulting from noise with a short correlation time.From the slow rate and P open / P closed = . ± .
5, we obtainthe rates k + = ( . ± . ) s − and k − = ( . ± . ) s − .We use the elastic model that is described in the next sec-tion to estimate the force and the energy needed to buckle FIG. 1. A) Negative staining EM image showing a portion of a microtubule microtubule and an assembly of the ODA complex. Globular blobsare regularly aligned along the microtubule. Scale bar: 100 nm. B) Fourier transform of EM images shows a 24 nm periodicity of ODA onmicrotubules. 1/4 nm − layer lines derived from microtubules are clearly observed (scale unit: 1/24 nm − ). C) Length distribution of ODApatches at different mixing ratios between ODA and microtubules. The peak length is around 100–200 nm irrespective of the mixing ratio. the filaments. With a typical length of l = µ m and EI = × − Nm , Eq. (2) gives F ≈ H = . µ m, we further calculate the elas-tic energy of the buckled state as F ∆ s ≈ × − Nm ≈ k B T . Changes in elastic energy that exceed the thermalenergy by two orders of magnitude prove that the beating isactively driven by molecular motors, i.e., that we assembledan active system. Theory and Simulation.
The shapes of the two bent filaments (Fig. 4A) and theforces that the dyneins need to produce to enter the bent con-figuration can be calculated by linear elasticity theory if weassume that the shape is quasi-static and that the deflectionsare small. In contrast to earlier models [28], we allow bothfilaments to bend. Because both ends are force-free, the force in filament 1 is exactly opposite to that in filament 2. Thecurvature in each filament is proportional to the local bendingmoment
EI y (cid:48)(cid:48) i ( x ) = F i y i ( x ) . (1)The resulting equation is solved with the ansatz y = A sin kx , y = B sinh kx with k = (cid:112) F / EI . The boundary condition at l leads to the equation tan kl = tanh kl with the lowest non-trivial solution kl = . F = . π EIl . (2)This equation can be used to estimate the force produced bythe motors that is needed to buckle the filaments. Notably,the prefactor in the buckling load of 1 . .
046 for one pinned and one clampedend [29]. As expected, clamping one end to a flexible fila-ment leads to a lower critical load than clamping it to a fixeddirection in space.
FIG. 2. A) Micrographs of bending cycle of two microtubules forming a synthoneme. Scale bar: 10 µ m B) Schematic representation of thefilament buckling. Initially, the filaments (green) are straight and the dynein motors (red) enter the active state. The force produced by thedyneins buckles the filament on which they are attached. The buckling changes the crossing angle between the microtubules, which reducesthe number of dyneins that can bind to both of them. The length difference between the filament segments, ∆ s ,and the distance H can be derived as functions of the crossingangle ϕ (see SI). Dynamical model.
The behavior of the system over timeobserved during the experiments can be described by a dy-namical model. The two filaments (each of length L ) areclamped at the minus end (Fig. 4B). Filament 1 is bearing dynein motors between length L and L , at a line density ρ .Each motor can be in the attached or detached state. Attach-ment can take place in the overlap zone l ± d / ϕ , where d is a characteristic distance between filaments that the motorscan bridge. In that zone, the attachment rate of the motors is k on . However, we use a lower constant k for two reasons:(i) a reduced attachment rate for the motors that align end-to FIG. 3. A) Maximal distance between the filaments in the buckled region ( H ), as defined in Fig. 2, as function of time. B) Distribution ofdistances H between the filaments. As the distribution is clearly bimodal, we designated the two states as open and closed. C) Normalizedautocovariance function C HH ( τ ) = ( (cid:104) H ( t + τ ) H ( t ) (cid:105) − (cid:104) H (cid:105) ) / (cid:10) ( H ( t ) − (cid:104) H (cid:105) ) (cid:11) . end along one filament indicates the cooperativity between themotors; (ii) the effective attachment rate is strongly reducedby thermal fluctuation when the motors are simultaneously inthe detached state. For a motor loaded with force f we use adetachment rate k off = k exp ( α f ) , where α is a parameterrepresenting the inverse characteristic detachment force.A motor attached on filament 1 with load f moves towardsthe minus end of filament 2 with velocity v = d ( ∆ s ) / d t deter-mined by a linear force-velocity relationship f = f s ( − v / v m ) (3)with the parameters f s (stall force) and v m (unloaded velocity).When n motors are attached, they share the load equally suchthat F ( l ) = n f .We explain the oscillatory cycle of the filaments observedin the experiments through the following stages: First, all mo-tors are detached and the first attachment takes place randomlywith the rate k . This increases the binding rate of remainingmotors to k on . After a short time, the total motor force n f s sur-passes the buckling force F ( l ) , where l is the distance to the first bound motor. The straight state becomes unstable. Byconsidering the duty ratio of stalled motors (fraction of timespent in the attached state) η = k on k on + k exp ( α f s ) , (4)the condition of buckling is η f s ρ ( L − L ) > F ( L ) = . π EIL . (5)The initial buckling instability is followed by the growth ofthe bulge, driven by the sliding action of motors in the overlapzone. During this phase, the crossing angle ϕ increases, whichreduces the length and the number of motors in the overlapzone, leading to a metastable state, where the force balance isreached at an angle ϕ when ηρ f s d / ϕ = F ( l ) .Through random detachment of motors, a “catastrophicfailure” can take place when detachment of motors leads toan increased load on the remaining ones, further increasing FIG. 4. Theoretical description of the active synthoneme. A) Elastic model. Two filament segments of different lengths are pinned to eachother at x = x = l . They are parameterized with the functions y ( x ) and y ( x ) . The x -axis represents the direction of theforce. The condition for the pinned end at x = y ( ) = y ( ) =
0. At the clamped end, the condition is y ( l ) = y ( l ) and y (cid:48) ( l ) = y (cid:48) ( l ) . B)Active model: two filaments are clamped in the origin. Filament 1 is decorated with motors from length L to length L . Motors can bind tofilament 2 if the distance between the filaments is smaller than d (grey rectangle). C) Snapshots from a stochastic simulation. The black linesshow two filaments, red and green circles show bound and free motors, respectively. The upper panels shows the filaments before binding, themiddle panel the onset of buckling and the lower panel a stalled state before catastrophic detachment of motors. D) The distance between thefilaments H as a function of time from the simulation. E) Distribution of distances H from the simulation. As in the experiment, a stronglybimodal distribution is visible. F) Autocorrelation function of the distance H as a function of time. their detachment rate. We assess the stability of a state withthe following consideration. At a constant total force F , ini-tially distributed over n attached motors, the on-off dynamicsis given by the master equation˙ n = ( N − n ) k on − nk off e α F / n . (6) Its stability is determined by the derivative ∂ ˙ n ∂ n = − k on + (cid:18) α Fn − (cid:19) k off e α F / n (7)which is positive when α f s n / n > / ( − η ) . As a roughestimate, we expect an instability when α f s (cid:38) CONCLUSION
The reconstituted minimal axoneme, i.e. the synthoneme,that we present in this study is a one-of-a-kind result resem-bling the natural system with its beating behavior. All crucialcomponents of our synthoneme are assembled in-vitro in abottom-up approach. We show that the cooperativity of thedynein motors to arranging on the filament as well as to ac-tuating the buckling can be reconstituted in-vitro. Althoughthe amplitude and frequency of oscillations are still well be-low those of natural cilia, we have shown that the basic func-tionality can be established with a far smaller number of pro-teins. Specifically, while cilia contain several hundred dif-ferent proteins, our synthetic axoneme works with only threecomponents (tubulin, ODA, ODA-DC). The observation thatsynthetic systems consisting only of molecular motors andfilaments can reproduce the basic movement necessary forcilia/flagella beating also provides clues about the amount ofcomplexity needed by the ancestor cilia to first achieve beat-ing motility. Indeed, some organisms like the male gamete ofthe parasitic protozoan
Diplauxis hatti have a motile axonemewith only three doublets instead the classical “9 + 2” structure[30]. This suggests that bending behavior could be producedby simpler structures that have filaments and motors. Futurerefinements will lead to a convergence between the syntheticand the natural cilium. This will provide a systematic way ofdissecting the elusive beating mechanism.Besides the potential of this system for answering impor-tant questions about ciliary beating, our synthetic cilium mayencourage the technological development of molecular ma-chines for fluid transport at micro- and nanoscale. Most pre-vious attempts to build artificial cilia have concentrated onmagnetic [31, 32], electrostatic [33] or optical [34] actua-tion mechanisms to produce motion similar to the natural one.These studies showed hydrodynamic entrainment between ad-jacent structures and creation of metachronal waves. How-ever, these systems are unrelated to biological cilia. In thefuture our system will also be developed as multi-cilia systemby using axoneme seeds as the base and aligning them and wewill achieve the synchronization of axonemal beating.
MATERIALS AND METHODSPreparation of the crude dynein extract
Demembranated axonemes are suspended in 0.6M KClcontaining HMDEK solution to extract crude dynein sample(see SI for more details about preparation). After spinningdown the axonemes for 5 min, the supernatant is desaltedwith the overnight dialysis against HMDEK solution (Spec-tra/Por Dialysis Membrane, MWCO:100-500D, Biotech CE).The concentration of the crude dynein extract is measuredwith Bradford method and the concentration used during theexperiments was 0.02 mg/ml.
Preparation of dynein–MT complexes
The flow chamber was build with Teflon-treated cover-slips as previously described in [35] and spaced with double-coated tape (80mm thick, W-12; 3M, St. Paul, MN) to preventany nonspecific binding of proteins onto the surface. Micro-tubules growing close to each other and with the same po-larity were obtained by using fragments of demembranatedaxonemes prepared by rigorous pipetting as polymerizationseeds. The ODA–MT complexes are reconstituted in the flowcell by flowing the components one after the other. Briefly,in the flow cell a small amount of axonemes are attached onthe bottom of the flow cell. After 5-min incubation, the flowcell is washed with 1% (w/v) Pluronic ® F127 in BRB80 (80mM PIPES, 1 mM MgCl , 1 mM EGTA, pH 6.8 with KOH)and is incubated for 5 min. After washing the chamber withBRB80, fluorescently-labeled (Cy3–labeled) porcine tubulin(3% labeling) is introduced into the flow cell, polymerizedin the presence of 1 mM GTP, 50% DMSO, 1mM MgCl at 37 ◦ C for 30 min and stabilized with 7 µ M taxol. Aftermicrotubule polymerization, diluted crude-dynein extract isintroduced into the flow cell and incubated for 5 min. Thenon-bound protein is eliminated by washing the chamber withbuffer and afterwards 1mM ATP is perfused into the chamberto trigger the activity.
Imaging and tracking
Fluorescence images of the MT-ODA complex are acquiredusing an inverted fluorescence microscope Ti-E (Nikon,Japan) equipped with a 60 × CFI Apochromat objective(N.A.=1.49, Nikon, Japan) and the confocal unit (CSU-X1,YOKOGAWA, Japan). The data is recorded with an iXon Ul-tra EMCCD camera (Andor Japan, Japan). The images areacquired at a frequency of 10 Hz. The movement of the fila-ments over times was tracked manually and a third order poly-nomial was fitted to the data by using a purpose-written MAT-LAB code.
Acknowledgements
E.B., I.G., and R.G. acknowledgesupport from the MaxSynBio Consortium which is jointlyfunded by the Federal Ministry of Education and Researchof Germany and the Max Planck Society. E.B. acknowl-edges support from the Volkswagen Stiftung (priority call“Life?”). A.V. acknowledges support from the SlovenianResearch Agency (grant no. P1-0099). K.O. acknowl-edges MEXT/JSPS KAKENHI, grant numbers 26440089,17K07376 and JP16H06280, the Takeda Science Foundationand Hyogo Science and Technology Association that partlysupported the project. ∗ [email protected] † [email protected][1] Satir, P. & Christensen, S. T. Overview of structure and functionof mammalian cilia. Annu. Rev. Physiol. , 377–400 (2007).[2] Gilpin, W., Bull, M. S. & Prakash, M. The multiscale physicsof cilia and flagella. Nat. Rev. Phys. , 74–88 (2020).[3] Loiseau, E. et al. Active mucus–cilia hydrodynamic couplingdrives self-organization of human bronchial epithelium.
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Chlamydomonas reinhardtii . Axonemes and theirdemembranation.
Axonemes were obtained from
Chlamydomonas reinhardtii according to the dibucaine method [36, 37].
C. reinhardtii wild type strain (137c mt-) and the outer-arm less mutant( oda1 ) were cultured in 4 liters of the liquid TAP mediumunder continuous illumination at 20 ◦ C for 4 days with airbubbling. Cells were harvested by centrifugation at 1692 × g(3000 rpm, R10A3 rotor, Himac CR22E) for 6 min, andthen re-suspended in 40 ml ice-cold HMDS (30 mM HEPES-NaOH, 5 mM MgSO , 1 mM dithiothreitol (DTT), 4% su-crose, pH 7.4). All procedures described below were con-ducted at 4 ◦ C or on ice unless otherwise stated. The cell sus-pension was moved to a 50-ml conical centrifuge tube and 2.5mM (final concentration) dibucaine HCl (Wako, 167-15111)was added. The suspension was pipetted rapidly in and out of10-ml Falcon disposable plastic pipettes for 30 s. Afterwards200 µ l of 100 mM EGTA was added and the solution was gen-tly resuspended several times. The cell bodies were removedby centrifugation at 1670 × g (3000 rpm, RS-4 rotor, KUB-OTA 6800) for 6 min, the supernatant was transferred to a new50-ml conical centrifuge tube and centrifuged again as above.The cell-free supernatant was centrifuged at 27720 × g (15,000rpm, RSR20-2 rotor Himac CR21) for 12 min. The resultingpellet was resuspended in 1.5 ml of HMDEK (30 mM HEPES-NaOH, 5 mM MgSO , 1 mM DTT, 1 mM EGTA, 50 mMpotassium-acetate, pH 7.4) and demembranated by adding 15 µ l of 20% Nonidet P-40 (NP-40, Nacalai Tesque). After 5min-incubation, the suspension was centrifuged at 21130 × g(15,000 rpm, FA-45-24-11 rotor, Eppendorf 5452R) for 5 min,and resuspended in 1.5 ml HMDEK. This procedure was re-peated twice to remove detergent. Axonemes were collectedby centrifugation as described above. An aliquot of the de-membranated oda1 axonemes was used to prepare the seedsof microtubule polymerization. Suspension of the axonemeswas gently homogenized with a Teflon pestle and pipetting.The resultant suspension was centrifuged at 3380 × g at 4 ◦ Cfor 10 min. The pellet was resuspended with a small amountof HMEDK solution. Intrinsic dyneins of the seeds were de-activated and the sliding among doublet microtubules was in-hibited with the treatment of ethylene glycol bis(succinimidylsuccinate) (Thermo Fisher Scientific, 21565).
Preparation of of the crude dynein extract.
For the extraction of ODAs and docking complex fromthe
Chlamydomonas reinhardtii wild-type axonemes we fol-low the method described in previous works [20, 38]. Asreference, we prepared high-salt extract from oda1 (outer-arm less mutant) axonemes. Demembranated axonemes wereresuspended in 0.6M KCl containing HMDEK solution toextract crude dynein sample. After spinning down the ax- onemes at 21130 × g (15,000 rpm, FA-45-24-11 rotor, Eppen-dorf 5452R) for 5 min, the supernatant was desalted withthe overnight dialysis against HMDEK solution (Spectra/PorDialysis Membrane, MWCO:100-500D, Biotech CE). Theconcentration of the crude dynein extract was measured withBradford method and it was around 0.02 mg/ml. High-saltextract from the demembranated axonemes contains varioustypes of proteins [38]. Therefore, protein components of thedynein-microtubule complex should be examined with SDS-PAGEs. Spinning down the crude dynein extract with micro-tubules in the presence of 1mM ATP partially pulled downthe outer-dynein arms and related proteins with microtubules.Using oda1 axonemes, we repeated the same procedure onthe axonemes and high-salt extracts. The resultant super-natants and pellets of the centrifugations were examined withthe SDS-PAGE and the contents of oda1 were compared withthose of wild type. Inner arm dyneins, components of thecentral pair apparatus and radial-spoke components remain insupernatant under this condition (Fig. S1). Thus, our proce-dure provided ODA-DC-MT complex which contained no in-ner arm dyneins but only outer arm dyneins. Negative staining electron microscopy on dynein-MT complex.
To evaluate the formation of ODA arrays on a microtubule,we examined the structure of dynein-MT complex with anelectron microscope. Structural similarity of this complexto the axoneme has been reported in previous studies andwas examined by negative staining electron microscopy. Itshowed that microtubules were periodically decorated withODA dyneins. The crude dynein extract of 200 µ g/ml wasmixed with taxol-stabilized microtubules (200 µ g/ml) at thevarious ratios (10:1, 1:1, 1:2 and 1:10). After 30-min incu-bation, the small aliquot of the mixture (5 µ l) was applied onto a carbon grid and washed with MMEK for EM (30 mMMOPS-NaOH, 5 mM MgSO , 1 mM DTT, 1 mM EGTA, 50mM KCl, pH 7.4). Fixation with 2% glutaraldehyde, washingwith MMEK and staining with 1.4% uranyl-acetate with 100 µ g/ml bacitracin. The sample was examined with JEM-1400(JEOL, Japan) with 80kV acceleration voltage and the im-ages of the samples were collected with 4K camera (US4000,Gatan). Typical electron micrographs are shown in Fig. S3.Coverage of the microtubules with ODA-DC complex wasevaluated with image analysis. To extract the 24 nm structuralrepeat of dynein-ODA-DC from the electron micrographs, thecustom-built band-pass filter was applied to them. The mergerof the original and filtered image clearly shows the presenceof dynein-DC complex. The length of the complex and mi-crotubule length in the image field were measured. ELASTIC MODEL
In this section we derive the relationships between thecrossing angle ϕ , the length difference ∆ s and the distance0between filaments H (Fig. 3A in main text). We start withthe solution derived in the main text, where the filamentsshapes are described by y = A sin kx and y = B sinh kx , with kl = . AB = sinh kl sin kl = − . . (S1)In the linear approximation, the opening angle at the pinnedend is ϕ = y (cid:48) ( ) − y (cid:48) ( ) = Ak − Bk = Ak (cid:18) − sin kl sinh kl (cid:19) = . Ak . (S2)Also in the linear approximation, the contour length of fila-ment i ( i = ,
2) can be calculated as s i = (cid:90) l (cid:113) + ( y (cid:48) i ) d x ≈ (cid:90) l (cid:2) + ( y (cid:48) i ) (cid:3) d x (S3) and the difference as ∆ s = (cid:90) l (cid:2) ( y (cid:48) ( x )) − ( y (cid:48) ( x )) (cid:3) d x = lk ( A − B )= sinh kl + sin kl sinh kl − sin kl l ϕ = . l ϕ . (S4)Finally, we define the maximum distance between the fila-ments H = max ( y − y ) . The condition for maximality is y (cid:48) ( x m ) − y (cid:48) ( x m ) = kx m cosh kx m = cos kl cosh kl (S5)with the solution kx m = . H = y ( x m ) − y ( x m ) = . l ϕ . These relationships are used in the main text toestimate the elastic energy of the two-filament system. Theyare also needed for the stochastic simulation.1 FIG. S1. Preparation of the outer-dynein arm-microtubule complex. A) Procedure of dynein-crude extraction. PPT means a precipitate B)The high-salt crude dynein extract from
Chlamydomonas reinhardtii wild type axonemes, oda1 axonemes and centrifuged dynein-microtubulecomplex were analyzed by SDS-PAGE with silver staining. Since only inner arm dyneins exist in oda1 axonemes, the high salt extract didnot contain outer arm dyneins. In contrast, the extract from wild-type axonemes contains both outer-arm dynein and inner-arm dyneins. Theglycerol cushion in the centrifugation can separate inner-arm dynein from microtubules in the presence of ATP but outer arm dyneins stayedwith microtubules. Lane 1: molecular weight markers. Lane 2: no dynein exists in oda1 -extract-MT complex. No light chains and Intermediatechains of inner-arm dyneins were found. Lane 3: Removal of ATP from the complex pulled inner-arm dyneins of oda1 extract into pellet withmicrotubules. Lane 4: Inner arm dyneins were found in the pellet when being centrifuged without cushion. Lane 6: Dyneins found in thepellet even in the presence of ATP and cushion but no light chains and Intermediate chains of inner-arm dyneins were found. This observationsuggests that only outer arm dyneins remained on microtubules and these dyneins formed the complex with microtubules via dynein-dockingcomplex. C) High-molecular region of 3% SDS-PAGE. Lane 1: The microtubule pellet in the presence of ATP and glycerol cushion. Nodynein heavy chain was found in the pellet. Lane 2: Inner arm dynein heavy chains were found. Lane 5: Even in the presence of ATP, onlyouter arm dyneins were associated with microtubules. These observations suggest that our procedure enabled the ODA-DC-MT complex tocontain no inner arm dyneins but only outer arm dyneins. S and P indicate a precipiate and supernatant, respectively. FIG. S2. Schematic representation of the assembly of a minimal synthetic axoneme with the minimal (a) and maximal (b) distance betweenthe polymerized microtubules. FIG. S3. Taxol-stabilized microtubules were mixed with crude dynein extract at various mixing ratios and observed with negative stainingelectron microscopy (acceleration voltage 80kV, magnification 25k). FIG. S4. Average length (A) and density (B) of dynein patches on microtubules as a function of mixing ration of crude dynein extract (4 - 400 µ g/ml) to microtubules (40 µµ