Emergence of flagella-like oscillations in single microtubules driven by collective dynein transport

  1. Shivani A. Yadav
  2. Neha Khetan
  3. Dhruv Khatri
  4. Chaitanya A. Athale

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Abstract

Flagellar and ciliary oscillations result from a combination of stereotypical axonemal geometry, collective mechanics of motors, microtubules (MTs), elastic linkers and biochemical regulation. However, the minimal essential components and constraints resulting in flagellar oscillations remain unclear. Here, we demonstrate that periodic, low-frequency waves of flagella-like oscillations in vitro emerge from a ATP-driven collective molecular motor transport of MTs clamped at one end. The spontaneous oscillations arise without any external forcing and can be explained by an in silico model of molecular motor binding driven MT bending and buckling followed by motor detachment driven ‘recovery’ stroke. We demonstrate that transitions in single MT patterns between flapping, flagellar-beating and looping are determined solely by the self-organization of collective motor transport and filament elasticity.

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    Reply to the reviewers

    Manuscript number: RC-2023-01991

    Corresponding author(s): Chaitanya A. Athale

    General Statements [optional]

    *We are grateful to the editors sending our manuscript out to review, and the reviewers for the careful reading and critical comments. In the following sections we describe our plan for revisions that will address the comments of the reviewers. We have added these in a point-wise manner. In summary most of the comments are addressable with additional experiments, simulations and data analysis. These will indeed serve to strengthen the findings without altering the fundamental findings. However, we would require upto 90 days to make these changes. *

    Description of the planned revisions

    Reviewer #1 Evidence, reproducibility and clarity

    __Summary: __This work combines in-vitro experiments and numerical modeling to study the dynamics ofmicrotubules, driven by molecular motors. In this bottom-up approach, molecular motors areimmobilized on the surface and microtubule filaments are anchored to the surface from one end. The dynamics results in "beating like" motion of the anchored microtubules. The authors establish aphase diagram of the different dynamical patterns of "beating like" motions by varying the molecular motor density and the length of the microtubule anchored to the surface. They use a numerical framework that captures the observed patterns.

    Our response: We are grateful to the reviewer for the careful reading and agree with the summary of our work. In the following sections we detail how we plan to address the specific comments.

    Major comments:

    1. Overall the experiments and results are well described and claims are supported by the data.

    Both experimental and numerical methods are presented in a way that they can be reproduced.

    Our response: We are grateful for the reviewer’s assessment about our findings and presentation of the results.

    Minor comments:

    1. A key feature of beating cilia is the asymmetry of the beat pattern (fast stroke and slow recovery). It might be interesting to use the kymographs or the Phy vs time analysis to see whether or not this feature exists in this simplified experimental model.

    Our response: We agree with the reviewer that it could be of interest to examine whether the dynamics of the tip-angle phi (φ) shows a difference between the strokes at onset and return, to compare to the fast-slow asymmetry observed in cilia. This will be approached in two ways:

    1. We will obtain more data from more fields of view

    2. Use the time-derivative of the tip-angle, phi (φ) dynamics to examine whether the onset and return strokes are asymmetric and how this compares to ciliary dynamics.

    3. We will also analyze the tangent angle to the contour, psi (ψ) plots with time (y-axis) and MT length (x-axis).

    A qualitative analysis of a few time-series suggests indeed that the onset v/s return stroke of the ‘beating’ is likely to be asymmetric in the manner qualitatively distinct from cilia and flagella, that appear to be symmetric. This would suggest we avoid the term flagella-like to describe the dynamics.

    2. Also, the beating frequency is very low (mHz) compared to real cilia/flagella (~Hz). Would it be possible to use the model to predict which parameter would need to be tuned to reach more

    physiologically relevant beating frequencies?

    Our response: We agree that the oscillations we observe have a frequency thousand fold lower as compared toflagella and cilia and have highlighted this in our discussion. When we modified motor velocity and stall forces, we found only a marginal increase in frequency of oscillations by a factor of 2-5, but not 10-fold or more. We also attempted in simulations to mimic kinesin-like properties. However we do not see a dramatic improvement. This suggests an involvement of higher-order organization of the filament. Indeed we plan to perform simulations that test the following scenarios not already tested:

    1. the role of microtubule bundling factors resulting in 2-, 3-, and higher order complexes of MTs

    2. varying the bending rigidity of the microtubules within ranges of what may be experimentally feasible with differences reported for taxol and GMPCPP filaments

    3. altering the duty ratio of the motor

    These will be in the nature of “what if” simulations that could provide the basis of future experimental design to test such predictions. This comment is similar to one by the other reviewers.

    Significance

    This study is part of the field of in-vitro reconstitution, from a minimal set of components, that aims to reproduce a biological function to identify and understand the minimal physical/biophysical mechanisms underlying a function. This study might be of interest for the people who address questions of the self-organization of cytoskeletal elements in minimal systems.

    Our response: We agree with the assessment of the reviewer of the significance of the study and the readership that might be most interested in this work.

    *The main limitation of this study relies on the claim of reproducing a flagella-like motion. Indeed, the frequency of the described oscillations is in the mHz range while the frequency of cilia is in the range of few Hz to tens of Hz. This suggests that the mechanism at play in such a reconstituted system is not the one that drives beating in real cilia/flagella. Yet, this limitation also applies to other studies in the field (Vilfan et al. 1999, Guido et al. 2022 ...). *

    Our response: We agree with the reviewer that the 10^3 to 10^4 difference in oscillation frequency with that observed in cilia is striking. Indeed our claim was limited to the wavelike nature of the oscillation of the free end of a clamped microtubule driven by molecular motors producing a buckling instability, release and re-engagement of motors. Therefore it is evident we are missing many components in our minimal system as compared to cilia. However, we would like to emphasize for now that the beating is only qualitatively comparable to cilia and flagella. So far we have not compared the two waveforms. As a part of our revision plan, we aim to objectively describe the quantitativeaspects that could strengthen our claim of a similarity or lack thereof in wave-forms.

    Indeed this limitation is also observed in the work of Vilfan et al. (2019) and Guido et al. (2022). However, we believe with changes to the experimental setup and a robust and tractable model we have improved on these studies.

    References:

    Vilfan A, Subramani S, Bodenschatz E, Golestanian R, Guido I (2019). Flagella- like Beating of a Single Microtubule. Nano Lett 19(5), 3359–3363.

    Guido I, Vilfan A, Ishibashi K, Sakakibara H, Shiraga M, Bodenschatz E, Golestanian R, Oiwa K (2022). A synthetic minimal beating axoneme. Small e2107854.

    My second concern is that the added value with regards to state of art is not clearly explicit. I'm thinking about the work of the Isabelle Guido's team where they have more complex reconstituted systems (a pair of 2 microtubules); or the work of Pascal Martin's lab where the design of the system allows to capture more complex mechanisms such as myosin density waves, which result infrequency beat of 0.1Hz.

    Our response: We agree that the advances of our study can be highlighted. In the following points we highlight the value added to prior art:

    1. In previous work, MT bundles have been shown to produce synchronized base-to-tip oscillations in vitro driven by kinesin in presence of crowdants (Sanchez et al., 2011). However, the study lacked control over MT length,, something we have addressed in our study.

    2. Cilia reconstitution with MT length and motor density control (Sasaki et al., 2018) are closer to control of the system but because of the complexity it is hard to distinguish what effect emerged from which componen.

    3. The generation of a bending wave driven by outer dynein arm (ODA) combined with pairs of MTs nucleated from Chlamydomonas axonemal fragments (Guido et al., 2022) was probably a close mimic of a minimal system; it not only lacked lacked variation in motor density and length but failed to show oscillations, with S-shaped buckling patterns observed.

    As a result it is reasonable to state that this work is a distinct improvement on previous work. In some senses it provides a consistency check on the previous results and at the other with a model and novel order-parameter an opportunity to improve our understanding.

    References:

    1. Vilfan A, Subramani S, Bodenschatz E, Golestanian R, Guido I (2019). Flagella-like Beating of a Single Microtubule. Nano Lett 19(5), 3359–3363.

    2. Sanchez T, Welch D, Nicastro D, Dogic Z (2011). Cilia-like beating of active microtubule bundles. Science 333(6041), 456–9.

    3. Sasaki R, Kabir AMR, Inoue D, Anan S, Kimura AP, Konagaya A, Sada K, Kakugo A (2018). Construction of artificial cilia from microtubules and kinesins through a well-designed bottom-up approach. Nanoscale 10(14), 63236332.

    4. Guido I, Vilfan A, Ishibashi K, Sakakibara H, Shiraga M, Bodenschatz E, Golestanian R, Oiwa K (2022). A synthetic minimal beating axoneme. Small e2107854.

    Reviewer #2 Evidence, reproducibility and clarity Summary:

    The authors use a modified version of conventional gliding assays to induce microtubule bending, buckling, looping and cyclic beating (which they term "flagella-like") via clamping the plus ends of gliding microtubules to the surface. They find that the pattern of motion depends on different factors such as microtubule length and motor density. They build a simple computational model that predicts transitions between microtubule motion patterns depending on these parameters.

    Our response: We agree with the assessment of the reviewer summarizing our work in terms of the approach taken and the inferences.

    Major comments:

    - Overall, the experimental data is extremely sparse. As far as I can see, there are only two replicas for the lower motor density. It is not clear to me how the authors define the boundaries in the

    experimental phase diagram in Fig. 7. To build a phase diagram - where one axis corresponds to the motor density - on just two experiments is not convincing. I would need to see more experiments covering a larger range of motor densities and at least three replica per condition.

    Our response: The comment refers to Fig. 7, whose purpose was to answer the question- can we test the phase diagram predicted in simulations by comparing to experiment? The answer was provided with representative data, in order to demonstrate that the model is qualitatively validated.

    The reviewer is asking for a systematic experimental test that rigorously demonstrates such a match between simulation and experiment. To this end, the phase diagram may not be the ideal form for such a test. We will attempt to examine the beating frequency and wave-transition in line with a comment by reviewer #3, as a measure of experiment-theory validation.

    We agree with the reviewer that our data could be enriched with replicates, with more densities of the motor. We will then analyze all the experimental data using common metrics to compare to simulations.

    - It is not clear to me why the proportion of pinned vs. free microtubule segments should affect the beating pattern. I would expect that the free microtubule segment does not "feel" the length of the clamped segment, if it is indeed fixed all along its length and unable to move / bend. The simulations use only two anchor points at the pinned tip. The segment in between the anchor points bends, which could affect how the free microtubule segment behaves. To support the claim that it is indeed the proportion of the lengths of the pinned vs. free segments and not simply the length of the free segment alone that influence the beating pattern, I would expect to

    (1) see the corresponding and thoroughly quantified experimental data that verifies this simulation-based prediction. Fig. 5C is based on only three microtubules and it is not clear how long the segments are.

    (2) the entire pinned segments in the simulation should be fixed. This should also be compared to experimental data, where the lengths of the free segments are the same and only the lengths of the pinned segments

    vary.

    Our response:* O*riginally the intention of comparing pinned length changes was based on experimental design, in which we incubated biotinylated tubulin to obtain longer or shorter clamped plus-ends. The contrast between a point-pinning and a longer segment is based on beam bending and buckling theory, corresponding to the difference between a swivelling point of immobilization (pinning) and a clamped end (clamped). However, we agree with the reviewer that beyond the pining scenario, once a segment is pinned the only thing really driving the beating is the free length. To address the specific comment we aim to add simulation calculations that will include a fixed clamp and increasing free length demonstrating that the primary driver in changing dynamics (so long as a segment is clamped) is the free length.

    (1) To address the question of experimental comparison we will examine more data with increasing free segment lengths for the same density of motors and plot the dynamics, as well as characterize the oscillations with frequency estimation.

    (2) This relates to the earlier part of this comment and we aim to re-run the filament clamped segment simulations to make it consistent with expectation and theory from related papers in the field, with only the free-segment length varied.

    - In relation to my previous comments: I would expect a direct comparison between the simulation-based prediction that the beating pattern changes with microtubule length and motor density in a quantitative manner, where all pinned microtubules observed experimentally are analyzed. The figures are often based on single observations.

    Our response: The experimental phase diagram had representative beating MTs, as compared to simulations. We agree that showing more statistics on these patterns could help. We aim to perform more experiments and analyze more data, which will be systematically plotted to make statistically relevant inferences of patterns as a function of density and length of MT.

    - The authors report that the pinned microtubules typically undergo 2-3 cycles of beating. This

    number is very low, and I am hesitant to call it "flagella-like" cyclic beating. Is this due to the dynein motors being much slower than e.g. kinesis? To confirm this and support the generality claimed by the authors, I would like to see experiments with a different, faster motor. If other motors are not readily available to the authors, this would imply a substantial amount of time and effort though.

    Our response: The slower velocity of yeast cytoplasmic dynein is indeed one the contributing factors for the slow oscillations seen. In preliminary experiments with kinesin we indeed see a faster oscillation, but still in the 10 mHz range. These experiments will be added to the revised manuscript.

    - Please perform statistical analysis of the experimental data.

    Our response: Most of the data, while statistical, is not being compared for means (e.g. simulation v/s experiment). However we will analyze the frequency as a function of length and density and examine differences based on standard statistical tests.

    Minor comments:

    - Number of replicates and samples should be indicated in the figures.

    Our response: With additional analyzed data and new experiments we will have more datasets and

    Significance

    - The approach to clamp the plus ends of gliding microtubules in order to induce buckling, bending and beating is elegant and should be easily transferable to other groups who may be interested in this method, since it is straightforward to adapt conventional gliding assays to induce pinning.

    Our response: We agree with this assessment of the reviewer.

    - The study could potentially be interesting to an audience studying flagella-like systems. Since the system is simple and based on in vitro components with defined parameters, it could serve as a basis for studying more complex systems or testing the influence of particular proteins associated with flagella. However, I do not see a major advance regarding our understanding of flagella or similar structures based on the manuscript. In combination with the model, I see it majorly as a useful tool, providing methodological advance. It would be desirably to make the computational model available to the public.

    Our response: We agree that this system of minimal in vitro components could in future be made more complex in a step-wise manner. Once the manuscript is accepted after review, we have intended to make the code available in OpenSource. The source code of Cytosim already is OpenSource and can be downloaded here: https://gitlab.com/f-nedelec/cytosim.

    - The computational model seems useful and straightforward to me, yet my background is purely experimental and I cannot judge the model in detail.

    Our response: The computational model is indeed straightforward, and is based on a set of C++ codes that are OpenSource and those with a computational training have tested it in multiple studies both by us and other labs.

    - In my view, the most important limitation of the manuscript is its lack of thorough experimental data to support the claims made by the authors. In its current state, the manuscript seems rather preliminary and I see the need for significant additional experimental evidence.

    Our response:* W*e plan to take the reviewers criticism on board and perform new experiments, analyses and simulations to address this gap of additional experiments. These experiments we believe will go to strengthen the manuscript, but not fundamentally alter the result.

    Reviewer #3 *(Evidence, reproducibility and clarity (Required)): *

    -Summary:

    *This manuscript reports experimental in vitro gliding assays demonstrating bending oscillations when single microtubules are anchored at their plus end and compressed beyond a buckling threshold by dynein molecular motors immobilized on a solid substrate. Together with numerical simulations based on the well-established Cytosim software, the authors identify three main classes of motile behavior under the control of microtubule length and motor density: aperiodic fluctuations (flapping), periodic beating with bending traveling waves over at least part of the filament length, and looping behaviors where the microtubule can curl on itself near its free tip. The authors claim that these movements are reminiscent of the beating movements of eukaryotic cilia and flagella and may provide useful information of the mechanism underlying the oscillatory instability. *

    Our response: We are grateful to the reviewer for a careful reading and have in the following sections outlined our plan for revision in response to the specific comments.

    *- Major comments: *

    1. The observed oscillations show only a few cycles (up to only 4, but often 2-3 (Fig. 1-2)) and are in addition very noisy. Oscillations thus appear to happen only transiently, i.e. do not show a dynamic steady state on timescale much larger than the oscillation period. Demonstrating the emergence of true (and stable) regular oscillations thus remains a challenge, in contrast to the authors' claim. The large variability of behavior from filament to filament (as seen in SV3), as well as in a single filament over time, also makes it difficult to achieve a robust quantitative description of these movements (see below).

    Our response: We have observed at times 4 and at times more cycles but we believe this is limited by the fact that mechanical pulling on the streptavidin-biotin linkage could result in occasional detachment of the filament from the surface. Stable oscillations of the form that the reviewer is pointing to may not emerge due to practical challenges and may require an alternative experiment such as optical tweezer to clamp the filament for a longer period. This is currently beyond the scope of the study, but could be attempted in future.

    Regarding the variability, we are aiming to analyze more data that has already been recorded and is also being acquired. These additional datapoints will allow for more representative statistics. The variability should tell us more about the nature of the system. We will estimate frequency of oscillations as a parameter for comparison along with our order parameter (span). This is similar to the comment by reviewer #2.

    2. Overall, the amount of experimental control seems relatively limited, for there is systematic variation of microtubule length (free or pinned) and only two motor densities have been explored.

    Our response: We will address this shortcoming by performing more experiments, with a few more motor densities of intermediate value. This will be supplemented with additional data analysis.

    • *One wonders why the motor density has not been more extensively varied and what determines the range of densities that can be achieved. What happens if the density gets larger than 50/µm^2? Do the filaments fail to remain anchored? Is buckling still permitted at high motor density? *

    Our response: The range of densities are obtained after the experiment, since this is not a patterning system. At times the density is either too low, and the filaments do not beat, or too high and they detach. This results in only two reported densities, less than perhaps desirable as pointed out by the reviewer. Now that we know what densities work, we aim for a fine-grained scan in the same range expected to produce regular oscillations.

    We will titrate the motors to obtain intermediate densities in the range that we have already found to result in stable oscillations with between 4-5 periods and hope to address this question.

    • *Important fundamental issues remain here unfortunately untouched in experiments and are also only qualitatively discussed in simulations (bottom of p11 and Fig. 4), namely the dependence of the frequency and wavelength of wave-like beating as a function of motor density and microtubule length. These limitations result from a lack of control over the microtubule lengths and that only two motor densities have been tested. Using the natural variability in length of the anchored filaments may be potentially used to study length effects but then a relatively large amount of data will be required to reliably conclude that filaments ensembles of different mean lengths reliably show different behaviors. Similarly, I do not see where in the data one can see that increasing motor density actually controls the oscillation frequency, as concluded from simulation data (but not analyzed quantitatively). *

    Our response: We plan to systematically analyze the frequency, which we have already demonstrated we can measure. The dependence on MT length and density will be tested and added as additional data. We will perform experiments with more motor densities to address that aspect too. We will also run additional simulations and compare outputs. This will help to address the comment and is in line with suggestions by the other reviewers too.

    3. The authors repeatedly claim that the movements they observe are "flagella-like". However, the comparison remains vague as there is no quantitative assessment of the similarity or dissimilarity between the movements observed here and biological beating of flagella or cilia (e.g. using data in Riedel-Kruse et al HSFP Journal 2007. DOI:10.2976/1.2773861 as a reference).

    Our response: We have compared frequency of oscillations from previous literature but find them to be extremely disparate – by a factor of 1,000. We will use the suggested references to find geometric properties that could test our claim of flagella-like in terms either of waveforms, symmetry of beating or the dynamics or tip-behavior.

    • *What does it mean to resemble flagellar beating? It would be desirable to be more explicit/quantitative and not be ashamed to point to differences (could be event more instructive) as well as to similarities. Note that oscillations of the tangent angle in flagella of the bull sperm are nearly sinusoidal, and are thus smooth, with no snaps (Riedel-Kruse et al HSFP 2007), thus challenging the claimed resemblance between bending oscillations in this work and the flagellar beat. *

    __Our response: __This is similar to the previous point. We agree that a quantitative comparison between the dynamics we observe of single filaments and of bonafide flagella, could strengthen the findings of this manuscript. We will use multiple metrics such as the tangent angle-with time of the free end, and the average angle along the flagella (as reported by Riedel-Kruse et al.) to make a more concrete comparison.

    • *In my opinion, the authors should tone done the resemblance of their system with cilia and flagella and be much more quantitative about the detailed features of the observed movements in their in-vitro assay. *

    __Our response: __We will take the reviewers comment on board and discuss the work in the absence of the flagellar connection since indeed there is no direct link so far- our comparison with flagella-like systems will be moved to the discussion section with a qualitative comparison of waveforms as this reviewer and others have suggested.

    • *In the present gliding assay, motors produce compressive tangential forces on the microtubule, which can result in buckling and thus in an elastic load applied by the filament to the motor with a component perpendicular to the filament. Instead, flagellar motors produce force dipoles that result in neighboring-filament sliding which is then converted in bending of the filament bundle as a result of elastic constrains. Symmetries of the problem thus seem very different. It is also worth noting that many (but not all) models of the flagellar beat actually assume a constant inter-filament distance so that there is no effective normal force acting on the motors to detach them, yet faithfully reproduce beating waveforms (e.g. Camalet and Jülicher New J of Phys (2000) DOI: 10.1088/1367-2630/2/1/324; Riedel-Kruse et al HSFP J (2010)). More generally, whether the present study provides any useful information to inform our current understanding of the flagellar beat is not clear to me and the authors' claim that it may be the case is not motivated enough. Accordingly, the statement (P19) "qualitative transitions (...) expected from not just the minimal but even the potentially complex flagellum" is not justified. *

    __Our response: __This distinction will be more elaborately discussed in the revised discussions section and similar to the previous point, we will avoid reference to flagella-like behavior.

    4. I could not find a detailed statistical account of the total number of filaments that was used for the paper, how many fell in the four classes of movement (swiveling, fluctuations, beating, and looping) identified by the authors, and whether the population in each class could actually be controlled experimentally, e.g. by varying motor density or microtubule length. This gave the unfortunate impression that the conclusions were based on cherry picking, which is troublesome considering the large variability in behavior between filaments and the ambition of the authors to provide a state diagram of the dynamics (Fig. 7). To reach clear conclusions, one parameter must be changed while the others remain fixed. For instance, to discuss the effects of the pinned length, one would like to fix the total microtubule length (but then the free length varies) or vary the pinned length with constant free length (thus changing the total microtubule length). I understand that this might be difficult (in experiments), but the authors should then acknowledge these limitations and mitigate their conclusions. In principle, if the yield of the experiment (number of anchored filaments per slide) were sufficient, one could to address these issues by classifying the filaments in ensembles of a given properties (e.g. same total length by variable pinned length). To reach this goal, there is a need to obtain a sufficiently large quantity of data. The reader gets an estimate on the order of 10 usable filaments per slide (video SV3 and inset in Fig. 2D), with only a few replicates (4 experiments at 46/µm^2 and 2 experiments at 27/µm^2). The authors talk about "representative filaments" throughout the text but there is no detail about the ensemble of filaments that show a given behavior and the number of filaments that are used to reach a given conclusion is not given. Length distributions for the free and pined ends of the microtubules, for the maximal amplitude of tangent-angle oscillations, and other measures that characterize the microtubule movements (curvature, wave speed) ought to be given, provided that enough data has been collected to compute reliable ensemble averages.

    __Our response: __For now we have only considered the average behavior with the dynamics observed from multiple fields of view, combined in terms of MT lengths and motor densities. Since Fig. 7 was meant to be representative and therefore a qualitative comparison with simulation predictions, replicates were not added. However, in response to reviewer’s question, we will analyze more data and add it in the supplementary material, in order to support the statistical validity of our claims- that are not based on purely selective evidence.

    *5. The effect of motor density on beating properties, in particular frequency, is discussed in simulations but not clearly demonstrated in experiments. One cannot conclude that experiments confirm the prediction of the theory in this respect. *

    __Our response: __Currently we have used a novel metric for the type of oscillation and pattern, the span-parameter (S). However, this was meant to capture large qualitative changes observed in experiment and simulation in terms of patterns.

    In response to this comment, we will also analyze the dominant frequency of filaments using FFT on the tip-angles from multiple conditions of MT length and motor density. The scaling of frequency with length and motor density will be compared to simulation predictions. The comparison will then allow an additional quantitative comparison between experiment and simulation.

    *- Minor comments: *

    6. More extensive quantitative analysis of the waveform of oscillation (noisy sinusoid vs. sawtooth or relaxation oscillations?) and bending wave propagation (speed and curvature vs position along the filament) is needed. In particular, it is claimed that the filaments "snap" and thus evince a "recovery stroke" (e.g. p7). I agree that snaps are evident in some of the videos, and are expected at low motor density. However, I would expect the movements to get smoother at higher motor density, as shown in simulations (looping regime). In any case, one could use the analysis of the tip or (better) tangent angle as a function of time to assess whether 'snaps' indeed occur; due to noise, snapping behavior is not so clear in the data provided in Fig. 1D-E.

    __Our response: __We agree with the reviewer that “snap-back” movement arising from potentially low motor density scenarios changes when the motor density is increased to a more smooth motion. We have observed this, and will characterize it quantitatively to make this point more clear. The tip-dynamics will be analyzed for velocity and symmetry to make this point more apparent.

    *7. Because the tips of the microtubules are "sticky" due to their biotinylated tips, I wonder whether the histogram of gliding velocity of the microtubules that are not anchored is modified, i.e shifted toward lower velocities, as compared to that of bare gliding microtubules. This is assuming that a majority of the microtubules are equipped with biotinylated "heads"; this information ought to be provided in the Methods if, as the author claim, the biotinylated tips can be visualized. Analysis of gliding velocities (e.g. in video SV3) could potentially reveal the enhanced interaction between the microtubules and the surface. *

    __Our response: __We will analyze the instantaneous gliding velocity and test the hypothesis that some filaments may be transiently immobile, while others may move unhindered at typical gliding assay velocities (50 to 80 nm/s).

    *8. Demonstrating that the anchoring strategy has actually improved the chance to anchor a microtubule, as compared to random anchoring to surface defects that occur naturally in gliding assays, would be welcome. *

    __Our response: __We will analyze the frequency histogram of gliding assay velocities and compare them to the filament-oscillation scenario with biotinylated filaments. We expect to see a zero-velocity mode in the clamped filament scenario and only transient (and therefore less frequent) pinned or clamped filaments. This is already our qualitative observation but we will seek to quantify it.

    *9. The simulations should be analyzed more quantitatively and extensively to study how motor density and microtubule length affect the wavelength and frequency of oscillations in the wave-like beating regime, going beyond what can be achieved experimentally. In particular, one could compute the speed of the bending waves, asses how it varies during wave progression from base to tip of the microtubule, describe the increase in the magnitude of tangent-angle and curvature oscillation as a function of curvilinear abscissa. *

    __Our response: __We have now analyzed the frequency and amplitude of filament oscillations in simulations. This will in the next step be used to look for trends as a function of MT length and motor density. We hope indeed to look beyond what experimentally achievable ranges might be, including measuring the propagation of the bending wave along the contour as suggested by the reviewer.

    *- Suggestions to help improving the presentation: *

    *1. First section of the results (p5-7): this section is full of methological details that get in the way of the description of the actual result (Fig. 1). I would suggest moving these details (e.g. there is not need here to explain how the motors are attached to the substrate, which you use cytoplasmic yeast dynein, and other details). *

    __Our response: __We will rewrite the manuscript to improve the clarity and move the methods to the section dedicated to the methodology.

    *2. The top of P9 could also be moved to Discussion section. *

    __Our response: __We will move the page 9 text referred to into the discussion.

    *3. P12-13: I also find that the Results section mixes results with discussion, which is not very effective. I would again move elements of discussion (here associated with bending energies) to the Discussion section and focus on results only. *

    __Our response: __We have done so due perhaps to a requirement from an earlier round of reviews. However, we will be happy to separate results from discussion- for example the reference to bending energies.

    *4. Throughout the result section: Move any comparison to actual flagellar dynamics to a dedicated section in Discussion. *

    __Our response: __The flagellar discussion will be moved out of the results section entirely unless we invoke the analysis of bonafide flagella.

    5. P12: doesn't the increase of the clamped length reduce the length of the free length, moving in the state diagram toward regions of shorter filaments. One wonders whether the clamped length really matter as long as the filament is clamped near the plus end. I would naively expect that it is the free-filament length that maters rather than the total length or the faction of the filament that is clamped.

    __Our response: __We agree with the reviewer with one caveat- filaments pinned at one end (point pinning) are distinct from those with long segments clamped. However, the reviewer is correct in pointing out cases where filaments have a substantial clamp, the free length is more important. We will revise our figures and results section to clarify this.

    *6. Figure 4: this figure shows very interesting simulation data that, in my opinion could be much more extensively studied. In particular, one could plot the oscillation frequency, the bending-wave speed, and wavelength as a function of the filament length and the motor density. Also, to characterize the beating waveform more in detail, it would be worth computing how the magnitude of tangent-angle oscillation increases with the curvilinear abscissa for representative examples of waveforms in the three regimes (see again in Riedel-Kruse et al HSFP 2007. DOI: 10.2976/1.2773861 or Pochitaloff et al Nat Phys 2022 DOI: 10.1038/s41567-022-01688-8). *

    __Our response: __We have performed fourier series analysis to obtain dominant frequencies. This will indeed be applied to the simulations in Fig. 4 in order to examine the rich dynamics, as well as provide a point of quantitative comparison to exepriments.

    *7. Figure 5: the way to display the data in A-B (simulations) and C-D (experiments) does not allow for an easy comparison between simulations and experiments. I would use beating patterns and kymographs of the tangent angle for both. *

    __Our response: __We are in the process of revising Fig. 5 in order to examine the effect of free MT length on oscillations and will put experimental and simulation analyses that match each other in the nature of the analysis. The analysis itself will be elaborated to include aspects such as average tangent angle as a function of arc-length (Riedel-Kruse et al., 2007) along with frequency.

    *8. Figure 6: the way to present the experimental beating patterns is no so clear (thick colored lines). I would recommend showing black lines resulting from automatic tracking of the microtubule. *

    __Our response: __The data in Fig. 6 is raw data projected in order to provide a picture within the limits of magnification. In order to address this comment we will project the tracked contour of the filament and that will result in a finer and better resolved image.

    *9. Legend of Fig. S1: the panels (D) and (E) of the figure are not called properly. *

    __Our response: __We will rectify the issue of sub-figure callouts.

    *10. Fig. S3: use the same scale in the different panels of (a) and (b) to allow for an easier comparison. It would also be nice to show videos of the simulated motion. *

    __Our response: __The current differences were in order for visual clarity and the modified axis values are mentioned. We will revise Fig. S3 simulation outputs where filaments are projected on the same axis for consistency.

    *11. Fig. S4: Hard to read, in particular the motors are not visible. Would be better to have the patterns in black on a white background. The panels look like screen shots. *

    Our response: The unbound motors have been deliberately made invisible for clarity. We can provide a figure update with the motors made visible again.

    *12. Fig.S5: indicate in the title that this figure deals with results of simulations. The legend refers to color bars but the figure is in grey scale. *

    __Our response: __Colorbar is indeed in grayscale. The legend entry will be modified to read “grayscale bar”.

    *Reviewer #3 (Significance (Required)): *

    *The motile phenomena reported here are qualitatively already well known in the field. Indeed, anyone who has performed a gliding assay, with microtubules or actin filaments has probably seen undulating or spiraling filaments accidentally anchored on surface defects. Accordingly, the topic has already been somewhat adressed in previous publications (e.g. Bourdieu et al Phys Rev Lett 1995; Sekimoto et al Phys rev Lett 1995; Vilfan et al Nanoletter 2019). As a matter of fact, microtubules anchored on defects in standard gliding assay can show oscillations very similar to those shown here. However, the lack of control over filament anchoring has precluded a systematic experimental study of the oscillatory filament dynamics. It is worth noting that ther bottom-up approaches have used filament bundles instead of single filaments, either with microtubules and kinesin motors (Sanchez et al Science 2011) or actin filaments and myosin motors (Pochitaloff et al Nature Phys 2022). These assays evince more regular oscillations (over tens of cycles) and waveforms that more closely resemble those of eukaryotic flagella than reported here. *

    __Our response: __We agree with this summary of our work, and will highlight the possible reasons why it differs from the work of Pochitaloff et al.

    *Here, the authors have developed an experimental strategy to increase the chance of anchoring single filaments' plus end to the substrate, potentially allowing for more control of the experimental conditions that lead to the emergence of oscillations (but see my criticisms above). Anchoring is made more likely, because short segments of biotinylated tubulin are added to the end of bare microtubules to make them stick to the substrate, which has been functionalized with streptavidin. A similar protocol had been reported before in the literature to study buckling of single microtubules by single kinesin motors (Gittes et al Biophys J 1996), but is here used at larger motor densities on the substrate. There is unfortunately no quantification of the success of the approach. *

    __Our response: __We propose to perform more experiments and analyze the data more quantitatively using multiple measures described in the literature and cited by this reviewer. We believe these changes will adequately address the concerns.

    *The comparison of the experimental data to Cytosim simulations is, to my knowledge, novel and a clear asset of the work, although this comparison could be more effective, as detailed above. *

    __Our response: __We will add a more complete quantitative comparison to supplement the already provided qualitative comparison to address the comments.

    *The emergence of periodic wave-like beating oscillations in motor-filament systems is a classical problem in biophysics. This problem is particularly relevant in the context of eukaryotic cilia and flagellar beating in biology. The audience for the present work is thus potentially broad, although the simplistic and artificial nature of the in-vitro system, with only one microtubule, will probably appeal more to biophysicists and theoretical physicists than biologists. *

    __Our response: __We appreciate the effort of this reviewer to evaluate our work. We however believe that the relevance of this work could extend beyond purely biophysics and theoretical physics as claimed by the reviewer.

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    Referee #3

    Evidence, reproducibility and clarity

    Summary:

    This manuscript reports experimental in vitro gliding assays demonstrating bending oscillations when single microtubules are anchored at their plus end and compressed beyond a buckling threshold by dynein molecular motors immobilized on a solid substrate. Together with numerical simulations based on the well-established Cytosim software, the authors identify three main classes of motile behavior under the control of microtubule length and motor density: aperiodic fluctuations (flapping), periodic beating with bending traveling waves over at least part of the filament length, and looping behaviors where the microtubule can curl on itself near its free tip. The authors claim that these movements are reminiscent of the beating movements of eukaryotic cilia and flagella and may provide useful information of the mechanism underlying the oscillatory instability.

    Major comments:

    1. The observed oscillations show only a few cycles (up to only 4, but often 2-3 (Fig. 1-2)) and are in addition very noisy. Oscillations thus appear to happen only transiently, i.e. do not show a dynamic steady state on timescale much larger than the oscillation period. Demonstrating the emergence of true (and stable) regular oscillations thus remains a challenge, in contrast to the authors' claim. The large variability of behavior from filament to filament (as seen in SV3), as well as in a single filament over time, also makes it difficult to achieve a robust quantitative description of these movements (see below).

    2. Overall, the amount of experimental control seems relatively limited, for there is systematic variation of microtubule length (free or pinned) and only two motor densities have been explored.

    a) One wonders why the motor density has not been more extensively varied and what determines the range of densities that can be achieved. What happens if the density gets larger than 50/µm^2? Do the filaments fail to remain anchored? Is buckling still permitted at high motor density?

    b) Important fundamental issues remain here unfortunately untouched in experiments and are also only qualitatively discussed in simulations (bottom of p11 and Fig. 4), namely the dependence of the frequency and wavelength of wave-like beating as a function of motor density and microtubule length. These limitations result from a lack of control over the microtubule lengths and that only two motor densities have been tested. Using the natural variability in length of the anchored filaments may be potentially used to study length effects but then a relatively large amount of data will be required to reliably conclude that filaments ensembles of different mean lengths reliably show different behaviors. Similarly, I do not see where in the data one can see that increasing motor density actually controls the oscillation frequency, as concluded from simulation data (but not analyzed quantitatively).

    1. The authors repeatedly claim that the movements they observe are "flagella-like". However, the comparison remains vague as there is no quantitative assessment of the similarity or dissimilarity between the movements observed here and biological beating of flagella or cilia (e.g. using data in Riedel-Kruse et al HSFP Journal 2007. DOI: 10.2976/1.2773861 as a reference).

    a) What does it mean to resemble flagellar beating? It would be desirable to be more explicit/quantitative and not be ashamed to point to differences (could be event more instructive) as well as to similarities. Note that oscillations of the tangent angle in flagella of the bull sperm are nearly sinusoidal, and are thus smooth, with no snaps (Riedel-Kruse et al HSFP 2007), thus challenging the claimed resemblance between bending oscillations in this work and the flagellar beat.

    b) In my opinion, the authors should tone done the resemblance of their system with cilia and flagella and be much more quantitative about the detailed features of the observed movements in their in-vitro assay.

    c) In the present gliding assay, motors produce compressive tangential forces on the microtubule, which can result in buckling and thus in an elastic load applied by the filament to the motor with a component perpendicular to the filament. Instead, flagellar motors produce force dipoles that result in neighboring-filament sliding which is then converted in bending of the filament bundle as a result of elastic constrains. Symmetries of the problem thus seem very different. It is also worth noting that many (but not all) models of the flagellar beat actually assume a constant inter-filament distance so that there is no effective normal force acting on the motors to detach them, yet faithfully reproduce beating waveforms (e.g. Camalet and Jülicher New J of Phys (2000) DOI: 10.1088/1367-2630/2/1/324; Riedel-Kruse et al HSFP J (2010)). More generally, whether the present study provides any useful information to inform our current understanding of the flagellar beat is not clear to me and the authors' claim that it may be the case is not motivated enough. Accordingly, the statement (P19) "qualitative transitions (...) expected from not just the minimal but even the potentially complex flagellum" is not justified.

    1. I could not find a detailed statistical account of the total number of filaments that was used for the paper, how many fell in the four classes of movement (swiveling, fluctuations, beating, and looping) identified by the authors, and whether the population in each class could actually be controlled experimentally, e.g. by varying motor density or microtubule length. This gave the unfortunate impression that the conclusions were based on cherry picking, which is troublesome considering the large variability in behavior between filaments and the ambition of the authors to provide a state diagram of the dynamics (Fig. 7). To reach clear conclusions, one parameter must be changed while the others remain fixed. For instance, to discuss the effects of the pinned length, one would like to fix the total microtubule length (but then the free length varies) or vary the pinned length with constant free length (thus changing the total microtubule length). I understand that this might be difficult (in experiments), but the authors should then acknowledge these limitations and mitigate their conclusions. In principle, if the yield of the experiment (number of anchored filaments per slide) were sufficient, one could to address these issues by classifying the filaments in ensembles of a given properties (e.g. same total length by variable pinned length). To reach this goal, there is a need to obtain a sufficiently large quantity of data. The reader gets an estimate on the order of 10 usable filaments per slide (video SV3 and inset in Fig. 2D), with only a few replicates (4 experiments at 46/µm^2 and 2 experiments at 27/µm^2). The authors talk about "representative filaments" throughout the text but there is no detail about the ensemble of filaments that show a given behavior and the number of filaments that are used to reach a given conclusion is not given. Length distributions for the free and pined ends of the microtubules, for the maximal amplitude of tangent-angle oscillations, and other measures that characterize the microtubule movements (curvature, wave speed) ought to be given, provided that enough data has been collected to compute reliable ensemble averages.

    2. The effect of motor density on beating properties, in particular frequency, is discussed in simulations but not clearly demonstrated in experiments. One cannot conclude that experiments confirm the prediction of the theory in this respect.

    Minor comments:

    1. More extensive quantitative analysis of the waveform of oscillation (noisy sinusoid vs. sawtooth or relaxation oscillations?) and bending wave propagation (speed and curvature vs position along the filament) is needed. In particular, it is claimed that the filaments "snap" and thus evince a "recovery stroke" (e.g. p7). I agree that snaps are evident in some of the videos, and are expected at low motor density. However, I would expect the movements to get smoother at higher motor density, as shown in simulations (looping regime). In any case, one could use the analysis of the tip or (better) tangent angle as a function of time to assess whether 'snaps' indeed occur; due to noise, snapping behavior is not so clear in the data provided in Fig. 1D-E.

    2. Because the tips of the microtubules are "sticky" due to their biotinylated tips, I wonder whether the histogram of gliding velocity of the microtubules that are not anchored is modified, i.e shifted toward lower velocities, as compared to that of bare gliding microtubules. This is assuming that a majority of the microtubules are equipped with biotinylated "heads"; this information ought to be provided in the Methods if, as the author claim, the biotinylated tips can be visualized. Analysis of gliding velocities (e.g. in video SV3) could potentially reveal the enhanced interaction between the microtubules and the surface.

    3. Demonstrating that the anchoring strategy has actually improved the chance to anchor a microtubule, as compared to random anchoring to surface defects that occur naturally in gliding assays, would be welcome.

    4. The simulations should be analyzed more quantitatively and extensively to study how motor density and microtubule length affect the wavelength and frequency of oscillations in the wave-like beating regime, going beyond what can be achieved experimentally. In particular, one could compute the speed of the bending waves, asses how it varies during wave progression from base to tip of the microtubule, describe the increase in the magnitude of tangent-angle and curvature oscillation as a function of curvilinear abscissa.

    Suggestions to help improving the presentation:

    1. First section of the results (p5-7): this section is full of methological details that get in the way of the description of the actual result (Fig. 1). I would suggest moving these details (e.g. there is not need here to explain how the motors are attached to the substrate, which you use cytoplasmic yeast dynein, and other details).

    2. The top of P9 could also be moved to Discussion section.

    3. P12-13: I also find that the Results section mixes results with discussion, which is not very effective. I would again move elements of discussion (here associated with bending energies) to the Discussion section and focus on results only.

    4. Throughout the result section: Move any comparison to actual flagellar dynamics to a dedicated section in Discussion.

    5. P12: doesn't the increase of the clamped length reduce the length of the free length, moving in the state diagram toward regions of shorter filaments. One wonders whether the clamped length really matter as long as the filament is clamped near the plus end. I would naively expect that it is the free-filament length that maters rather than the total length or the faction of the filament that is clamped.

    6. Figure 4: this figure shows very interesting simulation data that, in my opinion could be much more extensively studied. In particular, one could plot the oscillation frequency, the bending-wave speed, and wavelength as a function of the filament length and the motor density. Also, to characterize the beating waveform more in detail, it would be worth computing how the magnitude of tangent-angle oscillation increases with the curvilinear abscissa for representative examples of waveforms in the three regimes (see again in Riedel-Kruse et al HSFP 2007. DOI: 10.2976/1.2773861 or Pochitaloff et al Nat Phys 2022 DOI: 10.1038/s41567-022-01688-8).

    7. Figure 5: the way to display the data in A-B (simulations) and C-D (experiments) does not allow for an easy comparison between simulations and experiments. I would use beating patterns and kymographs of the tangent angle for both.

    8. Figure 6: the way to present the experimental beating patterns is no so clear (thick colored lines). I would recommend showing black lines resulting from automatic tracking of the microtubule.

    9. Legend of Fig. S1: the panels (D) and € of the figure are not called properly.

    10. Fig. S3: use the same scale in the different panels of (a) and (b) to allow for an easier comparison. It would also be nice to show videos of the simulated motion.

    11. Fig. S4: Hard to read, in particular the motors are not visible. Would be better to have the patterns in black on a white background. The panels look like screen shots.

    12. Fig.S5: indicate in the title that this figure deals with results of simulations. The legend refers to color bars but the figure is in grey scale.

    Significance

    • The motile phenomena reported here are qualitatively already well known in the field. Indeed, anyone who has performed a gliding assay, with microtubules or actin filaments has probably seen undulating or spiraling filaments accidentally anchored on surface defects. Accordingly, the topic has already been somewhat adressed in previous publications (e.g. Bourdieu et al Phys Rev Lett 1995; Sekimoto et al Phys rev Lett 1995; Vilfan et al Nanoletter 2019). As a matter of fact, microtubules anchored on defects in standard gliding assay can show oscillations very similar to those shown here. However, the lack of control over filament anchoring has precluded a systematic experimental study of the oscillatory filament dynamics. It is worth noting that ther bottom-up approaches have used filament bundles instead of single filaments, either with microtubules and kinesin motors (Sanchez et al Science 2011) or actin filaments and myosin motors (Pochitaloff et al Nature Phys 2022). These assays evince more regular oscillations (over tens of cycles) and waveforms that more closely resemble those of eukaryotic flagella than reported here.

    • Here, the authors have developed an experimental strategy to increase the chance of anchoring single filaments' plus end to the substrate, potentially allowing for more control of the experimental conditions that lead to the emergence of oscillations (but see my criticisms above). Anchoring is made more likely, because short segments of biotinylated tubulin are added to the end of bare microtubules to make them stick to the substrate, which has been functionalized with streptavidin. A similar protocol had been reported before in the literature to study buckling of single microtubules by single kinesin motors (Gittes et al Biophys J 1996), but is here used at larger motor densities on the substrate. There is unfortunately no quantification of the success of the approach.

    • The comparison of the experimental data to Cytosim simulations is, to my knowledge, novel and a clear asset of the work, although this comparison could be more effective, as detailed above.

    • The emergence of periodic wave-like beating oscillations in motor-filament systems is a classical problem in biophysics. This problem is particularly relevant in the context of eukaryotic cilia and flagellar beating in biology. The audience for the present work is thus potentially broad, although the simplistic and artificial nature of the in-vitro system, with only one microtubule, will probably appeal more to biophysicists and theoretical physicists than biologists.

  3. Review Commons

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    Referee #2

    Evidence, reproducibility and clarity

    Summary:

    The authors use a modified version of conventional gliding assays to induce microtubule bending, buckling, looping and cyclic beating (which they term "flagella-like") via clamping the plus ends of gliding microtubules to the surface. They find that the pattern of motion depends on different factors such as microtubule length and motor density. They build a simple computational model that predicts transitions between microtubule motion patterns depending on these parameters.

    Major comments:

    • Overall, the experimental data is extremely sparse. As far as I can see, there are only two replicas for the lower motor density. It is not clear to me how the authors define the boundaries in the experimental phase diagram in Fig. 7. To build a phase diagram - where one axis corresponds to the motor density - on just two experiments is not convincing. I would need to see more experiments covering a larger range of motor densities and at least three replica per condition.

    • It is not clear to me why the proportion of pinned vs. free microtubule segments should affect the beating pattern. I would expect that the free microtubule segment does not "feel" the length of the clamped segment, if it is indeed fixed all along its length and unable to move / bend. The simulations use only two anchor points at the pinned tip. The segment in between the anchor points bends, which could affect how the free microtubule segment behaves. To support the claim that it is indeed the proportion of the lengths of the pinned vs. free segments and not simply the length of the free segment alone that influence the beating pattern, I would expect to (1) see the corresponding and thoroughly quantified experimental data that verifies this simulation-based prediction. Fig. 5C is based on only three microtubules and it is not clear how long the segments are. (2) the entire pinned segments in the simulation should be fixed. This should also be compared to experimental data, where the lengths of the free segments are the same and only the lengths of the pinned segments vary.

    • In relation to my previous comments: I would expect a direct comparison between the simulation-based prediction that the beating pattern changes with microtubule length and motor density in a quantitative manner, where all pinned microtubules observed experimentally are analyzed. The figures are often based on single observations.

    • The authors report that the pinned microtubules typically undergo 2-3 cycles of beating. This number is very low, and I am hesitant to call it "flagella-like" cyclic beating. Is this due to the dynein motors being much slower than e.g. kinesis? To confirm this and support the generality claimed by the authors, I would like to see experiments with a different, faster motor. If other motors are not readily available to the authors, this would imply a substantial amount of time and effort though.

    • Please perform statistical analysis of the experimental data.

    Minor comments:

    • Number of replicates and samples should be indicated in the figures.

    Significance

    • The approach to clamp the plus ends of gliding microtubules in order to induce buckling, bending and beating is elegant and should be easily transferable to other groups who may be interested in this method, since it is straightforward to adapt conventional gliding assays to induce pinning.

    • The study could potentially be interesting to an audience studying flagella-like systems. Since the system is simple and based on in vitro components with defined parameters, it could serve as a basis for studying more complex systems or testing the influence of particular proteins associated with flagella. However, I do not see a major advance regarding our understanding of flagella or similar structures based on the manuscript. In combination with the model, I see it majorly as a useful tool, providing methodological advance. It would be desirably to make the computational model available to the public.

    • The computational model seems useful and straightforward to me, yet my background is purely experimental and I cannot judge the model in detail.

    • In my view, the most important limitation of the manuscript is its lack of thorough experimental data to support the claims made by the authors. In its current state, the manuscript seems rather preliminary and I see the need for significant additional experimental evidence.

  4. Review Commons

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    Referee #1

    Evidence, reproducibility and clarity

    Summary:

    This work combines in-vitro experiments and numerical modeling to study the dynamics of microtubules, driven by molecular motors. In this bottom-up approach, molecular motors are immobilized on the surface and microtubule filaments are anchored to the surface from one end. The dynamics results in "beating like" motion of the anchored microtubules. The authors establish a phase diagram of the different dynamical patterns of "beating like" motions by varying the molecular motor density and the length of the microtubule anchored to the surface. They use a numerical framework that captures the observed patterns.

    Major comments:

    Overall the experiments and results are well described and claims are supported by the data. Both experimental and numerical methods are presented in a way that they can be reproduced.

    Minor comments:

    A key feature of beating cilia is the asymmetry of the beat pattern (fast stroke and slow recovery). It might be interesting to use the kymographs or the Phy vs time analysis to see whether or not this feature exists in this simplified experimental model.

    Also, the beating frequency is very low (mHz) compared to real cilia/flagella (~Hz). Would it be possible to use the model to predict which parameter would need to be tuned to reach more physiologically relevant beating frequencies ?

    Significance

    This study is part of the field of in-vitro reconstitution, from a minimal set of components, that aims to reproduce a biological function to identify and understand the minimal physical/biophysical mechanisms underlying a function. This study might be of interest for the people who address questions of the self-organization of cytoskeletal elements in minimal systems.

    The main limitation of this study relies on the claim of reproducing a flagella-like motion. Indeed, the frequency of the described oscillations is in the mHz range while the frequency of cilia is in the range of few Hz to tens of Hz. This suggests that the mechanism at play in such a reconstituted system is not the one that drives beating in real cilia/flagella. Yet, this limitation also applies to other studies in the field (Vilfan et al. 1999, Guido et al. 2022 ...).

    My second concern is that the added value with regards to state of art is not clearly explicit. I'm thinking about the work of the Isabelle Guido's team where they have more complex reconstituted systems (a pair of 2 microtubules); or the work of Pascal Martin's lab where the design of the system allows to capture more complex mechanisms such as myosin density waves, which result in frequency beat of 0.1Hz.

  5. Version published to 10.1101/2022.09.11.507451v1 on bioRxiv