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  1. Author Response

    Reviewer #1 (Public Review):

    Mitotic spindles are macromolecular machines that accurately segregate duplicate chromosomes between two daughter cells during cell division. To perform this task, spindles exert forces that are orchestrated in space and time. On the other hand, non-functioning spindles can generate chromosome segregation errors, which are present in cancers, miscarriages, and Down syndrome. Therefore, understanding spindle mechanics is a big biological challenge. In this elegant study, the authors explore the mechanical properties of the mitotic spindle. They combine a variety of experimental biophysical approaches, including microneedle manipulation and quantitative imaging, with theoretical modeling. By systematically exploring the shape of kinetochore fibers that are not manipulated, they find the force and moments that exist in the native spindles. Analyzing previously published data obtained by microneedle manipulations, where kinetochore fibers were mechanically perturbed, the authors observe a dramatic change in the shape of the kinetochore fibers. Comparing this observation and theoretical predictions, they discover a lateral anchorage near the chromosome. Taken together, this paper nicely demonstrates existence of lateral anchorage near chromosomes, offering exciting ideas about the balance of forces of the entire mitotic spindle.

    We appreciate the reviewer’s enthusiasm about the work and their thoughtful questions and suggestions to improve the manuscript.

    Major points:

    (1) In order to describe the shape of unmanipulated kinetochore fibers, the authors use a simple physical model in which they describe these fibers as a single elastic rod. They find that the observed shape is a consequence of compressive forces, or a combination of bending moments and perpendicular forces. However, it is well known that kinetochores are under the tension. For this reason, the plus end of kinetochore fibers should be under tension rather than under compression. In order to describe forces that shape unmanipulated kinetochore fibers, the authors should revise the model by setting the tensile force at the plus end of the kinetochore fiber.

    We thank the reviewer for their comment on this important point .

    (2) The authors compare the shapes of inner and outer kinetochore fibers. By using the model, they find that the forces and moments are similar for both, the inner and outer kinetochore fibers, whereas the difference arises because these fibers have a different length. In classical beam theory, we distinguish between buckling (caused by a compressive force) and bending (caused by a bending moment). In the case of buckling, which is caused by a same critical force, different curvatures can be obtained, whereas in the case of bending the curvature is proportional to the bending moment. Based on the data presented by the authors, it seems that their model operates in the buckling regime. It would be important to elaborate on this more systematically. Also, one should warn the reader that in the case of bending, the inner and outer kinetochore fibers will be characterized by different bending moments.

    We thank the reviewer for raising this nuanced point on the shape generation mechanisms in inner and outer k-fibers. We believe that the mechanisms that the reviewer suggested are valid ways to generate varying k-fiber deflections in the scenario where the k-fiber end-to-end length is held fixed. However, we argue that the natural variability in the lengths of inner vs. outer k-fibers is alone sufficient to give rise to diverse k-fiber shapes without requiring the end-forces to change.

    We added a new Appendix section 1.4 (pages S4-S5 in the revised appendix) in our revised submission where we provide the details of our argument. We demonstrate analytically that when only a moment at the pole is present and held at a fixed value, then the normalized maximum deflection scales linearly with the k-fiber’s end-to-end length (Appendix 1 – figure 3a,b). And in the case where both a moment at the pole and an axial force are present and held at fixed values, the dependence on k-fiber length is stronger (faster than linear), thereby allowing for a wide range of k-fiber deflections created with identical end-forces (Appendix 1 – figure 3c,d).

    Reviewer #2 (Public Review):

    Suresh and co-workers apply classical beam bending theory to analyze shapes of the microtubule bundles that push and pull on mitotic chromosomes and drive chromosome separation in dividing cells. The bundles attach at one end to chromosomes via specialized protein assemblies called kinetochores, and at the other end they are associated with spindle poles. The shapes of these k-fiber bundles are analyzed in unperturbed control cells and in cells where the bundles have been forcibly deformed using microneedles. From their analysis, the authors infer the extent and nature of mechanical anchorage at each end of the bundles, finding that anchorage is more extensive and more restrictive at the kinetochore-attached ends compared to the pole-proximal ends. Anchorage at the pole-proximal ends is apparently limited to the bundle tips, allowing some swiveling of the bundles around the poles. In contrast, the kinetochore-attached ends appear to have "lateral anchorage", i.e. force-bearing connections to the sides of the bundles, that extend several micrometers away from the kinetochores. This lateral anchorage resists swiveling of the bundles around their kinetochore-attached ends.

    A major strength of this study is its high degree of novelty. The microneedle data on which the analyses are based have been published previously, but are entirely unique - based on classic, groundbreaking experiments performed nearly half a century ago on cells from grasshoppers and mantids, and now being done only in the Dumont lab, in mammalian cells for the first time, and with the benefit of modern fluorescence and molecular perturbation techniques. Such a unique and interesting dataset certainly deserves careful analytical scrutiny, which is the focus of this new paper.

    The application here of classical beam theory to analyze k-fiber shapes is also clever, apparently well done, and well described. The unique approach provides a direct way to assess the extent to which k-fiber bundles are mechanically linked to surrounding material, including to non-k-fiber microtubules and potentially to neighboring k-fibers. The main conclusion that lateral anchorage of the k-fibers in the local vicinity (within a few micrometers) of kinetochores is needed to explain the shapes that the k-fibers adopt during manipulations seems well justified by the data and analyses - particularly by the negative curvatures measured near the kinetochore-attached ends, and the tendency for the orientations of the kinetochore-proximal portions to be maintained even 1 to 3 micrometers away from the kinetochore-attached ends. The assumptions of the analysis also seem mostly reasonable and are clearly explained. Under these assumptions, the analysis shows convincingly that forces and moments applied only at kinetochore-attached ends would be insufficient to explain the observed shapes.

    We appreciate the reviewer’s enthusiasm about the work and their thoughtful questions and suggestions to improve the manuscript.

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  2. Evaluation Summary:

    This manuscript presents a creative, unique, and well-explained theoretical analysis of the shapes adopted by chromosome-attached microtubule bundles during manipulation with glass microneedles inside dividing cells. The overall conclusion is that the bundles are laterally anchored to other structures in the mitotic apparatus within several micrometers of their chromosome-attached ends, but relatively freer at their pole-proximal ends. This interesting work should appeal broadly to cell biologists and biophysicists.

    (This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)

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  3. Reviewer #1 (Public Review):

    Mitotic spindles are macromolecular machines that accurately segregate duplicate chromosomes between two daughter cells during cell division. To perform this task, spindles exert forces that are orchestrated in space and time. On the other hand, non-functioning spindles can generate chromosome segregation errors, which are present in cancers, miscarriages, and Down syndrome. Therefore, understanding spindle mechanics is a big biological challenge. In this elegant study, the authors explore the mechanical properties of the mitotic spindle. They combine a variety of experimental biophysical approaches, including microneedle manipulation and quantitative imaging, with theoretical modeling. By systematically exploring the shape of kinetochore fibers that are not manipulated, they find the force and moments that exist in the native spindles. Analyzing previously published data obtained by microneedle manipulations, where kinetochore fibers were mechanically perturbed, the authors observe a dramatic change in the shape of the kinetochore fibers. Comparing this observation and theoretical predictions, they discover a lateral anchorage near the chromosome. Taken together, this paper nicely demonstrates existence of lateral anchorage near chromosomes, offering exciting ideas about the balance of forces of the entire mitotic spindle.

    Major points:

    (1) In order to describe the shape of unmanipulated kinetochore fibers, the authors use a simple physical model in which they describe these fibers as a single elastic rod. They find that the observed shape is a consequence of compressive forces, or a combination of bending moments and perpendicular forces. However, it is well known that kinetochores are under the tension. For this reason, the plus end of kinetochore fibers should be under tension rather than under compression. In order to describe forces that shape unmanipulated kinetochore fibers, the authors should revise the model by setting the tensile force at the plus end of the kinetochore fiber.

    (2) The authors compare the shapes of inner and outer kinetochore fibers. By using the model, they find that the forces and moments are similar for both, the inner and outer kinetochore fibers, whereas the difference arises because these fibers have a different length. In classical beam theory, we distinguish between buckling (caused by a compressive force) and bending (caused by a bending moment). In the case of buckling, which is caused by a same critical force, different curvatures can be obtained, whereas in the case of bending the curvature is proportional to the bending moment. Based on the data presented by the authors, it seems that their model operates in the buckling regime. It would be important to elaborate on this more systematically. Also, one should warn the reader that in the case of bending, the inner and outer kinetochore fibers will be characterized by different bending moments.

    Was this evaluation helpful?
  4. Reviewer #2 (Public Review):

    Suresh and co-workers apply classical beam bending theory to analyze shapes of the microtubule bundles that push and pull on mitotic chromosomes and drive chromosome separation in dividing cells. The bundles attach at one end to chromosomes via specialized protein assemblies called kinetochores, and at the other end they are associated with spindle poles. The shapes of these k-fiber bundles are analyzed in unperturbed control cells and in cells where the bundles have been forcibly deformed using microneedles. From their analysis, the authors infer the extent and nature of mechanical anchorage at each end of the bundles, finding that anchorage is more extensive and more restrictive at the kinetochore-attached ends compared to the pole-proximal ends. Anchorage at the pole-proximal ends is apparently limited to the bundle tips, allowing some swiveling of the bundles around the poles. In contrast, the kinetochore-attached ends appear to have "lateral anchorage", i.e. force-bearing connections to the sides of the bundles, that extend several micrometers away from the kinetochores. This lateral anchorage resists swiveling of the bundles around their kinetochore-attached ends.

    A major strength of this study is its high degree of novelty. The microneedle data on which the analyses are based have been published previously, but are entirely unique - based on classic, groundbreaking experiments performed nearly half a century ago on cells from grasshoppers and mantids, and now being done only in the Dumont lab, in mammalian cells for the first time, and with the benefit of modern fluorescence and molecular perturbation techniques. Such a unique and interesting dataset certainly deserves careful analytical scrutiny, which is the focus of this new paper.

    The application here of classical beam theory to analyze k-fiber shapes is also clever, apparently well done, and well described. The unique approach provides a direct way to assess the extent to which k-fiber bundles are mechanically linked to surrounding material, including to non-k-fiber microtubules and potentially to neighboring k-fibers. The main conclusion that lateral anchorage of the k-fibers in the local vicinity (within a few micrometers) of kinetochores is needed to explain the shapes that the k-fibers adopt during manipulations seems well justified by the data and analyses - particularly by the negative curvatures measured near the kinetochore-attached ends, and the tendency for the orientations of the kinetochore-proximal portions to be maintained even 1 to 3 micrometers away from the kinetochore-attached ends. The assumptions of the analysis also seem mostly reasonable and are clearly explained. Under these assumptions, the analysis shows convincingly that forces and moments applied only at kinetochore-attached ends would be insufficient to explain the observed shapes.

    One potential limitation of the study is its assumption that flexural rigidity is constant along the entire length of the k-fibers. Arrangements of microtubules in k-fiber bundles from a handful of cell types, including PtK cells like those used here, are available from prior EM tomography studies (e.g., O'Toole 2020 Mol Biol Cell). In some instances, it appears that near the poles the bundles contain fewer microtubules than near the kinetochores, possibly becoming tapered into narrower, less rigid structures. If the flexural rigidity of the k-fiber bundles were reduced near the pole-proximal ends, could the deformed shapes be explained without invoking lateral anchorage specifically at the kinetochore-attached ends? Could models with uniform lateral anchorage, or with no lateral anchorage then explain the observed shapes?

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