Progressive chromosome shape changes quantified during cell divisions

  1. Yasutaka Kakui
  2. Yoshiharu Kusano
  3. Tereza Clarence
  4. Maya Lopez
  5. Toru Hirota
  6. Bhavin S. Khatri
  7. Frank Uhlmann

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Abstract

Mitotic chromosomes give genome portions the required compaction and mechanical stability for faithful inheritance during cell divisions. Here, we record human chromosome dimensions from their appearance in prophase over successive times in a mitotic arrest. Chromosomes first appear long and uniformly thin. Then, individual chromosome arms become discernible, which continuously shorten and thicken - the longer a chromosome arm, the thicker it becomes. The observed chromosome arm length to width relationship can be described by a power law with progressively increasing exponent. In the search for a molecular explanation of this behavior, the popular loop extrusion model provides no obvious means by which longer arms become thicker. Instead, we find that simulations of an alternative loop capture model recapitulate key features of our observations, including the gradually developing arm length to width relationship. Our analyses portray chromosomes as out-of-equilibrium structures in the process of transitioning towards, but on biologically relevant time scales not typically reaching, steady state.

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    *Reviewer #1 (Evidence, reproducibility and clarity (Required)):

    Summary: This manuscript authored by Kakui and colleagues aims to understand on how mitotic chromosomes get their characteristic, condensed X shape, which is functionally important to ensure faithful chromosome segregation and genome inheritance to both daughter cells. The authors focus on the condensin complex, a central player in chromosome condensation. They ask whether it condenses chromosomes through a now broadly popular "loop-extrusion" mechanism, in which a chromatin-bound condensin complex reels chromatin into loops until it dissociates or encounters a roadblock on the polymer (another condensin or some other protein complex), or through an alternative, "diffusion-capture" mechanism, in which a chromatin-bound condensin complex forms loops by encountering another chromatin-bound condensin until they dissociate from DNA (or from each other.) The authors measured the progressive changes in the shape of mitotic chromosomes by taking samples at given time points from synchronized and mitotically arrested cells and found that while all chromosomes become more condensed and shorter, their width correlated with the length of the chromosome arms. They also observed that chromosome compaction/shortening evolves on a time scale much longer than the interval between the onset of chromosome condensation and the start of chromosome segregation, suggesting that chromatin condensation does not reach its steady-state during an unperturbed mitosis. The observed width-length correlation could be described by a power law with an exponent that increases with the time (i.e. chromosome condensation). The authors also performed polymer simulations of the diffusion-capture mechanism and found that the simulations semi-quantitatively recapitulate their experimental observations. Major Comments My most substantial comments focus on somewhat technical details of the image analysis approaches taken and the polymer models employed. However, as all reported data are derived from those details, I feel it is crucial to address them. *

    We thank the reviewer for their suggestions on how to improve our image analysis and polymer modelling experiments. We are keen to develop both aspects of our manuscript with additional experiments as detailed below.

    Definition/measurement of chromatin arms width and length. The approach taken to manually threshold an "arm" object and then fitting it with a same-area ellipse is not an ideal approach to gauge length and width of the arm, for the following reasons: (1) An ellipse appears to do a poor job approximating many of the objects that we see in the zoom-in insets of Fig.1. Importantly, for somewhat bent shapes we see in the insets it likely strongly underestimates the length of the arms; this approach also presents potential problems for measuring width as well (see 2 and 3 here). (2) One concern is that, due to the diffraction limit, a cylindrical fluorescent object could appear somewhat wider at the mid-length than the real underlying cylinder or the poles; this effect could become more pronounced as the object gets brighter and shorter. (3) Forcing the fit to an ellipse to objects that are not truly rod-shaped can drive an overestimation of the width of the object, and I suspect that this effect also might correlate with the length and brightness of the object. (4) Given 1-3 above, I think the approach the authors used for the first two time points, while not perfect, is better suited and likely more robust while avoiding these caveats. Moreover, why the authors cannot use this same approach (but just for each arm separately) for the later (30+ min) time points as they used for first two is unclear. This point is underscored by the observation that there is a drastic difference in the results between the first two and all subsequent points. When the authors compared the two approaches at the 30 min time point (where width-length dependence is still weak) in different cell lines they did indeed see different results (Fig. S2), although they concluded that the difference was acceptable. * While the manuscript was under review, we have developed an improved pipeline to measure chromosome widths. As suggested by the reviewer, this approach is based on the method used for the first two time points. An additional improvement allows us to take automated measurements along the entire chromosome arm length, instead of being restricted to straight segments. We propose to use the improved algorithm to repeat the measurements at later time points.

    Along these lines, the difference between short and long arms for the chromosome in the insets of Fig.1 are quite subtle, except maybe at 180 and 240 min. On a related note, it might be informative to compare data for the two sister chromatid arms (as the underlying polymer has the same length) long vs long and short vs short and long vs short to help establish the robustness of the approach. *

    The chromosome arm width differences are clear and measurable. We will select insets that illustrate the arm width differences in a more representative way, and we will furthermore conduct the suggested analyses on subsets of chromosome arms to test the robustness of our approach.

    Regarding the power-law distribution, it is hard to judge based on the presented data whether it is a really good description of the data or not. In Fig.1c, the points for a given time can barely be distinguished, while in Fig.1b the authors plot individual time points in the panels, but the fits and points are overlapping so much that it is challenging to the main trends described by the clouds. The most informative approach for the reader would be to provide confidence intervals of the best fit parameters for all parameters that were varied in the fit. As the authors make some conclusions based on the power-law exponent values they observed, it would be helpful to know how confident we are in those values. *

    Confidence intervals of the power law exponents will be provided.

    The conclusion that short arms equilibrate faster based on Fig.3a is not fully convincing. For example, in a scenario where ~1.5 microns is the equilibrium length for all arms, and that the longest arms equilibrate the fastest - you would see the same qualitative pattern for quantiles, not much change in low percentiles, while you would observe a decrease in the values for the high percentiles. The authors might be right, but Fig. 3A does not unambiguously demonstrate that it is so based on this evidence alone. *

    Our reasoning is based on the observation that the shortest percentiles do not change or do not change rapidly after 30 minutes, while the longest percentiles are clearly still relaxing towards a steady state. We will repeat this analysis with the new measurements, obtained in response to point 1.

    As for chromosome roundness, typically in image analysis, roundness is defined through the ratio of (perimeter)2/area; it might be better to use "aspect ratio" for the metrics used by the authors. And, perhaps, one should expect that shorter (measured, not necessarily by polymer contour length) arms should have a higher width/length ratio? If one selects for more round objects, there should be no surprise that the width and length get almost proportional. Given all of this, I am not sure whether width/aspect ratio serves as a good proxy for the chromatin condensation progression, which is how the authors are employing this data in the manuscript as written. *

    We thank the reviewer for alerting us to an alternatively used definition of ‘roundness’. We will consider this concern, with one solution being to use ‘width-length ratio’ in its place.

    For the diffusion-capture model simulations, I think the results of the simulation would strongly depend on the assumptions of the probability to associate and the time scale of dissociation of the beads representing the condensin complex. For example, for a very strong association one might expect that all condensin will end up in one big condensate, even in the case of a long polymer. This is not explored/discussed at all. Did the authors optimize their model in any way? If not, how have they estimated the values they used? Moreover, perhaps this is an opportunity to learn/predict something about condensin properties, but the authors do not take advantage of this opportunity. *

    We in fact explored the consequences of altering diffusion capture on and off rates when we initially developed the loop capture simulations, and we will report on the robustness of our model to the probability of dissociation as part of our revisions.

    In addition, the authors did some checks to show that the steady-state results of the simulations do not depend on the initial conditions. However, as some of the results reported concern the polymer evolution to the steady state (Fig.6b-c), they also need to examine whether these results depend on the chosen initial conditions (or not), and if they do, what is the rationale for the choices the authors have made? *

    The current manuscript contains a comparison of steady states reached after simulations were started from elongated or random walk initial states (see Supplementary Figure 4). We will provide better justification for the choice of a 4x elongated initial state, which approximates the initial state observed* in vivo*.

    A more thorough discussion of other possible models, beyond diffusion-capture model considered here, would be beneficial to the reader. First, the authors practically discard the possibility of the loop-extrusion model to explain their observations (although they never explicitly state this in the abstract or discussion). However, they neither leveraged simulations to rigorously compare models nor included some other substantiated arguments to explain why they prefer their model. This is important, as one of the major findings here is that the chromatin never reaches steady state for condensation, making it challenging to intuit what one should expect in this very dynamic state. Second, the authors, while briefly mentioning that there might be some other mechanisms contributing to the mitotic chromosome reshaping, do not really discuss those possibilities in a scholarly way. For example, work by the Kleckner group has suggested an involvement of bridges between sister chromatids into their shortening dynamics (Chu et al. Mol Cell 2020). Third, the authors do not discuss how they envision the interplay between the different SMC complexes - cohesin, condensin I and condensin II - as they act on the same chromatin polymer, or at least acknowledge a possible role that this interplay might contribute to the observed time dependencies. The reviewer raises important points, which we are keen to explore by performing loop extrusion simulations, as well as in an expanded discussion section.

    Reviewer #1 (Significance (Required)):

    Significance: The question the authors are trying to address is fundamental and important. While loop extrusion-driven mitotic chromosome organization is a popular model, considering alternative models is always crucial, especially when one can find experimental observations that allow us to discriminate between possible models. The main limitations are: 1) the performance of the approach the authors take to measure chromosome shape is in question and 2) the main competitive model (loop extrusion) is not modeled. If all shortcomings are addressed this work may provide strong evidence for the diffusion-capture model and thus advance our mechanistic understanding of mitotic processes, which will be of broad interest to the fields of genome and chromosome biology. We are happy to hear that the reviewer agrees that our work ‘may provide strong evidence for the diffusion-capture model and thus advance our mechanistic understanding of mitotic processes’. See above for how we propose to address the two main limitations.

    Reviewer #2 (Evidence, reproducibility and clarity (Required)):

    SUMMARY The authors tracked the progression of mitotic chromosome compaction over time by imaging chromatin spreads from HeLa cells that were released from G2/M arrest. By measuring the mitotic chromosome arms' width and length at different times post-release, the authors demonstrated that the speed at which the chromosome arms reach an equilibrium state is dependent on their length. The authors were able to recapitulate this observation using polymer simulations that they previously developed, supporting the model of loop capture as the mechanism for mitotic chromosome compaction.

    MAIN COMMENTS This is a straightforward paper that supports an alternative mechanism (relative to the highly popular loop-extrusion) model for chromosome compaction. My comments are meant to help the manuscript reach a wider audience.

    I suggest that "equilibrium" be replaced with "equilibrium length" since it is the only equilibrium parameter of concern. *

    The reviewer is correct, and we will implement this change, also taking into account the reasoning of reviewer 3 that ‘steady state’ is a better term to describe a final shape that is maintained by an active process.*

    In the results, it may help to describe how loop capture and loop extrusion are incorporated into the simulations, using terminology that non-experts can understand. Such a description should be accompanied by figures that can be related to the other figures (color scheme, nomenclature if possible). *

    Following from the reviewer’s suggestion, we will provide schematics of the loop capture and loop extrusion mechanisms.*

    OTHER COMMENTS P5: Is it possible the chromosome-spread processing may distort the structures of the chromosomes? *

    We will compare chromosome dimension in live cells with those following spreading to investigate this possibility.*

    Please clarify whether mitosis can complete after drug removal at the various treatment intervals. *

    Drug treatment and removal is often used as an experimental tool. We will perform a control experiment to explore whether mitosis can indeed complete after drug removal under our experimental conditions.*

    P6: "Our records are not, therefore, meant as an accurate absolute measure of individual arms. Rather, fitting allows us to sample all chromosome arms and deduce overall trends of chromosome shape changes over time" It would be better to state this sentence earlier in this paragraph, or earlier in the section so that readers' expectations are curbed when they're reading the detailed analysis plan. *

    Note that we will employ an additional image analysis method, in response to comments from reviewer 1, which should lead to more reliable width measurements.*

    P6: "As soon as individual chromosome arms become discernible (30 minutes), longer chromosome arms were wider, a trend that became more pronounced as time progressed." Implies that at early time points, when the lengths of the arms were unknown, the longer arms were equal or narrower than the short arms. I think it's more accurate to say that as soon as the arms were resolved, the longer arms appeared wider. *

    We will adopt the reviewers’ more accurate wording.*

    P7: Is there a functional consequence to the long arms not equilibrating before anaphase onset? *

    The reviewer raises an interesting question, which we will explore in our revised discussion. One consequence of not reaching ‘steady state’ is that ‘time in mitosis’ becomes a key parameter that defines compaction at anaphase onset.*

    P13: "In a loop capture scenario, we can envision how condensin II sets up a coarse rosette architecture, with condensin I inserting a layer of finer-grained rosettes." This should be illustrated in a figure. *

    We will consider such a figure, though the roles of two condensin complexes is peripheral to our current study. Investigating the consequences of two distinct condensins for chromosome formation will provide fertile ground for future investigations. *

    FIGURES Fig. 1: "...while insets show chromosomes at increasing magnification over time" sounds like the microscope magnification is changing over time. Please change "magnification" to "enlargement". Alternatively, if the goal of the figure is to illustrate the shape/dimensions change of the chromosomes over time, wouldn't it be better to keep all the enlargements at the same scale? *

    During the revisions, we will explore whether to show the insets at the same magnification, or to adjust the wording as suggested by the reviewer.*

    Fig. 2a plot: Does the distribution of normalized intensities really justify a Gaussian fit? I see a double Gaussian. *

    The chosen example indeed resembles a double Gaussian. We will explore whether this is due to noise in the measurement and a poor choice of an example, or whether a double Gaussian fit is indeed merited.*

    Please label the structures that resemble "rosettes". Good idea, which we will implement.

    Lu Gan

    Reviewer #2 (Significance (Required)):

    General - This is a simulation-centric study of mammalian chromosome compaction that supports the loop-capture mechanism. It may be viewed as provocative by some readers because loop-extrusion has dominated the chromosome-compaction literature in the past decade. The only limitation, which is best addressed by future studies, is the absence of more direct molecular evidence of loop capture in situ. Though this same limitation applies to studies of the loop-extrusion mechanism.

    Advance - It is valuable for the field to consider alternative mechanisms. In my opinion, the dominant one has been studied to death by indirect methods without a direct molecular-resolution readout in situ. While the field awaits better experimental tools, more mechanisms should be explored.

    Audience - The chromosome-biology community (both bacterial and eukaryotic) will be interested.

    Expertise - My lab uses cryo-ET to study chromatin in situ.

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

    In this manuscript, Kakui et al. measured the length/width relationships of mitotic chromosomes in human cells that had entered mitosis for different durations. This simple measurement revealed very interesting behaviors of mitotic chromosomes. They found that the longer chromosome arms were wider than shorter ones. Mitotic chromosoms became progressively wider over time, with shorter ones reached the final state faster than the longer ones. They then built a loop-capture polymer model, which explained the time-dependent increase of width/length ration rather well, but did not quite explain the final roundness of chromosomes.

    I suggest the following points for the authors to consider.

    Major points (1) There is no experimental evidence that the loop capture mechanism is condensin-depdendent. Can the authors deplete condensin I or II or both and measure chromosome length and width in similar assays? This will link their models to molecular players. *

    Such analyses have been conducted by others, and we will provide a brief survey with relevant references to the literature in our revised introduction.*

    (2) It seems rather intuitive to me that if one defines the spacing the condensin-binding sites, then the loop sizes will be the same between shorter and longer chromosomes. It then follows that shorter chromosomes are rounder. Is it that simple? If not, can the authors provide a better explanation. *

    The reviewer makes an interesting point that roundness (width-length ratio), is greater for shorter chromosome arms, even if chromosome width is constant. We will make this clear in the revised manuscript.*

    (3) If the loop sizes are the same between shorter and longer chromosomes, why can't loop extrusion model explain this phenomenon? If one assumes that condensin is stopped by the same barrier element and has the same distrution at the loop base, this should produce the same outcome as loop capture. *

    The key feature of loop extrusion is the formation of a linear condensin backbone, resulting in a bottle brush-shaped chromosome. This arrangement prevents further equilibration of loops into a wider structure, as occurs in the loop capture mechanism by rosette rearrangements. These differences will be better explained, using a schematic, in the revised manuscript.*

    Minor points (1) "We are aware that this approximation underestimates the length of the longest chromosome arms and overestimates the length of the shortest arms." should be "We are aware that this approximation underestimates the length of the longer chromosome (q) arms and overestimates the length of the shorter (p) arms.". Right? *

    In fact, this comparison applies to all longer and shorter arms, not only pairs of p and q arms, which we will clarify.*

    (2) Some scientists argue that the final chromosome conformation might be kinetically driven. Even if the short chromosomes have reached the final roundness, this doesn't necessarily mean that they have reached equilibrium in cells. "Steady state" might be a better term to describe the chromosomes in vivo, as there are clearly energy-burning processes. *

    The reviewer is right that the term ‘equilibrium’ can be seen as misleading, which we will replace with ‘steady state’.*

    Reviewer #3 (Significance (Required)):

    I find the paper intellectually stimulating and a pleasure to read. It suggests a plausible explanation for mitotic chromosome formation. As such, it will be of great interest to scientists in the chromatin field.

    Reviewer #4 (Evidence, reproducibility and clarity (Required)):

    The take home message of this study is that chromosome structure can be attained through mechanisms of looping that do not require an explicit loop extrusion function. As the authors states, alternative models of loop capture have been proposed, dating from 2015-2016. THese models show DNA chains through simply Brownian diffusion can adopt a loop structure (citation 27, 28 and similarly Entropy gives rise to topologically associating domains Vasquez et al 2016 DOI: 10.1093/nar/gkw510).*

    The reviewer makes an excellent point in that entropy considerations, e.g. depletion attraction, likely contribute to the efficiency of loop capture. We will refer to this principle, including a citation to the Vasquez et al. study, in the revised manuscript.

    In this study, the authors go through careful and well-documented chromosome length measurements through prophase and metaphase. The modeling studies clearly show that loop capture provides a tenable mechanism that accounts for the biological results. The results are clearly written and propose an important alternative narrative for the foundation of chromosome organization.

    Reviewer #4 (Significance (Required)):

    The study is important because it takes a reductionist approach using just Brownian motion and loop capture to ask how well the fundamental processes will recapitulate the biological outcome. The fact that loop capture can account for the arm length to width relationships on biological time scales is important to report to the community. The work is extremely well done and the analysis of chromosome features is thorough and well-documented.*

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    Referee #4

    Evidence, reproducibility and clarity

    The take home message of this study is that chromosome structure can be attained through mechanisms of looping that do not require an explicit loop extrusion function. As the authors states, alternative models of loop capture have been proposed, dating from 2015-2016. THese models show DNA chains through simply Brownian diffusion can adopt a loop structure (citation 27, 28 and similarly Entropy gives rise to topologically associating domains Vasquez et al 2016 DOI: 10.1093/nar/gkw510).

    In this study, the authors go through careful and well-documented chromosome length measurements through prophase and metaphase. The modeling studies clearly show that loop capture provides a tenable mechanism that accounts for the biological results. The results are clearly written and propose an important alternative narrative for the foundation of chromosome organization.

    Significance

    The study is important because it takes a reductionist approach using just Brownian motion and loop capture to ask how well the fundamental processes will recapitulate the biological outcome. The fact that loop capture can account for the arm length to width relationships on biological time scales is important to report to the community.

    The work is extremely well done and the analysis of chromosome features is thorough and well-documented.

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    Referee #3

    Evidence, reproducibility and clarity

    In this manuscript, Kakui et al. measured the length/width relationships of mitotic chromosomes in human cells that had entered mitosis for different durations. This simple measurement revealed very interesting behaviors of mitotic chromosomes. They found that the longer chromosome arms were wider than shorter ones. Mitotic chromosoms became progressively wider over time, with shorter ones reached the final state faster than the longer ones. They then built a loop-capture polymer model, which explained the time-dependent increase of width/length ration rather well, but did not quite explain the final roundness of chromosomes.

    I suggest the following points for the authors to consider.

    Major points

    1. There is no experimental evidence that the loop capture mechanism is condensin-depdendent. Can the authors deplete condensin I or II or both and measure chromosome length and width in similar assays? This will link their models to molecular players.
    2. It seems rather intuitive to me that if one defines the spacing the condensin-binding sites, then the loop sizes will be the same between shorter and longer chromosomes. It then follows that shorter chromosomes are rounder. Is it that simple? If not, can the authors provide a better explanation.
    3. If the loop sizes are the same between shorter and longer chromosomes, why can't loop extrusion model explain this phenomenon? If one assumes that condensin is stopped by the same barrier element and has the same distrution at the loop base, this should produce the same outcome as loop capture.

    Minor points

    1. "We are aware that this approximation underestimates the length of the longest chromosome arms and overestimates the length of the shortest arms." should be "We are aware that this approximation underestimates the length of the longer chromosome (q) arms and overestimates the length of the shorter (p) arms.". Right?
    2. Some scientists argue that the final chromosome conformation might be kinetically driven. Even if the short chromosomes have reached the final roundness, this doesn't necessarily mean that they have reached equilibrium in cells. "Steady state" might be a better term to describe the chromosomes in vivo, as there are clearly energy-burning processes.

    Significance

    I find the paper intellectually stimulating and a pleasure to read. It suggests a plausible explanation for mitotic chromosome formation. As such, it will be of great interest to scientists in the chromatin field.

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    Referee #2

    Evidence, reproducibility and clarity

    Summary

    The authors tracked the progression of mitotic chromosome compaction over time by imaging chromatin spreads from HeLa cells that were released from G2/M arrest. By measuring the mitotic chromosome arms' width and length at different times post-release, the authors demonstrated that the speed at which the chromosome arms reach an equilibrium state is dependent on their length. The authors were able to recapitulate this observation using polymer simulations that they previously developed, supporting the model of loop capture as the mechanism for mitotic chromosome compaction.

    Main Comments

    This is a straightforward paper that supports an alternative mechanism (relative to the highly popular loop-extrusion) model for chromosome compaction. My comments are meant to help the manuscript reach a wider audience.

    I suggest that "equilibrium" be replaced with "equilibrium length" since it is the only equilibrium parameter of concern.

    In the results, it may help to describe how loop capture and loop extrusion are incorporated into the simulations, using terminology that non-experts can understand. Such a description should be accompanied by figures that can be related to the other figures (color scheme, nomenclature if possible).

    Other comments

    P5: Is it possible the chromosome-spread processing may distort the structures of the chromosomes?

    Please clarify whether mitosis can complete after drug removal at the various treatment intervals.

    P6: "Our records are not, therefore, meant as an accurate absolute measure of individual arms. Rather, fitting allows us to sample all chromosome arms and deduce overall trends of chromosome shape changes over time" It would be better to state this sentence earlier in this paragraph, or earlier in the section so that readers' expectations are curbed when they're reading the detailed analysis plan.

    P6: "As soon as individual chromosome arms become discernible (30 minutes), longer chromosome arms were wider, a trend that became more pronounced as time progressed." Implies that at early time points, when the lengths of the arms were unknown, the longer arms were equal or narrower than the short arms. I think it's more accurate to say that as soon as the arms were resolved, the longer arms appeared wider.

    P7: Is there a functional consequence to the long arms not equilibrating before anaphase onset?

    P13: "In a loop capture scenario, we can envision how condensin II sets up a coarse rosette architecture, with condensin I inserting a layer of finer-grained rosettes." This should be illustrated in a figure.

    Figures

    Fig. 1: "...while insets show chromosomes at increasing magnification over time" sounds like the microscope magnification is changing over time. Please change "magnification" to "enlargement". Alternatively, if the goal of the figure is to illustrate the shape/dimensions change of the chromosomes over time, wouldn't it be better to keep all the enlargements at the same scale?

    Fig. 2a plot: Does the distribution of normalized intensities really justify a Gaussian fit? I see a double Gaussian.

    Please label the structures that resemble "rosettes".

    Lu Gan

    Significance

    General This is a simulation-centric study of mammalian chromosome compaction that supports the loop-capture mechanism. It may be viewed as provocative by some readers because loop-extrusion has dominated the chromosome-compaction literature in the past decade. The only limitation, which is best addressed by future studies, is the absence of more direct molecular evidence of loop capture in situ. Though this same limitation applies to studies of the loop-extrusion mechanism.

    Advance It is valuable for the field to consider alternative mechanisms. In my opinion, the dominant one has been studied to death by indirect methods without a direct molecular-resolution readout in situ. While the field awaits better experimental tools, more mechanisms should be explored.

    Audience The chromosome-biology community (both bacterial and eukaryotic) will be interested.

    Expertise My lab uses cryo-ET to study chromatin in situ.

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    Referee #1

    Evidence, reproducibility and clarity

    Summary: This manuscript authored by Kakui and colleagues aims to understand on how mitotic chromosomes get their characteristic, condensed X shape, which is functionally important to ensure faithful chromosome segregation and genome inheritance to both daughter cells. The authors focus on the condensin complex, a central player in chromosome condensation. They ask whether it condenses chromosomes through a now broadly popular "loop-extrusion" mechanism, in which a chromatin-bound condensin complex reels chromatin into loops until it dissociates or encounters a roadblock on the polymer (another condensin or some other protein complex), or through an alternative, "diffusion-capture" mechanism, in which a chromatin-bound condensin complex forms loops by encountering another chromatin-bound condensin until they dissociate from DNA (or from each other.)

    The authors measured the progressive changes in the shape of mitotic chromosomes by taking samples at given time points from synchronized and mitotically arrested cells and found that while all chromosomes become more condensed and shorter, their width correlated with the length of the chromosome arms. They also observed that chromosome compaction/shortening evolves on a time scale much longer than the interval between the onset of chromosome condensation and the start of chromosome segregation, suggesting that chromatin condensation does not reach its steady-state during an unperturbed mitosis. The observed width-length correlation could be described by a power law with an exponent that increases with the time (i.e. chromosome condensation). The authors also performed polymer simulations of the diffusion-capture mechanism and found that the simulations semi-quantitatively recapitulate their experimental observations.

    Major Comments

    My most substantial comments focus on somewhat technical details of the image analysis approaches taken and the polymer models employed. However, as all reported data are derived from those details, I feel it is crucial to address them.

    1. Definition/measurement of chromatin arms width and length. The approach taken to manually threshold an "arm" object and then fitting it with a same-area ellipse is not an ideal approach to gauge length and width of the arm, for the following reasons: (1) An ellipse appears to do a poor job approximating many of the objects that we see in the zoom-in insets of Fig.1. Importantly, for somewhat bent shapes we see in the insets it likely strongly underestimates the length of the arms; this approach also presents potential problems for measuring width as well (see 2 and 3 here). (2) One concern is that, due to the diffraction limit, a cylindrical fluorescent object could appear somewhat wider at the mid-length than the real underlying cylinder or the poles; this effect could become more pronounced as the object gets brighter and shorter. (3) Forcing the fit to an ellipse to objects that are not truly rod-shaped can drive an overestimation of the width of the object, and I suspect that this effect also might correlate with the length and brightness of the object. (4) Given 1-3 above, I think the approach the authors used for the first two time points, while not perfect, is better suited and likely more robust while avoiding these caveats. Moreover, why the authors cannot use this same approach (but just for each arm separately) for the later (30+ min) time points as they used for first two is unclear. This point is underscored by the observation that there is a drastic difference in the results between the first two and all subsequent points. When the authors compared the two approaches at the 30 min time point (where width-length dependence is still weak) in different cell lines they did indeed see different results (Fig. S2), although they concluded that the difference was acceptable. Along these lines, the difference between short and long arms for the chromosome in the insets of Fig.1 are quite subtle, except maybe at 180 and 240 min. On a related note, it might be informative to compare data for the two sister chromatid arms (as the underlying polymer has the same length) long vs long and short vs short and long vs short to help establish the robustness of the approach.
    2. Regarding the power-law distribution, it is hard to judge based on the presented data whether it is a really good description of the data or not. In Fig.1c, the points for a given time can barely be distinguished, while in Fig.1b the authors plot individual time points in the panels, but the fits and points are overlapping so much that it is challenging to the main trends described by the clouds. The most informative approach for the reader would be to provide confidence intervals of the best fit parameters for all parameters that were varied in the fit. As the authors make some conclusions based on the power-law exponent values they observed, it would be helpful to know how confident we are in those values.
    3. The conclusion that short arms equilibrate faster based on Fig.3a is not fully convincing. For example, in a scenario where ~1.5 microns is the equilibrium length for all arms, and that the longest arms equilibrate the fastest - you would see the same qualitative pattern for quantiles, not much change in low percentiles, while you would observe a decrease in the values for the high percentiles. The authors might be right, but Fig. 3A does not unambiguously demonstrate that it is so based on this evidence alone.
    4. As for chromosome roundness, typically in image analysis, roundness is defined through the ratio of (perimeter)2/area; it might be better to use "aspect ratio" for the metrics used by the authors. And, perhaps, one should expect that shorter (measured, not necessarily by polymer contour length) arms should have a higher width/length ratio? If one selects for more round objects, there should be no surprise that the width and length get almost proportional. Given all of this, I am not sure whether width/aspect ratio serves as a good proxy for the chromatin condensation progression, which is how the authors are employing this data in the manuscript as written.
    5. For the diffusion-capture model simulations, I think the results of the simulation would strongly depend on the assumptions of the probability to associate and the time scale of dissociation of the beads representing the condensin complex. For example, for a very strong association one might expect that all condensin will end up in one big condensate, even in the case of a long polymer. This is not explored/discussed at all. Did the authors optimize their model in any way? If not, how have they estimated the values they used? Moreover, perhaps this is an opportunity to learn/predict something about condensin properties, but the authors do not take advantage of this opportunity. In addition, the authors did some checks to show that the steady-state results of the simulations do not depend on the initial conditions. However, as some of the results reported concern the polymer evolution to the steady state (Fig.6b-c), they also need to examine whether these results depend on the chosen initial conditions (or not), and if they do, what is the rationale for the choices the authors have made?
    6. A more thorough discussion of other possible models, beyond diffusion-capture model considered here, would be beneficial to the reader. First, the authors practically discard the possibility of the loop-extrusion model to explain their observations (although they never explicitly state this in the abstract or discussion). However, they neither leveraged simulations to rigorously compare models nor included some other substantiated arguments to explain why they prefer their model. This is important, as one of the major findings here is that the chromatin never reaches steady state for condensation, making it challenging to intuit what one should expect in this very dynamic state. Second, the authors, while briefly mentioning that there might be some other mechanisms contributing to the mitotic chromosome reshaping, do not really discuss those possibilities in a scholarly way. For example, work by the Kleckner group has suggested an involvement of bridges between sister chromatids into their shortening dynamics (Chu et al. Mol Cell 2020). Third, the authors do not discuss how they envision the interplay between the different SMC complexes - cohesin, condensin I and condensin II - as they act on the same chromatin polymer, or at least acknowledge a possible role that this interplay might contribute to the observed time dependencies.

    Significance

    The question the authors are trying to address is fundamental and important. While loop extrusion-driven mitotic chromosome organization is a popular model, considering alternative models is always crucial, especially when one can find experimental observations that allow us to discriminate between possible models. The main limitations are: 1) the performance of the approach the authors take to measure chromosome shape is in question and 2) the main competitive model (loop extrusion) is not modeled. If all shortcomings are addressed this work may provide strong evidence for the diffusion-capture model and thus advance our mechanistic understanding of mitotic processes, which will be of broad interest to the fields of genome and chromosome biology.

  6. Version published to 10.1101/2024.11.19.623756v2 on bioRxiv
  7. Version published to 10.1101/2024.11.19.623756v1 on bioRxiv