PRC1 resists microtubule sliding in two distinct resistive modes due to variations in the separation between overlapping microtubules

  1. Daniel Steckhahn
  2. Shane Fiorenza
  3. Ellinor Tai
  4. Scott Forth
  5. Peter R Kramer
  6. Meredith Betterton

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Abstract

Crosslinked cytoskeletal filament networks provide cells with a mechanism to regulate cellular mechanics and force transmission. An example in the microtubule cytoskeleton is mitotic spindle elongation. The three-dimensional geometry of these networks, including the overlap length and lateral microtubule spacing, likely controls how forces can be regulated, but how these parameters evolve during filament sliding is unknown. Recent evidence suggests that the crosslinker PRC1 can resist microtubule sliding by two distinct modes: a braking mode and a less resistive coasting mode. To explore how molecular-scale mechanisms influence network geometry in this system, we developed a computational model of sliding microtubule pairs crosslinked by PRC1 that reproduces the experimentally observed braking and coasting modes. Surprisingly, we found that the braking mode was associated with a substantially smaller lateral separation between the crosslinked microtubules than the coasting mode. This closer separation aligns the PRC1-mediated forces against sliding, increasing the resistive PRC1 force and dramatically reducing sliding speed. The model also finds an emergent similar average sliding speed due to PRC1 resistance, because higher initial sliding speed favors the transition to braking. Together, our results highlight the importance of the three-dimensional geometric relationships between crosslinkers and microtubules.

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  1. Version published to 10.1101/2024.12.31.630898v4 on bioRxiv
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    Reply to the reviewers

    We appreciated the constructive suggestions from the reviewers, and the explanation of the contribution of the manuscript. We have revised the manuscript in accordance with their suggestions, as discussed below.

    __Reviewer #1 (Evidence, reproducibility and clarity (Required)): __ This manuscript presents a computational analysis of PRC1, a passive microtubule crosslinker important for cell division, with a focus on its role in resisting force generation within antiparallel bundles, whose sliding is promoted by active kinesin motors. Using a previously developed simulator and several assumptions, the authors successfully recapitulated the two modes of PRC1 sliding resistance - coasting and braking - that were previously observed in in vitro reconstruction assays. The simulation also reproduces the redistribution of PRC1 within the overlap region as microtubules transition into the braking mode, a phenomenon also observed experimentally. An interesting outcome of the simulation is the change in spacing between the microtubules: The distance narrows as the sliding polymers switch from the coasting to the breaking mode, associated with an increased tilt of PRC1.

    Major comments: I find that this manuscript makes a valuable contribution to the cytoskeletal community, as the role of interfilament spacing in polymer assembly has been relatively underexplored, except for more classic studies such as those on muscle contraction and flagellar beating. What I had difficulty fully visualizing the model was the behavior of PRC1 during the coasting and braking modes. In my understanding, if individual heads of PRC1 bind and unbind to and from microtubules while microtubules that they crosslink slide apart, PRC1 should experience greater stretching and thus tilt more at higher sliding speeds. When the sliding slows down, the relative polymer position changes less within a given time, and PRC1 unbinding and re-binding would more easily reset their tilt to an equilibrium angle. However, the authors' simulation shows the opposite: PRC1 exhibits a greater tilt during the braking mode. This seems counterintuitive and a more detailed description and interpretation would worth. I suggest that the authors include a schematic illustrating the configuration of individual PRC1 molecules (e.g., angle and stretch) within the ensemble, particularly during their transition phase. This would greatly help readers grasp how this important protein ensemble switches its mechanical mode depending on polymer sliding and geometry.

    We thank the reviewer for the comments on the contribution of the results of the manuscript. Braking typically initiates at higher sliding speeds, when PRC1 do experience greater stretching and tilt more as the reviewer writes. As sliding slows down, the ability of PRC1 to unbind, re-bind, and rest their tilt to the equilibrium angle is restricted by the small distance between the microtubules: PRC1 binding will tend to occur tilted in the direction of sliding, and molecules tilted in this direction promote close separations, keeping overlaps braking. To clarify why braking overlaps are stable we added text and figure 4H. Steric interactions within the clusters at the overlap edges also restrict rebinding. To illustrate the behavior of PRC1 molecules during the transition from coasting to braking , we have added in figure 4A a schematic derived from simulation data of the microtubule and PRC1 positions, separations, and tilts during the transition from coasting to braking.

    Minor comments:

    1. How was the bimodal velocity distribution (Fig. 1D) obtained experimentally? Were the individual data averaged over time from the start to the end of individual sliding events? If so, does mode switching within a pair lead to under/over-estimate of the coasting and braking speeds?

    These data are reproduced from Alfieri et al. Current Biology 2021. In that paper, we acquired this data by observing the sliding separation of PRC1-crosslinked microtubule pairs and recorded two distinct velocities for each pair: the “bundled” velocity when overlap>0 and PRC1 was engaged in crosslinking and then the “escaped” velocity once the two microtubules had separated. In the vast majority of cases (>90%) each of these velocities was well measured by fitting a slope to the kymograph, as there were only very minor deviations from a linear position-versus-time relationship (e.g. we rarely saw acceleration or deceleration within an individual pair). In the rare (

    Line 158 includes typo.

    We thank the reviewer for pointing out this typo, which has been corrected.

    The fixed-separation simulation in Fig. 3D is important for demonstrating the causality. How was the average speed (V_avg) calculated in this case? Specifically, do microtubule pairs that slide at coasting mode maintain a high speed over the entire sliding event when the inter-filament spacing is fixed at a large distance?

    We thank the reviewer for raising this point, which was not clear in the original manuscript. In the fixed-separation simulation of Fig 3D the average speed is calculated for the whole simulation. We have clarified this in the figure 3 caption. We have also added a supplementary figure showing the velocity distribution. The coasting pairs do maintain high speed over the event.

    In my understanding, the attractive and repulsive lateral forces exerted by PRC1 with positive and negative tilts arise because PRC1 has a natural tilt relative to the perpendicular. Is this correct? It would be helpful to illustrate this assumption in a figure to clarify the molecular behavior being modelled.

    The reviewer raises an important point that we have clarified in the revised manuscript. The linear (spring stretch/compression) force is the primary contributor to the attractive lateral force in both braking and coasting states. The torsional force that arises from the natural tilt of PRC1 does contribute significantly to repulsion between microtubules in the coasting state. We have clarified this in the text and added a supplementary figure showing the energy and forces from PRC1 molecules as a function of angle.

    In the paragraph starting from line 258, the authors discuss Ase1 and the yeast spindles. What is the relevance to PRC1 particularly in considering that Ase1 exerts an entropic force within the confined microtubule bundles to resist sliding (e.g., Lasky et al., 2015)?

    We thank the reviewer for raising this important point. It is true that Ase1 has been shown to generate entropic forces that work to push against microtubule sliding, while this specific behavior has not been observed for PRC1. We believe that such forces are likely to arise when Ase1 is in a coasting-like mode and the individual crosslinkers are free to diffuse within the confines of the overlap, which is the mechanism Lansky et al. propose. In this paragraph of the discussion, we are highlighting the experimental observation that microtubule-microtubule spacing significantly reduces as a yeast cell proceeds from metaphase to anaphase, with late anaphase MT separations measured to be ~15nm, similar to what we predict for microtubule pairs that have engaged in a braking mode. We therefore speculate that a coasting-to-braking transition may be more generally applicable across different spindle types, at least when involving MAP65 family members such as Ase1 and PRC1. In the yeast spindle, then, we speculate that when microtubule separation is larger, Ase1 would be arranged in a coasting-like mode of binding, capable of generating entropic forces. Later, it is possible the molecules switch to a more braking-like mode, where MT-MT spacing reduces significantly as shown in EM data from yeast spindles. It will be useful in the future to acquire similar data from mammalian spindles to determine if late anaphase midzone separation also compacts when PRC1 is present, which would further validate our predictions. We have clarified the discussion of this point in the revision.

    Fig. 1B, C would benefit from additional labels, as the colors in the images do not match those in the accompanying cartoon.

    We thank the reviewer for the suggestion, and have added additional labels.

    Reviewer #1 (Significance (Required)):

    As in my major comments above. My expertise is experimental biophysics on microtubules and motors.

    __Reviewer #2 (Evidence, reproducibility and clarity (Required)): __The paper presents simulations of sliding antiparallel microtubules linked by PRC1 crosslinking proteins. It aims to reproduce and explain experimental observations by Alfieri et al. that suggested that PRC1 could adopt two distinct modes of resistive force production against kinesin-driving sliding forces.

    The model which the authors propose is that antiparallel sliding leads to the accumulation of PRC1 at the edges, which results in higher tilt angles of PRC1 molecules and consequently smaller microtubule separation. In the higher tilt regime PRC1 can exert more braking forces since, its angle with the Microtubules is smaller. To my understanding the key parameters for this model to work it the spontaneous tilt angle, and torsional spring that PRC-1's structure encodes. The authors demonstrates that for reasonable values very good agreement with experimental observations can be reached. The simulations are done in the CYlAks framework, which the Betterton group developed and validated in earlier work. The discussion is clear and readable

    Major Comment: While the paper goes at great length to successfully reproduce experiments, it is not discussed how sensitive the model is to changes in parameters. In particular it remains unclear how sensitive the model is to changes in the torsional spring that is being used to model PRC-1. Given that this is key to the findings presented here, I would have hoped for a more extensive discussion of the relevant physics. In particular It should be discussed how non-linearities and asymmetries in the torsional spring would affect the phenomenon identified here.

    We appreciate the reviewer’s suggestion to examine sensitivity to variation in model parameters. We note that we do present in Figure 2 a smaller exploration of parameter space; when key values are modulated by an order of magnitude, we find differences in the simulated outputs (e.g. enhanced or reduced tip clustering in response to changes in MAP diffusion or end binding). We also note the supplementary information includes the effect of varying parameters including the strength and asymmetry of the torsional spring, which addresses the specific concern noted. Given the length of the current manuscript, we propose to delay a more extensive study of parameter sensitivity to future work.

    (Very) Minor remark: the orientation of PRC-1 molecules is inconsistent between figures.

    We thank the reviewer for pointing this out. We have edited the figures to make the orientation consistent.

    __Reviewer #2 (Significance (Required)): __ PRC-1 is an important cross-linking protein in cell division, and its mechanics is at the center of much current research interest. As such this paper is timely. The key physics that is interesting here is the link between geometry, PRC1-arrangements and geometry of the MT network. The authors reproduce successfully the experimental observations, with reasonable parameters. But a parameter study that exposes the physics at play, and would help the reader generalize the concepts at play is missing.

    In its current state the paper will be of interest to experimentalists and theoreticians working on cytoskeletal filament networks. But it could be even more so, if the authors sought to generalize beyond the experiment at hand.

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

    The manuscript by Steckhahn and colleagues is a computational study of the mechanics of microtubule interactions with an essential mitotic crosslinker, PRC1. PRC1 is known to act as a molecular clutch, resisting the sliding of antiparallel microtubules in order to maintain mitotic spindle integrity. The present study aims to explain the recently discovered two modes of action of this clutch: a weakly resistant 'coasting' mode and a highly resistant 'braking' mode. The authors employ their previously developed Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) model to carry out Monte Carlo/Langevin dynamics simulations of microtubule sliding, driven by a mitotic kinesin and resisted by an ensemble of PRC1 crosslinkers, with explicit account of their diffusion, binding-unbinding kinetics, stretching-compression, and volume-exclusive interactions. Their reasonable model successfully reproduces the bimodal distribution of microtubule sliding rates, and offers a simple explanation of the two modes of action of the crosslinkers. According to the authors' conclusion, in the coasting mode PRC1 molecules are almost perpendicular to the microtubules, while the microtubules are separated by about 30 nm (close to the rest length of PRC1). When the overlap between the sliding microtubules shrinks, the PRC1 molecules cluster, which facilitates their tilting. This has two effects: a projection of force bringing microtubules closer together appears, and a projection of resistive force along the microtubule axis becomes substantial, enabling more efficient 'braking'.

    The key conclusions are convincing, clearly stated, and supported by data. The simulation techniques are justified and well described. I have no concerns about the technical side of this study.

    We thank the reviewer for their clear summary of the results of the paper.

    Reviewer #3 (Significance (Required))

    I believe this is a useful piece of work, which clarifies some important aspects of the PRC1 mechanism of action by showing that a simple but rigorous mechanical consideration is sufficient to explain the observed bimodal behavior of the mitotic crosslinkers. The findings could be interesting to biophysicists and cells biologists, interested in cytoskeleton and cell division.

  3. Review Commons

    Note: This preprint has been reviewed by subject experts for Review Commons. Content has not been altered except for formatting.

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    Referee #3

    Evidence, reproducibility and clarity

    The manuscript by Steckhahn and colleagues is a computational study of the mechanics of microtubule interactions with an essential mitotic crosslinker, PRC1. PRC1 is known to act as a molecular clutch, resisting the sliding of antiparallel microtubules in order to maintain mitotic spindle integrity. The present study aims to explain the recently discovered two modes of action of this clutch: a weakly resistant 'coasting' mode and a highly resistant 'braking' mode. The authors employ their previously developed Cytoskeleton Lattice-based Kinetic Simulator (CyLaKS) model to carry out Monte Carlo/Langevin dynamics simulations of microtubule sliding, driven by a mitotic kinesin and resisted by an ensemble of PRC1 crosslinkers, with explicit account of their diffusion, binding-unbinding kinetics, stretching-compression, and volume-exclusive interactions. Their reasonable model successfully reproduces the bimodal distribution of microtubule sliding rates, and offers a simple explanation of the two modes of action of the crosslinkers. According to the authors' conclusion, in the coasting mode PRC1 molecules are almost perpendicular to the microtubules, while the microtubules are separated by about 30 nm (close to the rest length of PRC1). When the overlap between the sliding microtubules shrinks, the PRC1 molecules cluster, which facilitates their tilting. This has two effects: a projection of force bringing microtubules closer together appears, and a projection of resistive force along the microtubule axis becomes substantial, enabling more efficient 'braking'. The key conclusions are convincing, clearly stated, and supported by data. The simulation techniques are justified and well described. I have no concerns about the technical side of this study.

    Significance

    I believe this is a useful piece of work, which clarifies some important aspects of the PRC1 mechanism of action by showing that a simple but rigorous mechanical consideration is sufficient to explain the observed bimodal behavior of the mitotic crosslinkers. The findings could be interesting to biophysicists and cells biologists, interested in cytoskeleton and cell division.

  4. Review Commons

    Note: This preprint has been reviewed by subject experts for Review Commons. Content has not been altered except for formatting.

    Learn more at Review Commons

    Referee #2

    Evidence, reproducibility and clarity

    The paper presents simulations of sliding antiparallel microtubules linked by PRC1 crosslinking proteins. It aims to reproduce and explain experimental observations by Alfieri et al. that suggested that PRC1 could adopt two distinct modes of resistive force production against kinesin-driving sliding forces.

    The model which the authors propose is that antiparallel sliding leads to the accumulation of PRC1 at the edges, which results in higher tilt angles of PRC1 molecules and consequently smaller microtubule separation. In the higher tilt regime PRC1 can exert more braking forces since, its angle with the Microtubules is smaller. To my understanding the key parameters for this model to work it the spontaneous tilt angle, and torsional spring that PRC-1's structure encodes. The authors demonstrates that for reasonable values very good agreement with experimental observations can be reached. The simulations are done in the CYlAks framework, which the Betterton group developed and validated in earlier work. The discussion is clear and readable

    Major Comment:

    While the paper goes at great length to successfully reproduce experiments, it is not discussed how sensitive the model is to changes in parameters. In particular it remains unclear how sensitive the model is to changes in the torsional spring that is being used to model PRC-1. Given that this is key to the findings presented here, I would have hoped for a more extensive discussion of the relevant physics. In particular It should be discussed how non-linearities and assymetries in the torsional spring would affect the phenomenon identified here.

    (Very) Minor remark: the orientation of PRC-1 molecules is inconsistent between figures.

    Significance

    PRC-1 is an important cross-linking protein in cell division, and its mechanics is at the center of much current research interest. As such this paper is timely. The key physics that is interesting here is the link between geometry, PRC1-arrangements and geometry of the MT network. The authors reproduce successfully the experimental observations, with reasonable parameters. But a parameter study that exposes the physics at play, and would help the reader generalize the concepts at play is missing.

    In its current state the paper will be of interest to experimentalists and theoreticians working on cytoskeletal filament networks. But it could be even more so, if the authors sought to generalize beyond the experiment at hand.

  5. Review Commons

    Note: This preprint has been reviewed by subject experts for Review Commons. Content has not been altered except for formatting.

    Learn more at Review Commons

    Referee #1

    Evidence, reproducibility and clarity

    This manuscript presents a computational analysis of PRC1, a passive microtubule crosslinker important for cell division, with a focus on its role in resisting force generation within antiparallel bundles, whose sliding is promoted by active kinesin motors. Using a previously developed simulator and several assumptions, the authors successfully recapitulated the two modes of PRC1 sliding resistance - coasting and braking - that were previously observed in in vitro reconstruction assays. The simulation also reproduces the redistribution of PRC1 within the overlap region as microtubules transition into the braking mode, a phenomenon also observed experimentally. An interesting outcome of the simulation is the change in spacing between the microtubules: The distance narrows as the sliding polymers switch from the coasting to the breaking mode, associated with an increased tilt of PRC1.

    Major comments:

    I find that this manuscript makes a valuable contribution to the cytoskeletal community, as the role of interfilament spacing in polymer assembly has been relatively underexplored, except for more classic studies such as those on muscle contraction and flagellar beating. What I had difficulty fully visualizing the model was the behavior of PRC1 during the coasting and braking modes. In my understanding, if individual heads of PRC1 bind and unbind to and from microtubules while microtubules that they crosslink slide apart, PRC1 should experience greater stretching and thus tilt more at higher sliding speeds. When the sliding slows down, the relative polymer position changes less within a given time, and PRC1 unbinding and re-binding would more easily reset their tilt to an equilibrium angle. However, the authors' simulation shows the opposite: PRC1 exhibits a greater tilt during the braking mode. This seems counterintuitive and a more detailed description and interpretation would worth. I suggest that the authors include a schematic illustrating the configuration of individual PRC1 molecules (e.g., angle and stretch) within the ensemble, particularly during their transition phase. This would greatly help readers grasp how this important protein ensemble switches its mechanical mode depending on polymer sliding and geometry.

    Minor comments:

    1. How was the bimodal velocity distribution (Fig. 1D) obtained experimentally? Were the individual data averaged over time from the start to the end of individual sliding events? If so, does mode switching within a pair lead to under/over-estimate of the coasting and braking speeds?
    2. Line 158 includes typo.
    3. The fixed-separation simulation in Fig. 3D is important for demonstrating the causality. How was the average speed (V_avg) calculated in this case? Specifically, do microtubule pairs that slide at coasting mode maintain a high speed over the entire sliding event when the inter-filament spacing is fixed at a large distance?
    4. In my understanding, the attractive and repulsive lateral forces exerted by PRC1 with positive and negative tilts arise because PRC1 has a natural tilt relative to the perpendicular. Is this correct? It would be helpful to illustrate this assumption in a figure to clarify the molecular behavior being modelled.
    5. In the paragraph starting from line 258, the authors discuss Ase1 and the yeast spindles. What is the relevance to PRC1 particularly in considering that Ase1 exerts an entropic force within the confined microtubule bundles to resist sliding (e.g., Lasky et al., 2015)?
    6. Fig. 1B, C would benefit from additional labels, as the colors in the images do not match those in the accompanying cartoon.

    Significance

    As in my major comments above. My expertise is experimental biophysics on microtubules and motors.

  6. Version published to 10.1101/2024.12.31.630898v3 on bioRxiv
  7. Version published to 10.1101/2024.12.31.630898v2 on bioRxiv
  8. Version published to 10.1101/2024.12.31.630898v1 on bioRxiv