Measurements and simulations of microtubule growth imply strong longitudinal interactions and reveal a role for GDP on the elongating end

  1. Joseph M Cleary
  2. Tae Kim
  3. Annan SI Cook
  4. Lauren A McCormick
  5. William O Hancock
  6. Luke M Rice

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    Evaluation Summary:

    The authors use interference reflection microscopy to image a growing microtubule for long intervals at high frame rates, overcoming a limitation of fluorescence. Using careful quantitative analysis, the authors find that the kinetics of dynamic instability are "slow", in contrast to the "rapid kinetics" previously reported. This work provides new mechanistic insight into the mechanism of microtubule growth and is of interest to biologists and physicists interested in cytoskeletal filament dynamics.

    (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 #2 agreed to share their name with the authors.)

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Abstract

Microtubule polymerization dynamics result from the biochemical interactions of αβ-tubulin with the polymer end, but a quantitative understanding has been challenging to establish. We used interference reflection microscopy to make improved measurements of microtubule growth rates and growth fluctuations in the presence and absence of GTP hydrolysis. In the absence of GTP hydrolysis, microtubules grew steadily with very low fluctuations. These data were best described by a computational model implementing slow assembly kinetics, such that the rate of microtubule elongation is primarily limited by the rate of αβ-tubulin associations. With GTPase present, microtubules displayed substantially larger growth fluctuations than expected based on the no GTPase measurements. Our modeling showed that these larger fluctuations occurred because exposure of GDP-tubulin on the microtubule end transiently ‘poisoned’ growth, yielding a wider range of growth rates compared to GTP only conditions. Our experiments and modeling point to slow association kinetics (strong longitudinal interactions), such that drugs and regulatory proteins that alter microtubule dynamics could do so by modulating either the association or dissociation rate of tubulin from the microtubule tip. By causing slower growth, exposure of GDP-tubulin at the growing microtubule end may be an important early event determining catastrophe.

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  1. Version published to 10.7554/elife.75931 on eLife
  2. eLife

    Author Response:

    Reviewer #1:

    The authors perform very careful growth speed and growth fluctuation analysis of microtubules growing in vitro in the presence of either GMPCPP or GTP. This is essentially a re-examination of highly cited work published by Gardner et al in 2011. The quality of the current analysis is improved compared to previous work, because the authors use a label-free imaging method providing higher signal-to-noise-ratio data and allowing longer imaging at higher time resolution, and because the fluctuation analysis is technically more advanced. The main conclusions are that growth fluctuations are lower than previously published by Gardner et al., however in the presence of GTP they are still higher than expected, as reported previously, but less dramatically different than proposed previously. The authors propose a kinetic model that includes the possibility of GTP hydrolysis causing a hypothetical (but plausible) slowdown of tubulin addition when a GDP tubulin is exposed at the microtubule end to explain the larger growth fluctuations in the presence of GTP. This is an important study proposing a new model for the origin of the natural growth fluctuations of microtubules. In the future, this work will also have an impact on our understanding of how regulators of microtubule polymerization act. Overall this is a carefully performed study, with especially the experimental and data analysis part being of very high quality.

    Questions that the authors might want to address:

    1. Can the measured growth fluctuations in the presence of GMPCPP be explained by an even simpler 1-dimensional single protofilament growth model? Or is indeed a 2-dimensional model required that the authors use here.

    We thank the reviewer for their point that is now addressed as part of the broader explanation of the introduction. This helps give context to the need for the 2D model in the first place in lieu of the canonical 1D polymer model for growth. Earlier work (Gardner et al., “Rapid microtubule assembly kinetics”, Cell 2011) also demonstrated that 1D models are more limited in the magnitude of fluctuations that they can produce.

    1. Can the measured taper of growing microtubule ends be used to further constrain the fits to the data?

    This is an excellent point and should be achievable in principle. However, in the context of our simple model, we were unable to identify a set of parameters that could simultaneously recapitulate growth rates, growth fluctuations, and end taper. This is a limitation of our study that we acknowledge. We suspect that at least one additional state in the model will be required to improve its ability to predict end taper. This will be the subject of future work in our laboratories.

    1. The authors mention that they choose the optimal kon from the fits to the GMPCPP data also for the fits to the GDP data, if this reviewer understood correctly. Is this justified, given that the longitudinal interactions are probably different in a GMPCPP and a GTP lattice?

    The reviewer does understand the choice correctly: we used the same on-rate constant for fitting to the growth rates in GTP and GMPCPP. We think this is well- justified. First, 1D analyses (see Fig 1C and 3B) of the concentration-dependent growth rates yields apparent on-rate constants of 3.1 μM-1s-1 ± 0.6 and 2.3 μM-1s-1 ± 1.2 for microtubules grown with GMPCPP and GTP, respectively. These apparent on-rate constants fall within error of each other. Second, large changes in affinity like we observed between GMPCPP and GTP, are commonly assumed to manifest themselves in off-rate constants, not on-rate constants. Third, in the absence of evidence to the contrary, it just seems simpler to assume that GTP- and GMPCPP- bound tubulin will have similar on-rate constants for binding to the microtubule end. We added a sentence to be more this more explicit about this point.

    1. How reliably can the kinetic model of the authors predict the GTP hydrolysis rate at growing microtubule ends and how does this rate compare to previously published measurements or models?

    This is an interesting question from the reviewer. The GTPase rate constant we used here (0.08 s-1) falls at the lower end of the rather large range of values obtained in prior studies (range: 0.07 - 1 s-1). As we and others have noted previously, the relatively simple biochemical model we used does not capture the observed dependence of catastrophe frequency on tubulin concentration (e.g. Kim and Rice, MBoC 2019; also VanBuren et al., 2005). More complex models are better able to recapitulate this concentration-dependence, and in principle one could use measured catastrophe frequencies and/or GTP cap sizes as constraints on model fits. However, in the present work we chose to use the simplest model, and this is why we focused on trends with GTPase rate as opposed to one specific rate. We appreciate the opportunity to clarify this point, and we added a sentence to emphasize that we focused on trends with increasing GTPase rate rather than on a particular value of the GTPase rate.

    Reviewer #3:

    This paper applies rigorous quantitative microscopy to an open problem in biophysics, namely the kinetics of microtubule dynamic instability. Previous studies that analyzed these kinetics found them to be "fast", which is to say that tubulin binds very frequently to the end of a microtubule, but falls off almost as frequently (Gardner et al. Cell 2011). This "rapid self-assembly kinetics" is arguably the prevailing conceptual framework for microtubule polymerization. In contrast, the present study finds the kinetics of polymerization to be "slow", with infrequent binding events that persist for longer periods of time. The conceptual shift from "fast" to "slow" has significant implications, in particular for the mechanisms of microtubule polymerases.

    The difference in results from Gardner et al. Cell 2011 comes from 2 places. First, the authors use interference reflection microscopy (IRM) instead of fluorescence. Using IRM allows them to image growing microtubules for long time intervals at high frame rates. Thus, a single microtubule can generate a long plot of length versus time, in contrast to Gardner, who concantenated many short traces together to create a long plot. Second, the authors apply sub-pixel drift correction to their movies and show conclusively that pixel-based drift correction contributes to the appearance of "fast kinetics". Figure 1 (and its supplements) are an outstanding example of technical rigor, where different analyses are displayed side-by-side to justify the conclusion of slow kinetics, particularly for the growth of GMPCPP-tubulin.

    With GTP-tubulin in the reaction, growth is significantly more variable. To explain the increased variability, the authors use a computational model to test a particular hypothesis, namely that the tubulin at the very end of a microtubule can be in the GDP state, and that these terminal GDP-subunits have a reduced affinity for incoming dimers. In other words, the simulations argue that exposure of a GDP subunit at tip could "poison" that protofilament, and because that protofilament now lags behind the others, the microtubule end position fluctuates. But the manuscript is missing an experimental corrolary for their model of GDP exposure. And there are other potential explanations for why GTP-tubulin growth could be more variable than GMPCPP-tubulin growth. For example, we know that GMPCPP microtubules are stiff and uniformly 14-pf. Perhaps growth fluctuations are linked to tubulin's flexibility, which is included as a parameter in some computational models (e.g., Zakharov Biophys J 2015). The modeling here has demonstrated that GDP exposure is sufficient to explain growth variation, but they have not demonstrated that it is necessary, which would require experiments. The authors should spend part of their discussion considering alternative models and arguing explicitly for why trans-acting nucleotide makes sense.

    We added a sentence to the ‘Limitations of the model’ section to provide additional kinds of model alterations than were already listed.

    We also added a sentence to be more explicit about why we favor trans-acting GTP.

    The idea that GDP exposure could "poison" a protofilament end reminded me of eribulin and Doodhi et al., Curr Biol 2016. After all, eribulin is a bona fide poison (err, microtubule-targeting anti-cancer drug). Doodhi et al. defined the binding site for eribulin as the terminal end of b-tubulin, meaning that it blocks incoming subunits. They showed that the drug perturbed dynamic instability significantly, induced catastrophes, created "split EB comets", etc. Is the poisoning effect of eribulin related to the poisoning effect of GDP-exposure? Are eribulin and GDP-exposure both explainable as alterations in longitudinal affinity? A discussion of this comparison would be interesting.

    These are interesting questions. It’s not clear (to us, at least) that eribulin can be taken as equivalent to GDP-exposure. Indeed, there are interesting differences in the effects observed from different plus-end modulating compounds (GDP, eribulin, and even Darpin). These different modulators have the ability to limit protofilament elongation by blocking the terminal β-tubulin interface but give rise to different effects that probably depend on the lifetime of the blocked state and perhaps also other allosteric effects. For the sake of simplicity, we would prefer not to incorporate these ideas into the manuscript.

    Lastly, the relationship of to the authors' previous computational work (Piedra et al. MBoC 2016) needs further elaboration. In Piedra et al., their model allows GTP exchange into the poisoned GDP-terminal subunit. In this manuscript, the exchange is disallowed, which is the same as saying that its rate is 0. Is this reasonable? In Fig. 3B of Piedra, they plot how catastrophe frequency is affected by the rate of GDP->GTP exchange. If exchange is slow, then the impact of exchange on catastrophes is minimal. Is the same true for growth? The current manuscript should be viewed as an opportunity to elaborate on Piedra to the extent possible. It's clear in Piedra that the GTPase rate itself matters in terms of the sensitivity of catastrophes to GDP->GTP exchange rates. The authors write "a finite rate of exchange would only modulate the amount of GDP on the microtubule end for a given GTPase rate; it would not eliminate the 'poisoning' effect of GDP exposure that increases fluctuations in growth rate." But the interesting question is the sensitivity of the growth rate to the finite rate of GDP->GTP exchange.

    As one might expect, if the rate of GDP->GTP exchange is too fast, the effects on growth rate and fluctuations vanish (because exchange effectively becomes instantaneous). If the rate of exchange is too slow, there is no change from the ‘no exchange’ simulations. At intermediate rates of exchange, the magnitudes of the effects on growth rate and fluctuations decreases as the exchange rate increases. We saw no evidence for a regime where growth rates but not growth fluctuations (or vice versa) were affected. We prefer to not dwell on this in the present manuscript, but we hope to revisit the question experimentally in the future.

  3. eLife

    Evaluation Summary:

    The authors use interference reflection microscopy to image a growing microtubule for long intervals at high frame rates, overcoming a limitation of fluorescence. Using careful quantitative analysis, the authors find that the kinetics of dynamic instability are "slow", in contrast to the "rapid kinetics" previously reported. This work provides new mechanistic insight into the mechanism of microtubule growth and is of interest to biologists and physicists interested in cytoskeletal filament dynamics.

    (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 #2 agreed to share their name with the authors.)

  4. eLife

    Reviewer #1 (Public Review):

    The authors perform very careful growth speed and growth fluctuation analysis of microtubules growing in vitro in the presence of either GMPCPP or GTP. This is essentially a re-examination of highly cited work published by Gardner et al in 2011. The quality of the current analysis is improved compared to previous work, because the authors use a label-free imaging method providing higher signal-to-noise-ratio data and allowing longer imaging at higher time resolution, and because the fluctuation analysis is technically more advanced. The main conclusions are that growth fluctuations are lower than previously published by Gardner et al., however in the presence of GTP they are still higher than expected, as reported previously, but less dramatically different than proposed previously. The authors propose a kinetic model that includes the possibility of GTP hydrolysis causing a hypothetical (but plausible) slowdown of tubulin addition when a GDP tubulin is exposed at the microtubule end to explain the larger growth fluctuations in the presence of GTP. This is an important study proposing a new model for the origin of the natural growth fluctuations of microtubules. In the future, this work will also have an impact on our understanding of how regulators of microtubule polymerization act. Overall this is a carefully performed study, with especially the experimental and data analysis part being of very high quality.

    Questions that the authors might want to address:

    1. Can the measured growth fluctuations in the presence of GMPCPP be explained by an even simpler 1-dimensional single protofilament growth model? Or is indeed a 2-dimensional model required that the authors use here.

    2. Can the measured taper of growing microtubule ends be used to further constrain the fits to the data?

    3. The authors mention that they choose the optimal kon from the fits to the GMPCPP data also for the fits to the GDP data, if this reviewer understood correctly. Is this justified, given that the longitudinal interactions are probably different in a GMPCPP and a GTP lattice?

    4. How reliably can the kinetic model of the authors predict the GTP hydrolysis rate at growing microtubule ends and how does this rate compare to previously published measurements or models?

  5. eLife

    Reviewer #2 (Public Review):

    This is a very thorough and clear study, in which the authors used IRM to measure time series for growing MT lengths with high resolution and accuracy and for long time intervals. This precision and duration of measurements allowed them to quantify not only the growth rates, but also fluctuations of these rates. Then, they turned to thier previously used computational Monte Carlo model, which considers MT lattice and assigns rates of arrival and affinities to tubulin dimers depending on local MT tip geometry: there is a difference whether the tubulin is binding to the lonely protofilament tip, or into the 'corner', with added lateral interaction.

    The elegant part of the study is this: it is impossible to fit the model parameters uniquely from just average growth kinetics, but fluctuation measurements give the additional constraint, which allows to make an interesting and novel conclusion: the dimers bind to the protofilament tips slowly but tightly, so basically the MT growth can be accounted for by individual tip growth.

    All these results were obtained in the absence of hydrolysis. Then, the authors use GTP tubulin and find that the fluctuations increase drastically. Their model can only fit the measurements assuming that sometimes a GDP-subunit occurs at the MT tip, and this hinders the growth. This is somewhat at odds with what researchers think, but I find this conclusion logical.

  6. eLife

    Reviewer #3 (Public Review):

    This paper applies rigorous quantitative microscopy to an open problem in biophysics, namely the kinetics of microtubule dynamic instability. Previous studies that analyzed these kinetics found them to be "fast", which is to say that tubulin binds very frequently to the end of a microtubule, but falls off almost as frequently (Gardner et al. Cell 2011). This "rapid self-assembly kinetics" is arguably the prevailing conceptual framework for microtubule polymerization. In contrast, the present study finds the kinetics of polymerization to be "slow", with infrequent binding events that persist for longer periods of time. The conceptual shift from "fast" to "slow" has significant implications, in particular for the mechanisms of microtubule polymerases.

    The difference in results from Gardner et al. Cell 2011 comes from 2 places. First, the authors use interference reflection microscopy (IRM) instead of fluorescence. Using IRM allows them to image growing microtubules for long time intervals at high frame rates. Thus, a single microtubule can generate a long plot of length versus time, in contrast to Gardner, who concantenated many short traces together to create a long plot. Second, the authors apply sub-pixel drift correction to their movies and show conclusively that pixel-based drift correction contributes to the appearance of "fast kinetics". Figure 1 (and its supplements) are an outstanding example of technical rigor, where different analyses are displayed side-by-side to justify the conclusion of slow kinetics, particularly for the growth of GMPCPP-tubulin.

    With GTP-tubulin in the reaction, growth is significantly more variable. To explain the increased variability, the authors use a computational model to test a particular hypothesis, namely that the tubulin at the very end of a microtubule can be in the GDP state, and that these terminal GDP-subunits have a reduced affinity for incoming dimers. In other words, the simulations argue that exposure of a GDP subunit at tip could "poison" that protofilament, and because that protofilament now lags behind the others, the microtubule end position fluctuates. But the manuscript is missing an experimental corrolary for their model of GDP exposure. And there are other potential explanations for why GTP-tubulin growth could be more variable than GMPCPP-tubulin growth. For example, we know that GMPCPP microtubules are stiff and uniformly 14-pf. Perhaps growth fluctuations are linked to tubulin's flexibility, which is included as a parameter in some computational models (e.g., Zakharov Biophys J 2015). The modeling here has demonstrated that GDP exposure is sufficient to explain growth variation, but they have not demonstrated that it is necessary, which would require experiments. The authors should spend part of their discussion considering alternative models and arguing explicitly for why trans-acting nucleotide makes sense.

    The idea that GDP exposure could "poison" a protofilament end reminded me of eribulin and Doodhi et al., Curr Biol 2016. After all, eribulin is a bona fide poison (err, microtubule-targeting anti-cancer drug). Doodhi et al. defined the binding site for eribulin as the terminal end of b-tubulin, meaning that it blocks incoming subunits. They showed that the drug perturbed dynamic instability significantly, induced catastrophes, created "split EB comets", etc. Is the poisoning effect of eribulin related to the poisoning effect of GDP-exposure? Are eribulin and GDP-exposure both explainable as alterations in longitudinal affinity? A discussion of this comparison would be interesting.

    Lastly, the relationship of to the authors' previous computational work (Piedra et al. MBoC 2016) needs further elaboration. In Piedra et al., their model allows GTP exchange into the poisoned GDP-terminal subunit. In this manuscript, the exchange is disallowed, which is the same as saying that its rate is 0. Is this reasonable? In Fig. 3B of Piedra, they plot how catastrophe frequency is affected by the rate of GDP->GTP exchange. If exchange is slow, then the impact of exchange on catastrophes is minimal. Is the same true for growth? The current manuscript should be viewed as an opportunity to elaborate on Piedra to the extent possible. It's clear in Piedra that the GTPase rate itself matters in terms of the sensitivity of catastrophes to GDP->GTP exchange rates. The authors write "a finite rate of exchange would only modulate the amount of GDP on the microtubule end for a given GTPase rate; it would not eliminate the 'poisoning' effect of GDP exposure that increases fluctuations in growth rate." But the interesting question is the sensitivity of the growth rate to the finite rate of GDP->GTP exchange.

  7. Version published to 10.1101/2021.11.24.469935v1 on bioRxiv