1. Structural Biology and Molecular Biophysics
  2. Cell Biology
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Autocatalytic microtubule nucleation determines the size and mass of Xenopus laevis egg extract spindles

  1. Franziska Decker
  2. David Oriola
  3. Benjamin Dalton
  4. Jan Brugués  Is a corresponding author
  1. Max Planck Institute of Molecular Cell Biology and Genetics, Germany
  2. Center for Systems Biology Dresden, Germany
  3. Max Planck Institute for the Physics of Complex Systems, Germany
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Cite as: eLife 2018;7:e31149 doi: 10.7554/eLife.31149

Abstract

Regulation of size and growth is a fundamental problem in biology. A prominent example is the formation of the mitotic spindle, where protein concentration gradients around chromosomes are thought to regulate spindle growth by controlling microtubule nucleation. Previous evidence suggests that microtubules nucleate throughout the spindle structure. However, the mechanisms underlying microtubule nucleation and its spatial regulation are still unclear. Here, we developed an assay based on laser ablation to directly probe microtubule nucleation events in Xenopus laevis egg extracts. Combining this method with theory and quantitative microscopy, we show that the size of a spindle is controlled by autocatalytic growth of microtubules, driven by microtubule-stimulated microtubule nucleation. The autocatalytic activity of this nucleation system is spatially regulated by the limiting amounts of active microtubule nucleators, which decrease with distance from the chromosomes. This mechanism provides an upper limit to spindle size even when resources are not limiting.

https://doi.org/10.7554/eLife.31149.001

eLife digest

When cells divide, they first need to create a copy of their genetic material, which they then evenly distribute between their daughter cells. This is done by a complex of proteins known as the mitotic spindle, which divides the chromosomes that carry the genetic material in the form of genes. The mitotic spindle is mainly made of tubulin proteins that are arranged to form hollow cable-like filaments, called the microtubules. Microtubules are dynamic structures that can grow or shrink by adding or removing tubulin proteins. Unlike the spindle, which can ‘live’ up to hours, the microtubules only live for about 20 seconds and need to be constantly renewed to maintain the structure.

To successfully distribute the genetic material, spindles need to have the right length. Previous research has shown that the length of a spindle adapts to the size of a cell – the larger the cells, the larger the spindles. However, in very large cells, such as the cells of an embryo when they first divide, spindles have an upper size limit. It is thought that specific proteins produced by the chromosomes help to regulate the formation of new microtubules and thereby also influence the size of the spindle. However, until now it was not clear how exactly they do so and if this also sets the upper size limit.

To further investigate microtubule renewal and its relation to spindle size, Decker et al. used spindles assembled in cell extracts from the eggs of the African clawed frog. The results showed that the new microtubules grow off the existing ones, like new branches of a tree. The branching happens when the established microtubules interact with specific molecules emitted by the chromosomes, and the concentration of these molecules decreases with distance from the chromosomes. This concentration gradient regulates how many microtubules grow at different distances from the chromosomes and so sets the size of spindles.

These findings help us to understand how biological structures are built out of dynamic and short-lived components. Moreover, a better understanding of how mitotic spindles grow might eventually help to develop new treatments for cancer and other diseases.

https://doi.org/10.7554/eLife.31149.002

Introduction

A general class of problems in biology is related to the emergence of size and shape in cells and tissues. Reaction diffusion mechanisms have been broadly successful in explaining spatial patterns in developmental biology as well as some instances of intracellular structures (Turing, 1952; Howard et al., 2011). The mitotic spindle, a macromolecular machine responsible for segregating chromosomes during cell division, is thought to be a classic example of such reaction diffusion processes. A diffusible gradient of the small GTPase Ran emanating from chromosomes has been shown to trigger a cascade of events that result in the nucleation of microtubules, the main building blocks of the spindle (Kaláb et al., 2006; Caudron et al., 2005). The spatial distribution of microtubule nucleation is key for understanding size and architecture of large spindles. This is because microtubules in these spindles are short and turnover rapidly in comparison to the entire structure (Redemann et al., 2017; Brugués et al., 2012; Needleman et al., 2010). The mechanisms underlying the spatial regulation of microtubule nucleation, however, are still unclear (Prosser and Pelletier, 2017; Petry, 2016). One possibility is that the interplay between Ran-mediated nucleation and microtubule turnover governs spindle assembly (Kaláb et al., 2006; Caudron et al., 2005). However, the role of the Ran gradient in determining spindle size is still controversial. For instance, in cell culture systems, the length scale of the Ran gradient does not correlate with spindle size (Oh et al., 2016). A second possibility is that autocatalytic growth accounts for spindle assembly via microtubule-stimulated microtubule nucleation (Petry et al., 2013; Goshima et al., 2008; Loughlin et al., 2010; Ishihara et al., 2016). However, autocatalytic mechanisms suffer from the fact that their growth is hard to control. Although autocatalytic growth can be regulated by limiting the catalyst, such mechanisms are unlikely to function in the large cells of developing eggs such as Xenopus, where resources are not limiting (Crowder et al., 2015). Understanding the role of microtubule nucleation in setting the size of spindles is limited by the fact that little is known about the rate, distribution, and regulation of microtubule nucleation in spindles (Prosser and Pelletier, 2017; Petry, 2016). This is partly because of the lack of methods to measure microtubule nucleation in spindles. Here, we measured microtubule nucleation in spindles assembled in Xenopus laevis egg extract using laser ablation. We show that microtubule nucleation is spatially dependent and requires physical proximity to pre-existing microtubules. Our findings are consistent with a theoretical model in which autocatalytic microtubule nucleation is regulated by the amount of the active form of spindle assembly factors. This mechanism provides a finite size for spindles even when resources are not limiting.

Results

Microtubule nucleation is spatially regulated

Microtubules grow from the plus ends while minus ends remain stable (Howard, 2001). Thus, the location of minus ends functions as a marker for microtubule nucleation. However, in spindles microtubules constantly flux towards the poles (Mitchison, 1989), and measuring the location of a microtubule minus end at a particular time does not correspond to its original site of nucleation (Brugués et al., 2012). To decouple microtubule transport from microtubule nucleation, we inhibited kinesin-5 (Eg5) in spindles assembled in Xenopus laevis egg extracts. This inhibition stops microtubule transport and leads to the formation of radially symmetric monopolar spindles (monopoles) that have a similar size as regular spindles (Miyamoto et al., 2004; Skoufias et al., 2006) (Figure 1A, Figure 1—figure supplement 1 and Video 1). The location of minus ends in these monopoles corresponds to the location of microtubule nucleation.

Figure 1 with 3 supplements see all
Microtubule nucleation in monopolar spindles is spatially regulated.

(A) Fluorescence image of a monopolar spindle (left), and single-molecule fluorescent tubulin and EB1-GFP (right). (B) Circular laser cut and corresponding differential intensity depolymerization front at different times. (C) Radial sum of differential intensities at different time points (from dark to light blue) of one cut at a radius of 19 μm from the center. The area under each curve equals the mass of microtubules depolymerized per time interval of 2 s. (D) Nucleation profile of monopolar spindles (N = 117 cuts, mean ± SD).

https://doi.org/10.7554/eLife.31149.003
Video 1
EB1-GFP comets in monopolar spindles.

Pre-assembled monopolar spindles (200 μM STLC) were imaged after adding 0.2 µg/ml EB1-GFP. Individual frames were recorded every second with subsequent averaging of 3 frames.

https://doi.org/10.7554/eLife.31149.007

Three independent measurements show that inhibiting microtubule transport does not affect dynamic parameters of microtubules. First, microtubules in these structures polymerize at 20.9 ± 5.1 µm/min (N = 7 monopoles, Figure 1A and Video 1), which is indistinguishable from the polymerization velocity in spindles, 22.7 ± 8.4 µm/min (N = 4 spindles). Second, microtubules from monopolar and control spindles depolymerize at the same velocity (33.5 ± 6.4 µm/min and 35.9 ± 7.3 µm/min respectively, see Figure 1—figure supplement 2). Third, microtubule lifetime distributions of monopolar spindles, measured by single-molecule microscopy of tubulin dimers, give an average lifetime of 19.8 ± 2.2 s, consistent with similar measurements in regular spindles (Needleman et al., 2010) (Methods and materials and Video 2).

Video 2
Tubulin speckles in a monopolar spindle.

Pre-assembled monopolar spindles (200 µM STLC) were visualized by adding 1 nM purified Atto565 frog tubulin. Images were taken every second with subsequent averaging of 4 frames.

https://doi.org/10.7554/eLife.31149.008

To localize microtubule nucleation events, we measured the density of minus ends in monopolar spindles by analyzing synchronous waves of microtubule depolymerization from laser cuts similar to Ref. (Brugués et al., 2012). Briefly, cut microtubules rapidly depolymerize from the newly generated plus ends, while the new minus ends remain stable. The minus end density at the location of the cut can then be obtained from the decrease of the microtubule depolymerization wave, but as opposed to Ref. (Brugués et al., 2012), our method resolves the minus end locations with a single laser cut (see Figure 1B–C, Figure 1—figure supplement 3, Figure 2—figure supplement 1, Video 3Video 4; a detailed explanation of the method can be found in the Methods and materials and Appendix 1). We define the microtubule nucleation profile at a distance r from the center of the monopole as the number of minus ends per unit length at r divided by 2πr. We measured the microtubule nucleation profile across the entire structure by performing laser cuts at different distances from the center of the monopoles. These measurements revealed that microtubule nucleation extends throughout monopoles, with the highest nucleation near the center and monotonically decreasing far from the center (see Figure 1D), indicating that the strength of microtubule nucleation is spatially regulated.

Video 3
Depolymerization wave after a cut in a fluorescently labeled monopole.

200 µM STLC, 150 nM Atto565-tubulin. Images were acquired every 500 ms.

https://doi.org/10.7554/eLife.31149.009
Video 4
Fluorescence intensity loss after a cut in a fluorescently labeled monopole as the depolymerization wave propagates.

200 µM STLC, 150 nM Atto565-tubulin. We calculated the differential intensities for a time interval of 2 s. For purposes of visualization, negative intensity values were set to zero.

https://doi.org/10.7554/eLife.31149.010
Video 5
Tubulin speckles in a monopolar spindle (200 µM STLC) treated with 30 µg/mg anti-MCAK antibodies.

The field of view only shows a quarter of the entire structure. Speckles were created by adding 1 nM purified Atto565 frog tubulin to pre-assembled structures. In every movie, four frames were averaged during the acquisition.

https://doi.org/10.7554/eLife.31149.011
Video 6
EB1-GFP comets in MCAK-inhibited monopoles.

Pre-assembled monopolar spindles (200 µM STLC) were treated with 30 µg/mg anti-MCAK antibodies and imaged after adding 0.2 µg/ml EB1-GFP.

https://doi.org/10.7554/eLife.31149.012

Microtubule nucleation depends on the stability of microtubules

Several mechanisms have been proposed to regulate microtubule nucleation. From a biophysical perspective, these mechanisms can be categorized into two scenarios: (i) microtubule-dependent nucleation, in which a pre-existing microtubule stimulates the nucleation of a new microtubule, or (ii) microtubule-independent nucleation, in which factors other than pre-existing microtubules (e.g. diffusible cues in the cytoplasm) stimulate nucleation (Prosser and Pelletier, 2017; Petry, 2016; Petry et al., 2013; Goshima et al., 2008; Clausen and Ribbeck, 2007; Ishihara et al., 2014a; Carazo-Salas et al., 2001).

If microtubule nucleation depends on pre-existing microtubules, altering microtubule stability should change the nucleation profile – a microtubule that exists for a longer time would have a higher probability to stimulate the creation of more microtubules. To test this scenario, we increased microtubule stability by inhibiting the depolymerizing kinesin MCAK (Walczak et al., 1996) using antibodies. MCAK inhibition led to a dramatic increase in monopole size (see Figure 2A). Both the average length and stability of microtubules increased threefold after inhibition (Figure 2B–C and Figure 2—figure supplement 1) as assessed by laser ablation (8.0 ± 0.3 µm versus 23.6 ± 3.6 µm, see Methods and materials and [Brugués et al., 2012]) and single microtubule lifetime imaging (19.8 ± 2.2 s versus 60.4 ± 4.4 s), Video 2Video 5 and Supplementary Figure 2. These measurements are consistent with MCAK modifying the catastrophe rate (Walczak et al., 1996; Tournebize et al., 2000). We measured microtubule nucleation in this perturbed condition and found that the nucleation profile extends further from the center of the monopole, has a larger amplitude, and decays over a larger distance with respect to control monopoles (Figure 2D). Therefore, the number and spatial distribution of nucleated microtubules does indeed scale with microtubule stability in monopolar spindles, which is inconsistent with microtubule-independent nucleation. One possibility is that MCAK-inhibition could by itself increase nucleation independently of microtubules. However, this would only lead to an overall increase of the amplitude of microtubule nucleation, which alone would not be sufficient to account for the dramatic change in the spatial dependence of the nucleation profile we observe in Figure 2D. Thus, microtubule nucleation in these structures depends on the presence and dynamics of microtubules.

Figure 2 with 1 supplement see all
Microtubule nucleation depends on the stability of microtubules.

(A) Inhibition of MCAK leads to larger steady-state monopoles. Scale bar = 20 µm (B) Microtubule length distributions measured from laser ablation and fitted to an exponential (mean ± SD). (C) Normalized histograms of microtubule lifetimes of control (N = 5331 speckles, five structures) and MCAK-inhibited monopoles (N = 7289 speckles, three structures), and corresponding first-passage time fits (see Methods and materials). (D) Nucleation profile of control (N = 117 cuts) and MCAK-inhibited monopoles (N = 74 cuts) in arbitrary units that are consistent in both structures (mean ± SD). The inset shows both nucleation profiles multiplied by the circumference length at each radius, which corresponds to the total microtubule nucleation at that distance from the center of the monopole.

https://doi.org/10.7554/eLife.31149.013

Microtubule nucleation requires physical proximity to pre-existing microtubules

The presence and dynamics of microtubules could alter microtubule nucleation in two ways: microtubules could nucleate indiscriminately in the cytoplasm without requiring microtubules, but their presence concentrates active nucleators through transient interactions with microtubules (Oh et al., 2016), or alternatively, microtubules could directly nucleate new microtubules, requiring active nucleators to bind to microtubules to initiate nucleation. In the latter case, the presence of a microtubule is essential for the nucleation process, whereas in the former, microtubules can still nucleate in the absence of microtubules. To test whether microtubule nucleation requires physical proximity to pre-existing microtubules (e.g., a branching process [Petry et al., 2013]), we locally blocked microtubule polymerization by adding inert obstacles near the center of monopoles, at locations where nucleation should be expected according to our measurements (Figures 2D and 3A, and Video 7). These localized obstacles cannot prevent the diffusion of nucleators, but would prevent microtubules that polymerize towards them to extend further. Consistent with microtubule-stimulated nucleation, the presence of these obstacles inhibited nucleation of new microtubules behind the obstacles, as in a shadow cast by light, whereas microtubules nucleated further around the obstacles, creating a sharp boundary, see Figure 3A. These results suggest that monopolar spindles grow to a size larger than an individual microtubule by microtubule-stimulated microtubule nucleation in physical proximity to pre-existing microtubules, which creates an autocatalytic wave of microtubule growth.

Figure 3 with 2 supplements see all
Microtubule nucleation requires physical proximity to pre-existing microtubules.

(A) Inert obstacles (fluorocarbon oil microdroplets or polystyrene beads) immobilized to coverslips selectively block microtubule nucleation. Left: Schematic outcomes depending on whether new microtubules are nucleated in physical proximity from pre-existing microtubules (top) or not (bottom). Middle: Two time points of a microtubule structure with labeled tubulin (red) and EB1-GFP (green) growing around immobilized frog sperm chromosomes. The oil microdroplet is highlighted with a dashed ellipse. Right: Normalized line profiles of shadow regions behind six different obstacles (colored dots). The intensity profiles were normalized to the average intensity outside the obstacles and rescaled to the radius of the obstacle. Gray lines show mean ± SD. (B) Left: Addition of RanQ69L to extract homogeneously activates nucleation and creates mini asters after 20 min (22). Middle: Addition of RanQ69L to monopoles leads to immediate growth of new microtubules from the pre-existing monopoles. Right: Quantification of radial fluorescence intensity profiles at different time points of the growing monopole shown in the middle.

https://doi.org/10.7554/eLife.31149.015
Video 7
Monopole growing against an obstacle.

The microtubule structure is labeled with tubulin Atto565 (red) and EB1-GFP (green) and grows around immobilized frog sperm chromosomes. The bead is attached to the surface and highlighted with an arrow.

https://doi.org/10.7554/eLife.31149.018

The amount of active nucleators limits the autocatalytic growth of spindles

For a microtubule structure to have a finite size through an autocatalytic process, each microtubule at the periphery must create on average less than one microtubule at steady state, otherwise the number of microtubules would increase exponentially and the structure would grow unbounded (Ishihara et al., 2016). However, measurements of the temporal evolution of microtubule mass in spindles show indeed an initial phase of exponential growth (Figure 3—figure supplement 1 and (Clausen and Ribbeck, 2007; Dinarina et al., 2009). This is also consistent with the observation of microtubules creating more than one microtubule on average when inducing bulk microtubule branching by adding TPX2 and constitutively active Ran (RanQ69L) in extracts (Petry et al., 2013). These observations raise the question of how spindles reach a finite size through autocatalytic growth (as in the control and MCAK-inhibited monopoles). One possibility is that microtubule dynamics change as a result of limiting amounts of tubulin or microtubule-associated proteins (Good et al., 2013; Hazel et al., 2013). However, since our cell-free system is not confined, availability of tubulin and microtubule-associated proteins is not limiting. Furthermore, inhibiting MCAK leads to larger monopoles with a microtubule polymerization velocity that is indistinguishable from smaller control monopoles (20.9 ± 5.1 µm/min and 18.8 ± 5.4 µm/min respectively, Video 6, Video 1, Figure 3—figure supplement 2 and Table 1), suggesting that the availability of tubulin appears not to be diffusion-limited. Finally, microtubule dynamics do not change spatially throughout MCAK-inhibited monopoles (Figure 3—figure supplement 2), indicating that spatial variations of tubulin amount or microtubule dynamics cannot explain the finite size of these structures.

Another possibility is that microtubule nucleation is limiting. It has been shown that RanGTP is required for spindle assembly. RanGTP is created only in the vicinity of chromosomes (through the ran nucleotide exchange factor RCC1), which in turn releases spindle assembly factors (SAFs) responsible for nucleating microtubules (Kaláb et al., 2006; Caudron et al., 2005). Since the active SAFs are naturally limited by their spatially restricted generation, a limiting amount of an active microtubule nucleation factor would therefore be a good candidate as the limiting component for both autocatalytic growth and size regulation. To test this idea, we added constitutively active Ran (RanQ69L), to pre-existing monopolar spindles. A limiting pool of active nucleators implies that (i) activating nucleators everywhere in the cytoplasm would lead to unbounded microtubule growth in the monopole (similar to large interphase asters in embryos [Wühr et al., 2010]), and (ii) new microtubules should nucleate from the pre-existing microtubules of the structure. Adding RanQ69L to pre-existing monopoles immediately started nucleation of new microtubules preferentially at the edge of the pre-existing structures in a wave-like fashion, consistent with microtubule-stimulated growth (Figure 3B and Videos 8 and 9). This result further suggests that other limiting components that regulate microtubule dynamics alone cannot account for this growth. Taken together, these measurements show that the amount of active nucleators, which is limited by the availability of RanGTP, limits the size of monopolar spindles and is responsible for the bounded growth of these structures.

Video 8
Ran asters after addition of 30 µM RanQ69L to extract.

Microtubules were labeled with 150 nM Atto565-tubulin. Movie starts 20 min after adding RanQ69L.

https://doi.org/10.7554/eLife.31149.019
Video 9
Growth of pre-existing monopoles after addition of 10 µM RanQ69L.

Monopolar spindles (200 µM STLC, labeled with 150 nM Atto565-tubulin) were imaged on a PLL-g-PEG passivated slide immediately after adding RanQ69L. Scale bar = 20 µm.

https://doi.org/10.7554/eLife.31149.020

Autocatalytic microtubule nucleation model

To test whether a limited pool of active nucleators can quantitatively account for the size and microtubule nucleation in these structures, we developed a biophysical model of autocatalytic microtubule nucleation (see Figure 4A and Appendix 1). In our model, inactive nucleators are present throughout the cytoplasm and can be activated at the surface of chromosomes, which is a simplification of the activation of SAFs by RanGTP. The total amount of active nucleators depends on the balance between the rate of activation at the chromosomes and the rate of inactivation (accounting for sequestration, hydrolysis, or other processes). Once activated at the chromosomes, nucleators can diffuse in the cytoplasm, bind, and unbind from microtubules. When bound to microtubules, active nucleators can nucleate new microtubules at a certain rate, and the newly nucleated microtubules maintain the same polarity as the mother microtubule (Petry et al., 2013). This process leads to an autocatalytic wave as a consequence of the self-replicating activity of an extended object. In contrast to a reaction diffusion process, the front propagation is independent of microtubule diffusion and only depends on microtubule dynamics.

Figure 4 with 1 supplement see all
Model for microtubule-stimulated nucleation.

(A) Inactive nucleators (orange circles) are activated around DNA. As active nucleators diffuse (green circles), they can bind and unbind microtubules (red lines). Once bound, they can nucleate a new microtubule with a certain probability. Active nucleators become inactive at a constant rate. (B) Radial microtubule density profiles measured from fluorescent images (mean ± SD, Nmonopoles = 40 (blue), Na-MCAK = 18 (gray)) and corresponding model fit to the MCAK-inhibited and prediction to control monopoles (see Appendix 1). The ratio of the microtubule densities for control and MCAK-inhibited monopoles was determined using structures from the same extract reaction. (C) Parameter-free rescaling of the microtubule density profiles predicted by the model: ρC=ρMexp[(1/M-1/C)x], where ρC, C and ρM, M are the density and length of microtubules for the control and MCAK-inhibited structures, respectively, and x is the distance from the center of the structure. In the graph, blue corresponds to the density profile of control monopoles and gray to the rescaled density profile of MCAK-inhibited monopoles. (D) Data and predictions (orange) for the nucleation profiles of control (blue) and MCAK-inhibited monopoles (gray) up to a global nucleation amplitude, and flux-corrected regular spindles (green) (mean ± SD, Ncontrol = 117 , Na-MCAK = 74, Nspindle = 36 cuts).

https://doi.org/10.7554/eLife.31149.021

In our model, the amount and dynamics of active nucleators are the same for both control and MCAK-inhibited monopoles, leading to the prediction that the two microtubule density profiles would only differ in a parameter controlling the microtubule length or lifetime (see Appendix 1). In particular, both profiles should scale to each other without any fitting parameters by changing the microtubule length as measured independently by laser ablation. To test this prediction, we measured the radial profile of microtubule density of control and MCAK-inhibited monopoles (Figure 4B): These microtubule density profiles are qualitatively different –the density of MCAK-inhibited monopoles increases initially and decreases after reaching a maximum, whereas the control monopole decreases monotonically from the origin. Remarkably, both profiles collapse into each other after the parameter-free rescaling of the MCAK-inhibited monopole predicted by the model (see Appendix 1 and Figure 4C). To test the model beyond scaling, we fit the MCAK-inhibited profile with two independent parameters and an arbitrary amplitude of the density profile, which agrees quantitatively with the data (see Appendix 1 and Figure 4B). By fixing all parameters to the values obtained by this fit (which are the same for the control monopole, see Appendix 1, Table 2) and using the measured average microtubule length for the control monopole (Methods and materials, Table 1), the model predicts the control monopole microtubule profile. Finally, we can also predict the MCAK-inhibited and control microtubule nucleation profiles from the fitted parameters up to an arbitrary amplitude (common for both profiles) (Figure 4D). Remarkably, this prediction is also consistent with flux-corrected microtubule nucleation in regular spindles obtained by laser ablation (see Methods and materials, Figure 4D green circles, Videos 10 and 11), showing that the same nucleation mechanism holds for regular spindles. Thus, our model for autocatalytic microtubule nucleation accounts for both the microtubule density and nucleation profiles.

Table 1
Measurements of microtubule dynamics in spindles and monopoles.
https://doi.org/10.7554/eLife.31149.023
Microtubule dynamicsSpindleMonopoleMCAK-inhibited monopole
Lifetime (s)16 ± 220 ± 260 ± 4
Polymerization velocity (μm/min)23 ± 821 ± 519 ± 5
Depolymerization velocity (μm/min)36 ± 733 ± 646 ± 8
  1. Reference Needleman et al., 2010.

Table 2
Parameters used in the model of autocatalytic microtubule nucleation.
https://doi.org/10.7554/eLife.31149.024
ParameterSymbolValueProcedure
Microtubule turnover rate control monopole (s-1)ΘC0.05 ± 0.01Single molecule microscopy
Microtubule turnover rate MCAK-inhibited monopole (s-1)ΘM0.016 ± 0.001Single molecule microscopy
Microtubule length control monopole (μm)C8.0 ± 0.3Laser ablation
Microtubule length MCAK-inhibited monopole (μm)M24 ± 4Laser ablation
Length scale gradient unbound nucleators (μm)u24.9 ± 0.5Fit to the model
Branching parameter (dimensionless)α2.38 ± 0.01Fit to the model
Microtubule density at the center of the monopole (a.u.)ρ(0)4058 ± 64Fit to the model
Video 10
Depolymerization waves after a cut in a fluorescently labeled spindle.

150 nM Atto565-tubulin. Images were acquired every 500 ms.

https://doi.org/10.7554/eLife.31149.025
Video 11
Fluorescence intensity loss after a cut in a fluorescently labeled spindle as the depolymerization waves propagate.

150 nM Atto565-tubulin. We calculated the differential intensities for a time interval of 2 s. For visualization purposes, negative intensity values were set to zero.

https://doi.org/10.7554/eLife.31149.026

Discussion

Our data and model are consistent with an autocatalytic mechanism in which microtubule-stimulated microtubule nucleation controls growth in Xenopus laevis egg extract spindles. This process is spatially regulated by a gradient of active nucleators that is established by the interplay between the Ran gradient and microtubule dynamics. Microtubules regulate the nucleator activity because they act as the substrate where active nucleators need to bind to nucleate microtubules. Chromatin acts as a trigger for an autocatalytic wave of microtubule nucleation, and at the same time limits spindle size by controlling the amount of active nucleators through RanGTP. This suggests that the amount of active Ran can tune spindle length, and resolves its controversial relation to spindle length regulation: while a diffusion and inactivation process has a characteristic length scale independent of the amplitude of the gradient – set by the ratio of the squared root of the diffusion and inactivation rate – here we show that both the length scale and amplitude of the gradient of nucleators are involved in regulating the size and mass of spindles. Since the length scale of the gradient is amplified by microtubule-stimulated nucleation, the relevant length scale for setting the size is the distance at which a microtubule generates one or fewer microtubules. Our proposed mechanism therefore allows regulation of spindle size and mass by two means, although microtubule nucleation is the principal control parameter, microtubule dynamics can still fine tune the spindle length (Reber et al., 2013). Although our results are restricted to Xenopus laevis spindles, we hypothesize that a similar mechanism may also apply to other spindles with a large number of microtubules. This would be consistent with the fact that components involved in microtubule branching have been identified in many eukaryotic systems (Dasso, 2002; Hsia et al., 2014; Sánchez-Huertas and Lüders, 2015). However, further experiments are needed to test this hypothesis.

An autocatalytic nucleation process implies that microtubule structures are capable of richer dynamical behaviors than those arising from the classic view of random nucleation in the cytoplasm via a diffusible gradient. Beyond producing finite-sized structures like spindles and ensuring that new microtubules keep the same polarity as the pre-existing ones, it also allows for a rapid switch into unbounded wave-like growth if nucleators become active throughout the cytoplasm. Indeed, the growth of large interphase asters has been hypothesized as a chemical wave upon Cdk1 activation (Chang and Ferrell, 2013; Ishihara et al., 2014b). These properties, characteristic of excitable media, provide a unified view for the formation of spindles and large interphase asters in embryos (Ishihara et al., 2014a) within a common nucleation mechanism. However, microtubule nucleation differs from regular autocatalytic processes in reaction-diffusion systems such as Fisher-waves and Turing mechanisms (Turing, 1952; Fisher, 1937) in that its growth does not rely on diffusion or advection. Instead, the process of branching displaces the center of mass of the structure. Thus, it emerges as consequence of the finite extension and dynamics of the reactant (microtubules). The interplay between autocatalytic growth and fluxes driven by motors could lead to general principles of pattern formation and cytoskeletal organization in cells.

Methods and materials

Cytoplasmic extract preparation, spindle assembly and biochemical perturbations

Cytostatic factor (CSF)-arrested Xenopus laevis egg extract was prepared as described previously (Hannak and Heald, 2006; Murray, 1991). In brief, unfertilized oocytes were dejellied and crushed by centrifugation. After adding protease inhibitors (LPC: leupeptin, pepstatin, chymostatin) and cytochalasin D (CyD) to a final concentration of 10 µg/ml each to fresh extract, we cycled single reactions to interphase by adding frog sperm (to 300–1000 sperm/µl final concentration) and 0.4 mM Ca2+ solution, with a subsequent incubation of 1.5 hr. While fresh CSF extract containing LPC and CyD was kept on ice, all incubation steps were performed at 18–20°C. The reactions were driven back into metaphase by adding 1.3 volumes of fresh CSF extract (containing LPC and CyD). Spindles formed within 1 hr of incubation. To inhibit kinesin-5 (Eg5) in spindles, S-Trityl-L-Cysteine (STLC) was added to the reactions to a final concentration of 200 µM . Transitions to monopolar spindles were observed within 30–60 min of incubation. To inhibit the depolymerizing kinesin MCAK in monopolar spindles, we added anti-MCAK antibodies to a final concentration of 30 µg/ml (kind gift from R. Ohi). MCAK-inhibited structures reached their steady-state after 20 min. Alternatively, we added RanQ69L (kind gift from K. Ishihara) to pre-formed monopoles to a final concentration of 30 or 10 µM and imaged immediately. In the control reactions, the same concentrations were added to extract reactions in the absence of pre-formed structures and imaged after 20 min incubation. The lower the RanQ69L concentration the later Ran asters formed. Conversely, if a pre-existing structure was present, microtubule nucleation immediately started at the periphery with subsequent growth of the structure. The growth of pre-existing monopolar spindles stopped with the appearance of Ran asters in bulk (after 20 min depending on the concentration of RanQ69L), consistent with the sequestering of the additional nucleators activated by RanQ69L. Prior to imaging, Atto565 labeled purified porcine tubulin (purified according to Ref. [Castoldi and Popov, 2003]) and Höchst 33342 were added to the reactions to a final concentration of 150 nM and 16 µg/ml, respectively, to visualize microtubules and DNA.

Image acquisition

Control and MCAK-inhibited monopolar spindles were imaged using a Nikon spinning disk microscope (Ti Eclipse), an EMCCD camera (Andor iXon DU-888 or DU-897), a 60 × 1.2 NA water immersion objective, and the software AndorIQ for image acquisition. The room was kept at constant 20C. Monopolar spindles after the addition of RanQ69L were imaged using a Nikon wide-field epifluorescence microscope (Ti Eclipse), an sCMOS camera (Hamamatsu Orca Flash 4.0), and a 20 × 0.75 NA objective. In this case, image acquisition was performed using µManager (Edelstein et al., 2014). The growth of microtubule structures in the presence of obstacles was imaged using a Nikon total internal reflection fluorescence (TIRF) microscope (Ti Eclipse), equipped with an Andor iXon3 DU-897 BV back-illuminated EMCCD camera, a 100 × 1.49 NA oil immersion objective, and the Nikon software NIS elements.

Laser cutting procedure and image analysis

The femtosecond laser ablation setup was composed of a mode-locked Ti:Sapphire laser (Coherent Chameleon Vision II) oscillator coupled into the back port of the Nikon spinning disk microscope and delivering 140 fs pulses at a repetition rate of 80 MHz. Cutting was performed using a wavelength of 800 nm and typically a power of 150 mW before the objective. The sample was mounted on a piezo stage that positioned the sample in 3D with sub-micrometer precision. The laser cutting process was automatically executed by a custom-written software that controlled the mechanical shutter in the beam path and moved the piezo stage to create the desired shape of the cut. Lines and circular cuts were performed in several planes to cover a total depth of 1–2 µm around the focal plane. We adapted the size and geometry of the cut shapes to each spindle or monopolar structure. Cutting was finished within 2 s. Images were acquired at least every 0.5 s during the cutting procedure as well as for 1 min after the cut. The depolymerization wave typically disappeared within 30 s. Each microtubule structure was cut only once.

We analyzed the depolymerization waves using a custom-written Python code. Briefly, for a given cut at position r, we subtracted the intensities of images (raw data) with a time difference δt of 2–3 s to get the differential intensities I(x,ϕ,t;r), where x is the radial coordinate, ϕ is the angle, and t is the time after the cut (see Figure 1B and Figure 1—figure supplement 3). I corresponds to the quantity of microtubules that depolymerized during the time interval δt. Next, we integrated the differential intensities over ϕ and plotted these integrals with respect to the radial coordinate x. The depolymerization wave appears as a peak that is traveling towards the center of the monopole and broadening over time (see Figure 1C). We fitted Gaussians to these peaks and plotted the area under these Gaussians over time A~(t,r) (see Laser ablation method and Figure 1—figure supplement 3C). We fitted an exponential to the area decays over distance from the cut, and normalized the decays by the amplitude at the location of the cut. The slope at the position of the cut is proportional to the number of minus ends at this location (see Laser ablation method). To take the local microtubule density into account, we multiplied the normalized slopes at the position of the cut by the averaged angular integral of the microtubule fluorescence intensity at this position. This gives the amount of minus ends per unit length nc(y,r) at y given a cut performed at r. To obtain the two dimensional minus end density (number per unit length squared), we divided by 2πr, which corresponds to the nucleation profile (notice that the nucleation profile has arbitrary units). Averaged microtubule density profiles were obtained from 82 and 12 fluorescence profiles of monopoles and MCAK-inhibited monopoles, respectively. Additionally, we used angular fluorescence profiles of control and MCAK-inhibited structures from the same extract reaction to determine the ratio between these two nucleation profiles and enable a reliable comparison. Finally, in order to obtain the microtubule length distribution, we fitted an exponential function to nc(y,r) as a function of the cut distance r. The slope of nc(y,r) at r is proportional to the number of microtubules with minus ends at y and plus ends at r (see Appendix 1), which after normalization gives the microtubule length distribution.

Laser cuts in bipolar spindles were similarly analyzed. Instead of circular cuts, we performed linear cuts perpendicular to the long axis of the spindle, which induced two depolymerization waves traveling towards the poles (due to the mixed polarity of microtubules). The waves were analyzed by integrating the differential intensities along the direction of the cut and plotting these integrals as a function of spindle length. This again lead to the depolymerization waves appearing as peaks that are traveling towards the poles and broadening over time. The subsequent analysis is exactly the same as for monopolar spindles continuing by fitting Gaussians to these peaks as described above.

Analysis of microtubule dynamics

The microtubule polymerization velocity was measured by adding EB1-GFP to extract reactions to a final concentration of 0.2 µg/ml and analyzing kymographs drawn along the growth direction of a microtubule (40 kymographs from seven control monopoles obtained from different reactions on two different days, 68 kymographs from five MCAK inhibited monopoles obtained from different reactions on the same day). Microtubule depolymerization velocities were obtained by analyzing the velocity of the fronts after the laser cuts. The maxima of the fitted Gaussians (see Laser cutting procedure and image analysis) were used to determine the position of the depolymerization front as a function of time, which was fitted to a linear function. The slope corresponded to the depolymerization velocity of the cut microtubules, which was found to be constant for each laser cut. We measured microtubule lifetimes by adding Atto565 purified frog tubulin (purified according to Ref. [Groen and Mitchison, 2016]) to a final concentration of 1 nM and subsequent tracking of the speckles using the MOSAIC suite, (Sbalzarini and Koumoutsakos, 2005) (5331 speckles from five monopoles from different reactions of 3 different days, 7289 speckles from 3 MCAK-inhibited monopoles from different reactions of the same day). We included only those speckles that appeared and disappeared during the length of the movie (10 min). To calculate the average lifetime of microtubules, we used the lifetime distribution 𝒫(t) of a diffusion and drift process to fit it to our data according to 𝒫(t)t-3/2e-t/τ, where τ/4 is the expected lifetime of a microtubule of average length, Ref. (Bicout, 1997; Needleman et al., 2010). A summary of the different measured values is given in Table 1.

Obstacle assay to block microtubule nucleation

Coverslips were cleaned by sonication in 2% Hellmanex and used to assemble parafilm channels of 3 mm width. Every step of the assay was completed by an incubation at room temperature (10 min up to several hours) and washing of the channel with BRB80 (80 mM PIPES, 1 mM MgCl2, 1 mM EGTA). Channels were subsequently filled with anti-biotin antibodies, Puronic F-127 to block the remaining surface, biotinylated Xenopus laevis sperm, biotinylated fluorocarbon oil microdroplets (produced as described in Ref. [Lucio et al., 2015]) or biotinylated polystyrene beads acting as inert obstacles, and freshly prepared extract including Atto565 labeled purified porcine tubulin (150 nM final), EB1-GFP (0.2 µg/ml final), and sodium orthovanadate (0.5 mM final concentration). Image acquisition was performed on a TIRF microscope.

Measuring the microtubule mass over time

To measure the microtubule mass over time, we added frog sperm to extract and immediately started to acquire z-stacks around the DNA over time. After subtracting the background, we integrated the fluorescence intensity of the labeled microtubules over all z-planes and plotted it as a function of time.

Passivation of coverslips with PLL-g-PEG

Passivation of coverslips with Poly-L-lysine-g-polyethylene glycol (PLL-g-PEG) was performed according to Ref. (Field et al., 2017). In brief, coverslips were placed in a drop of 0.1 mg/ml PLL-g-PEG in 10 M HEPES pH 7.4 on Parafilm for 20 min at room temperature. They were then washed three times in distilled water and dried with a nitrogen jet.

Appendix 1

Laser ablation method

We quantify the total amount of microtubule depolymerization as a function of time t from a cut at a distance r from the center of the monopolar spindle between two frames separated by δt by summing the total differential intensity (see Figure 1B,C, and Figure 1—figure supplement 1),

(1) A~(t,r)=nd(t,r)vdσfδt,

where nd(t,r) is the total number of depolymerizing microtubules from the cut at r, vd the depolymerization velocity and σf the fluorescence per unit length of microtubule. We define the total microtubule depolymerization rate by A(t,r)=A~(t,r)/δt. The integrated differential intensity along the angular coordinate ϕ has a very well defined peak along the x radial coordinate that moves as a function of time (see Figure 1C and Figure 1—figure supplement 1), allowing to express the total microtubule depolymerization rate as a function of the position of the peak y(t) with respect to the monopole center, A(y,r) (see Figure 1—figure supplement 1). As the front moves, the total microtubule depolymerization rate decreases (see Figure 1C). The derivative with respect to the position of the front is: 

(2) dA(y,r)dy=-dnd(y,r)dyvdσf=nc(y,r)vdσf.

Where nc(y,r) is the number of minus ends per unit length at a distance y from the center, from microtubules cut at a distance r. Therefore,

(3) nc(y,r)=1vdσfdA(y,r)dy

The number of minus ends per unit length nc(y,r) is related to the number density of microtubules ρ(y,η), with minus ends at y and plus ends at η (number per unit length squared), by:

(4) nc(y,r)=rρ(y,η)dη

The actual number of minus ends (number per unit length) at a position r, n(r), which is proportional to the total microtubule nucleation at that location in the absence of transport, is by definition rρ(r,η)dη, where we integrate for all possible lengths of microtubules with minus ends at r. This quantity is related to the number of minus ends of microtubules cut at r evaluated at the position of the cut, nc(r,r):

(5) n(r)rρ(r,η)dη=nc(r,r)

In order to obtain the two-dimensional density of minus ends (or nucleation profile) in the polar geometry of the monopole, we divide n(r) by 2πr. Finally, we can obtain the probability distribution P(y,) of microtubules with minus ends at a position y and length as:

(6) P(y,)=ρ(y,+y)0ρ(y,+y)d.

In the particular case of monopolar spindles, since microtubule transport is inhibited P(y,)P() and the microtubule length distribution does not depend on the position of the minus ends. This was experimentally verified and it is shown in Figure 2—figure supplement 1.

Appendix 2

Physical model for autocatalytic microtubule nucleation

We consider a simplified model of autocatalytic microtubule nucleation. We define the microtubule bound and unbound populations of active nucleators (or active SAFs) as nb(x,t) and nu(x,t), respectively. When unbound, active nucleators can diffuse with diffusion coefficient D and become inactive with rate k0. Active nucleators can bind to microtubules with rate kb and unbind with rate ku. A bound nucleator, can nucleate a microtubule from a pre-existing microtubule with rate kbra. The average position at which an active nucleator will bind to a microtubule can be estimated as follows: We assume that nucleators can bind anywhere along a microtubule. Since our measurements showed that microtubule lengths are exponentially distributed with an average length (Figure 2B), a nucleator will bind on average at a distance from the minus end of the mother microtubule. Thus, the average location of nucleation coincides with the average location of the plus end of the mother microtubule. The density of microtubule plus ends is transported at the polymerization velocity vp (Dogterom and Leibler, 1993). Finally, we define the microtubule mass density as ρ(x,t)=0ρ~(x,l,t)dl, where ρ~ is the distribution of microtubules with length l at time t and plus ends at x. In our simplified description microtubules grow at velocity vp and disappear after a characteristic turnover rate Θ. We want to highlight the difference between vp and the front velocity of the growing structure. The latter depends on kbra and vanishes in the absence of autocatalytic nucleation (Figure 4—figure supplement 1). Given the previous considerations, the dynamics of the system read:

(7)tnu=D2nukbbnuρ+kunbk0nu(8)tnb=kbbnuρkunb(9)tρ=vpρ+kbranbΘρ

where b is a characteristic binding length scale for the active nucleators. Next, we will consider a one-dimensional problem with the spatial coordinate x being the radial coordinate from the center of the monopolar spindle. A more involved two-dimensional description of the problem is found to lead to similar results. Unbound nucleators are assumed to be activated with constant rate Γ at the surface of chromatin in the center of the monopole (x=0) (see Figure 4A). This leads to a boundary condition for the flux of active nucleators at the chromosomes which is expressed as -Dxnu|x=0=Γ. At steady state, Equation 8 leads to nb(x)=0nu(x)ρ(x), where 0bkb/ku. Using the last expression into Equation 7 and the boundary condition at x=0, at steady state we obtain: 

(10) nu(x)=Ae-x/u

where A=ΓDk0 is the amplitude of the gradient, proportional to the rate of activation Γ at the chromosomes, and uD/k0 is the characteristic length scale of the gradient of unbound active nucleators. Finally, by using Equation 9 we find the steady state microtubule density:

(11) ρ(x)=λ(x)e-x/

where λ(x)=ρ(0)exp[α(1-e-x/u)] is a lifetime-independent function, ρ(0) is the density of microtubules at x=0 and αΓ0kbravk0 is a dimensionless parameter. Since only bound nucleators can nucleate new microtubules, the nucleation process requires an initial source of microtubules acting as seeds for the autocatalytic growth. In our simplified model, this initial source corresponds to the boundary condition ρ(0). The origin of these seed microtubules could be due to spontaneous microtubule nucleation in the cytoplasm, centrosomes, or RanGTP-mediated nucleation in close proximity to chromosomes. One possibility is that the concentration of RanGTP close to the site of its production at the chromosomes is high enough to trigger spontaneous nucleation in the cytoplasm similar to the the case when constitutively active RanQ69L is added at sufficiently high concentration to the extract without pre-existing microtubule structures (Figure 3B). However, our measurements on microtubule nucleation in control and MCAK-inhibited structures shows that microtubule-independent microtubule nucleation is not sufficient to explain spindle growth or the spatial dependence of microtubule nucleation, and that microtubule independent nucleation can be accounted for as a boundary condition, suggesting that it is very localized in space.

There are two main length scales in the system: u which is dictated by the gradient of unbound active nucleators and does not depend on microtubule lifetime, and which is the mean microtubule length. From our results, the inhibition of the motor protein MCAK affects the lifetime Θ and length (see Figure 2B and C), thus not changing λ(x). Therefore, the model predicts that if the control monopole profile is given by ρC(x)=λ(x)e-x/C, the perturbed monopole profile reads ρM(x)=λ(x)e-x/M. The ratio of the two profiles follows:

(12) ρC(x)ρM(x)=exp[x(1M-1C)].

In Figure 4B, the MCAK-inhibited microtubule profile is fitted to Equation 11 with fitting parameters α and lu (notice that ρ(0) only rescales the arbitrary amplitude), while the parameter M is measured from laser ablation measurements in MCAK-inhibited monopoles. Conversely, the microtubule density profile for control monopoles is predicted by using Equation 11 or Equation 12 without the need of any fitting parameter, taking C as the measured mean microtubule length from control monopoles. Finally, the fits on Figure 4D for the microtubule nucleation profiles are done using the expression for nb(x) and adjusting the prefactor. A summary of the parameters used in the model and the procedure used to obtain them is specified in Table 2.

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Decision letter

  1. Andrea Musacchio
    Reviewing Editor; Max Planck Institute of Molecular Physiology, Germany

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your article "Autocatalytic microtubule nucleation determines the size and mass of spindles" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by Andrea Musacchio as the Senior and Reviewing Editor. The reviewers have opted to remain anonymous.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

In this paper, the authors use mono polar spindles (obtained for instance by Eg5 knockdown) to evaluate the position of minus-ends in Xenopus egg extract spindles, and thus to evaluate the mechanism of microtubule nucleation, and its effect on spindle size. The authors show that the monopolar spindle density profile can be understood as an autocatalytic mechanism that is regulated by a gradient of active nucleators. This is achieved by laser ablation experiments triggering a wave of depolymerisation. Measurements of the properties of the depolymerisation wave profile allow to access quantitative information on the nucleation profiles and length distribution of the microtubules. Comparison between control spindles and spindles with MCAK inhibition, which have longer and longer-lived microtubules, is consistent with the regulated autocatalytic mechanism. The paper concludes with a computational model to account for the control and MCAK inhibition conditions. The model is well explained and nicely done, and makes a strong contribution to the paper. In conclusion, the reviewers consider this an interesting and elegant study. However, they also identify the following important points that should be addressed in a revised version of the manuscript.

Essential revisions:

1) A table of parameters, together with values that are determined in the study, should be added. For instance, it is unclear what parameters are obtained from the model fit in Figure 4B.

2) While the theoretical modelling seems generally reasonable, some aspects remain unclear. Before Equation 7 the authors argue that since a nucleator can bind anywhere on microtubules with average length l, they bind on average at distance l from the end of the mother microtubule – why is it not l/2 then? They then argue that the center of mass velocity is given by v=l theta with theta the turn-over rate. Can the authors explain in more details where this relation comes from? In particular, one reviewer is surprised that the branching rate does not enter this formula; is it the case that there is still a velocity at 0 branching rate for instance?

3) In Figure 3C, it is unclear from the legend what exactly is being plotted. The authors should clarify this point.

4) Since only bound nucleators are nucleating new microtubules, it seems that the whole process would not start without the formation of initial microtubules by a process distinct from the autocatalytic mechanism described in the paper. Can the authors discuss what may control the density at x=0? Is it different in the control and MCAK-inhibited conditions?

5) After Equation 1, the sentence "this rate has a very well peak that moves as a function of time, Figure 1C" is confusing. The rate Ã(t, r) is already integrated with respect to distance away from the cut, so presumably Figure 1C does not directly inform about the shape of the function as a function of r. Is this correct? If not, please explain.

6) In Figure 2B, the x-axis says "distance from the central"; do the authors actually mean "microtubule length L"?

7) After Equation 6, the authors mention that P(y, l) does not depend on y. Is that something that can be verified from experimental measurements?

8) In Figure 1D, the two nucleation profiles for control and a-MACK conditions are plotted in arbitrary units. Are these arbitrary units defined in a consistent way, such that the difference in magnitude of the two plots is meaningful? If so, it would be helpful to clarify this in the manuscript.

9) Throughout the paper, the authors generalize the results to "mitotic spindles" or in some cases "large spindles". However, the mechanisms described here may be particular to Xenopus egg extract spindles, in which branched microtubule nucleation has been observed. The authors should be careful either to limit conclusions to the system described here, rather than to all mitotic spindles in general, or to explain how the results may apply in other mitotic spindles, which may not show branched microtubule nucleation, and/or where microtubule nucleation may occur exclusively at spindle poles or centrosomes.

10) The authors state that the location of minus ends in the monopolar spindles exactly corresponds to the location of microtubule nucleation, because microtubule transport is completely eliminated in the absence of Eg5. This is a major assumption in the paper, and experimental verification that no microtubule transport occurs in the absence of Eg5, and that the minus ends are exact readouts for the location of microtubule nucleation, is important.

11) The authors state that their method of laser cutting and analysis resolves the minus end locations with a single laser cut, allowing the authors to measure the "microtubule nucleation profile" (units a.u./length2). It would be helpful to provide a bit more detail regarding the method in the main text and so that the reader can follow the experiment, and, in addition, a better definition and description of "microtubule nucleation profile" would allow the reader to better understand the results in Figure 1D. Right now, these key results are too briefly explained in the main text, and not understandable.

12) The authors measured microtubule nucleation under conditions in which MCAK was inhibited, and found that the number and spatial spread of nucleated microtubules was increased. From these experiments, it was concluded that microtubule nucleation depended upon the presence and dynamics of microtubules. However, can the authors exclude that the nucleation process itself is not altered by MCAK inhibition, such that stabilization of microtubule nuclei by inhibition of MCAK would lead to increased nucleation, similar to but not dependent on the presence of additional microtubule density in the presence of MCAK?

13) The description of the experiments in Figure 2D, in which an "inert obstacle" was added to block microtubule polymerization, should be better detailed in the main text. Further, while the one sample image is convincing, there was no quantification of this result, nor detail on how the location of the obstacle relative to the center of the monopole would alter these results. This needs to be addressed.

14) From the RanQ69L experiments, in which new microtubules were nucleated at the edge of pre-existing structures (one experiment shown, no quantification), the authors conclude that the amount of active nucleators limit the size of monopolar spindles. This conclusion would be greatly strengthened by measuring the size of the monopoles as a function of the concentration of active nucleators.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Autocatalytic microtubule nucleation determines the size and mass of spindles" for further consideration at eLife. Your revised article has been favorably evaluated by Andrea Musacchio as the Senior and Reviewing Editor, and two reviewers.

The reviewers praised your effort in revising the manuscript, but there are two remaining issues that need to be addressed before acceptance, as outlined below. The required changes are textual and do not require re-review, but I kindly ask you to consider the reviewers' points very carefully:

1) One thing that remains unclear is the definition of the velocity v. The explanations given by the authors seem confusing, and the authors should clarify this in the manuscript, maybe with the help of a schematic. What is not clear is that (i) in their reply to the referees, the authors state that v is the velocity due to the branching process, but end by saying that in the absence of branching there is still a non-zero velocity. This sounds contradictory and needs to be clarified. (ii) It is unclear if this velocity is different or equal to the velocity of polymerisation of individual filaments. (iii) If the velocity is indeed associated to the microtubule mass flow as stated by the authors, it is not clear how this velocity can be independent from the branching rate. It sounds natural to think that a moving filament decorated with many branches will not create the same mass flow as an undecorated filament. These points should be clarified in the text, possibly with the aid of a schematic.

2) While the authors generalize the results to "mitotic spindles" or in some cases "large spindles", the mechanisms described here rely on branched microtubule nucleation, which, to the reviewer's knowledge, has only been observed in Xenopus egg extract spindles. Thus, the reviewer thinks that it is important to limit the conclusions and paper title to systems in which branched microtubule nucleation has actually been observed, since the model relies specifically on this assumption, rather than to all mitotic spindles in general. It appears that the authors address this concern by hypothesizing that branched microtubule nucleation could potentially also happen in mitotic spindles from other organisms, without supporting data. In the absence of new data to demonstrate that branching microtubule nucleation is a general mechanism across multiple organisms, this argument is not convincing, and the paper and title should be rewritten with more exact language to limit the conclusions specifically to spindles, such as the Xenopus egg extract spindle, in which branched microtubule nucleation has been observed.

https://doi.org/10.7554/eLife.31149.031

Author response

Essential revisions:

1) A table of parameters, together with values that are determined in the study, should be added. For instance, it is unclear what parameters are obtained from the model fit in Figure 4B.

We thank the reviewers for their comments. We added two tables in the Materials and methods (Table 1 and 2) specifying the values obtained for microtubule dynamics measurements and the parameters used in the model, as well as the procedure used to obtain them. In Figure 4B, two main parameters (𝛼 and ℓu) are obtained by fitting the model to the microtubule density profile for the MCAK-inhibited monopole. A third parameter ⍴(0) which determines the amplitude of the profile is also fit to the MCAK-inhibited monopole data. Despite this amplitude is given in arbitrary units, the intensity profiles for the control and perturbed monopoles were obtained from the same extract reactions. Thus, their ratio is quantified and the same amplitude parameter ⍴(0) is used for the two different profiles. These three parameters (⍴(0), 𝛼 and ℓu) obtained from the MCAK-inhibited monopole data are used to predict the control monopole microtubule density, as well as the nucleation profiles in Figure 4D (except for the prefactor in the nucleation profile that cannot be obtained from fitting the density profiles directly).These parameters are specified in Table 2.

2) While the theoretical modelling seems generally reasonable, some aspects remain unclear. Before Equation 7 the authors argue that since a nucleator can bind anywhere on microtubules with average length l, they bind on average at distance l from the end of the mother microtubule – why is it not l/2 then?

The key point is that microtubules are dynamic, and therefore the probability of an active nucleator to bind close to the minus end is larger than close to the plus end, since the binding site close to the minus end lives for longer than the binding site close to the plus end. Given that the length distribution of microtubules is exponentially distributed with mean length ℓ, this implies that the profile of active nucleators bound to a microtubule is also exponentially distributed with a length scale ℓ. Therefore, on average, active nucleators will bind at a distance ℓ from the microtubule minus end.

This calculation is slightly different from calculating the average position of a fluorescent speckle incorporated in a dynamic microtubule of average length ℓ. In this case the answer is ℓ/2 because speckles can only be incorporated at the plus end, while active nucleators can bind all along the microtubule. We made this point now clearer in the Materials and methods.

They then argue that the center of mass velocity is given by v=l theta with theta the turn-over rate. Can the authors explain in more details where this relation comes from? In particular, one reviewer is surprised that the branching rate does not enter this formula; is it the case that there is still a velocity at 0 branching rate for instance?

In our model, the velocity v is the speed at which the microtubule mass flows due to the branching process. This is calculated by considering the average center of mass distance between the newborn microtubule from its mother microtubule divided by the microtubule lifetime. As mentioned in Appendix 2, subsection “Physical model for autocatalytic microtubule nucleation”, since the microtubule length is exponentially distributed with length ℓ, the average branching distance is precisely ℓ. We want to highlight the difference between the microtubule mass flux velocity and the front velocity. The latter depends on the branching rate kbra and should be zero in the absence of branching. In a similar model of autocatalytic microtubule growth, the front velocity was explicitly calculated and depended on the branching rate [see Ishihara et al. 2016]. In our case, the steady state front velocity is zero as the structures reach a finite size, although v is different from zero. If the branching rate is reduced, the number of branching events is reduced, but the microtubule flux for a given branching process is the same. In the absence of branching (kbra = 0), using Equation 9 in Appendix 2, we find an exponential profile for the microtubule density with length scale ℓ, which corresponds to the case of a single microtubule at the origin.

We included some comments in the appendix highlighting the fact that v does not correspond to the front velocity and does not depend on the branching rate.

3) In Figure 3C, it is unclear from the legend what exactly is being plotted. The authors should clarify this point.

We assume the reviewers refer to Figure 4C and not Figure 3C. We first apologize for the brevity of the explanation and we agree with the reviewers that Figure 4C is somehow unclear. In this figure we show evidence supporting our model exemplified by testing Equation 12 in the Materials and methods section (or Figure 4C caption). The experimentally measured microtubule density profile of the anti-MCAK monopole is multiplied by the exponential factor exp[x(1/ℓM-1/ℓC)] to find the predicted control density profile according to the model, where ℓM is the average length of a microtubule in the anti-MCAK monopole and ℓC is the average length of microtubule in a control monopole. Since these two parameters are measured using laser ablation (see Table 2), the exponential factor is known and there are no fitting parameters. The blue curve shows the experimental control profile (same as in Figure 4B) whereas the gray curve shows the predicted control profile, using Equation 12 together with the anti-MCAK profile from Figure 4B. We included some remarks on the explanation both on the main text and on the caption of Figure 4 to better explain the plots.

4) Since only bound nucleators are nucleating new microtubules, it seems that the whole process would not start without the formation of initial microtubules by a process distinct from the autocatalytic mechanism described in the paper. Can the authors discuss what may control the density at x=0? Is it different in the control and MCAK-inhibited conditions?

We agree with the reviewers that autocatalytic microtubule nucleation requires initial seed microtubules to trigger the growth of the structure. This initial density corresponds to ⍴(0). As suggested by the reviewers the mechanism setting ⍴(0) is different than autocatalytic nucleation. The origin of these seed microtubules can be due to spontaneous microtubule nucleation in the cytoplasm, centrosomes, or RanGTP-mediated nucleation in close proximity to chromosomes. One possibility is that the concentration of RanGTP close to the site of its production at the chromosomes is high enough to trigger spontaneous nucleation in the cytoplasm similar to the case when constitutively active RanQ69L is added at sufficiently high concentration to the extract without pre-existing microtubule structures. However, our work shows that microtubule-independent microtubule nucleation is not sufficient to explain spindle growth or the spatial dependence of microtubule nucleation, and that microtubule independent nucleation can be accounted for as a boundary condition, suggesting that it is very localized in space. We added this discussion in the model section of Appendix 2.

Regarding the microtubule density at x=0, i.e. ⍴(0), it is the same for both profiles and it can be obtained by fitting the model to one of the experimentally measured microtubule density profiles (see Table 2). In particular, in our analysis we fit this value in the MCAK-inhibited profile and use it to predict the measured control profile. Therefore, our model is consistent with the microtubule density profile being the same for the control and perturbed case at the origin x=0. We have better emphasized this point in the main text.

5) After Equation 1, the sentence "this rate has a very well peak that moves as a function of time, Figure 1C" is confusing. The rate Ã(t, r) is already integrated with respect to distance away from the cut, so presumably Figure 1C does not directly inform about the shape of the function as a function of r. Is this correct? If not, please explain.

The reviewers are correct, there was a confusion on the definition of A(t,r). This quantity is integrated over the angular and radial coordinates. We corrected this part in Appendix 1 subsection “Laser ablation method”.

6) In Figure 2B, the x-axis says "distance from the central"; do the authors actually mean "microtubule length L"?

Thank you for pointing this out. This is a typo that we fixed in the new version.

7) After Equation 6, the authors mention that P(y, l) does not depend on y. Is that something that can be verified from experimental measurements?

As mentioned in Equation 6 in Appendix 1, given that microtubule transport is inhibited, the microtubule length distribution in monopoles should theoretically not depend on the position of the minus-ends y. This is in contrast to the microtubule length distribution in spindles, where there exists a clear dependence of the mean microtubule length along the spindle long axis due to microtubule transport, and becomes homogenous upon inhibition of microtubule transport (see Brugués et al. 2012). We verified this experimentally and we now included a new supplementary figure (Figure 2—figure supplement 1) showing how P(y,ℓ) is independent of y.

8) In Figure 1D, the two nucleation profiles for control and a-MACK conditions are plotted in arbitrary units. Are these arbitrary units defined in a consistent way, such that the difference in magnitude of the two plots is meaningful? If so, it would be helpful to clarify this in the manuscript.

Yes, these arbitrary units are consistently defined by using angular fluorescence (average microtubule density) profiles of control and MCAK-inhibited structures from the same extract reaction to determine the ratio between these two and enable a reliable comparison. We added this clarification in the caption of the corresponding figure (Figure 2).

9) Throughout the paper, the authors generalize the results to "mitotic spindles" or in some cases "large spindles". However, the mechanisms described here may be particular to Xenopus egg extract spindles, in which branched microtubule nucleation has been observed. The authors should be careful either to limit conclusions to the system described here, rather than to all mitotic spindles in general, or to explain how the results may apply in other mitotic spindles, which may not show branched microtubule nucleation, and/or where microtubule nucleation may occur exclusively at spindle poles or centrosomes.

We agree with the reviewers that such mechanism may not apply to all types of mitotic spindles, especially spindles with a small amount of microtubules (~10) as in the case of fission yeast. However, we argue that several evidences support the fact that this mechanism might apply to the majority of eukaryotic mechanisms, where the number of microtubules forming the spindles is on the order of 104-105 microtubules, and in spindles that are larger than the length of individual microtubules. Components involved in microtubule branching (e.g., augmin) and in the Ran pathway (e.g., RCC1) have been identified in many eukaryotic organisms (mainly metazoans) [Dasso, 2002; Hsia et al. 2014; Sánchez-Huertas and Lüders, 2015; Kamasaki et al. 2013; Savoian and Glover 2014; Goshima et al.2008]. Moreover, microtubule-dependent microtubule nucleation has been recently proposed to account for size regulation in human tissue culture cells [Oh et al. 2016]. Therefore, we hypothesize that spatially regulated autocatalytic microtubule nucleation could also apply to other organisms, especially those with spindles consisting of more than a few thousand microtubules and lengths larger than their microtubule average length. To validate this hypothesis, further experiments in other organisms will need to be performed. We now included some elements of the previous discussion at the end of the manuscript.

10) The authors state that the location of minus ends in the monopolar spindles exactly corresponds to the location of microtubule nucleation, because microtubule transport is completely eliminated in the absence of Eg5. This is a major assumption in the paper, and experimental verification that no microtubule transport occurs in the absence of Eg5, and that the minus ends are exact readouts for the location of microtubule nucleation, is important.

We performed a quantitative analysis of the velocity distribution of the Video 2 showing that tubulin speckles do not significantly move in monopoles. We added this analysis as a new panel in Figure 1—figure supplement 1. Tracking individual tubulin speckles we evaluated the velocity distribution along the x and y-components given a certain cartesian coordinate frame. We obtained 0.09 ± 0.03 μm/min in the x-component and 0.08 ± 0.04 μm/min in the y-component (mean ± SDM, n = 717 speckles). The mean velocity of the speckles was found to be 0.13 ± 0.08 μm/min, which is negligible compared with the microtubule transport in spindles (Sawin et al., 1992 (2.10 ± 0.36 µm/min); Maddox et al., 2003 (2.3 ± 0.6 µm/min); Miyamoto et al., 2004 (around 2 µm/min); Cameron et al., 2011 (around 2.5 µm/min in spindle center); Brugués et al., 2012 (2.5 µm/min)). Furthermore, to our knowledge, the maximum reported minus-end polymerization velocity in X. laevis extract is 0.3 μm/min [Hendershott et al. 2014]. This speed is negligible compared to the polymerization dynamics of the plus ends (vp≈ 24 µm/min, vd≈ 37 µm/min), and would imply an error of 100 nm over the average lifetime of a microtubule (~20 s). Additionally, the videos of the cuts are of the order of 30 s and therefore, the uncertainty in the cut position after the data analysis is already larger than the error minus-end polymerization/depolymerization would introduce.

11) The authors state that their method of laser cutting and analysis resolves the minus end locations with a single laser cut, allowing the authors to measure the "microtubule nucleation profile" (units a.u./length2). It would be helpful to provide a bit more detail regarding the method in the main text and so that the reader can follow the experiment, and, in addition, a better definition and description of "microtubule nucleation profile" would allow the reader to better understand the results in Figure 1D. Right now, these key results are too briefly explained in the main text, and not understandable.

We agree with the reviewers that the definition of the microtubule nucleation profile was not clearly stated in the main text and we included now the explicit definition. We define the microtubule nucleation profile at a distance r from the center of the monopole as the number of minus ends per unit length at r divided by 2πr. We still prefer to keep the laser ablation method in the supplement since we believe that properly explaining it would require a long discussion that would interfere with the readability of the manuscript. However, we have added a few more sentences in the main text so that the reader can understand the essential elements of the method.

12) The authors measured microtubule nucleation under conditions in which MCAK was inhibited, and found that the number and spatial spread of nucleated microtubules was increased. From these experiments, it was concluded that microtubule nucleation depended upon the presence and dynamics of microtubules. However, can the authors exclude that the nucleation process itself is not altered by MCAK inhibition, such that stabilization of microtubule nuclei by inhibition of MCAK would lead to increased nucleation, similar to but not dependent on the presence of additional microtubule density in the presence of MCAK?

One possibility is that MCAK-inhibition could by itself increase nucleation independently of microtubules. However, this would only lead to an overall increase of microtubule nucleation, which alone would not be sufficient to account for the dramatic change in the spatial dependence of the nucleation profile we observe in Figure 2D. Thus, microtubule nucleation in these structures depends on the presence and dynamics of microtubules. An additional evidence supporting the fact that MCAK inhibition is not affecting the overall nucleation amplitude is that the microtubule density at the origin ⍴(0) is found to be the same for the control and perturbed monopoles. We added this discussion in the main text.

13) The description of the experiments in Figure 2D, in which an "inert obstacle" was added to block microtubule polymerization, should be better detailed in the main text. Further, while the one sample image is convincing, there was no quantification of this result, nor detail on how the location of the obstacle relative to the center of the monopole would alter these results. This needs to be addressed.

We added an additional panel in Figure 3 in the main text together with a new video. The new panel in the main text shows the quantification of how an obstacle affects the MT density profiles, at distances ranging from 11 to 30 µm from the center. The analysis considers n=6 obstacles and shows a clear valley at the obstacle position which corresponds to the casted shadow observed in the videos. We plan to further investigate how the obstacle position alters the results in a follow up paper; however, our present data do not show a dependence on the distance. We added a video that shows a monopole growing against an obstacle (Video 7).

14) From the RanQ69L experiments, in which new microtubules were nucleated at the edge of pre-existing structures (one experiment shown, no quantification), the authors conclude that the amount of active nucleators limit the size of monopolar spindles. This conclusion would be greatly strengthened by measuring the size of the monopoles as a function of the concentration of active nucleators.

The main reason to perform these experiments was to show that the activation of more nucleators leads to outgrowth of pre-existing structures, which suggests that the amount of active nucleators is limiting in normal spindles. As suggested by the reviewers, we have added a new panel in Figure 3 from the main text that quantifies the growth of the monopole displayed in the same figure.

Unfortunately it is challenging to measure the size of monopoles as a function of RanQ69L concentration because it is difficult to measure a steady state size. This is a consequence of the appearance of mini asters at some point during the monopole growth that presumably sequester nucleators or other components (such as tubulin or MAPs). When we did a titration of RanQ69L using the same extract reaction we made the following observations:

60 µM: Spontaneous nucleation occurred everywhere in the cytoplasm and motor action immediately formed mini Ran asters (similar to the control image and movie shown in Figure 3B left and Video 8). The density of Ran asters was high enough that they dragged out microtubules from the pre-existing monopole such that they did not grow but instead got ripped apart within ~15 min.

30 µM and 15 µM: Monopoles grew until Ran asters appeared everywhere. The higher the RanQ69L concentration the earlier Ran asters appeared. Then the growth of monopoles stopped, presumably due to either depletion of nucleators in the mini asters, or some other component (e.g., tubulin or MAPs).

10 µM: This is the concentration shown in Figure 3B right. For this preparation of extract Ran asters appeared very late in the cytoplasm and thus the monopole had maximal growth. We now included a quantification for this case showing how the front advances.

5 µM: For this concentration the monopoles almost did not grow. Most likely because the RanQ69L concentration was too low to effectively increase the nucleation from pre-existing monopoles. No Ran asters were formed in the cytoplasm.

Finally, it is worth mentioning that other authors also reported difficulties and variability between extracts in RanQ69L experiments [Maresca et al. 2009]. Despite the difficulties in quantifying the titration of the RanQ69L experiments, the conclusions of this experiment remain the same, i.e., increasing the amount of active nucleators leads to the growth of the monopolar structure, implying that active nucleators limit the growth of these structures.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

The reviewers praised your effort in revising the manuscript, but there are two remaining issues that need to be addressed before acceptance, as outlined below. The required changes are textual and do not require re-review, but I kindly ask you to consider the reviewers' points very carefully:

1) One thing that remains unclear is the definition of the velocity v. The explanations given by the authors seem confusing, and the authors should clarify this in the manuscript, maybe with the help of a schematic. What is not clear is that (i) in their reply to the referees, the authors state that v is the velocity due to the branching process, but end by saying that in the absence of branching there is still a non-zero velocity. This sounds contradictory and needs to be clarified. (ii) It is unclear if this velocity is different or equal to the velocity of polymerisation of individual filaments. (iii) If the velocity is indeed associated to the microtubule mass flow as stated by the authors, it is not clear how this velocity can be independent from the branching rate. It sounds natural to think that a moving filament decorated with many branches will not create the same mass flow as an undecorated filament. These points should be clarified in the text, possibly with the aid of a schematic.

We have clarified the confusion between polymerization velocity and front velocity in the text and with a schematic (Figure 4—figure supplement 1). In our simplified description, the velocity v appearing in the density equation is the polymerization velocity. The front velocity is a consequence of both the polymerization of microtubules and the branching process. This distinction becomes clearer in the new figure.

2) While the authors generalize the results to "mitotic spindles" or in some cases "large spindles", the mechanisms described here rely on branched microtubule nucleation, which, to the reviewer's knowledge, has only been observed in Xenopus egg extract spindles. Thus, the reviewer thinks that it is important to limit the conclusions and paper title to systems in which branched microtubule nucleation has actually been observed, since the model relies specifically on this assumption, rather than to all mitotic spindles in general. It appears that the authors address this concern by hypothesizing that branched microtubule nucleation could potentially also happen in mitotic spindles from other organisms, without supporting data. In the absence of new data to demonstrate that branching microtubule nucleation is a general mechanism across multiple organisms, this argument is not convincing, and the paper and title should be rewritten with more exact language to limit the conclusions specifically to spindles, such as the Xenopus egg extract spindle, in which branched microtubule nucleation has been observed.

As suggested by the reviewer, we changed the title of the paper to include Xenopus laevis egg extract and restrict our results to this system. In the Discussion we made more explicit that the possibility that this mechanism may be shared by other organisms is hypothetical and needs to be tested.

https://doi.org/10.7554/eLife.31149.032

Article and author information

Author details

  1. Franziska Decker

    1. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
    2. Center for Systems Biology Dresden, Dresden, Germany
    3. Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing
    Competing interests
    No competing interests declared
    ORCID icon 0000-0002-3241-6575
  2. David Oriola

    1. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
    2. Center for Systems Biology Dresden, Dresden, Germany
    3. Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
    Contribution
    Formal analysis, Methodology, Writing—review and editing
    Competing interests
    No competing interests declared
    ORCID icon 0000-0002-8356-7832
  3. Benjamin Dalton

    1. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
    2. Center for Systems Biology Dresden, Dresden, Germany
    3. Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
    Contribution
    Investigation, Methodology
    Competing interests
    No competing interests declared
  4. Jan Brugués

    1. Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
    2. Center for Systems Biology Dresden, Dresden, Germany
    3. Max Planck Institute for the Physics of Complex Systems, Dresden, Germany
    Contribution
    Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Visualization, Methodology, Writing—original draft, Project administration, Writing—review and editing
    For correspondence
    brugues@mpi-cbg.de
    Competing interests
    No competing interests declared
    ORCID icon 0000-0002-6731-4130

Funding

Human Frontier Science Program (CDA00074/2014)

  • Jan Brugués

European Molecular Biology Organization (ALTF 483-2016)

  • David Oriola

Deutsche Forschungsgemeinschaft

  • Franziska Decker

Max-Planck-Gesellschaft (Open-access funding)

  • Franziska Decker
  • David Oriola
  • Benjamin Dalton
  • Jan Brugués

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We acknowledge A A Hyman, M Loose, S Grill, T Quail, K Ishihara, R Farhadifar, G Pigino, F Jug, C Norden, F Jülicher and I Patten for fruitful discussions and careful revision of the manuscript. We also thank J Rosenberger for helping on the coding for laser ablation. We kindly thank R Ohi and K Ishihara for providing us the anti-MCAK antibodies and RanQ69L, respectively. We thank Heino Andreas for frog maintenance and the Light Microscopy Facility (LMF) at MPI-CBG for providing TIRF microscopy. This work was supported by the Human Frontiers Science Program (CDA00074/2014, to JB), EMBO (ALTF 483–2016, to DO), the ELBE postdoctoral program (BD), and a DIGS-BB fellowship provided by the DFG (FD).

Ethics

Animal experimentation: All animals were handled according to the directive 2010/63/EU on the protection of animals used for scientific purposes, and the german animal welfare law under the license document number DD24-5131/367/9 from the Landesdirektion Sachsen (Dresden) - Section 24D.

Reviewing Editor

  1. Andrea Musacchio, Reviewing Editor, Max Planck Institute of Molecular Physiology, Germany

Publication history

  1. Received: August 11, 2017
  2. Accepted: January 9, 2018
  3. Accepted Manuscript published: January 11, 2018 (version 1)
  4. Version of Record published: February 15, 2018 (version 2)
  5. Version of Record updated: February 19, 2018 (version 3)

Copyright

© 2018, Decker et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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