Three-dimensional structure of kinetochore-fibers in human mitotic spindles

  1. Robert Kiewisz  Is a corresponding author
  2. Gunar Fabig
  3. William Conway
  4. Daniel Baum
  5. Daniel Needleman
  6. Thomas Müller-Reichert  Is a corresponding author
  1. Experimental Center, Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Germany
  2. Department of Physics, Harvard University, United States
  3. Department of Visual and Data-Centric Computing, Zuse Institute Berlin, Germany
  4. Department of Molecular and Cellular Biology, Harvard University, United States
  5. John A. Paulson School of Engineering and Applied Sciences, Harvard University, United States
  6. Center for Computational Biology, Flatiron Institute, United States

Abstract

During cell division, kinetochore microtubules (KMTs) provide a physical linkage between the chromosomes and the rest of the spindle. KMTs in mammalian cells are organized into bundles, so-called kinetochore-fibers (k-fibers), but the ultrastructure of these fibers is currently not well characterized. Here, we show by large-scale electron tomography that each k-fiber in HeLa cells in metaphase is composed of approximately nine KMTs, only half of which reach the spindle pole. Our comprehensive reconstructions allowed us to analyze the three-dimensional (3D) morphology of k-fibers and their surrounding MTs in detail. We found that k-fibers exhibit remarkable variation in circumference and KMT density along their length, with the pole-proximal side showing a broadening. Extending our structural analysis then to other MTs in the spindle, we further observed that the association of KMTs with non-KMTs predominantly occurs in the spindle pole regions. Our 3D reconstructions have implications for KMT growth and k-fiber self-organization models as covered in a parallel publication applying complementary live-cell imaging in combination with biophysical modeling (Conway et al., 2022). Finally, we also introduce a new visualization tool allowing an interactive display of our 3D spindle data that will serve as a resource for further structural studies on mitosis in human cells.

Editor's evaluation

This paper will be an incredible resource for cell biologists. The authors use sophisticated reconstructions of kinetochore–fibers within human metaphase spindles using electron tomography and then analyze their ultrastructure and organization. The findings lead to compelling models with clear implications for kinetochore–fiber and spindle self–organization.

https://doi.org/10.7554/eLife.75459.sa0

Introduction

Chromosome segregation during cell division is carried out by microtubule (MT)-based spindles (Anjur-Dietrich et al., 2021; McIntosh et al., 2013; Oriola et al., 2018; Prosser and Pelletier, 2017). While mitotic spindles can contain thousands of MTs, only a fraction of those highly dynamic filaments is associated with the kinetochores (Redemann et al., 2017). These MTs are called kinetochore microtubules (KMTs) and function to establish a physical connection between the chromosomes and the rest of the spindle (Flemming, 1879; Khodjakov et al., 1997; Maiato et al., 2004; Musacchio and Desai, 2017; Rieder, 1981; Rieder and Salmon, 1998).

The regulation of KMT dynamics in mitotic spindles has been studied in great detail in a number of different systems, including the early Caenorhabditis elegans embryo, Xenopus egg extracts and mammalian tissue culture cells (DeLuca et al., 2006; Dumont and Mitchison, 2009; Farhadifar et al., 2020; Inoué and Salmon, 1995; Kuhn and Dumont, 2019; Long et al., 2020). However, our understanding of the ultrastructure of KMTs in mammalian k-fibers is rather limited due to a low number of three-dimensional (3D) studies on spindle organization. Earlier 3D studies on mammalian spindles applied several techniques. Some studies used serial thin-section transmission electron microscopy (TEM) (Khodjakov et al., 1997; Mastronarde et al., 1993; McDonald et al., 1992; McEwen and Marko, 1998; Sikirzhytski et al., 2014) or partial 3D reconstruction by electron tomography (O’Toole et al., 2020; Yu et al., 2019). Other studies used scanning electron microscopy to analyze the ultrastructure of mitotic spindles (Hoffman et al., 2020; Nixon et al., 2017; Nixon et al., 2015). However, these prior studies did not present comprehensive 3D reconstructions of mammalian mitotic spindles. Nevertheless, by applying serial thin-section TEM it was reported that k-fibers in PtK1 cells are composed of about 20 KMTs (McDonald et al., 1992; McEwen et al., 1997). In contrast, tomographic analysis of RPE1 cells revealed 12.6 ± 1.7 KMTs per k-fiber (O’Toole et al., 2020). Moreover, different cell types can exhibit a wide range of chromosome sizes, which could be an important factor in modulating the number of attached KMTs (Moens, 1979). This variation in the reported numbers of KMTs per k-fiber as well as a lack of complete 3D models of human mitotic spindles motivated us to perform an in-depth analysis of the k-fiber organization and KMT length distribution in the context of whole mitotic spindles in human tissue culture cells.

It was shown that mitotic KMTs exhibited various patterns of organization in different species. Single KMTs are connected to the kinetochores in budding yeast (Winey et al., 1995), while multiple KMTs are connected to dispersed kinetochores in nematodes (Oegema et al., 2001; O’Toole et al., 2003; Redemann et al., 2017). Multiple KMTs connected to kinetochores are also observed in human cells. However, KMTs in these cells are organized into bundles, termed ‘kinetochore-fibers’ (k-fibers), which are attached to a single region on each chromosome (Begley et al., 2021; Godek et al., 2015; Inoue, 1953; Metzner, 1894; Mitchison and Kirschner, 1984; O’Toole et al., 2020).

Three different simplified models of k-fiber organization can be drawn. Firstly, a direct connection between kinetochores and spindle poles can be considered (Figure 1A), in which all KMTs in a given k-fiber have approximately the same length and are rigidly connected (Ris and Witt, 1981). Secondly, an indirect connection may be considered (Figure 1B), In such a model, none of the KMT minus ends would be directly associated with the spindle poles, thus KMTs would show differences in their length and connect to the poles purely by interactions with non-KMTs in the spindle. Such an indirect connection was previously reported for a subset of k-fibers in PtK1 and PtK2 cells (Sikirzhytski et al., 2014). Thirdly, the kinetochore-to-spindle pole connection may be neither direct nor indirect, thus showing a semi-direct pattern of connection, in which only some of the KMTs in a given k-fiber are associated with the spindle pole while others are not (Figure 1C). Previously, we have shown such a semi-direct pattern of KMT anchoring into the spindle network for the first embryonic mitosis in C. elegans (Redemann et al., 2017). Some KMTs in this nematode system are indeed directly associated with the spindle poles, while others are not. As far as the length of the KMTs in mammalian cells is concerned, a difference in their length had previously been reported for PtK1 cells (McDonald et al., 1992; Sikirzhytski et al., 2014). We, therefore, wondered how the anchoring of k-fibers into the spindle network is achieved in mammalian cells.

Models of k-fiber organization in mammalian mitosis.

(A) Direct connection with KMTs (red lines) spanning the distance between the kinetochore and the spindle pole. Chromosomes are shown in blue with kinetochores in red. The mother (m) and the daughter centriole (d) of the spindle pole are indicated. All KMTs are assumed to have similar lengths. (B) Indirect connection showing KMTs linking the kinetochore and the spindle pole by association with non-KMTs (yellow lines). K-fibers in this model are composed of KMTs with different lengths, and none of the KMTs is directly associated with the spindle pole. (C) Semi-direct connection showing KMTs of different lengths. Some KMTs are directly associated with the spindle pole, while others are not. In this model, KMTs show a difference in length.

Here, we aimed to determine the number and length of KMTs and the positioning of their putative minus ends in human HeLa cells. We further aimed to analyze the organization of k-fibers and the interaction of KMTs with non-KMTs in whole mammalian spindles. Focusing on the metaphase stage, we applied serial-section electron tomography to produce large-scale reconstructions of entire mitotic spindles in HeLa cells. To achieve this, we developed software tools for a quantitative in-depth analysis of both KMTs and non-KMTs (Kiewisz and Müller-Reichert, 2021; https://github.com/RRobert92/ASGA). We found that k-fibers in HeLa cells display a previously unexpected variable morphology. The k-fibers indeed contain KMTs of different lengths (a semi-direct type of connection with the spindle pole) and show an uncoupling of KMT minus ends at the site of preferred interaction with the spindle poles. For better visualization of KMT organization and k-fiber morphology, we introduce here a new 3D visualization tool that allows the interested reader to interactively display the 3D data (https://cfci.shinyapps.io/ASGA_3DViewer/).

Results

K-fibers are composed of approximately nine KMTs

For our large-scale analysis of mammalian k-fibers, we acquired data on metaphase spindles in HeLa cells by serial-section electron tomography (Figure 2A–B). To visually inspect the quality of our samples, we extracted slices of regions of interest (Figure 2—figure supplement 1). We also used the tomogram data to reconstruct full spindles in 3D for quantitative analysis of the spindle morphology (Figure 2—videos 1–3). In preparation for this quantitative analysis, we applied a Z-factor to our 3D models to correct for a sample collapse that had occurred during the acquisition of the tomographic data (Figure 2—figure supplement 2). In our three full reconstructions, we segmented all MTs, the chromosomes and the spindle poles (including the centrioles). Each of these metaphase spindles was composed of approximately 6300 MTs (6278 ± 1614 MTs, mean ±STD; Figure 2C–E; Table 1, Table 2) and had an average pole-to-pole distance of 9.0 ± 1.7 µm (mean ±STD; Figure 2—figure supplement 3A-B; Table 1).

Figure 2 with 10 supplements see all
Three-dimensional reconstruction of metaphase spindles by large-scale electron tomography.

(A) Tomographic slice showing a HeLa cell (spindle #1) in metaphase. The chromosomes (ch) and the spindle poles (p) are indicated. (B) Three-dimensional reconstruction of the same spindle as shown in A. The stacking of the serial tomograms used to generate a three-dimensional model of the spindle with the MTs (white lines) is visualized. The segmented chromosomes are shown in blue. (C) Three-dimensional model of the spindle as shown in A. The total number of all MTs is given in the upper right corner. The non-KMTs (yellow lines) and KMTs (red lines) are shown. (D) Full 3D model of metaphase spindle #2. (E) Full 3D model of metaphase spindle #3. (F) Extraction of KMTs from the 3D reconstruction as shown in C. The number of KMTs is given in the upper right corner. KMT plus and minus ends are shown by white spheres. (G) KMTs extracted from spindle #2. (H) KMTs extracted from spindle #3. Scale bars, 1 µm.

Table 1
Characterization of the 3D-reconstructed metaphase spindles in HeLa cells.
Data setSpindle pole distance [µm]Inter-kinetochore distance [µm]*No. of MTs in the tomographic volumeNo. of kinetochoresNo. of KMTsNo. of non-KMTsNo. of k-fibers
Spindle #17.161.08 ± 0.20
(n=43)
488492797
(16.3%)
4087
(83.7%)
92
Spindle #210.391.24 ± 0.21
(n=50)
80471101,102
(13.7%)
6945
(86.3%)
110
Spindle #39.481.03 ± 0.27
(n=40)
590490680
(11.5%)
5224
(88.5%)
90
  1. *

    Numbers are given as mean ± STD.

Table 2
Tomographic data sets as used throughout this study.
Data setOriginal data setMontage (X/Y)No. of serial sections[300 nm each]Estimated tomographic volume [µm3]Data set size [Gb]
Spindle #1T_04752 × 32259846.5
Spindle #2T_04792 × 32999677.9
Spindle #3T_04942 × 33590471.9

We then annotated the KMTs in our reconstructions based on the association of the putative MT plus ends with kinetochores. MTs that were arranged in parallel and made end-on contact at a single ‘spot’ on the chromosomes were defined as KMTs being part of the same k-fiber. For this publication, these bundled KMTs were considered the ‘core’ of the k-fibers. Possible interactions of these KMTs with other MTs (referred to as non-KMTs) in the spindle were subject to subsequent steps of our in-depth spindle analysis. In our tomographic data sets, we identified between 90 and 110 k-fibers per cell, which included on average 859 ± 218 KMTs (mean ±STD, n=3; Figure 2F–H; Figure 2—videos 4–6; Table 1) in each spindle. Thus, only ~14% of all MTs in the reconstructed spindles were KMTs. The majority of annotated KMTs displayed open flared ends at the kinetochore (Figure 2—figure supplement 4), consistent with previous observations on the morphology of KMT plus ends in mammalian cells (McIntosh et al., 2013). We took advantage of these extracted k-fibers to further analyze the distance between the sister k-fiber ends in each data set. For this, we calculated the median position of the KMT plus ends at each k-fiber and then determined the distance between the median KMT plus-end positions of sister k-fibers (Figure 2—figure supplement 3C-D; Table 1). The average distance between the sister k-fiber ends was 1.13 ± 0.24 µm (mean ±STD, n=292). The similarity in the median distance between sister k-fiber ends in the three reconstructions indicated to us that the selected pre-inspected spindles were indeed cryo-immobilized at a similar mitotic stage, thus allowing a further comparative quantitative analysis of our 3D models.

Next, we extracted individual k-fibers from our full 3D reconstructions to visualize their overall morphology (Figure 3A; Figure 3—videos 1–6). Our serial-section approach enabled us to follow each KMT in each k-fiber in 3D. This was achieved by semi-automatic stitching of the corresponding ends over section borders (Figure 3—figure supplement 1; Lindow et al., 2021). In addition to this semi-automatic stitching, each KMT in our reconstructions was manually checked for a proper end identification. The individual k-fibers showed remarkable variability in their overall shape. Some k-fibers were rather straight, while others were very curved. At the kinetochores, k-fibers showed a compacted appearance, while k-fibers were considerably broader at their pole-proximal end. Interestingly, some KMT minus ends extended beyond the position of the centrioles (Figure 3A, k-fibers #I - #III).

Figure 3 with 9 supplements see all
Morphology of k-fibers and number of KMTs associated per kinetochore.

(A) Examples of individual sister k-fibers extracted from the full 3D reconstruction of metaphase spindle #1. The numbering of these examples (corresponding to the supplementary videos) is given in the upper right corners. KMTs are shown as red lines. The ends of the KMTs are indicated by white spheres, centrioles are shown as cylinders (gray). Scale bar for all examples, 1.5 µm. (B) Histogram showing the frequency of detected KMTs per kinetochore. This plot includes data from all three spindle reconstructions. The dashed line (black) indicates the average number of KMTs per kinetochore (n=292). (C) Graph showing the number of KMTs associated per kinetochore plotted against the distance between sister k-fibers (n=292). The Pearson’s correlation coefficient for each data set and the average coefficient for all data sets are given. (D) Graph showing the difference (delta) in the number of KMTs associated with the respective sister kinetochores plotted against the distance between the kinetochore-proximal ends of k-fiber pairs (n=292). The Pearson’s correlation coefficient for each data set and the average coefficient for all data sets are given.

We further investigated the number of KMTs associated per kinetochore (Figure 3B; Figure 3—figure supplement 2A; Table 3) and found that the k-fibers were composed of around nine KMTs (8.5 ± 2.2, mean ±STD, n=292). To exclude the possibility that the average number of KMTs attached to kinetochores is influenced by a possible stretch of the sister kinetochores, we plotted both the number of attached KMTs and the difference (delta) in the number of KMTs associated with the respective sister kinetochore against the distance between the kinetochore-proximal ends of k-fiber pairs. We did not observe a correlation between these parameters (Figure 3C–D; Pearson’s correlation coefficients were 0.04 and 0.29) and concluded that the number of KMT attachments to kinetochores in metaphase is not influenced by a variation in the inter-kinetochore distance. Another variable with a possible influence on the number of attached KMTs to the outer kinetochores could be the position of the k-fibers within the metaphase spindle. Because spindles show a rounded appearance at metaphase, a difference in the number of attached MTs to the outer kinetochores could be influenced by the overall spindle shape. To analyze such a possible positional effect, we considered the cross-section of the metaphase plate as an ellipse and defined a central, an intermediate and a peripheral zone on this ellipse (Figure 3—figure supplement 3A). By determining the position of the kinetochores on the 3D-reconstructed metaphase plate, we then annotated each k-fiber in our three data sets to one of these regions (Figure 3—figure supplement 3B-M). Keeping the roundedness of spindles at metaphase in mind, we indeed observed that k-fibers positioned in the center are rather straight, while peripheral k-fibers are more curved. However, we did not find a difference in the number of attached KMTs for these three different regions (Figure 3—figure supplement 3N; Table 5) and concluded that also the position of the k-fibers within the spindle has no effect on the average number of KMTs per k-fiber.

Table 3
Quantitative analysis of KMTs and non-KMTs.
Data setLength of KMTs [µm]*Length of non- KMTs [µm]*No. of KMTs per kinetochore*No. of KMTs in the MT-centrosome interaction area*Mean KMT minus-end distance to poles [µm]% of KMTs associated with poles% of non-KMTs associated with poles
Spindle #13.59
(±1.57)
2.13
(±1.67)
8.04
(±1.86)
5.0
(±1.8)
1.7261.244.3
Spindle #23.82
(±1.97)
1.95
(±1.60)
9.75
(±2.18)
3.1
(±2.3)
2.8731.528.6
Spindle #34.27
(±1.93)
2.07
(±1.93)
7.49
(±1.91)
4.1
(±2.0)
2.1254.241.9
  1. *

    Numbers are given as mean ±STD.

We were also interested in measuring the density and spacing of KMTs at the kinetochore, thus allowing subsequent analysis of KMT density along the k-fiber length. Because kinetochores show lower contrast in high-pressure frozen material compared to conventionally prepared samples (McEwen et al., 1998b), we indirectly measured the size of the kinetochores in our spindles by determining the cross-sectional area of the k-fibers (i.e. by encircling the KMTs) close to the outer kinetochore plate. The measured average kinetochore area was 0.10 ± 0.07 µm2 (mean ±STD; Figure 3—figure supplement 2B-C). We then analyzed the density of KMTs at the outer kinetochores by counting the number of KMTs within the determined areas, which was 112 ± 60 KMTs/µm2 (mean ±STD, n=292; Figure 3—figure supplement 2D; Table 3). In addition, we observed an average center-to-center distance between neighboring KMTs of 74 ± 22 nm (mean ±STD, n=292; Figure 3—figure supplement 2E; Table 4). Considering an MT diameter of 25 nm, this corresponds to an average wall-to-wall spacing of about 50 nm between the KMTs at the outer kinetochore. Thus, following our initial visual inspection of k-fibers, the KMTs tend to be highly compacted at the outer kinetochore.

Table 4
Quantitative analysis of k-fiber organization.
Data setKMT density at the kinetochore [KMT/µm2]*KMT-KMT distance at the kinetochore [nm]*Global tortuosity of KMTs*% of curved KMTsArea of k-fibers [µm2]*% of KMTs in a k-fibers*
Spindle #1122
(±62)
67
(±20)
1.11
(±0.11)
39.80.08
(±0.1)
64
(±27)
Spindle #299
(±45)
78
(±23)
1.07
(±0.07)
28.40.09
(±0.11)
70
(±25)
Spindle #3117
(±72)
76
(±23)
1.13
(±0.13)
47.10.12
(±0.24)
59
(±29)
  1. *

    Numbers are given as mean ±STD.

We also measured the length of the KMTs in our reconstructed k-fibers and observed a broad distribution of KMT lengths with an average value of 3.87 ± 1.98 µm (mean ±STD, n=2579; Figure 4A; Figure 4—figure supplement 1A; Table 3). Our analysis revealed the existence of relatively short KMTs in central, intermediate and peripheral k-fibers that were not associated with the spindle poles (Figure 4—figure supplements 23; Table 5). Indeed, about 20 ± 4% of the KMTs had lengths less than 2 µm. Our analysis also showed relatively long KMTs (about 39 ± 10%) that were longer than the half spindle length. Some of these long KMTs showed a pronounced curvature at their pole proximal end, thus connecting to the ‘back side’ of the spindle poles (see also Figure 3A, k-fiber #I - #III; Figure 3—videos 1–3).

Figure 4 with 3 supplements see all
Analysis of MT length distribution.

(A) Histogram showing the length distribution of KMTs from all data sets (n=2579). The dashed line indicates the average length of KMTs. (B) Histogram showing the length distribution of non-KMTs (n=14458). The dashed line indicates the average length of non-KMTs.

Table 5
Quantitative analysis of k-fiber positioning in the spindle.
RegionLength of KMTs [µm]*No. of KMTs per kinetochore*No. of KMTs at MT-centrosome interaction areaMean KMT minus-end distance to poles [µm]*No. of KMTs associated with poles*Global tortuosity of KMTs*
Central3.5
(±1.7)
8.2
(±2.4)
162
(~48%)
2.0
(±1.3)
4.3
(±2.3)
1.08
(±0.08)
Intermediate3.6
(±1.7)
8.6
(±2.1)
266
(~49%)
2.1
(±1.3)
4.6
(±1.9)
1.11
(±0.12)
Peripheral3.9
(±2.0)
8.6
(±2.4)
730
(~45%)
2.5
(±1.6)
4.1
(±2.0)
1.10
(±0.10)
  1. *

    Numbers are given as mean ±STD.

  2. Number and percentage of KMTs is shown.

We continued our study by further analyzing the pole proximal ends (from now on called minus ends). As a first step, we annotated each KMT minus end in our spindle reconstructions. The development of appropriate software allowed us then to determine both the distance of the KMT minus ends to the nearest spindle pole and the relative position of the KMT minus ends along the pole-to-kinetochore axis (Figure 5A; Kiewisz and Müller-Reichert, 2021). In addition, we were also interested in the percentage of the KMT minus ends that were directly associated with the spindle poles. Similar to our previously published analysis of spindle morphology in the early C. elegans embryo (Redemann et al., 2017), we defined a MT-centrosome interaction area. For this, we plotted the distribution of all non-KMT minus-end distances to the nearest spindle pole. The distribution peaked ~1 µm from the pole and then fell before plateauing in the spindle bulk. To find the edge of this MT-centrosome interaction area, we fit a Gaussian to the distribution peak and defined the cutoff distance for the edge of the MT-centrosome interaction area as twice the half-width, which was 1.7 µm from the mother centriole. (Figure 5B, gray area). In other words, KMTs with their minus ends positioned at 1.7 µm or less to the center of the nearest mother centriole (i.e. inside this MT-centrosome interaction zone) were defined to be directly associated with a pole, while KMT minus ends positioned farther than this cut-off distance of 1.7 µm were called indirectly associated with the spindle pole. We then measured the distance of each KMT minus end to the nearest mother centriole (Figure 5C; Figure 5—figure supplement 2A). Taking our determined cut-off value into account, we found that only 49% (±15.5%, ±STD, n=3) of the KMT minus ends were positioned within the defined MT-centrosome interaction area. This is in accord with our observation that the average number of KMTs per k-fiber at the spindle pole (4.1 ± 2.0, mean ±STD; Figure 5—figure supplement 3; Table 3) was lower compared to the average number of KMTs per k-fiber at the kinetochore (8.5 ± 2.2, mean ±STD; Figure 3B). All in all, this suggested to us that only half of the KMTs in HeLa cells are directly connected to the spindle pole, while the other half of the KMTs are indirectly connected.

Figure 5 with 4 supplements see all
Analysis of MT minus ends.

(A) Measurement of MT minus-end positioning. A KMT (red line) with its ends (red circles) and a non-KMT (yellow line) with its ends (yellow circles) are shown. The distance of both the KMT and the non-KMT minus ends to the center of the mother centriole was calculated. The relative position of the KMT minus ends along the pole-to-kinetochore axis and the non-KMT minus ends along the pole-to-pole axis was also determined (P1, pole 1; P2, pole 2; K, kinetochore). (B) Determination of the MT-centrosome interaction area. Graph showing the number of non-KMT minus ends plotted against their distance to the pole (i.e. to the center of the mother centriole). The determined area of the interaction of non-KMTs with the centrosome and the half-width of this area is indicated in gray. The border of the MT-centrosome interaction area (right dashed line) was determined by identifying twice the half-width of the distribution peak of the minus-end distances. (C) Histogram showing the distribution of the KMT minus-end distances to the center of the mother centriole (n=2579). The MT-centrosome interaction area as defined in B is indicated by a gray area (dashed line shows the border of this area). (D) Histogram showing the relative position of the KMT minus ends on the pole-to-kinetochore axis (n=2579). The position of the spindle pole (p = 0, dashed line) and the kinetochore (K = 1) is indicated. The approximated MT-centrosome interaction area is indicated in gray. (E) Histogram showing the distribution of the non-KMT minus-end distances to the center of the mother centriole (n=14458). The MT-centrosome interaction area is indicated in gray. (F) Plot showing the relative position of the non-KMT minus ends on the pole-to-pole axis (n=14458). The position of the spindle poles (P1 = 0, P2 = 1). The approximated MT-centrosome interaction area is shown in gray.

Interestingly, we also observed that the number of KMT minus ends associated with the spindle poles was significantly higher in k-fibers positioned in the center compared to those at the periphery of the mitotic spindle. In addition, the average length of KMTs in central k-fibers and their minus-end distance to the spindle pole were significantly lower compared to those observed in peripherally positioned k-fibers (Figure 5—figure supplement 4; Table 5). This suggested to us that the position of the k-fibers within the spindle affects the ultrastructure of the individual KMTs.

We next investigated the relative position of the KMT minus ends on the pole-to-kinetochore axis. For this, we defined the approximate relative position of the MT-centrosome interaction area on the pole-to-kinetochore axis (Figure 5D; Figure 5—figure supplement 1; Figure 5—figure supplement 2B; Table 3). The approximated relative position was calculated as an average for all KMTs and ranged from –0.2 to 0.2. We found that the KMT minus ends that were positioned within the MT-centrosome interaction zone showed a peak position close to the center of the spindle poles. In contrast, KMT minus ends outside this interaction area did not show a preferred position but rather displayed a flat relative distribution on the pole-to-kinetochore axis. This analysis confirmed our initial visual 3D inspection of the KMTs, revealing that the k-fibers in HeLa cells are not composed of compact bundles of KMTs of the same length but rather show KMTs of different lengths, thus confirming previously published data (McDonald et al., 1992; O’Toole et al., 2020).

For comparison, we also analyzed the length distribution of non-KMTs in the spindles. Non-KMTs had an average length of 2.0 ± 1.7 µm (mean ±STD; n=14458; Figure 4B; Figure 4—figure supplement 1B) showing a high number of very short (<2 µm) and a low number of long MTs (>half spindle length). In addition, 38 ± 9% of the non-KMT minus ends were localized in the defined MT-centrosome interaction zone and the remaining ~60% were located in the bulk of the spindle (Figure 5E; Figure 2—figure supplement 2C; Table 3). In addition, the distribution plot of the relative position of the non-KMT minus ends on the pole-to-pole axis showed two peaks at the spindle poles (Figure 5F; Figure 5—figure supplement 2D). Overall, this indicated to us that the non-KMTs show a very high number of very short MTs that is different from the flatter length distribution of KMTs.

KMT tortuosity is higher at the spindle poles than at the kinetochores

Previous work on the flexibility and the rigidity of MTs indicated that these polymers are able to search the spindle space for a binding partner, bend and continue to grow in a modified direction to avoid obstacles or react to pushing/pulling forces. It was further shown that the flexibility of MTs is dependent on their length (Pampaloni et al., 2006). Therefore, we were interested in whether long KMTs are more curved compared to short KMTs. As a measure, we decided to analyze the tortuosity of individual KMTs in our 3D models. Tortuosity is the ratio of the total length of a curve (the spline length of a given KMT) to the distance between its ends. Straight KMTs, therefore, have a tortuosity of 1, while a quarter circle has a tortuosity of around ~1.1 and a half-circle of around ~1.6 (Figure 6A). Because the tortuosity of KMTs might not be homogeneous throughout the spindle, we aimed to measure both their global and local tortuosity in our 3D reconstructions, that is, the tortuosity of the KMTs along their entire length and also in defined segments of a length of 500 nm along the k-fibers, respectively (Figure 6B–C).

Figure 6 with 4 supplements see all
Global and local tortuosity of KMTs.

(A) Schematic illustration of tortuosity (T) as given for a straight line, a quarter of a circle, and a half of a circle. (B) Schematic illustration of global tortuosity (Tg) of KMTs given by the ratio of the spline length (Lx) to the 3D distance between the KMT ends illustrated by gray circles (Ly). (C) Schematic illustration of KMT local tortuosity (Tl) as given by division segments with a length of 500 nm. (D) Three-dimensional model of k-fibers (spindle #1) showing the global tortuosity of KMTs as indicated by color coding (top left corner). (E) Histogram showing the frequency of tortuosity for KMTs (n=2579). The Pearson’s correlation coefficient is given for each reconstructed spindle. The black dashed line indicates the average KMT tortuosity. The percentage ratio of ‘straight’ to ‘curved’ KMTs is also given. (F) Perspective view as shown in D. Straight KMTs (tortuosity of 1.0–1.1; red) and curved KMTs (tortuosity ≥1.1; white) are highlighted. (G) Correlation of global tortuosity and length of KMTs (n=2579). The Pearson’s correlation coefficient is given for each reconstructed spindle. The gray line indicates the local regression calculated by the loess method. (H) Three-dimensional model of k-fibers (from spindle #1) showing the local tortuosity of KMTs as indicated by color-coding. (I) Correlation of the local tortuosity of KMTs with the relative position along the pole (P)-to-kinetochore (K) axis (n=2579). Scale bars, 1 µm.

Firstly, we analyzed the global tortuosity of the KMTs. For this, we applied a color code to our 3D models to visualize differences in the curvature of individual KMTs (Figure 6D; Figure 6—videos 1–3). For all data sets, we observed an average value of KMT tortuosity of 1.1 ± 0.1 (mean ±STD, n=2579). We found that 62 ± 8% of the KMTs showed a tortuosity of lower than 1.1 and 38 ± 10% of the KMTs displayed a tortuosity higher than 1.1 (Figure 6E; Table 4). We also observed that straight KMTs (tortuosity <1.1) were predominantly located in the center of the spindle, while curved KMTs (tortuosity >1.1) were located more at peripheral spindle positions (Figure 6F; Figure 6—figure supplement 1, Table 5). Furthermore, the global tortuosity of KMTs was correlated with their length. As expected, short KMTs were straighter, while long KMTs were more curved (R = 0.68; p = 2.2e-16; Figure 6G). In addition, 75 ± 6% of the KMTs with a tortuosity higher than 1.1 were longer than the half-spindle length. Secondly, we also investigated the local tortuosity of the KMTs. For each KMT, we applied the same color code as used for the analysis of global tortuosity (Figure 6H). Then we plotted the tortuosity value for each 500 nm segment against the position on the pole-to-kinetochore axis (Figure 5—figure supplement 1). Our analysis revealed that the tortuosity of KMTs was not uniform along the pole-to-kinetochore axis. Importantly, the local tortuosity of the KMTs was weakly correlated with the relative position of the KMT segments on the pole-to-kinetochore axis. The local tortuosity slowly and constantly increased from the kinetochores towards the spindle poles (R = –0.13; p = 2.2e-16; Figure 6I). Extending previously published knowledge, we concluded that KMTs have a higher tortuosity at the spindle poles compared to the kinetochores.

K-fibers are broadened at spindle poles

Our tortuosity measurements revealed that individual KMTs in the mitotic spindle are rather curved at positions close to the spindle poles. Therefore, we were also interested in analyzing how the curvature of individual KMTs might shape the overall structure of the k-fibers, particularly at their pole-proximal ends. For this, we determined the cross-section areas of k-fibers along their entire length (Figure 7A; Figure 7—figure supplement 1). In the interest of precision, we analyzed the cross-sections of k-fibers by calculating polygonal areas, allowing a quantitative geometrical analysis without a prior assumption about their shape. Cross-sections of k-fibers showed an average polygonal area of 0.097 ± 0.161 µm2 (mean ±STD, n=292). We then continued by plotting the values for these polygonal areas against the relative position on the pole-to-kinetochore axis (Figure 7B; Table 4). We measured an average polygonal area of 0.034 ± 0.019 µm2 at the kinetochores, 0.149 ± 0.210 µm2 in the middle of the spindles, and 0.092 ± 0.146 µm2 at the spindle poles. Compared to the position at the kinetochore, the average polygonal area of the k-fibers was about fourfold higher in the middle of the spindles and roughly threefold higher at the spindle poles. Moreover, the cross-section polygonal area of the k-fibers showed a higher spread of values at the spindle poles compared to the kinetochores, thus reflecting the observed broadened appearance of the k-fibers at the spindle poles.

Figure 7 with 1 supplement see all
Shape of k-fibers.

(A) Schematic illustration of the analysis of polygonal areas as obtained from k-fiber cross-sections. KMTs are shown as lines (red), KMT ends as spheres (light red). Cross-sections of the given k-fiber are shown as blue squares (top). The median position of all KMTs in a cross-section is indicated as a yellow circle (bottom). (B) Distribution of the k-fiber polygonal area along with the relative position on the pole [P]-to-kinetochore [K] axis (n=292). (C) Schematic illustration of the k-fiber density analysis. For each k-fiber, a radius at the kinetochore was estimated by calculating a minimum circle enclosing all KMTs (top). The determined radius was then enlarged by factor 2 to account for k-fiber flexibility. Along with the k-fiber, the number of KMTs enclosed in the selected radius was then measured (bottom). (D) Distribution of the percentage of KMTs enclosed in the k-fiber along with the relative position along the pole [P]-to-kinetochore [K] axis (n=292). For each reconstructed spindle, data sets are presented as polynomial lines showing local regression calculated with the loess method. Average values with standard deviations are shown in gray. The approximated MT-centrosome interaction areas are shown in gray with the position of the poles indicated by dashed lines (B and D).

To further characterize the arrangement of the KMTs in the k-fibers, we also set out to measure the number of the KMTs along the length of the k-fibers (Figure 7C). For each k-fiber, we defined a circle enclosing all KMTs at the kinetochore. We then measured the number of KMTs that were included in this defined k-fiber circle and plotted the percentage of the enclosed KMTs against the relative position along the pole-to-kinetochore axis. We observed a variation in the percentage of enclosed KMTs along the k-fiber length. As defined, the highest percentage of enclosed KMTs was observed at the outer kinetochore. However, at the spindle poles, roughly only 64% of the KMTs were enclosed (Table 4). Thus, the density of KMTs in the k-fibers at the spindle poles was decreased compared to the one observed at the outer kinetochore (Figure 7D). From all these analyses, we concluded that k-fibers display a higher tortuosity and a lower KMT density close to the spindle poles compared to the kinetochore positions, thus leading to a broadened appearance of their pole-proximal ends.

KMTs primarily associate with non-KMTs at spindle poles

So far, we had concentrated only on an analysis of KMT morphology and considered these bundled MTs as the ‘core structure’ of the k-fibers. Likely, the observed organization of KMTs in k-fibers is the result of KMTs interacting with other non-KMTs in the spindle, thus contributing to the maturing of k-fibers (Almeida et al., 2021). Therefore, we also aimed to investigate patterns of association of KMTs with the neighboring non-KMTs in our 3D reconstructions. Moreover, we were particularly interested in localizing such KMT/non-KMT associations in the spindles to map the detected positions of MT-MT interaction on the pole-to-kinetochore axis. In general, we considered two types of interactions between MTs. Firstly, we analyzed potential interactions between MT ends with neighboring MT lattices, which could be mediated by MT minus-end associated molecular motors such as dynein (Tan et al., 2018) or kinesin-14 (Molodtsov et al., 2016), by other MT-associated proteins such as HDAC6 (Ustinova et al., 2020), Tau (Bougé and Parmentier, 2016), or by Ɣ-tubulin (Rosselló et al., 2018). Secondly, we considered MT-MT lattice interactions, which might be established by molecular motors such as kinesin-5 (Falnikar et al., 2011) or PRC1 (Mollinari et al., 2002; Polak et al., 2017).

Both types of interactions are also shown here by using our new 3D visualization tool (Kiewisz and Müller-Reichert, 2022; https://cfci.shinyapps.io/ASGA_3DViewer). The aim of applying this tool is to enable an illustration of the 3D complexity of such KMT/non-KMT associations. Readers are encouraged to visit this website for a display of our spindles in 3D, thus allowing to view k-fibers, KMTs and also non-KMTs in an interactive way.

We started our analysis by investigating possible KMT minus-end associations with either KMT or non-KMT lattices (Figure 8). For this, we annotated all KMT minus ends in our 3D reconstructions and measured the distance of each minus end to a neighboring MT lattice. We then determined association distances (i.e. 25, 30, 35, 45, 50, 75, and 100 nm) to quantify the number of associations occurring within these given interaction distances (Kellogg et al., 2016; Redwine et al., 2012). From this, we further determined the percentage of all KMT minus ends that were associated with non-KMT lattices according to selected association distances (Figure 8—figure supplement 1; Table 6 and Table 7). As expected, we observed that the number of KMT minus ends associated with adjacent MT lattices increased at larger association distances. Considering 35 nm as an example of a possible interaction distance between two MTs connected by a single dynein motor (Amos, 1989), we observed that only 32.6 ± 5.5% of all KMT minus ends were associated with other MTs (for a visualization of the pattern of association see Figure 8—figure supplements 12; Figure 8—video 1). Moreover, all KMT minus ends that were not associated with the spindle poles (i.e. those positioned farther than 1.7 µm away from the centrioles) only 32.8 ± 24.9% showed an association with other MT lattices at a given distance of 35 nm (Figure 8—figure supplement 1). This suggested that for an interaction distance of 35 nm roughly only 30% of the KMT minus ends in k-fibers were associated with the MT network. Further considering larger distances of association between KMT minus ends and neighboring MT lattices, we also observed that not all KMT minus ends were associated with neighboring MTs even at a value of 100 nm (Table 6 and Table 7).

Figure 8 with 6 supplements see all
Association of KMTs with the MT network.

(A) Graph showing the number of KMT minus ends associated with KMT lattices within 35 nm of interaction (n=2579). Numbers of KMT minus ends are normalized by the density of surrounding MTs and plotted against the relative position on the pole-to-kinetochore axis (P, pole; K, kinetochore). The approximated MT-centrosome interaction area is shown in gray with the position of the pole indicated by a dashed line. The percentage of KMT associations located in the MT-centrosome interaction area is given. (B) Bar plot showing the normalized number of KMT minus ends associated with non-KMT lattices within 35 nm distance (n=2579). (C) Graph showing the number of KMT lattices associated with other KMT minus ends plotted along the relative position on the pole-to-kinetochore axis and normalized by the spindle density (n=2579). (D) Graph displaying the number of KMT lattices associated with non-KMT minus ends (n=2579). Moving averages with a period of 0.05 along the pole-to-kinetochore axis are shown as black lines.

Table 6
Analysis of the association of KMT minus ends with other neighboring KMT lattices.
Data setAnalysisInteraction distances [nm]
253035455075100
Spindle #1No. of KMTs3768112204238306330
% of KMTs4.99.115.027.332.040.944.1
Spindle #2No. of KMTs203768142177266290
% of KMTs1.93.56.313.216.524.827.1
Spindle #3No. of KMTs132766116135199218
% of KMTs1.94.09.817.220.029.532.3
Table 7
Analysis of the association of KMT minus ends with neighboring non-KMT lattices.
Data setAnalysisInteraction distances [nm]
253035455075100
Spindle #1No. of KMTs3782132217248353384
% of KMTs4.911.017.629.033.247.251.3
Spindle #2No. of KMTs245313353469525677732
% of KMTs22.929.233.043.849.063.268.3
Spindle #3No. of KMTs2864107198230355410
% of KMTs4.29.515.929.434.152.760.8

Next, we sought to map the positions of the detected associations of KMT minus ends with either KMT or non-KMT lattices within the reconstructed spindles. We determined the position of such associations in our spindles and then plotted the data against the relative position on the pole-to-kinetochore axis. For this, we normalized the pole-to-kinetochore axis by the MT density at each given position. We first plotted the normalized number of KMT minus-end associations with MT lattices against the relative position on the pole-to-kinetochore axis (Figure 8A; Figure 8—figure supplement 3A). KMT minus ends were distributed along the pole-to-kinetochore axis with a preference for positions at the spindle poles. As an example, for a given association distance of 35 nm, 60.7 ± 9.4% of the total number of associations were observed at the spindle poles. We then also determined the relative position of the KMT minus-end associations with non-KMT lattices (Figure 8B; Figure 8—figure supplement 3B). Similarly, the majority of the associations of KMT minus ends with non-KMT lattices were observed at the spindle poles. For the chosen distance of 35 nm, 44.7 ± 5.2% of these associations were observed at the spindle poles. Thus, the spindle poles appeared as the major sites for interaction of KMT minus ends with neighboring MT lattices.

Vice versa, we also determined the occurrence of either KMT or non-KMT minus ends in the vicinity of KMT lattices (Figure 8; Figure 8—figure supplement 4; Figure 8—video 2). At 35 nm or closer to the KMT lattice, we observed that on average 42 ± 8% of KMTs were associated with either KMT or non-KMT minus ends, with the majority of associations with non-KMT minus ends (Figure 8—figure supplement 3C-D; Table 8 and Table 9). Moreover, we also determined the relative position of these associations on the spindle axis. Again, more than half of the KMT lattices (59.8 ± 6.7%) associated with other MT minus ends were preferentially found at spindle poles (Figure 8C; Figure 8—figure supplement 3E). In contrast, only 39.1 ± 4.6% of non-KMTs associated with other MT minus ends were found at the poles (Figure 8D; Figure 8—figure supplement 3F). Again, this analysis indicated that the interaction of KMTs with other MTs preferentially takes place at the spindle poles regardless of the association distance. Notably, we could observe a peak of association between the KMT lattices and the non-KMT minus ends at a relative position of around 0.3 (Figure 8D), suggesting that the KMT lattices at this position are important for interactions with non-KMTs.

Table 8
Analysis of the association of KMT lattices with other neighboring KMT minus ends.
Data setAnalysisInteraction distances [nm]
253035455075100
Spindle #1No. of KMTs3971117210236336403
% of KMTs5%10%15%28%31%45%54%
Spindle #2No. of KMTs244686179237401470
% of KMTs2%4%8%17%22%37%43%
Spindle #3No. of KMTs142761127148227284
% of KMTs2%4%9%19%22%34%43%
Table 9
Analysis of the association of KMT lattices with other neighboring non-KMT minus ends.
Data setAnalysisInteraction distances [nm]
253035455075100
Spindle #1No. of KMTs81151223362415534577
% of KMTs11%20%30%48%55%71%77%
Spindle #2No. of KMTs51100173351433640717
% of KMTs5%9%16%33%40%59%67%
Spindle #3No. of KMTs3493176301348471507
% of KMTs5%14%26%44%51%69%75%

In addition, we were also interested in mapping the number and the length of MT-MT associations on the pole-to-pole axis in order to recognize specific patterns of interactions within the mitotic spindle. For a pairing length analysis as previously applied (McDonald et al., 1992; Winey et al., 1995), we defined 20 nm as a minimal length of interaction. For each MT, we also counted the number of continuous interaction segments over which they retained this minimal association proximity (Figure 9A). In addition, we also varied the distance between associated MTs by choosing values of 25, 30, 35, 45, and 50 nm. As expected, the peaks in the number of KMTs changed rapidly with an increase in the number and length of associations (Table 9 and Table 10). We then analyzed the association of KMTs with other MTs in the spindle by plotting the number of associations against the relative position on the pole-to-pole axis. We also normalized the number of associations by the MT density. With an increase in the considered association distance between MTs, we observed an increase in the number of associations at the spindle poles and a drastic decline in the number of these associations at positions in the middle of the spindle (Figure 9B; Figure 9—figure supplement 1A; Figure 9—video 1). We then also analyzed the association of non-KMTs with other MTs. In contrast to the previous analysis, by increasing the association distances we detected a considerable increase in the number of interactions near the spindle midplane. (Figure 9C; Figure 9—figure supplement 1B; Figure 9—video 2). This peak is of functional importance, most likely representing the region, where kinesin motors generate pushing forces (Shimamoto et al., 2015). We concluded from all these analyses that KMTs and non-KMTs differ in their spatial pattern of MT-MT association. KMTs strongly interact with neighboring MTs at the spindle poles, while non-KMTs show a broad region of MT-MT interaction within the middle of the spindle, potentially forming interpolar bundles (Mastronarde et al., 1993).

Figure 9 with 4 supplements see all
Positions of MT-MT associations.

(A) Schematic illustration showing the mapping of the number of MT-MT associations on the pole-to-pole axis (P1, position = 0; P2, position = 1). The number of associations is measured in defined segments (20 nm). KMTs are illustrated in red, non-KMTs in yellow, and areas of MT-MT association in gray. (B) Graph showing the number of KMTs associated with other MTs plotted against the relative position on the pole-to-pole axis. KMT number is normalized by the MT density. The defined association distances for KMTs with other MTs in the spindle are given in the insert. (C) Number of non-KMTs associated with neighboring MTs plotted against the relative position on the pole-to-pole axis.

Table 10
Average number of associations of KMTs and non-KMTs with MT lattices.
Data setMT typeInteraction distances [nm]
2530354550
Spindle #1*KMTs4.8
(±1.5)
8.6
(±2.5)
12.4
(±3.4)
18.8
(±4.9)
1.3
(±5.5)
Non-KMTs4.4
(±1.5)
7.0
(±2.6)
9.6
(±3.7)
13.0
(±5.4)
16.2
(±6.2)
Spindle #2*KMTs4.2
(±1.3)
5.8
(±1.8)
8.0
(±2.6)
13.3
(±4.1)
16.0
(±4.8)
Non-KMTs3.2
(±0.9)
4.0
(±1.3)
5.2
(±1.8)
8.2
(±3.1)
9.8
(±3.7)
Spindle #3*KMTs4.2
(±1.2)
8.0
(±2.3)
12.4
(±3.4)
18.6
(±4.8)
21.2
(±5.4)
Non-KMTs3.6
(±1.2)
5.2
(±2.3)
8.0
(±3.3)
11.6
(±4.7)
13.2
(±5.3)
All spindles*KMTs4.4
(±1.3)
7.4
(±2.3)
10.6
(±3.2)
16.4
(±4.7)
19.0
(±5.3)
Non-KMTs3.6
(±1.2)
5.4
(±2.2)
7.4
(±3.1)
10.8
(±4.5)
12.4
(±5.1)
  1. *

    Numbers are given as mean ±STD.

Finally, we were interested in how the distribution patterns of MT-MT associations change in relation to the position in the spindle. With our high-resolution 3D data sets covering all MTs in the spindle, we decided to investigate the number and the length of associations for both KMTs and non-KMTs as a function of the distance between MTs. Firstly, we analyzed the association of KMTs with any MT in the spindle (Figure 9—figure supplement 2A-D). As expected, with an increase in the considered distance between MTs, KMTs showed an increase in the number and also in the average length of interactions (Table 10 and Table 11). For a given MT-MT distance of 35 nm, each KMT associates on average with 10.6 ± 3.2 (mean ±STD, n=2579) other MTs in the spindle with an average association length of 145 ± 186 nm (±STD, n=2579). Secondly, we also analyzed the association of non-KMTs with any MT in the spindle. Non-KMTs showed a similar pattern of increase in the number and length of associations with increasing distances between individual MTs. For 35 nm, each non-KMT associates on average with 7.4 ± 3.1 (mean ±STD, n=16256) other MTs in the spindle with an average association length of 103±118 nm (mean ±STD, n=16256). With an increase in the distance between MTs, we observed that KMTs tend to show a higher number and a higher average length of associations compared to non-KMTs. Importantly, these results were consistent for all selected association distances (Figure 9—figure supplement 2E-F).

Table 11
Average length of associations of KMTs and non-KMTs with MT lattices.
Data setMT typeInteraction distances [nm]
2530354550
Spindle #*KMTs81.3
(±88.8)
119.7
(±151.1)
163.9
(±207.5)
241.3
(±301.9)
271.0
(±335.9)
Non-KMTs58.3
(±54.1)
78.3
(±79.9)
107.7
(±116.9)
165.1
(±195.1)
187.9
(±227.0)
Spindle #2*KMTs69.5
(±69.9)
93.2
(±107.0)
124.3
(±146.0)
207.8
(±252.3)
252.2
(±314,9)
Non-KMTs59.2
(±53.2)
73.2
(±71.9)
92.3
(±97.3)
145.8
(±170.5)
175.1
(±213.0)
Spindle #3*KMTs66.1
(±63.4)
97.3
(±117.8)
143.2
(±191.7)
231.3
(±321.2)
263.4
(±362.2)
Non-KMTs54.3
(±51.7)
74.5
(±86.4)
104.6
(±133.7)
165.6
(±218.7)
191.3
(±252.0)
All spindles*KMTs73.0
(±76.2)
104.6
(±129.2)
145.1
(±186.0)
225.6
(±292.3)
261.9
(±336.8)
Non-KMTs57.2
(±53.1)
75.4
(±80.5)
102.2
(±118.9)
159.1
(±197.2)
184.9
(±232.1)
  1. *

    Numbers are given as mean ±STD.

Discussion

Large-scale reconstruction by serial-section electron tomography (Fabig et al., 2020; Redemann et al., 2018; Redemann et al., 2017) allowed us to quantitatively analyze KMT organization in individual k-fibers and in the context of whole mitotic spindles.

Methodological considerations

For generating 3D reconstructions of spindles, we applied electron microscopy of plastic sections. The use of plastic sections suffers from the fact that samples undergo a collapse in the electron beam during imaging, and this is obvious by a reduction in the section thickness (Luther et al., 1988; McEwen and Marko, 1998; O’Toole et al., 2020). By expanding the complete stack of serial tomograms (Figure 2—figure supplement 2), it is possible to correct this loss in Z, and we did so for our three data sets covering whole metaphase spindles in HeLa cells.

Here, we used serial, semi-thick sections of plastic-embedded material for a 3D tomographic reconstruction of whole spindles. Although serial sectioning is never perfect, in that the section thickness within ribbons always shows some variability, we were able to produce data sets of remarkable similarity. This is true for our analysis of MT length distribution (Figure 4; Figure 4—figure supplement 1) and our measurements of minus-end distance to the spindle poles and minus-end positioning (Figure 5; Figure 5—figure supplement 2). In combination with a semi-automatic segmentation and stitching of MTs (Lindow et al., 2021; Weber et al., 2012), our approach enabled us to reliably model individual MTs over section borders, thus allowing a quantitative study of MT length and end-positioning in whole spindles. In the future, we will use this routine approach to quantify MT organization also in other mammalian systems, such as RPE1 and U2OS cells.

In electron microscopic images, centrosomes or spindle poles are visible by pairs of centrioles surrounded by electron-dense pericentriolar material (PCM). Since these membrane-less organelles do not show a clear boundary in thin sections or in electron tomograms, it is not immediately obvious how to define the edge of the spindle pole. Inspired by earlier studies on the early C. elegans embryo (O’Toole et al., 2003; Redemann et al., 2017; Weber et al., 2012), we determined the edge of the spindle pole from the density distribution of non-KMT minus ends in the spindle. The non-KMT minus-end density peaked a micron away from the pole and then fell before leveling off at constant non-KMT minus-end density in the spindle bulk. We defined the edge of the spindle pole as twice the half-width from the center of the non-KMT minus-end density peak. In the HeLa spindles, this was 1.7 µm from the mother centriole. We applied the same cutoff in a parallel study on the dynamics of mammalian k-fibers (see Figure 1 in Conway et al., 2022).

In this parallel study, we supplemented our electron tomography data on the KMT length distribution with light microscopic data. Essentially, our 3D reconstructions show a distribution of KMT length in metaphase that is strikingly similar to the distribution plot of KMT length as obtained by biophysical modeling in combination with light microscopy (see Figure 8B-D in Conway et al., 2022). All this shows that light and electron microscopy produces truly complementary data, although completely different methods of sample preparation and data analysis have to be applied.

KMT organization

Counting the total number of KMTs and non-KMTs in our spindles, we show that only ~14% of all MTs in the reconstructed spindles were KMTs. However, this percentage in the total number of all MTs corresponds to ~25% of the tubulin mass as measured in parallel by light microscopy (Conway et al., 2022). Comparing the average length of KMTs and non-KMTs, we also find that KMTs are on average twice as long as non-KMT. Thus, a higher value in the average length of KMTs versus non-KMTs contributes to a higher percentage in the tubulin mass of KMTs compared to all other MTs in the spindle.

The length distribution of KMTs in HeLa cells shows striking similarities to the distribution of KMTs observed in the early C. elegans embryo (Redemann et al., 2017). Both human KMTs attached to monocentric kinetochores and also nematode KMTs associated with dispersed holocentric kinetochores show a rather flat length distribution and a rather low number of both very short and very long KMTs. In contrast, non-KMTs in both systems show an exponential length distribution with a very high occurrence of very short MTs (around 57% of the non-KMTs and ~21% of KMT in HeLa cells were less than 2 µm in length). Exponential length distributions as found for non-KMTs are typical of dynamic instability kinetics (Burbank et al., 2007; Loiodice et al., 2019). The observed length distribution of KMTs, however, indicates a difference in dynamics and possibly higher stability of the plus-ends against MT depolymerization. Taken together, all this argues that KMTs in both spindles have distinct properties different from those of non-KMTs.

A difference in the properties between KMTs and non-KMTs is also obvious after a cold treatment of cells. Such treated cells show cold-stable k-fibers, while most of the non-KMTs undergo depolymerization upon exposure to cold (Maiato et al., 2004). Here, we can only speculate about this resistance to cold temperature. Likely, KMTs are stabilized by interaction with the kinetochores (Brinkley and Cartwright, 1975; DeLuca et al., 2006; Warren et al., 2020) and/or by KMT-KMT/KMT-non-KMT associations, possibly mediated by several MT-associated proteins (Agarwal, 2018). It is also possible that non-KMTs, involved in k-fiber maturation during mitosis (Maiato et al., 2004), contribute to such stabilization of k-fibers in mammalian cells.

Electron tomography revealed that on average nine KMTs are attached to each kinetochore in HeLa cells in metaphase. This result differs from previous observations in PtK1 cells (McEwen et al., 1997; O’Toole et al., 2020). In this marsupial cell line, about 20 KMTs were reported to connect to the kinetochores. This difference in the number of attached KMTs could be related to kinetochore size. As previously observed by light microscopy, kinetochores in HeLa cells are about half the size of kinetochores in PtK1 cells (Cherry et al., 1989). Similarly, kinetochore size in PtK1 cells was 0.157 ± 0.045 µm2 (mean ±STD) as observed by electron tomography (McEwen et al., 1998a), whereas kinetochores in HeLa cells, as determined indirectly in this study, have an estimated size of about 0.107 ± 0.075 µm2 (mean ±STD). Possibly, the area of the outer kinetochore might indirectly define the size and/or the number of available free binding sites for MTs (Drpic et al., 2018; Monda and Cheeseman, 2018). Concerning the number of kinetochore-attached MTs, it is interesting to note here that the number of KMTs per k-fiber is not related to the position of these KMTs in the spindles. In fact, central, intermediate and peripheral kinetochores show similar average numbers of attached KMTs. Thus, the peripheral position of k-fibers within the spindle accompanied by an increase in the global tortuosity has no effect on the number of KMTs in the k-fibers.

KMTs in our reconstructed k-fibers are of different lengths, confirming previous observations (McDonald et al., 1992; O’Toole et al., 2020; Sikirzhytski et al., 2014). In fact, many KMTs are relatively short (~20% of KMTs were shorter than 2 µm; Figure 4A), and half of the KMT minus ends are not positioned in the defined MT-centrosome interaction area. Per definition, these short KMTs in k-fibers are not directly associated with the spindle poles. Interestingly, only 5% of the analyzed k-fibers show a length distribution in which none of the analyzed KMTs is positioned in the MT-centrosome interaction area (Figure 5—figure supplement 3). When analyzing KMTs in the one-cell C. elegans embryo, we found that only about 20% of the KMT minus ends were located within 2 µm of their corresponding mother centriole. This suggested that the majority of KMTs in C. elegans do not contact the centrosomes. In agreement with previously published data (McDonald et al., 1992; O’Toole et al., 2020), our tomographic analysis of mammalian KMTs thus suggests that the k-fibers in HeLa cells mediate a semi-direct connection with the spindle poles, in which at least one KMT of the k-fibers is directly connected to the poles, while the other KMTs of the fiber are indirectly linked to non-KMTs (Figure 10). Thus, spindles in nematode embryos and in mammalian cells are similar in that anchoring of KMTs into the spindle network can be observed.

Model of a k-fiber showing a semi-direct connection between a kinetochore and a spindle pole.

(A–B) Three-dimensional views of a selected 3D-reconstructed k-fiber with an overlay area drawn around KMTs using the alpha shape method. The KMTs are shown as red lines and the ends are marked with red dots. The approximate position of the pole is indicated (p). The same k-fiber is shown from two different perspectives (X/Y view in A; Z/Y view in B). Scale bars, 1 µm. (C) Schematic model of a semi-direct connection between a kinetochore (chromosome in blue, paired kinetochores in dark red) and a spindle pole (MT-centrosome interaction area and centrioles in gray) as established by a single k-fiber. KMTs are shown as red lines, KMT ends as light red circles. (D) Model of the k-fiber (as shown in C) associated with the surrounding non-KMT network. Non-KMTs are shown as yellow lines, non-KMT ends as yellow circles. KMT-KMT interactions are indicated by light red areas, KMT-non-KMT interactions by light yellow areas.

Interestingly, we observed a difference in KMT length and their minus-end distance to the pole in central versus peripheral KMTs. Centrally located KMTs were shorter, and their minus ends showed a shorter distance to the mother centriole compared to peripheral KMTs. This difference is most likely related to the roundedness of the mitotic spindles (Taubenberger et al., 2020). To test whether the roundedness of spindles and the organization of KMTs in terms of KMT length and minus-end distribution are directly related, it would be interesting to analyze the organization of KMTs in spindles showing a lower degree of rounding up during mitoses such as in PtK1 (McDonald et al., 1992) and RPE1 cells (O’Toole et al., 2020).

Extending previous knowledge, we have shown that k-fibers in our reconstructions show a remarkable morphological variability, as obvious by a change in the circumference of the k-fibers along their entire length (Figure 10A–B). This variability in the circumference of the k-fibers is reflected in an increase in the local tortuosity of KMTs at positions close to the spindle poles. An increase in the tortuosity of KMTs at spindle poles might promote the anchoring of the broadened k-fibers into the non-KMT network through MT-MT interactions (Figure 10C–D).

Here, we consider the bundled KMTs as the ‘core’ of the k-fibers (Figure 10C). We used the annotated KMTs in our reconstruction to identify other non-KMTs associated with these KMTs. In other words, we annotated the KMTs in the spindles to ‘fish out’ other non-KMTs out of more than 6000 MTs to identify those non-KMTs that were positioned in the vicinity of the reconstructed KMTs. Explicitly, the results obtained from our approach do not exclude models of KMT organization, in which the k-fiber is a tight bundle that continues to the pole with changing composition of KMTs and associated non-KMTs along its length. In this sense, differences in either the length of KMTs or in the loss of KMTs from the k-fiber might simply reflect a MT exchange with the spindle (Figure 10D). Our consideration of KMTs as the cores of k-fibers is also not in disagreement with a dynamic change in k-fiber composition during the maturing of those fibers in metaphase (Begley et al., 2021; Maiato et al., 2004). Unfortunately, our 3D reconstructions can deliver only snapshots of the very dynamic mitotic process.

While both KMTs and non-KMTs show a clear correlation in the number and the average length of associations (Figure 9—figure supplement 2), both MT populations show differences in the position of these associations. In contrast to non-KMTs, KMTs show a high tendency to associate with non-KMTs at the spindle poles (Figure 8F–G; Figure 9C–D). This tendency to interact at spindle poles is independent of the chosen distance of MT interaction. In accord with the previously discussed broadening of the k-fibers at their pole-facing end, our results suggest that KMTs preferably associate with other MTs at the spindle poles. In contrast, non-KMTs show a flat pattern of interaction with other MTs at association distances of 25 and 35 nm. Moreover, an increase in the association distance from 35 nm to 50 nm, shows a higher tendency of non-KMTs to associate with MTs in the center of the spindle, very likely related to the organization of interpolar MTs in the center of the spindle (Figure 8—figure supplement 1F; Kajtez et al., 2016; Mastronarde et al., 1993; Vukušić et al., 2017). In general, it would be interesting to analyze the organization of these interpolar MTs, the structure of the KMTs in the k-fibers, and also the recognized patterns of MT-MT interaction during other stages of mitosis, for instance at anaphase. Patterns of the interaction of KMTs with non-KMTs might be more obvious during the segregation of the chromosomes.

Implications for models on spindle organization

As previously noted, we have combined our 3D reconstructions with additional live-cell imaging and biophysical modeling in a parallel publication (Conway et al., 2022). Combining data on the length and the position of KMT minus ends in spindles (as obtained here by electron microscopy), and the turnover and movement of tubulin in KMTs as generated by light microscopy, a model was proposed in which KMTs predominantly nucleate de novo at kinetochores, with KMTs growing towards the spindle poles. A major outcome of this parallel study is that KMTs in spindles grow along the same trajectories as non-KMTs and that both the KMTs and non-KMTs are well aligned throughout the spindle, leading to the assumption that spindles can be considered as active liquid crystals (Brugués and Needleman, 2014; Oriola et al., 2020). This might apply to both centrosomal mitotic as well as acentrosomal female meiotic spindles (Redemann et al., 2018; Redemann et al., 2017). Such liquid crystals can be characterized by the degree of local MT alignment, expressed by the nematic order parameter. Interestingly, the analyzed spindles show a high nematic order parameter (S = 0.81 ± 0.02) near the chromosomes, whereas the nematic order parameter (S = 0.54 ± 0.02) is lower at the spindle poles (Conway et al., 2022). Along this line, KMTs in our electron tomography study are well aligned in the middle of the spindle, while the order of the KMTs in the k-fibers is progressively lost at positions closer to the spindle poles. While KMTs are growing out from the kinetochores towards the centrosomes, the observed broadening of the k-fibers at the spindle poles might be a direct consequence of a decrease in the internal structural organization of the spindle trajectories (i.e. of the surrounding non-KMTs). In the future, it will be important to analyze k-fibers in other fully 3D-reconstructed mammalian spindles to advance the developed model on KMT outgrowth in the context of such well-defined trajectories.

Materials and methods

Key resources table
Reagent type (species) or resourceDesignationSource or referenceIdentifiersAdditional information
Strain, background (HeLa, Kyoto)Gerlich LabIMBA, Vienna, Austria--
Software, algorithmSerialEM
Boulder Laboratory for
3-Dimensional Electron Microscopy of cells
Colorado, USA
https://bio3d.colorado.edu/
Mastronarde, 2003
--
Software, algorithmIMOD
Boulder Laboratory for
3-Dimensional Electron Microscopy of cells
Colorado, USA
http://bio3d.colorado.edu/
Kremer et al., 1996
--
Software, algorithmAmira
Thermo Fisher Scientific, USA
https://www.zib.de/software/amira
Stalling et al., 2005
--
Software, algorithmASGA
Robert Kiewisz /
Müller - Reichert Lab
Dresden, Germany
https://github.com/RRobert92/
Kiewisz and Müller-Reichert, 2021
-https://kiewisz.shinyapps.io/ASGA
Software, algorithmASGA - 3D Viewer
Robert Kiewisz /
Müller - Reichert Lab
Dresden, Germany
https://github.com/RRobert92/
Kiewisz and Müller-Reichert, 2022
-https://cfci.shinyapps.io/ASGA_3DViewer/

Cell line

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For all experiments, we have used a HeLa Kyoto cell line obtained from Dr. Daniel Gerlich (IMBA, Vienna), which was given to the Gerlich lab by S. Narumiya (Kyoto, Japan; RRID: CVCL_1922) and validated using the Multiplex Human Cell Line Authentication test (MCA). Furthermore, the HeLa Kyoto cell line was checked for mycoplasma with a PCR test kit. This cell line was not on the list of commonly misidentified cell lines as maintained by the International Cell Line Authentication Committee.

Cultivation of cells

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HeLa cells (Guizetti et al., 2011) were grown in Dulbecco’s Modified Eagle’s Medium (DMEM) supplemented with 10% fetal bovine serum (FBS) and 100 units/ml of penicillin/streptomycin (Pen/Strep). Flasks were placed in a humidified incubator at 37°C with a supply of 5% CO2. For electron microscopy, cells in mitosis were enriched by applying the shake-off technique (Kiewisz et al., 2021). Flasks with cell confluency of 60–80% were shaken against the laboratory bench. The medium with detached cells was then collected, centrifuged at 1200 rpm for 3 min at room temperature, and resuspended in 1 ml of pre-warmed DMEM medium.

Electron tomography

Specimen preparation for electron microscopy

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Cultures enriched in mitotic HeLa cells were further processed for electron microscopy essentially as described (Guizetti et al., 2011; Kiewisz et al., 2021). Briefly, sapphire discs with a diameter of 6 mm were cleaned in Piranha solution (1:1 H2SO4 and H2O2, v/v), coated with poly-L-lysine (0.1% in ddH2O, w/v), and dried for 2 hrs at 60°C. Furthermore, the discs were coated with fibronectin (1:10 dilution in 1 x PBS, v/v) for 2 hr and stored in a humidified incubator until further used. The sapphire discs were then placed into custom-designed 3D-printed incubation chambers (Kiewisz et al., 2021). Subsequently, cells were seeded on the coated sapphire discs and incubated for 10 min in a humidified incubator at 37°C supplied with 5% CO2. This allowed the mitotic cells to re-attach to the surface of the coated sapphire discs and continue to divide.

High-pressure freezing and freeze substitution

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Cells were cryo-immobilized using an EM ICE high-pressure freezer (Leica Microsystems, Austria). For each run of freezing, a type-A aluminum carrier (Wohlwend, Switzerland) with the 100 µm-cavity facing up was placed in the specimen loading device of the EM ICE. The cavity of the type-A carrier was filled with 5 µl of DMEM containing 10% BSA. The carrier was then immediately closed by placing a 6 mm-sapphire disc with attached cells facing down on top of the type-A carrier. Finally, a spacer ring was mounted on top of the closed carrier, and freezing was started. Samples were frozen under high pressure (~2000 bar) with a cooling rate of ~20000°C/s (Reipert et al., 2004). Frozen samples were then opened under liquid nitrogen and transferred to cryo-vials filled with anhydrous acetone containing 1% (w/v) osmium tetroxide (EMS, USA) and 0.1% (w/v) uranyl acetate (Polysciences, USA). Freeze substitution was performed in either a Leica AFS or a Lecia AFS II (Leica Microsystems, Austria). Samples were kept at –90°C for 1 hr, warmed up to –30°C with increments of 5°C/hr, kept for 5 hrs at –30°C, and then warmed up to 0°C (increments of 5°C/hr). Finally, samples were allowed to warm up to room temperature. After freeze substitution, samples were washed three times with pure anhydrous acetone and infiltrated with Epon/Araldite (EMS, USA) using increasing concentrations of resin (resin:acetone: 1:3, 1:1, 3:1, then pure resin) for 1 hr each step at room temperature (Müller-Reichert et al., 2003). Samples were infiltrated with pure resin overnight and then embedded by using commercial flow-through chambers (Leica Microsystems, Austria) designed for sapphire discs of a diameter of 6 mm. Samples were polymerized at 60°C for 36 hr.

Pre-selection of staged cells

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To select cells in metaphase, resin-embedded samples were pre-inspected using an Axiolab RE upright brightfield microscope (Zeiss, Germany) with a 5 x and a 40 x objective lens (Zeiss, Germany). Selected cells in metaphase were sectioned using an EM UC6 ultramicrotome (Leica Microsystems, Austria). Ribbons of semi-thick (~300 nm) serial sections were collected on Formvar-coated copper slot grids, post-stained with 2% (w/v) uranyl acetate in 70% (v/v) methanol, followed by 0.4% (w/v) lead citrate (Science Services, USA) in double-distilled water. In addition, 20 nm-colloidal gold (British Biocell International, UK) was attached to the serial sections, serving as fiducial markers for subsequent electron tomography. The selected cells were then pre-inspected at low magnification (~2900 x) using either an EM906 (Zeiss, Germany) or a TECNAI T12 Biotwin (Thermo Fisher Scientific, USA) transmission electron microscope operated at either 80 or 120 kV, respectively.

Acquisition and calculation of tomograms

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Serial sections of the selected cells were then transferred to a TECNAI F30 transmission electron microscope (Thermo Fisher Scientific, USA) operated at 300 kV and equipped with a US1000 CCD camera (Gatan, USA). Using a dual-axis specimen holder (Type 2040, Fishione, USA), tilt series were acquired from –65° to +65° with 1° increments at a magnification of 4700 x and a final pixel size of 2.32 nm applying the SerialEM software package (Mastronarde, 2005; Mastronarde, 2003). For double-tilt electron tomography, the grids were rotated for 90 degrees and the second tilt series were acquired using identical microscope settings (Mastronarde, 1997). The tomographic A- and B-stacks were combined using IMOD (Kremer et al., 1996; Mastronarde and Held, 2017). For each spindle reconstruction, montages of 2×3 frames were collected. Depending on the orientation of the spindles during the sectioning process, between 22 and 35 serial sections were used to fully reconstruct the volumes of the three selected spindles (Table 9).

Segmentation of MTs and stitching of serial tomograms

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As previously published (Redemann et al., 2014; Weber et al., 2012), MTs were automatically segmented using the ZIB Amira (Zuse Institute Berlin, Germany) software package (Stalling et al., 2005). After manual correction of MT segmentation, the serial tomograms of each recorded cell were stitched using the segmented MTs as alignment markers (Lindow et al., 2021) Following this pipeline of data acquisition and 3D reconstruction, three complete models of HeLa cells in metaphase were obtained (Table 9). As also done in our previous study on mitosis in C. elegans (Redemann et al., 2017), we discarded MTs with one endpoint found within 100 nm from the border of a reconstructed tomogram. With high probability, these MTs were leaving the tomographic volume. These discarded MTs account for <1% of all traced MTs in all datasets. Therefore, we do not expect a relevant error in this analysis.

Z-correction of stacked tomograms

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Each stack of serial tomograms was expanded in Z to correct for a sample collapse during data acquisition (McEwen and Marko, 1998). We corrected this shrinkage by applying a Z-factor to the stacked tomograms (Figure 2—figure supplement 2; O’Toole et al., 2020). Taking the microtome setting of 300 nm, we multiplied this value by the number of serial sections. For each spindle, we also determined the thickness of each serial tomogram and then calculated the total thickness of the reconstruction. The Z-factor was then determined by dividing the actual thickness of each stack of tomograms by the total thickness as determined by the microtome setting. Such calculated Z-factors (1.3 for spindle #1, Figure 2B, C and F; 1.4 for spindle #2, Figure 2D and G; and 1.42 for spindle #3, Figure 2E and H) were then applied to our full spindle reconstructions. All quantitative data in this publication are given for the Z-expanded spindles. For comparison, values for the non-expanded spindles are also given in Table 12 and Table 13.

Table 12
Quantification of KMT ultrastructure before and after application of Z-expansion to the 3D models.
Data setLength of KMTs [µm]*Length of non- KMTs [µm]*No. of KMTs per kinetochore*No. of KMTs in the MT-centrosome interaction area*Mean KMT minus-end distance to poles [µm]No. of KMTs associated with poles [%]No. of non-KMTs associated with poles [%]
BeforeAfterBeforeAfterBeforeAfterBeforeAfterBeforeAfterBeforeAfterBeforeAfter
Spindle #13.23
(±1.49)
3.59
(±1.57)
2.03
(±1.6)
2.13
(±1.67)
8.04
(±1.86)
8.04
(±1.86)
4.1
(±1.8)
5.0
(±1.8)
1.161.7262.261.244.544.3
Spindle #23.69
(±1.87)
3.82
(±1.97)
1.85
(±1.55)
1.95
(±1.60)
9.75
(±2.18)
9.75
(±2.18)
2.4
(±2.0)
3.1
(±2.3)
2.472.8753.631.528.828.6
Spindle #34.03
(±1.79)
4.27
(±1.93)
1.91
(±1.80)
2.07
(±1.93)
7.49
(±1.91)
7.49
(±1.91)
3.4
(±1.8)
4.1
(±2.0)
1.352.1262.054.242.341.9
  1. *

    Numbers are given as mean ±STD.

Table 13
Quantification of k-fiber organization before and after application of Z-expansion to the 3D models.
Data setDensity of KMTs at the kinetochore [KMT/µm2]*KMT-KMT distance at the kinetochore [nm]*Global tortuosity of KMTs*% of curved KMTs*Area of k-fibers [µm2]*% of KMTs in a k-fibers*
BeforeAfterBeforeAfterBeforeAfterBeforeAfterBeforeAfterBeforeAfter
Spindle #1151
(±74)
122
(±62)
61
(±11)
67
(±20)
1.09
(±0.10)
1.11
(±0.11)
36.139.80.063
(±0.09)
0.08
(±0.1)
34
(±27)
64
(±27)
Spindle #2137
(±68)
99
(±45)
65
(±12)
78
(±23)
1.06
(±0.06)
1.07
(±0.07)
21.428.40.068
(±0.10)
0.09
(±0.11)
70
(±25)
70
(±25)
Spindle #3175
(±123)
117
(±72)
66
(±12)
76
(±23)
1.11
(±0.11)
1.13
(±0.13)
39.547.10.080
(±0.15)
0.12
(±0.24)
59
(±39)
59
(±29)
  1. *

    Numbers are given as mean ±STD.

Software packages

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We used the ZIB extension of the Amira software (Zuse Institute Berlin, Germany) for further quantitative analyses (Stalling et al., 2005). In addition, an automatic spatial graph analysis (ASGA) software tool was created for the quantification of KMT length and minus-end distribution (Kiewisz and Müller-Reichert, 2021). The ASGA software tool was also used to quantify the position of each k-fiber in the mitotic spindles and determine the tortuosity, the cross-section area, the shape and the density of KMTs in the k-fibers and the MT-MT interactions.

Staging of spindles

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For staging of the three reconstructed metaphase spindles, we determined the inter-kinetochore distance for each k-fiber pair. More precisely, we analyzed the distance between the paired outer kinetochores. For this, the closest neighboring sister kinetochores were determined. The center of each kinetochore was then defined as a median position of all KMT plus ends associated with each selected kinetochore, and the inter-kinetochore distance was then calculated as the 3D distance between the defined median centers of each kinetochore pair. For each mitotic spindle, the inter-kinetochore distance is given as the mean value (±STD). As an additional criterion for mitotic staging, the pole-to-pole distances were measured. For this, we analyzed the 3D distance between the centers of the manually segmented mother centrioles in each data set. This read-out was used to determine the spindle size at metaphase.

Classification of MTs

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MTs with their putative plus end associated with the chromosomes were defined as KMTs (Figure 2—figure supplement 2). Characteristically, these KMTs showed a parallel arrangement at the site of attachment to the chromosomes. Unfortunately, identification of individual kinetochores in our electron tomograms was hindered by the fact that prominent single and electron-dense KMT attachment sites, as described previously for conventionally fixed cells (McEwen et al., 1998b), were not always clearly visible after cryo-fixation by high-pressure freezing. All other MTs in our 3D reconstructions were classified as non-KMTs.

MT-centrosome interaction area

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For each non-KMT, the end closest to the nearest mother centriole was defined as the minus end. The absolute distance of each putative non-KMT minus end to the nearest mother centriole was measured in 3D. The number of the non-KMT minus ends was then plotted against their distance to the pole. We then fit a Gaussian distribution to the non-KMT minus-end density. We also defined the peak of the Gaussian distribution to determine its half-width. The border of spindle poles, termed here the border of the MT-centrosome interaction area, was defined as twice the half-width, which was 1.7 µm from the centrosome.

Position of MT minus ends

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To analyze the position of KMT and non-KMT minus ends in the metaphase spindles, two measurements were performed. Firstly, the 3D distance between the nearest mother centriole and the KMT and the non-KMT minus ends was determined. Secondly, the relative position of these ends on the pole-to-kinetochore and the pole-to-pole axis was determined. For each KMT minus end, the relative position is given as the normalized position between the mother centriole (position = 0) and the kinetochore (position = 1; Figure 5—figure supplement 1). For each non-KMTs minus end, the relative position is given as the normalized position between two spindle poles (pole1 = 0, and pole2 = 1; Figure 5A). The distribution of the relative positions of KMT and non-KMT minus ends (mean ±STD) is given for each data set. The number and percentage of KMT and non-KMT ends not associated with the spindle pole were defined as minus ends detected farther than the calculated MT-centrosome interaction area. To visualize an approximated MT-centrosome interaction area on both the pole-to-kinetochore and the pole-to-pole axis, we defined the relative position of the average border of this interaction area. The average border of this interaction area was defined as the average relative position of all KMTs and ranged from –0.2 to 0.2.

Length distribution of MTs

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The full length of each reconstructed KMT and non-KMT was measured, and the average (±STD) is given for each data set. We also analyzed the percentage of short versus long KMTs. For each data set, short KMTs were defined as those shorter than 1.7 µm in length. This threshold was chosen based on the MT-centrosome interaction area. Long KMTs were identified as KMTs longer than the half-spindle length for each given data set.

Defining kinetochore position

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To determine the position of each k-fiber in the mitotic spindle, a position model was created that is based on the location of each kinetochore on the metaphase plate. For this, the kinetochores of each spindle were projected in 2D space on the X/Z axis and an ellipse with a semi-major (called a-axis) and a semi-minor axis (called b-axis) was fitted onto all projected kinetochores. The fitted ellipse was then divided into three regions ranging from 0 to 50% (central region), 50 to 75% (intermediate region), and 75 to 100% (peripheral region). Kinetochores with associated k-fibers were then assigned to these three regions.

Global tortuosity of KMTs

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For the analysis of global KMT tortuosity, the ratio of the KMT spline length and the 3D distance between the plus and the minus end for each KMT was measured. The distribution of KMT tortuosity (mean ±STD) is given. In addition, the correlation of the tortuosity of KMTs with their length is given as a fitted polynomial line calculated as a local polynomial regression by the locally estimated scatterplot smoothing ‘loess’ method. A confidence interval for the created polynomial line was calculated with the t-based approximation, which is defined as the overall uncertainty of how the fitted polynomial line fits the population of all data points. Local polynomial regressions and confidence intervals for all data sets were calculated using the stat 4.0.3 R library (R Development Core Team, 2021).

Local tortuosity of KMTs

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For the calculation of the local tortuosity, each KMT was subsampled with segments of a length of 500 nm. Both the tortuosity and the relative position along the pole-to-kinetochore axis were measured for each segment. In addition, the correlation of local KMT tortuosity against the relative position is given. Local polynomial regressions and confidence intervals for all data sets were calculated using the stat 4.0.3 R library (R Development Core Team, 2021).

The polygonal cross-section area of k-fibers

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The cross-section area was calculated every 500 nm along each k-fiber. For each defined k-fiber cross-section, the KMT positions were mapped on a 2D plane, and the polygonal shape of the k-fiber cross-sections was calculated based on the position of the KMTs. The polygonal shape was calculated with the alpha shape algorithm (α = 10) using the ‘ashape3d’ function of the alphashape3d 1.3.1 R library (Lafarge and Pateiro-Lopez, 2020). The alpha shape is the polygonal shape formed around a given set of points (KMTs from a cross-section) created by a carving space around those points with a circle of a radius defined as α. The polygonal shape was then built by drawing lines between contact points. In order to calculate the area from the polygonal shape of a k-fiber cross-section, a polygonal prism was created by duplicating and shifting a polygonal shape 1 µm in the X/Y/Z dimension. This created a prism with a height of 1 µm. The volume of the created 3D object (prism) was then calculated using the alphashape3d 1.3.1 R library (Lafarge and Pateiro-Lopez, 2020). From this, a polygonal area could be calculated by dividing the prism volume (Vpp) by prism high (hpp = 1 µm). The distribution of the k-fiber polygonal area along the pole-to-kinetochore axis is given as a fitted polynomial line of local polynomial regression using the ‘loess’ method. Confidence intervals were calculated with the t-based approximation using the stat 4.0.3 R library (R Development Core Team, 2021).

Density of KMTs in k-fibers

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The density of KMTs in the k-fibers was calculated in segments of 500 nm length along the entire path of each fiber. To determine the percentage of KMTs that were enclosed in the k-fiber for each cross-section, the number of KMTs enclosed in the given k-fiber section and the circular area were determined. The radius of the circular area was calculated for each k-fiber at the position of KMT attachment to the kinetochores. The distribution of the k-fiber density along the pole-to-pole axis is given as a fitted polynomial line and a confidence interval calculated with the t-based approximation using the stat 4.0.3 R library (R Development Core Team, 2021).

Interaction of KMTs with non-KMTs

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A possible association between KMT minus ends and other MT lattices was measured by calculating the 3D distance between KMT ends and every MT lattice in the reconstructed spindle. An interaction between KMT minus ends and a MT lattice was identified when KMT minus ends were found within a given interaction distance to any MT lattice. The defined interaction distances were 25, 30, 35, 45, 50, 75, and 100 nm. To account for differences in the density of MTs along the pole-to-pole axis, each KMT interaction was normalized by calculating the local MT density around each KMT end. This was achieved by selecting a voxel of 0.001 µm3 with the KMT end in its center and calculating the local MT density by dividing the number of potential interactions by the voxel volume. For visualization, each KMT was labeled based on the type of detected interaction with KMTs or non-KMTs. KMTs without any interaction were also labeled. The percentage of KMTs with any interaction was measured and the average value for all data sets is given (mean ±STD).

To identify possible MT minus-end associations with KMT lattices, the 3D distances of the MT minus ends to KMT lattices were calculated. An association between MT minus ends and KMT lattices was detected when MT minus ends were positioned within defined interaction distances to the KMT lattices. Again, we considered the following interaction distances: 25, 30, 35, 45, 50, 75, and 100 nm. In addition, each interaction was normalized by the local MT density, as described above. The percentage of KMTs with any interaction was measured and the average from all datasets is given (mean ±STD).

To analyze the position of MT-MT associations, the relative position of MT minus ends on the pole-to-kinetochore axis was calculated. The relative position of each minus end is given as the position between the kinetochore (position = 1) and mother centriole (position = 0) along the spindle axis, normalized by the MT density.

Analysis of KMT-KMT distances

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The KMT-KMT distances at given k-fiber cross-sections were measured by a K-nearest neighbor estimation. An estimation was achieved by calculating a distance matrix between all selected KMTs. Each KMT-KMT connection was ranked according to its distance. Finally, for each KMT in a k-fiber, the closest KMT neighbors were selected. For each k-fiber, the mean KMT-KMT distance and the standard deviation were calculated.

Interaction of MTs

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The interaction between MTs was calculated in steps of 20 nm along each MT. For each MT segment, the distance to a neighboring MT was calculated. In addition, the length of interaction was analyzed for each detected MT-MT interaction. The length of interaction between MTs was calculated as a sum of the 20 nm segments. This analysis was performed for defined interaction distances of 25, 30, 35, 45, and 50 nm. The frequency plots for the average number of interactions per MT and the average length of interaction are given for each interaction distance. Each MT segment is labeled based on the number of interactions.

Error analysis

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For the tracing of MTs, the error associated with our approach was previously analyzed for the 3D reconstructions of mitotic centrosomes in the early C. elegans embryo using serial semi-thick plastic sections (Weber et al., 2012). Although the data on mammalian spindles is larger, the tomogram content of this current study is similar to the published centrosome data sets, and thus we assume that the error MT tracing lies in the same range of 5–10%. All traced MTs were manually verified. This was achieved by using the ‘filament editor’ tool in the ZIB extension of the Amira software that allowed us to create a flattened overview of the entire MT track, which was instrumental for quick validation of each MT. Both false-positive and negative tracings were corrected.

However, it is more difficult to estimate the error of the matching algorithm. Our standardized automatic stitching method has been described in detail in previous publications (Lindow et al., 2021; Redemann et al., 2014; Weber et al., 2012). In general, the stitching depends on the local density and properties of the MTs. For this reason, the stitched MTs were manually verified and corrected (Lindow et al., 2021). In particular, all KMTs in our reconstructions were checked for correct stitching across section borders. Examples of correct stitching of MTs at section borders are given in Figure 3—figure supplement 1. The quality of the analysis of the MTs, especially the KMTs, should therefore be influenced by minor errors. In our previous publications (Redemann et al., 2014; Weber et al., 2012), we estimated the overall quality of the stitching by analyzing the distribution of MT endpoints in the Z-direction (i.e. normal to the plane of the slice). We expect to find approximately the same density of MT endpoints along the Z-direction of each serial-section tomogram. This distribution is visualized in the Serial Section Aligner tool previously presented (Lindow et al., 2021). Therefore, if the density of endpoints after matching is approximately the same along the Z-direction of the serial-section tomograms, we can assume that the number of artificial points that have been introduced at the interfaces of the serial sections are negligible. This was visualized by projecting each spindle along the Y/Z axis (Figure 3—figure supplement 1).

Custom-designed software for the visualization of 3D data

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For better visualization of the 3D organization of KMTs in k-fibers, a platform was developed using the WebGL library (rgl 0.106.8 R library; Adler et al., 2021). This platform was implemented for the public and will allow readers to choose data sets from this publication for an interactive visualization of selected spindle features. For instance, users may choose to visualize the organization of k-fibers or KMTs and select for the analysis of MT-MT interactions. For an analysis of KMTs, users can select the following features of analysis such as length distribution, minus-end positioning, curvature, and number at the kinetochore. For the MT-MT interaction analysis, users can select different interaction distances. This platform is designed for the continuous addition of 3D reconstructions of spindles obtained from different systems and can be accessed as follows: https://cfci.shinyapps.io/ASGA_3DViewer/.

Data availability

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Tomographic data before and after the z-expansion has been uploaded to the TU Dresden Open Access Repository and Archive system (OpARA) and is available as open access: http://doi.org/10.25532/OPARA-128; http://dx.doi.org/10.25532/OPARA-177.

We released all datasets in Amira format. The tomographic data are also available in tiff format, which can be opened either with the ImageJ Fiji (Schindelin et al., 2012) or the IMOD (Kremer et al., 1996) open-source software packages. The MT-track files containing information about the segmented MTs were released in binary and ASCII format. To make this task easier for interested readers, the ASGA (Kiewisz and Müller-Reichert, 2021) open-source software, which is part of this publication, is supplied with small scripts written in R language, which allows users to read the ASCII format into an array. https://github.com/RRobert92/ASGA/blob/main/R/bin/Utility/Load_Amira.R.

The code used to perform quantitative analysis and visualization of MT organization in spindles has been uploaded to the GitHub repository and is available as open access under the GPL v3.0 license: https://github.com/RRobert92/ASGA; https://github.com/RRobert92/ASGA_3DViewer.

The supplementary high-resolution videos have also been uploaded to YouTube. l These movies can be found at this URL: https://youtube.com/playlist?list=PL-L6a60L11laVrVBFZqGi0wmULXD1b4Px.

Data availability

All Datasets were uploaded and ara available in OpaRA server: http://doi.org/10.25532/OPARA-128; http://doi.org/10.25532/OPARA-177. The code used to perform quantitative analysis and visualization of MT organization in spindles has been uploaded to the GitHub repository and is available as open access under the GPL v3.0 license: https://github.com/RRobert92/ASGA; (copy archived at swh:1:rev:142dcb882134954b9dc98f26044dd04a3893f181); https://github.com/RRobert92/ASGA_3DViewer, (copy archived at swh:1:rev:7594a85728f7fce05562d4f75fefee4d0f1935e4).

The following data sets were generated
    1. Kiewisz R
    (2021) OpaRA
    HeLa metaphase spindle tomographic data sets and analysis.
    https://doi.org/10.25532/OPARA-128
    1. Kiewisz R
    (2022) OpaRA
    HeLa metaphase spindle tomographic data sets and analysis for z-expansion data.
    https://doi.org/10.25532/OPARA-177

References

  1. Software
    1. Adler D
    2. Murdoch D
    3. Nenadic O
    4. Urbanek S
    5. Chen M
    6. Gebhardt A
    7. Bolker B
    8. Csardi G
    9. Srzelecki A
    10. Senger A
    (2021)
    RGL - 3D visualization device system for R using OpenGL
    CRAN.
  2. Software
    1. Lafarge T
    2. Pateiro-Lopez B
    (2020)
    alphashape3d: Implementation of the 3D Alpha-Shape for the Reconstruction of 3D Sets from a Point Cloud
    CRAN.
    1. Metzner R
    (1894)
    Beitrage zur granulalehre. I. Kern und kerntheilung
    Arch Anat Physiol 4:309–348.
  3. Book
    1. Stalling D
    2. Westerhoff M
    3. Hege HC
    (2005)
    Amira: a Highly Interactive System for Visual Data Analysis
    In: Hansen CD, Johnson CR, editors. The Visualization Handbook. Elsevier. pp. 749–767.

Decision letter

  1. Adèle L Marston
    Reviewing Editor; University of Edinburgh, United Kingdom
  2. Anna Akhmanova
    Senior Editor; Utrecht University, Netherlands
  3. J Richard McIntosh
    Reviewer; University of Colorado, Boulder, United States

Our editorial process produces two outputs: (i) public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "Three–dimensional structure of kinetochore–fibers in human mitotic spindles" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Anna Akhmanova as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: J Richard McIntosh (Reviewer #1).

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

Essential revisions:

1) The authors do not take account of the collapse in section thickness that occurs when plastic–embedded samples are treated with the beam of an electron microscope. This shape–change is not isotropic, because the film upon which the sections sit shrinks little, if at all, supporting the dimensions of the embedded material in two dimensions. The dimension perpendicular to the section plane is, however, unsupported, and the section collapses along that axis by about 40%. There is confidence that this situation pertains for the current data for two reasons. The full metaphase spindles, seen in cross–section, appear either elliptical or flattened, whereas both EM cross–sections of HeLa metaphases and light microscopic images of living spindles viewed down their axes are circular. Second, each kinetochore appears elliptical in this study, whereas in previous work with spindle cross–sections, human kinetochores are circular. The ellipticity of both the kinetochore and the metaphase plates is just about the degree expected, given the 30 – 40% collapse that others have measured for ET of plastic embedded material. The potential error caused by this distortion must be resolved in the paper. One way to address this would be to apply the asymmetric expansion to their model necessary to make it a better representation of an uncollapsed spindle, as other have previously done, then recalculate all their near–neighbor distributions on the data that have been brought into true. While we do not insist on this for this quite large amount of work, the authors must resolve this artefact in their reconstruction.

2) Another issue that should be considered is that the preference for KMTs to have non–KMTs as neighbors near the pole, which they report, is uncorrected for two structural issues: the increased density of MTs near the poles, which is a natural result of the essentially spherical shape of the metaphase spindle, and the fact that there are many more non–KMT in this region of the spindle than KMTs, so naturally KMTs have more non–KMTs as neighbors. This situation says nothing about the possibility of MT–MT interactions unless the proximity data are normalized for these two considerations.

3) When the observer is excising the tiny wafer of plastic that contains the cell for study from the thin layer of plastic in which it is embedded, it is all too easy to bend the plastic. This distorts the biological material in the plastic and may contribute to the torsion observed in the 3D reconstructions of spindle MTs. This small but important issue deserves mention.

4) The "textbook" models proposed and challenged in the text are not representative of the common understanding in the state of the field and the authors do not do enough to discuss the implications of their results or fit their results in the context of previous literature. Previous EM studies in mammalian spindles have already shown that k–fibers form semi–direct connections to the pole. The authors could instead emphasize other key findings in the paper, or provide more context as to why their main point about a semi–direct connection between kinetochores and poles in human cells is novel and exciting.

5) HeLa spindle lengths were previously reported to be ~12 µm, however, here they are reported to be significantly shorter in all spindles analyzed. The authors should clarify the origin of this discrepancy.

6) Figures 5, 7, and 8 should be better motivated. It would also help to discuss implications of findings, and to add summaries/models to the text or figure.

7) The paper lacks any discussion or estimation of potential errors –– tracking MTs or erroneous end declared/missed. An estimation/discussion of the errors should be provided so that the reader knows how much confidence there should be in this analysis.

8) The authors need to provide a better explanation of the use of the term K–fiber. The paper uses the term K–fiber to refer to the bundle of KMTs. This is making an unjustifiable assumption. The paper demonstrates that the KMTs often do not retain a tight cluster in going from KT to pole through premature termination of the KMTs and splay. Is this then the K–fiber? Is this consistent with the known structural integrity (eg under laser cutting) and high stability (cold stable) of K–fibers? An alternative model would be that the K–fiber is a tight MT bundle that continues to the pole with a changing composition of MTs along its length. The loss of KMTs from the bundle is then simply MT exchange with the spindle. The analysis is unclear on this point – proximity to MT lattices of the KMTs has weak dependence on distance along the spindle axis, suggesting bundles are present, but this needs more analysis.

9). How are so many minus ends generated in the spindle – 50% for KMTs, 30% for non–KT MTs. These terminated MTs are presumably crosslinked, and the fast dynamics of astral MTs suggests they must be nucleated in the spindle itself. This should be discussed.

10) Inclusion of more EM images to back up and support the conclusions.

Please also take note of specific points raised by individual reviewers below.Reviewer #1 (Recommendations for the authors):

Abstract: While K–fibers do connect kinetochore directly with the poles in many cells, in others the k–fiber connects with other spindle MTs, rather than the material at the pole. Even in cells with clearly defined poles, connection with other MTs may contribute to spindle mechanics (as is shown in this study). Therefore, it might set the reader's mind on the right course by replacing the first sentence with something like, "… provide a physical linkage between the chromosomes and the rest of the spindle."

Ln 112 I think you mean "Figure 2–movie supplements 1–3".

Ln 114 The observations of 14% of the MTs being KMTs, but those MTs accounting for 24% of the tubulin mass make an interesting discrepancy. I presume the difference in these numbers comes from the fact that KMTs are, on average longer than non–KMTs, but whatever the reason, it should be explained.

Figure 2 Supplement 1 Note that the legend to this figure is a repeat of the legend for figure 2, and there is no legend for this Figure In Figure 3B you call these kinetochores sisters 1 and 2. If you are confident that they are a pair, it might be more meaningful to your readers to call this pair of kinetochores sisters #1 and call the individual kinetochores 1A and 1B. I certainly don't insist on this nomenclature change, but it might help readers to follow you.

Figure 2 Supplement 2 In the legend (ln 884) you use the term "cross–section" to refer to tomographic slices that cut through a MT parallel to its axis. I find this confusing, because the cross–section of a MT is usually a slice cut perpendicular to the MT axis. Rephrase?

Ln 116 Were the Kinetochore–proximal ends of ALL KMTs flared, as shown? In previous publications many KMT plus ends were flared, but not all.

Ln 119 O'Toole et al. have examined the pole–proximal ends of KMTs in C. elegans and found that about half of these ends are open, half appeared to be capped, perhaps by the γ–tubulin ring complex. I wonder of your data would allow you to make comparable observations on KMTs in Hela cells? Mammalian spindle MTs flux toward the spindle pole, whereas comparable data for the C.e. embryonic spindle are (to my knowledge) not available. It would be very interesting to know if KMT minus ends in HeLa are capped or not. If capped, how can they flux?

Ln 120 Since there is no legend for Figure 2 Sup 1, I am making an inference about panel C on that figure, but it looks as if you use the 3D positions of each KMT associated with a single kinetochore to find a 3D average position, then call that the position of the kinetochore. This is not strictly true, because the plus ends of the KMTs are not AT the kinetochore, they commonly end outside the outer plate in the corona material. It would be valuable to find a wording that states more explicitly what you are doing, because the distances you present for the spacings of sister kinetochores are likely to be bigger than those measured by others with different definitions of the kinetochore.

Ln 128 "Site facing the pole" is imprecise and undefined.

Ln 134 and following. If I have understood you correctly, you estimated the size of each kinetochore by the area occupied by the KMTs that ended at approximately on region of the spindle because you did not see extra staining density in the chromatin or some other structural indicator of the kinetochore itself. That's OK, but you then go on to calculate the correlation between the number of KMTs and the size of the area they occupy and get a great correlation. But this is not meaningful. Of course, you get a good correlation because you are estimating the size of the kinetochore by the area occupied by the MTs. You then say that this is in good agreement with Cherry's observations on HeLa by LM, without saying what Cherry saw. I find this set of statements unhelpful for understanding K size.

Ln 902 There is something funny about the font for G of Graph and then P of Plot. Similar problems throughout this legend and others, so check the PDF carefully before it is posted.

Ln 903 Panel B does not show the distribution mentioned in the legend. It shows a related fact, which is important, but the distribution of minus ends is the subject of Figure 4. Have you computed it relative to a pole–to–pole axis, or the like? Perhaps relative to distance from the pole? The fact that so many KMTs do actually reach the pole is important and surprising to me. Based on K–fibers in PtK cells, I would have thought that more KMTs would have ended farther from the pole. Interesting.

Ln 910 As indicated by my comments relevant to the text derived from this figure, I don't see much value in this analysis, given the way you defined the position and size of the kinetochores.

Ln 160 and following. Your definition of the distance from the pole within which you call MT ends pole–interacting is clear, but your reasons for choosing this distance are not. In a sense this is a discussion point, and so how either you or Steffie decided this was the right distance might best be presented in that part of the paper. However, something should be said about it here, because in its current form, the distance chosen sounds completely arbitrary. Perhaps add a discussion paragraph and say here that this point is clarified in the discussion?

Ln 919 The end markers are circles, not spheres.

Ln 923 You map non–KMT end positions onto the pole–to–pole axis, which makes sense. You say that you map KMT end positions onto a kinetochore–to–pole axis, but that implies that you used a different axis for every kinetochore. Is that true? If so, you should say how these axes were determined, and a figure to show exactly what you mean should be added.

Figures 4D and G: Because you say "distance" in the text and on the abscissa, I presume this is what you have previously called "Euclidian distance", as suggested in 4A. Please be specific here because it is important for thinking about your data. In G, you again say distance, but here, I presume it is distance along the pole–to–pole axis, since that is how you describe it above. Thus, in your current labeling, the word distance means different things in these two panels. If I have this right, you should clean up the terminology. Note that again there are font problems at several places in the PDF.

Ln 942 Here again distance of KMT minus ends to poles is referred to simply as "distance". If this is a 3D Euclidian distance, as previously implied please change wording. Now in panel C, you are presenting distances as mapped onto the spindle axes, so these should be directly comparable to the distances you present for nonKMTs. If I'm right about this, I think you should say so explicitly. For example, Panels C and E are directly comparable, and the penetration of KMTs beyond the position of the mother centriole is nicely demonstrated. But now you state that E represents real distances (Euclidian?) and F is position on the axes. This implies that you measured distances from minus ends of nonKMTs to the centriole, which has not previously been mentioned. This needs clarification and explicit description with clearer words. Moreover, the shapes of these plots shown in Figure 4 sup1 F are remarkable for their symmetry, and this deserves comment and explanation.

Ln 180 This is the only reference to Figure 4 supple. 2, which is an interesting figure. I wonder why this information doesn't get more attention in the text.

Also relevant to this figure: here better than anywhere, one sees the elliptical shape of the cross sections of your spindle reconstructions. Given what one knows from light microscopy, this is almost certainly an artifact of electron tomography. I presume it is a result of the collapse of section thickness in the beam of the microscope. Some mention and explanation of this feature of your reconstructions belongs in the paper somewhere.

Ln 196 I find this title to be a bit of an exaggeration. Splay implies really flaring out. Yes, the area of the k–fiber encompassing polygons increases toward the pole, but I would describe it as a widening, not flaring or splaying.

Ln 225 You are using polygon here and below as an adjective. Should be polygonal.

General comment on the study of MT associations. Some of these statements and graphs need a bit more thought. Figures 7B and 7D show that the greater the distance between an MT end and an MT wall that is considered to be an "interaction", the greater the number of interactions there are. This point is almost trivial; it must be true. I don't see that it is worth two graphs. Said another way, the looser the criterion use for MT–MT interaction, the more interactions are seen. I don't think this needs to be demonstrated.

Ln 245 It might be worth mentioning MT–interacting proteins that are not motor enzymes, since some of these have been shown to be important for spindle structure and function.

Ln 255 The term association distance is introduced without any intellectual background. This may be a bit cryptic for people who have not been reading papers about spindle MTs and the ways structural studies have tried to identity MT–MT interactions. Perhaps add a sentence that rationalizes your interest in "interaction distance"? Perhaps a reference to others who have used this approach?

Ln 261 You say that most of these interactions occur near the pole, and you also say that many of the KMTs end before getting near the pole. Thus, the 41.4% of KMTs that have an end interacting with the wall of a non–KMT might be quite a large fraction of the KMTs that get into the polar area and are therefore in a position to have this kind of interaction. Can you look at this and clarify the point? For example, if you find a distance from the mother centriole that defines a hemisphere in which MT–MT distances are small, what fraction of the KMTs that get into that region have a tip interaction with a non–KMT.

Ln 270 and following. The observation that most of the MT–MT interactions (i.e., sites of close proximity) occurred near the spindle pole might be important, but a qualitative look at the 3D reconstructions suggests that the MT density is greater near the poles than farther away. By this I mean in a given spindle cross–section, how many MTs are there/unit area. If this number is higher near the poles, then the MTs must be closer to one another, so the increase in the number of MT proximities is a necessity, not a novel fact. This issue should be considered in the presentation of these data. Perhaps you could compute the MT density as a function of position along the spindle, then use this number at each position to normalize the distributions of interactions, thereby asking whether there is something in the data to indicate that the MTs are binding with one another, rather than simply being packed in. Also, the mechanical significance of KMT ends near KMTs is not clear to me.

Ln 276 You say, "as a result", but that phrase could be omitted. You are just describing what you saw.

Ln 290 Note that the number of non–KMTs/spindle cross–section exceeds the number of KMTs/cross section, and this is particularly true near the spindle poles. Thus, the fact that there are more associations between KMT ends and non–KMTs than with KMTs may simply be a consequence of this population difference. This could be calculated on the bases of the relative densities of the two kinds of MTs.

Ln 295 The fact that association frequencies are higher near the pole regardless of association distance may again be based simply on MT density.

Ln 296 In this context, I'm particularly interested in Figure 7, supple. 1E. This distribution of interactions between the walls of KMTs and the ends of non–KMTs does show its biggest peak at the pole, as stated, but there is a good indication of a second peak, not far from the kinetochores. This peak would be clearer if the data were presented as a running average, since the fluctuations seen make the bar graphs very spikey. Moreover, if the normalization, based on MT density were applied, it would reduce the polar peak but not the rise in frequency that is seen nearer to the kinetochores. As you know, this position along the spindle was identified structurally by O'Toole et al. as a place where the minus ends of overlapping MTs from the interzone (a subset of your non–KMTs) made association with the walls of KMTs. It is also the place where two groups using microbeams have identified places where KMTs receive a push from the spindle interzone. Thus, the gentle rise in your data may be very significant for the functional interactions between different classes of spindle MTs.

Ln 297 This discussion sounds just like what Mastronarde and others have called pairing length in their studies of yeast spindles. It might be well to use similar terminology to minimize confusion. Also, I think there might be a clearer way to describe what you have done. Here is my effort: "To measure the paraxial length over which MTs interacted, we defined 20 nm along the axis as a minimal length of interaction. For each pair of MTs that lay within a chosen interaction distance, we measured the number of 20 nm segments over which they retained this proximity."

Ln 305 I'm a little uncertain about what the words here mean. Are the "peaks of association" peaks in the number of 20 nm paring lengths that describe the pairing distances? Please clarify.

Figure 8 It seems as if the legends to 8B and C are switched.

Ln 305 and following. These words don't do justice to the very interesting distribution graphs you show in Figure 8. In the text, you don't discriminate between the classes of MTs that you break out in your graphs. For example, the words here describe what is shown in Figure 8B but not 8D. Please be specific about which MTs your words refer to.

Ln 309 You see no "hotspots" in your data for interactions between non–KMTs, but in Figure 8D there is a significant peak near the spindle midplane. (The label on the ordinate of this graph says non–KMTs interacting with all other MTs. I presume that you mean both other non–KMTs and KMTs. If this is not right, please be more specific.) Granted, the peak is higher for greater interaction distances, but studies in fission yeast suggest that the mean distance between MTs in the zone of overlap is greater than near the poles, and this the region where kinesin motors generate pushing forces. This peak may be of functional significance, and I think deserves mention in the text.

Ln 327 The term "spindle MTs" appears here without definition. Please clarify.

Ln 369 In the text and in Figure 9 it seems to me that you are under–representing the extent to which some KMTs reach the polar area. Your summary diagram shows only one MT of five making to the polar region, whereas both the images you show in the several movies for Figure 3 and your earlier text suggest that the fraction is closer to one–half. This diagram is important, because it is likely to be what gets cited and maybe even reaching textbook figures. Make sure it shows what you have actually seen.

Ln 383 This statement about strong indications of KMTs preferring to interact with non–KMTs is subject to the concern raised above that your data are not corrected for the greater number of non–KMTs. Make sure to do this normalization before making this claim.

Ln 472 No mention is made in the methods section of coping with the fact that plastic sections collapse during the early stages of exposure to the electron beam. Although there is some shrinkage in the plane of the section, the collapse of section thickness can be as much as 40%, and this affects 3–D geometry of the reconstruction. In my opinion, the fact that both the over–all shapes of your spindles and the shapes of each kinetochore fiber are oval, not circular, is a result of this collapse. Some labs expand the dimension perpendicular to the section plane to correct for this collapse. Was this correction applied here? If not, do you think it has impact on the distances observed between spindle MTs? Some discussion would be appropriate.

Ln 535 "was found within the interaction distance" would be clearer.

Ln 1099 The words, "This video shows" could be omitted from each of these legends with no loss.

Reviewer #2 (Recommendations for the authors):

Figure 1

–The authors should include the semi–direct connection between kinetochores and poles, since this has previously been shown.

Figure 2

– Figure legend 2C should indicate that microtubule number is in the upper right corner.

Figure 2–supplement 1.

– The figure legend is missing.

– Figure 2–supplement 1B indicates pole–to–pole distances of > 8µm for each spindle, with an average around 10.5 µm. However, Table 1 reports spindle pole distances of ~7, 10, and 9 µm. The authors should clarify this discrepancy.

Figure 3

– Line 140 in the text reports a KMT packing density of 0.07 KMT/µm2, and Table 3 reports similar KMT packing densities (0.06–0.09 KMT/µm2). However, Figure 3–supplement 1E reports KMT densities in the range of 25–75 KMTs/µm2. The correlation coefficient on lines 137–8 also doesn't match the correlation coefficient on Figure 3–supplement 1D.

– Authors should clarify the motivation for comparing inter–kinetochore distance and the number of MTs at the kinetochore, and what previous evidence might suggest a correlation (Figure 3C).

– Authors should define "neighborhood KMT–KMT" in the figure legend for Figure 3–supplement 1F.

Figure 4

– The authors make several conclusions about the composition of k–fiber bundles, for example, that k–fiber bundles are made up of varying KMT lengths. However, they only present gross KMT data. To directly conclude that individual bundles are made up of varying KMT lengths, they should show their KMT data grouped by k–fiber bundle.

– Relating to Figure 4–supplement 2N, the authors could explain the significance of finding more KMT minus–ends at spindle poles in central k–fibers compared to peripheral k–fibers, expanding on what the motivations were for this analysis and what might it say about global k–fiber organization. The authors could also consider plotting KMT length versus kinetochore region.

– The color of the outer kinetochore region does not match the colors of the images or plots, similarly in Figure 5.

Figure 5

– The authors could expand on their motivations for studying tortuosity of KMTs, and speculate on what their findings could imply about spindle organization.

Figure 6

– The polygon area analysis shown in Figure 6–supplement 1D is unclear and difficult to follow. The authors could clarify why this method was necessary.

– Line 229 confusingly states that the polygon area of the k–fiber was 5–fold lower at the pole–facing end of the fibers. It is unclear whether this is relative to the mid–position or to the kinetochore.

Figure 7 and Figure 8

– Some of the text in Figure 7 is too small to read.

– The authors could condense and clarify these figures, as well as compare their findings to previous work on KMT and non–KMT minus–end distributions (O'Toole et al. 2020).

– The authors could discuss more on the key differences found between kMTs and non–kMTs, specifically how the distributions of these two populations are related to their lifetime, organization in the spindle, and mechanistic differences.

– This overall section would benefit from a general summary in the text and model figure(s).

Reviewer #3 (Recommendations for the authors):

I would recommend a number of additions. Potentially too many for this paper. The most important are the error analysis and the K–fiber identification issue, whilst the interpretation of Figure 8 needs clearing up. Adding more context/discussion and showing tomograph images to support your analysis would be very helpful to your readers.

Additions to support analysis claims:

1. Measurement error analysis and discussion. The manuscript fails to address any issue with respect to errors – all biological data has errors, the question is how much and if it is biased (errors on average not zero). A discussion of accuracy and cautions for interpretation is thus essential. The key issues are whether:

a. MTs are tracked accurately and along their full length. In particular are microtubules cut prematurely. This could be addressed by analysis of the location of identified MT ends in the sections, in particular errors are more likely at the boundaries of the 300nm slices. Thus, if end density is uniform across the section this provides some reassurance that sectioning (and image morphing) is not causing an error in declaring a MT end when there is none. Since sectioning of the 3 cells is likely to have different orientations with respect to the spindle axis, error rates across sections could be assessed with regard to MT orientation. Secondly, can MTs be lost between sections – what is the invisible volume width between sections? Thirdly, examine both the + and – ends and ascertain if they are consistent with MT ends in EM. Since + ends at KTs are curved, it would be good to determine if all + ends in the spindle are curved; otherwise, there may be a signature of an erroneously declared end. Please show examples from the EM. Why wasn't end structure used to determine which are the + and – ends?

b. Are MT ends located accurately, and can you estimate the accuracy?

c. Are there lost volumes within sections, or rips, where the sample was destroyed/distorted by the slicing procedure. This would give blind spots in the analysis. What proportion of cell volume is lost and how is it handled in the analysis? Are MT ends called near these problematic volumes?

2. Confirm basic statistics with other modalities. To reassure the reader, quantities such as intersister distances, spindle length, KT number, sister–sister twist (wrt metaphase plate), metaphase plate width, kinetochore size, etc could be shown to be consistent with live imaging of the Kyoto HeLa cell line. Perhaps in a Table. It was good to see in Conway et al. the polarisation microscopy comparison.

3. Show EM/tomographs to illustrate results. Given this data has 2nm resolution, there is a lack of illustrations with the imaging data. Only examples of KMT + ends are shown in Figure 2 Supplement 2. A sequence of cross sections through a 'K–fibre bundle' would be helpful, marking the KMTs and nonKMTs. This would also help visualise the 'area' and KMT density quantification. An image (sequence) showing an example MT along its length might also be useful. These would allow the reader to see the MT/bundle environment. High resolution sections and/or movies through the spindle moving from the metaphase plate to pole would be good to see, annotated with KMTs in pseudo–colour for instance. Adding this ability to their visualisation tool might be helpful, and taking an idea from Google maps – flip between tomograph section image and analysis would be great. This could be made 3D showing MT orientations as a vector field.

Additional analyses, which this data should be amenable to, and likely add to the paper's conclusions:

4. Identify K–fiber bundles. You seem to identify the K–fiber with the bundle of KMTs. I don't think it can be used in this limited way. We know that K–fibres are mechanically distinct MT bundles attached to the KT, bent by forces created by KT attachments (rebounding when cut), MTs in the bundle are crosslinked and K–fibers are cold stable. Hence, can the authors identify nonKMTs that join the bundle (K–fibre) or demonstrate they are not there. These should be parallel to the KMTs with a long association length and be physically close to KMTs. You could use your transverse circle around KMTs to also compute the density of MTs – is that density constant despite loss of KMTs. Movies/image series along the bundle center line could then be constructed showing the bundle tomography image section with distance. Going beyond the KTs would also enable visualisation of bridging fibers, if any – this should complement the analysis of O'Toole et al. on mcMTs. You could then separate MTs into KMTs, mcMTs, and neither (you mention another paper on interdigitating MTs but this paper is weakened without addressing this point). If you find bridging fibers, what is typical geometry of merger to K–fibre and distance from KT?

5. Quantify + ends. There must be a substantial number of + ends of KMTs in the spindle. It would be good to confirm this. This could be used to examine if MT ends could be generated by breaking MTs – are there + and – ends in close proximity and along the spindle MT orientation, in particular do the KMTs – ends have a + end nearby?

6. The analysis of peripheral and central KTs (I don't like the word inner and outer) you do for tortuosity can be extended to other statistics – length, fraction KMTs meeting the pole, splay etc. It seems evident that peripheral KMTs will be longer and more likely to fail to reach the spindle pole.

7. You could analyse the angles of interaction of MT end–MT lattice interactions (within 35 nm). Your length association would suggest these are parallel.

8. You don't account for the change in MT density as you move towards the spindle poles. For instance, the increased MT associations towards the pole can reflect simply this increased MT density. It might also be useful to ascertain the angular dependence of the MTs around the spindle pole (at 1.53 microns). Is it homogeneous as one moves from the pole–pole axis and behind the pole – I suspect not? Is there evidence of clusters (possibly use a statistical test here). It might also be helpful to illustrate the density of MTs. I calculated that MTs would be separated at the spindle pole sphere on average by 148nm (if homogeneous), whilst your tightest bundling of KMTs is 60nm at KTs. Distances are thus very similar at 0.7 microns, close to the peak of the minus end density.

Add more context. The results are not discussed in context of existing literature, including relating results to

i) super–resolution studies, e.g. the twist and handedness of HeLa spindles (Tolic papers, twist appears weak or absent in spindles #1–3),

ii) live cell imaging such as the EB tracking (Yamashita et al. 2015). The detected EB spots are far lower than the number of MTs detected here. Can this be explained? How many + ends (away from poles) have you in the spindle bulk, not associated with KTs.

iii) There is also no discussion of bridging fibres; this has been in the literature for a decade and a confirmation/quantification (number MTs) would be very welcome. This of course would entail examining non–KMTs, as suggested above.

iv) You have 40% of minus ends away from the spindle poles. It would be good to have your interpretation of the processes that nucleate MTs, both nonKMT and KMT, away from the poles? Does this number make sense or is this evidence of poor MT tracking?

Data release.

Tomography data: It is fantastic that the tomography data is released. I would however suggest that there is guidance on which free software can load the Amira files, or release in alternative formats.

Tracks: it would be good if the MT traces were released as well. This would enable many people to analyse the networks without the high cost of analysing the tomography data themselves.

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

Thank you for resubmitting your work entitled "Three–dimensional structure of kinetochore–fibers in human mitotic spindles" for further consideration by eLife. Your revised article has been evaluated by Anna Akhmanova (Senior Editor) and a Reviewing Editor.

The manuscript has been greatly improved but there are some remaining points raised by the reviewers that the authors should consider before acceptance:

Reviewer #1 (Recommendations for the authors):

Kiewisz et al. have done a heroic job of revising their manuscript for resubmission. I appreciate the labor involved in recalculating all the images and interaction distances. Although the distances didn't change much, the images are a significant improvement, and the new data on near–neighbor MT–MT spacings are now more likely to stand the test of time. The revised neighbor distribution curves that are normalized for MT density are also a real improvement. All in all, this paper is now an excellent contribution to the literature and should be published as soon as possible. Below I mention a few issues that still strike my eye, but most of them are simple clarifications and so little work will be needed to make this manuscript a classic.

Critique

Ln 1300 Figure 8 is potentially an important figure, but I find two problems with its current version: the gray MTs on a black background are essentially invisible, and the dots in panels C and E are unexplained. This may be my display, but the authors should consider the points.

Figure 8 supplements. The lines representing MTs are so thin that they are hard to see on my screen, even when I blow each sub–image up to fill the screen. In your displays of whole spindles, it is clear why you must use narrow lines, but in these figures with only a few MTs displayed, you could increase the clarity of the images by just making each line a bit wider. Again, dots on the graphics are unexplained.

In 8Sup1, all I am seeing is KMTs in different colors. There don't seem to be any non–KMTs, and there are no sites of interaction displayed. I gather that this figure shows simply the trajectories of the KMTs that do interact, not the interactions themselves. Do you think this is the best way to show your point?

In 8Sup3, similar to Sup1. I think these figures would be more informative if you would show the interacting non–KMT and particularly the site of interaction. Simply coloring the whole MT erases that information.

Ln 331 You are right, of course, that the major peak in Figure 8, Sup2 G shows a major peak near the pole, like all the other associations, but the secondary peak farther from the pole is very noticeable in this display, and given the evidence from other groups that this kinetochore–proximal region may be an important site for interactions between the ends of non–KMTs and the walls of KMTs, I think this really deserves mention.

Figure 9, these MT–representing lines barely show up on my screen. A little thicker?

The legends for the Figure 9 supplement Figures need attention. The boxes are not referred to or explained, and again the sites of interaction are not clear. Supple. 2 legend text, "Number of KMTs plotted against the number of associations with other MTs in the spindle per individual KMT" doesn't match the labeling on those axes, so it's not clear what is being shown in these graphs.

Ln 371 and following, you state that the number of associations was 10.6, but it is not clear what this number means. Number/KMT, per k–fiber or what?

Ln 384 and following. I understand that the reworking of your images and numbers to accommodate the reviewers' suggestion of expanding the collapsed sections was a major amount of work, and probably pretty painful/annoying to do. Thus, adding this paragraph to the discussion is understandable, but as a reader coming to this version with a fresh point of view, I don't think it is necessary. You describe what you are going to do near the beginning of the paper, and you describe very nicely what you did in the methods section. It seems to me mentioning it again in the discussion over–emphasizes the point to, but this is for the authors to decide.

Ln 516 The statement that these and related data show that KMTs nucleate predominantly at kinetochores is true only for metaphase cells, and this limitation must be stated, otherwise it is misleading.

The addition of https://cfci.shinyapps.io/ASGA_3DViewer/ as a viewer tool is a major step in data sharing. Many thanks to the authors for developing this, because the Amira package is expensive. This addition will make their hard work much more useful to others.

Reviewer #2 (Recommendations for the authors):

The authors provide a substantially improved manuscript. We support publication. However, a number of issues (most small) remain and should be addressed before publication.

– Intro: The authors describe the three models of KMT–pole connections, but should situate known mammalian spindle structure work in the context of these models. More was known prior to this work than what was acknowledged.

– Figure 5B, 5S2B: legend and plot in 5B says centrosome interaction area was defined as a half–width of a peak from the center, but text lines 195 and 408 say "two fit half–widths from the center of the fit peak".

– Figure 5D: How can the MT–centrosome interaction area be highlighted in gray, if this distance is 1.7 µm but the P–KT length of each k–fiber is different? (i.e. the x–axis of this plot is a relative measurement, but MT–centrosome interaction distance is absolute).

– There is no Figure 5E.

– Figure 5G: Discrepancy with Figure 5A and 5G legend, where P2 is at a relative position of 1.00 vs. 1.2.

– Figure 4B, 4S1B, 5B, 5F, 5G, 9S2B, 9S2D: What criteria were used to decide which nKMTs to include? The total number from all three spindles is 16,256, based on Table 1, but these plots all include only 9957 (more than any individual spindle but far less than all three).

– Figure 5S4B legend does not match plot.

– Line 1254: What is meant by "A tortuosity of 1.1 is length."?

– Line 1255: What is meant by "The gray line indicates indicated by a dashed line."?

– Figure 6E–F: Color codes are reversed. Red corresponds to higher tortuosity in E but lower tortuosity in F, and vice versa with gray.

– Lines 231–236: A different motivation is needed for the tortuosity analysis. Tortuosity reports on microtubule curvature, but NOT twist–it doesn't tell us anything about 3D helicity that is consistent along a microtubule's length. It also seems that Figure 6 should have its own heading in the Results text, rather than being combined under the heading "K–fibers are broadened at spindle poles," since the correlation between tortuosity and spindle axis position is very weak and there is no other evidence in Figure 6 to support this statement.

– Figure 7S1D: They did not address our comment that the polygon area analysis is never motivated or explained, and is unclear.

– Figures 8–9: They did not change figures 8–9 (formerly 7–8) very much, as we suggested. Expanding their introduction to these figures in the text helps a little, but it's still hard to tell how these figures and sub–figures are making unique points.

– Figure 9A: This cartoon should be moved to Figure 9S2, because interaction length is not quantified in Figures 9 or 9S1.

– Figure 9S1: It's unclear what is being shown here or how it relates to Figure 9. Line 1375 says "This 3D model illustrates the association of KMT lattices with other KMT lattices minus ends". What are all the non–KMTs shown in these images? Are we looking at associations with lattices, with minus ends, or microtubules that interact for extended distances? Line 1376 says "The types of interactions are shown by color–coding," but what is the color code?

– Lines 497–498: What correlations is this sentence referring to? No correlations are shown in Figures 8 or 9.

https://doi.org/10.7554/eLife.75459.sa1

Author response

Essential revisions:

1) The authors do not take account of the collapse in section thickness that occurs when plastic–embedded samples are treated with the beam of an electron microscope. This shape–change is not isotropic, because the film upon which the sections sit shrinks little, if at all, supporting the dimensions of the embedded material in two dimensions. The dimension perpendicular to the section plane is, however, unsupported, and the section collapses along that axis by about 40%. There is confidence that this situation pertains for the current data for two reasons. The full metaphase spindles, seen in cross–section, appear either elliptical or flattened, whereas both EM cross–sections of HeLa metaphases and light microscopic images of living spindles viewed down their axes are circular. Second, each kinetochore appears elliptical in this study, whereas in previous work with spindle cross–sections, human kinetochores are circular. The ellipticity of both the kinetochore and the metaphase plates is just about the degree expected, given the 30 – 40% collapse that others have measured for ET of plastic embedded material. The potential error caused by this distortion must be resolved in the paper. One way to address this would be to apply the asymmetric expansion to their model necessary to make it a better representation of an uncollapsed spindle, as other have previously done, then recalculate all their near–neighbor distributions on the data that have been brought into true. While we do not insist on this for this quite large amount of work, the authors must resolve this artefact in their reconstruction.

Thank you for pointing this out. We are absolutely aware of this collapse in Z, and there is no doubt that there is a mass loss during imaging. We were, however, not completely sure about the correct factor that has to be applied to the collapsed sections. Following the request of reviewer #1 and referring to the publication by O’Toole et al. (2020), we have applied a Z-factor to each of our three data sets (Z-factors were: 1.3 for spindle #1, 1.4 for spindle #2 and 1.42 for spindle #3). We have mentioned this now in the main text (in the results, see new Figure 2-figure – supplement 2). This procedure is also described in the experimental procedures section. The corrected models are now shown in the new figures and supplied videos. After this expansion of the 3D models, we re-did our complete quantitative analysis of the spindle MTs. Essentially, all numbers only marginally changed, and all trends and conclusions remained unaltered. As suggested, we are also presenting the previously obtained quantifications in Tables 12-13, thus giving the interested reader the possibility to compare the data obtained before and after Z-extension of the 3D reconstructions.

2) Another issue that should be considered is that the preference for KMTs to have non–KMTs as neighbors near the pole, which they report, is uncorrected for two structural issues: the increased density of MTs near the poles, which is a natural result of the essentially spherical shape of the metaphase spindle, and the fact that there are many more non–KMT in this region of the spindle than KMTs, so naturally KMTs have more non–KMTs as neighbors. This situation says nothing about the possibility of MT–MT interactions unless the proximity data are normalized for these two considerations.

Taking the higher density of MTs at spindle poles into account, we have normalized the MT-MT interactions against the density of non-KMTs along the pole-to-kinetochore axis. The new figures show the normalized length distribution plots. Our claim that KMTs preferentially interact with non-KMTs at spindle poles remains the same.

3) When the observer is excising the tiny wafer of plastic that contains the cell for study from the thin layer of plastic in which it is embedded, it is all too easy to bend the plastic. This distorts the biological material in the plastic and may contribute to the torsion observed in the 3D reconstructions of spindle MTs. This small but important issue deserves mention.

There is a misunderstanding here about the preparation of our samples for electron tomography. Tomograms were not obtained after a re-mounting of thin layers of plastic. Here, the cells were grown and frozen on sapphire discs. The sapphire discs were removed after polymerization of the resin. Therefore, a bending of a thin layer of plastic prior to a re-mounting of the samples on dummy blocks is not an issue here. The observed torsion of the spindles is therefore not related to sample preparation!

4) The "textbook" models proposed and challenged in the text are not representative of the common understanding in the state of the field and the authors do not do enough to discuss the implications of their results or fit their results in the context of previous literature. Previous EM studies in mammalian spindles have already shown that k–fibers form semi–direct connections to the pole. The authors could instead emphasize other key findings in the paper, or provide more context as to why their main point about a semi–direct connection between kinetochores and poles in human cells is novel and exciting.

Thank you for pointing this out. After reading this comment, we realized that the semi-direct connection is not the main issue here as this has been published before our study. We only briefly mention this now in the introduction (and we clearly cite previous work on this). However, we think that the broadening of the k-fibers is indeed an unrecognized feature that needs to be reported. In the discussion we favor the interpretation that this broadening facilitates the interaction of KMTs with non-KMTs at positions close to the spindle pole. In the light of considering the mitotic spindle a liquid crystal with an intrinsic order, we discuss the possibility now that a broadening of the k-fibers could be directly related to a lower nematic order for the spindle poles compared to the kinetochore regions. In addition, we also link the minus-end morphology of the KMTs to our interpretation that KMTs grow out from the kinetochore towards the spindle poles. This way, we directly link the two submitted papers and provide context obtained from our parallel collaborative study.

5) HeLa spindle lengths were previously reported to be ~12 µm, however, here they are reported to be significantly shorter in all spindles analyzed. The authors should clarify the origin of this discrepancy.

We have used HeLa (Kyoto) cells obtained from the Gerlich lab (Vienna, Austria) that have been used previously for a cytokinesis study (Guizetti et al., 2001). This information has been added to the Materials and methods section. The discrepancy in spindle length reported for LM versus EM data is related to a dehydration step that is unavoidable in sample preparation for electron microscopy. Embedding of dehydrated samples is an issue related to all previous studies using plastic samples for either TEM or SEM. To minimize the effect of dehydration, we have performed a ‘mild dehydration’ (i.e., freeze substitution at the temperature of -80ºC). In addition, we have plotted the length distribution of KMTs against the relative position on the pole-to-kinetochore axis, so a change in the absolute number does not really change the interpretation of obtained EM data.

6) Figures 5, 7, and 8 should be better motivated. It would also help to discuss implications of findings, and to add summaries/models to the text or figure.

Thank you for pointing this out. We have tried to better motivate the studies associated with the figures mentioned above. We also have added aspects, related to these figures, in the discussion to better point out the implications of this work.

7) The paper lacks any discussion or estimation of potential errors –– tracking MTs or erroneous end declared/missed. An estimation/discussion of the errors should be provided so that the reader knows how much confidence there should be in this analysis.

This is a very important issue, thanks for bringing this up. We should have added a paragraph on this topic to the initially submitted manuscript. For this work, we applied a fully established image analysis pipeline, which includes an automatic segmentation of MTs, manual correction of false positive and negative ‘hits’ and an automatic stitching of MTs at section borders (modeling about section borders is now illustrated in the new Figure 3—figure supplement 1). Again, a paragraph of possible sources of errors should have been added, and we do so now in our revised manuscript. However, we would like to point out that we have published a number of large-scale reconstructions (for instance see, Redemann et al., 2017), in which we have discussed possible mistakes and errors already in more detail. We didn’t want to be repetitive here. Concerning the automatic stitching of MTs (as discussed in Weber et al., 2012) and the stitching of MTs at section borders (as discussed in depth in Lindow et al., 2021) we have added a new paragraph to Materials and methods. In addition, we also describe the requested expansion of our models in z (see also comments above and the new Figure 2-figure – supplement 2).

8) The authors need to provide a better explanation of the use of the term K–fiber. The paper uses the term K–fiber to refer to the bundle of KMTs. This is making an unjustifiable assumption.

We only partially agree with this comment. There is no unambiguous, universally agreed upon definition of a k-fiber. For the purpose of this paper, we first needed to ‘fish out’ KMTs from our 3D spindle reconstructions. For this, we were in need of a ‘hard criterium’ to do so and we did this by defining MTs with their putative plus ends associated with the chromosomes as KMTs. We consider these bundled KMTs as the ‘core’ of the k-fibers, and we clearly state this now in the main text of the manuscript. In a next step, we considered the non-KMTs in the vicinity of the KMTs. For further analysis and to avoid any bias here, we have chosen different ‘interaction distances’ to analyze the association of non-KMTs with the KMTs. We invested quite some time to detect a pattern of KMT/non-KMT association. Using the newly provided computer tool, the reader is encouraged to visualize the complex interaction pattern of KMTs with non-KMTs. We also provide three new figures to illustrate this issue (Figure 8—figure supplement 1 and 3 and Figure 9—figure supplement 1). However, we cannot and don’t exclude the interaction of KMTs with other neighboring non-KMTs. We mention this aspect now under cold-stabilization of k-fibers and ‘KMT maturation’ in the discussion.

The paper demonstrates that the KMTs often do not retain a tight cluster in going from KT to pole through premature termination of the KMTs and splay. Is this then the K–fiber? Is this consistent with the known structural integrity (eg under laser cutting) and high stability (cold stable) of K–fibers?

We don’t see how the core of KMTs versus a KMT/non-KMT bundle would necessarily show different data after laser cutting or cold stability. A number of MAPs can be considered here to achieve a stabilization of KMTs that run in parallel. In addition, a local modification of the KMT’s tubulin can’t be excluded as a possibility to provide stability. We consider these issues now in the discussion. In the future, it would be certainly interesting to look at the ultrastructure of cold-stabilized MTs and to further analyze the association of bundled KMTs with associated non-KMTs. However, we are convinced that this needs to be subject to a follow-up publication.

An alternative model would be that the K–fiber is a tight MT bundle that continues to the pole with a changing composition of MTs along its length. The loss of KMTs from the bundle is then simply MT exchange with the spindle. The analysis is unclear on this point – proximity to MT lattices of the KMTs has weak dependence on distance along the spindle axis, suggesting bundles are present, but this needs more analysis.

Certainly, this is a model to consider, and we have added this aspect to a new paragraph on the nature of k-fibers in our discussion. We now explicitly mention such an ‘exchange’ of MTs within the k-fiber in the discussion. However, it is unclear what objective criteria can be used to determine if particular MTs are or are not to be considered as being in a bundle. Again, we have added a new supplementary figure to illustrate the complexity of non-KMTs around KMTs. What makes a bundle a bundle? Certainly, MTs can not only be considered as bundles when they run in parallel. However, objective algorithms for such a non-KMT analysis are currently not available, and we plan to present a detailed analysis of non-KMT organization in a separate publication. Despite a detailed manual inspection of surrounding non-KMTs, we have so far been unable to see clear, qualitative indications of bundling non-KMTs. Because of a lack of unambiguous data on this point, we hesitate to make a definitive statement about this in our paper and to comment in an original publication on results obtained by other optical methods and in other labs! Finally, we don’t see why a weak dependence of KMTs with MT lattices along the spindle axis, suggests that non-KMT bundles are present. We believe that it would be best to address these issues in a future manuscript.

9). How are so many minus ends generated in the spindle – 50% for KMTs, 30% for non–KT MTs. These terminated MTs are presumably crosslinked, and the fast dynamics of astral MTs suggests they must be nucleated in the spindle itself. This should be discussed.

A short comment first, a crosslinking of MTs in the spindle is not visible in our electron tomograms obtained from plastic sections. Any statement on this point would be rather speculative. In addition, a given position of a minus end in the spindle is not necessarily the place of MT nucleation. MTs might be transported within spindles along tracks of neighboring MTs. So, we simply want to be careful here about statements on the sites of MT nucleation in spindles. However, it is not surprising that MTs are nucleated within the spindle and we comment now on this observation in our revised discussion and cite the appropriate papers. We also refer to our parallel collaborative work presented by Conway et al., in which the biophysics of KMT dynamics in the spindle is discussed in detail.

10) Inclusion of more EM images to back up and support the conclusions.

We have added more images to better illustrate the morphology of spindles in mitotic HeLa cells. We have added a new figure to illustrate the spindle poles and kinetochore MTs (for instance, see Figure 2—figure supplement 1). In this new figure, we present tomographic slices from our tomograms. However, we would like to point out here that these images are only very thin tomographic slices through whole spindles, so the reader can’t really appreciate the 3D information that is given by our 3D reconstructions. The ‘crowded environment’ of the spindles is not obvious in these thin slices showing only parts of whole KMTs and non-KMTs. To better illustrate the 3D complexity of the metaphase spindle in HeLa cells, we have introduced a platform that allows the interested readers to interactively look at various spindle features. We have added 3 new figures (Figure 8—figure supplement 1 and 3 and Figure 9—figure supplement 1) to illustrate the association of the KMTs of selected k-fibers with surrounding non-KMTs. We certainly hope that the interested reader will explore this new tool to appreciate the high density of MTs in spindles.

Please also take note of specific points raised by individual reviewers below.

Reviewer #1 (Recommendations for the authors):

Abstract: While K–fibers do connect kinetochore directly with the poles in many cells, in others the k–fiber connects with other spindle MTs, rather than the material at the pole. Even in cells with clearly defined poles, connection with other MTs may contribute to spindle mechanics (as is shown in this study). Therefore, it might set the reader's mind on the right course by replacing the first sentence with something like, "… provide a physical linkage between the chromosomes and the rest of the spindle."

Thank you, we have changed this in the abstract.

Ln 112 I think you mean "Figure 2–movie supplements 1–3".

This has been corrected. Sorry for this mistake.

Ln 114 The observations of 14% of the MTs being KMTs, but those MTs accounting for 24% of the tubulin mass make an interesting discrepancy. I presume the difference in these numbers comes from the fact that KMTs are, on average longer than non–KMTs, but whatever the reason, it should be explained.

Thank you for pointing this out. As given in the text, we have measured the average length of all KMTs and non-KMTs in our spindle reconstructions: average length is 3.87 ± 1.98 µm for KMTs and 2.0 ± 1.76 µm (mean ± STD; n = 9957) for non-KMTs. So, KMTs are on average almost twice as long as non-KMTs. We have shifted this issue to the discussion.

Figure 2 Supplement 1 Note that the legend to this figure is a repeat of the legend for figure 2, and there is no legend for this Figure

Sorry for this mistake. We solved this issue.

In Figure 3B you call these kinetochores sisters 1 and 2. If you are confident that they are a pair, it might be more meaningful to your readers to call this pair of kinetochores sisters #1 and call the individual kinetochores 1A and 1B. I certainly don't insist on this nomenclature change, but it might help readers to follow you.

We agree, this is a good suggestion and will help the reader to follow. We have changed this in the legend for Figure 3B.

Figure 2 Supplement 2 In the legend (ln 884) you use the term "cross–section" to refer to tomographic slices that cut through a MT parallel to its axis. I find this confusing, because the cross–section of a MT is usually a slice cut perpendicular to the MT axis. Rephrase?

Yes, this is not precise enough. We have changed this in the figure legend.

Ln 116 Were the Kinetochore–proximal ends of ALL KMTs flared, as shown? In previous publications many KMT plus ends were flared, but not all.

We will report on the end morphologies of KMTs in mitotic HeLa cells in a separate publication. We decided to analyze the MT ends in the context of depletion of the MT minus-end regulator, MCRS1. This is a collaboration with the lab of Isabelle Vernos (Barcelona, Spain). This parallel publication (Laguillo-Diego et al.) will be submitted also to ELife very soon.

Ln 119 O'Toole et al. have examined the pole–proximal ends of KMTs in C. elegans and found that about half of these ends are open, half appeared to be capped, perhaps by the γ–tubulin ring complex. I wonder of your data would allow you to make comparable observations on KMTs in Hela cells? Mammalian spindle MTs flux toward the spindle pole, whereas comparable data for the C.e. embryonic spindle are (to my knowledge) not available. It would be very interesting to know if KMT minus ends in HeLa are capped or not. If capped, how can they flux?

Yes, a similar analysis can be done. In fact, we did this already in the context of the parallel study (Laguillo-Diego et al.) on the morphology of MT minus ends in untreated and MCRS1-depleted HeLa cells. Indeed, KMT minus ends are heterogeneous showing either open or closed morphologies.

Ln 120 Since there is no legend for Figure 2 Sup 1, I am making an inference about panel C on that figure, but it looks as if you use the 3D positions of each KMT associated with a single kinetochore to find a 3D average position, then call that the position of the kinetochore. This is not strictly true, because the plus ends of the KMTs are not AT the kinetochore, they commonly end outside the outer plate in the corona material. It would be valuable to find a wording that states more explicitly what you are doing, because the distances you present for the spacings of sister kinetochores are likely to be bigger than those measured by others with different definitions of the kinetochore.

Formally, this is true. And yes, the presented distances for the spacings of sister kinetochores are bigger. We were interested in a comparison of the distance between the plus-ends of sister k-fibers. We now determine the ‘distance

between the median position of KMT plus-ends between pairs of sister k-fibers’. We hope that this is clearer now. Sorry again,

Ln 128 "Site facing the pole" is imprecise and undefined.

We have changed this to pole-proximal end.

Ln 134 and following. If I have understood you correctly, you estimated the size of each kinetochore by the area occupied by the KMTs that ended at approximately on region of the spindle because you did not see extra staining density in the chromatin or some other structural indicator of the kinetochore itself. That's OK, but you then go on to calculate the correlation between the number of KMTs and the size of the area they occupy and get a great correlation. But this is not meaningful. Of course, you get a good correlation because you are estimating the size of the kinetochore by the area occupied by the MTs. You then say that this is in good agreement with Cherry's observations on HeLa by LM, without saying what Cherry saw. I find this set of statements unhelpful for understanding K size.

We agree that we have to be clearer here! We were not primarily interested in the absolute size of the kinetochores in our spindles. This indirect measurement of KMT area was done to calculate the density and spacing of KMTs at the outer kinetochore (and along the length of k-fibers, later in the paper). We deleted the comparative statement about kinetochore size as measured by light microscopy and in other systems. We hope that this point is clearer now.

Ln 902 There is something funny about the font for G of Graph and then P of Plot. Similar problems throughout this legend and others, so check the PDF carefully before it is posted.

We checked the font size in all our graphs. Thank you for pointing this out.

Ln 903 Panel B does not show the distribution mentioned in the legend. It shows a related fact, which is important, but the distribution of minus ends is the subject of Figure 4. Have you computed it relative to a pole–to–pole axis, or the like? Perhaps relative to distance from the pole? The fact that so many KMTs do actually reach the pole is important and surprising to me. Based on K–fibers in PtK cells, I would have thought that more KMTs would have ended farther from the pole. Interesting.

Sorry that we caused some confusion here. To be clearer here, we have changed this figure. In panes A, we now show the length distribution (i.e., the measurements on the length) of KMTs and non-KMTs in a separate figure (Figure 4). In Figure 5A we now illustrate two measurements: First, we show the measurement of the absolute distances of the KMT and the putative non-KMT minus ends to the center of the nearest mother centriole. This is indicated by black arrows. The absolute values are given in µm. Second, we show the relative position of the KMT and of the putative non-KMT minus ends on the pole-to-kinetochore and on the pole-to-pole axis, respectively. As for the relative position of the KMTs on the pole-to-kinetochore axis, each KMT plus end was defined as position 1. We hope this is clear now in the new Figure 5 (and also in the new Figure 5—figure supplement 1 showing both spindle poles). In panel B, we explain how we determined the MT-centrosome interaction area. This was done to introduce a clear ‘border’ for an annotation of KMT minus ends as either directly or indirectly associated with the spindle poles. We have added a paragraph about this MT-centrosome interaction area to the discussion.

Ln 910 As indicated by my comments relevant to the text derived from this figure, I don't see much value in this analysis, given the way you defined the position and size of the kinetochores.

Is this comment related to the centrosomes instead of the kinetochores? Hopefully, our definition of the centrosome border is clearer now.

Ln 160 and following. Your definition of the distance from the pole within which you call MT ends pole–interacting is clear, but your reasons for choosing this distance are not. In a sense this is a discussion point, and so how either you or Steffie decided this was the right distance might best be presented in that part of the paper. However, something should be said about it here, because in its current form, the distance chosen sounds completely arbitrary. Perhaps add a discussion paragraph and say here that this point is clarified in the discussion?

We agree on this. The reason for choosing the border for this interaction area needs clarification and more explanation in the text. We tried to be clearer about this in the Results section (also in the figure legend) and have added a paragraph to the discussion. As also obvious in our previous publications on MTs in the early C. elegans embryo (O’Toole at al., 2003; Weber et al., 2012; Redemann et al., 2017), it is impossible to define a clear boundary for the membrane-less spindle poles in EM images. As a solution to this problem, we plotted the number of all putative non-KMT minus ends to the distance of theses minus ends to the nearest mother centriole (absolute values given in µm; these are not relative distances!). The border of the MT-centrosome interaction area (Figure 4B, right dashed line) was then determined by the bend in the histogram, where the peak plateaued (arrow). We hope this is clearer now.

Ln 919 The end markers are circles, not spheres.

Of course, you are right. Sorry, we have checked and changed this throughout our manuscript.

Ln 923 You map non–KMT end positions onto the pole–to–pole axis, which makes sense. You say that you map KMT end positions onto a kinetochore–to–pole axis, but that implies that you used a different axis for every kinetochore. Is that true? If so, you should say how these axes were determined, and a figure to show exactly what you mean should be added.

We agree, we need to better explain this, and it is also a good idea to add a figure here to show how we defined the kinetochore-to-pole axis. We defined this axis for each kinetochore. The spindle pole is always position 0, while the kinetochore is always position 1 on the half-spindle axis.

Figures 4D and G: Because you say "distance" in the text and on the abscissa, I presume this is what you have previously called "Euclidian distance", as suggested in 4A. Please be specific here because it is important for thinking about your data. In G, you again say distance, but here, I presume it is distance along the pole–to–pole axis, since that is how you describe it above. Thus, in your current labeling, the word distance means different things in these two panels. If I have this right, you should clean up the terminology. Note that again there are font problems at several places in the PDF.

Again, sorry for being unclear here. In Figure 4 (now Figure 5), we are talking about two types of measurements (see our comments above): first, about absolute distances; second, about relative positions on either the pole-to-kinetochore or the pole-to-pole axis. We have cleaned up the terminology. We hope that this is clearer now.

Ln 942 Here again distance of KMT minus ends to poles is referred to simply as "distance". If this is a 3D Euclidian distance, as previously implied please change wording. Now in panel C, you are presenting distances as mapped onto the spindle axes, so these should be directly comparable to the distances you present for nonKMTs. If I'm right about this, I think you should say so explicitly. For example, Panels C and E are directly comparable, and the penetration of KMTs beyond the position of the mother centriole is nicely demonstrated. But now you state that E represents real distances (Euclidian?) and F is position on the axes. This implies that you measured distances from minus ends of nonKMTs to the centriole, which has not previously been mentioned. This needs clarification and explicit description with clearer words. Moreover, the shapes of these plots shown in Figure 4 sup1 F are remarkable for their symmetry, and this deserves comment and explanation.

As mentioned above, we have modified Figure 4. In the new Figure 4, we talk about the length distribution of both KMTs and non-KMTs. In the new Figure 5, we now talk about our analysis of both KMT and non-KMT minus ends. Hopefully, this new presentation of the data is much clearer now. In addition, we have added a comment on the symmetry of the plot in Figure 4—figure supplement 1F (now Figure 5—figure supplement 2D).

Ln 180 This is the only reference to Figure 4 supple. 2, which is an interesting figure. I wonder why this information doesn't get more attention in the text.

We mention this point now in the text.

Also relevant to this figure: here better than anywhere, one sees the elliptical shape of the cross sections of your spindle reconstructions. Given what one knows from light microscopy, this is almost certainly an artifact of electron tomography. I presume it is a result of the collapse of section thickness in the beam of the microscope. Some mention and explanation of this feature of your reconstructions belongs in the paper somewhere.

Again, we took care of this collapse and present the z-corrected figures in the revised version of our manuscript.

Ln 196 I find this title to be a bit of an exaggeration. Splay implies really flaring out. Yes, the area of the k–fiber encompassing polygons increases toward the pole, but I would describe it as a widening, not flaring or splaying.

As requested, we now report on a ‘broadening’ of the pole-proximal ends of the k-fibers.

Ln 225 You are using polygon here and below as an adjective. Should be polygonal.

Thanks, we have changed this.

General comment on the study of MT associations. Some of these statements and graphs need a bit more thought. Figures 7B and 7D show that the greater the distance between an MT end and an MT wall that is considered to be an "interaction", the greater the number of interactions there are. This point is almost trivial; it must be true. I don't see that it is worth two graphs. Said another way, the looser the criterion use for MT–MT interaction, the more interactions are seen. I don't think this needs to be demonstrated.

We agree, this must be true. The point here is to show how the association patterns change by increasing in the interaction area. All in all, we have to say that the analysis of MT-MT interactions turned out to be very complex, and we decided to keep Figures 7 and 8 to explicitly show these complex interaction patterns. We fully agree that additional analysis will be necessary in the future.

Ln 245 It might be worth mentioning MT–interacting proteins that are not motor enzymes, since some of these have been shown to be important for spindle structure and function.

Thanks, this is a good point. We have added this information.

Ln 255 The term association distance is introduced without any intellectual background. This may be a bit cryptic for people who have not been reading papers about spindle MTs and the ways structural studies have tried to identity MT–MT interactions. Perhaps add a sentence that rationalizes your interest in "interaction distance"? Perhaps a reference to others who have used this approach?

Thanks, we have added a sentence here to better explain what we did here.

Ln 261 You say that most of these interactions occur near the pole, and you also say that many of the KMTs end before getting near the pole. Thus, the 41.4% of KMTs that have an end interacting with the wall of a non–KMT might be quite a large fraction of the KMTs that get into the polar area and are therefore in a position to have this kind of interaction. Can you look at this and clarify the point? For example, if you find a distance from the mother centriole that defines a hemisphere in which MT–MT distances are small, what fraction of the KMTs that get into that region have a tip interaction with a non–KMT.

We do not understand this comment. However, we think that a similar analysis is presented in the new Figure 8F and G.

Ln 270 and following. The observation that most of the MT–MT interactions (i.e., sites of close proximity) occurred near the spindle pole might be important, but a qualitative look at the 3D reconstructions suggests that the MT density is greater near the poles than farther away. By this I mean in a given spindle cross–section, how many MTs are there/unit area. If this number is higher near the poles, then the MTs must be closer to one another, so the increase in the number of MT proximities is a necessity, not a novel fact. This issue should be considered in the presentation of these data. Perhaps you could compute the MT density as a function of position along the spindle, then use this number at each position to normalize the distributions of interactions, thereby asking whether there is something in the data to indicate that the MTs are binding with one another, rather than simply being packed in. Also, the mechanical significance of KMT ends near KMTs is not clear to me.

Thank you. This is indeed an issue that needs to be considered. As suggested, we normalized the distribution of the MT-MT interactions.

Ln 276 You say, "as a result", but that phrase could be omitted. You are just describing what you saw.

Agreed, we have taken this phrase out.

Ln 290 Note that the number of non–KMTs/spindle cross–section exceeds the number of KMTs/cross section, and this is particularly true near the spindle poles. Thus, the fact that there are more associations between KMT ends and non–KMTs than with KMTs may simply be a consequence of this population difference. This could be calculated on the bases of the relative densities of the two kinds of MTs.

We took care of this aspect and normalized our graphs against the MT densities.

Ln 295 The fact that association frequencies are higher near the pole regardless of association distance may again be based simply on MT density.

We have considered this aspect by normalizing our data against the density of the surrounding MTs.

Ln 296 In this context, I'm particularly interested in Figure 7, supple. 1E. This distribution of interactions between the walls of KMTs and the ends of non–KMTs does show its biggest peak at the pole, as stated, but there is a good indication of a second peak, not far from the kinetochores. This peak would be clearer if the data were presented as a running average, since the fluctuations seen make the bar graphs very spikey. Moreover, if the normalization, based on MT density were applied, it would reduce the polar peak but not the rise in frequency that is seen nearer to the kinetochores. As you know, this position along the spindle was identified structurally by O'Toole et al. as a place where the minus ends of overlapping MTs from the interzone (a subset of your non–KMTs) made association with the walls of KMTs. It is also the place where two groups using microbeams have identified places where KMTs receive a push from the spindle interzone. Thus, the gentle rise in your data may be very significant for the functional interactions between different classes of spindle MTs.

Thank you for pointing this out. We have added the ‘moving average’ to this graph.

Ln 297 This discussion sounds just like what Mastronarde and others have called pairing length in their studies of yeast spindles. It might be well to use similar terminology to minimize confusion. Also, I think there might be a clearer way to describe what you have done. Here is my effort: "To measure the paraxial length over which MTs interacted, we defined 20 nm along the axis as a minimal length of interaction. For each pair of MTs that lay within a chosen interaction distance, we measured the number of 20 nm segments over which they retained this proximity."

Thank you for your elegant suggestion. We have changed this in our manuscript accordingly.

Ln 305 I'm a little uncertain about what the words here mean. Are the "peaks of association" peaks in the number of 20 nm paring lengths that describe the pairing distances? Please clarify.

Yes, this is related to the number of associations with a 20 nm-pairing length. We have corrected this.

Figure 8 It seems as if the legends to 8B and C are switched.

Thanks, we checked this and changed it accordingly.

Ln 305 and following. These words don't do justice to the very interesting distribution graphs you show in Figure 8. In the text, you don't discriminate between the classes of MTs that you break out in your graphs. For example, the words here describe what is shown in Figure 8B but not 8D. Please be specific about which MTs your words refer to.

Thank you. We have cleaned this up.

Ln 309 You see no "hotspots" in your data for interactions between non–KMTs, but in Figure 8D there is a significant peak near the spindle midplane. (The label on the ordinate of this graph says non–KMTs interacting with all other MTs. I presume that you mean both other non–KMTs and KMTs. If this is not right, please be more specific.) Granted, the peak is higher for greater interaction distances, but studies in fission yeast suggest that the mean distance between MTs in the zone of overlap is greater than near the poles, and this the region where kinesin motors generate pushing forces. This peak may be of functional significance, and I think deserves mention in the text.

Agreed, we have mentioned this in the text now.

Ln 327 The term "spindle MTs" appears here without definition. Please clarify.

We changed this to “any MT in the spindle”.

Ln 369 In the text and in Figure 9 it seems to me that you are under–representing the extent to which some KMTs reach the polar area. Your summary diagram shows only one MT of five making to the polar region, whereas both the images you show in the several movies for Figure 3 and your earlier text suggest that the fraction is closer to one–half. This diagram is important, because it is likely to be what gets cited and maybe even reaching textbook figures. Make sure it shows what you have actually seen.

Very good point. Thanks! We agree that the last schematic drawing should be a visual abstract/representation of our paper. We worked on this graph and made sure that 50% of the shown KMTs reach the pole. We also worked on the paragraph of the discussion covering this issue!

Ln 383 This statement about strong indications of KMTs preferring to interact with non–KMTs is subject to the concern raised above that your data are not corrected for the greater number of non–KMTs. Make sure to do this normalization before making this claim.

As suggested, we present out data now as normalized graphs, but the overall interpretation of our data remains the same.

Ln 472 No mention is made in the methods section of coping with the fact that plastic sections collapse during the early stages of exposure to the electron beam. Although there is some shrinkage in the plane of the section, the collapse of section thickness can be as much as 40%, and this affects 3–D geometry of the reconstruction. In my opinion, the fact that both the over–all shapes of your spindles and the shapes of each kinetochore fiber are oval, not circular, is a result of this collapse. Some labs expand the dimension perpendicular to the section plane to correct for this collapse. Was this correction applied here? If not, do you think it has impact on the distances observed between spindle MTs? Some discussion would be appropriate.

We completely agree that there is a collapse of the plastic sections during imaging. As stated in our comments to the ‘essential revisions’ (see above), we have corrected this collapse by applying a z-factor to our full 3D reconstructions. We have added a new figure illustrating this point (new Figure 2—figure supplement 2). We have also added a new paragraph to the Experimental Procedures, where we talk more about how this z-expansion was achieved. Basically, we followed the procedure as described in O’Toole et al. (2020). Essentially, the numbers in our analyses changed only marginally! For clarity, we are showing the data obtained before and after z-expansion in Table 12 and 13.

Ln 535 "was found within the interaction distance" would be clearer.

We changed this to “were positioned“.

Ln 1099 The words, "This video shows" could be omitted from each of these legends with no loss.

We have deleted these words from all video legends.

Reviewer #2 (Recommendations for the authors):

Figure 1

–The authors should include the semi–direct connection between kinetochores and poles, since this has previously been shown.

We agree. As requested, we have added this to Figure 1.

Figure 2

– Figure legend 2C should indicate that microtubule number is in the upper right corner.

We have indicated this in the figure legend.

Figure 2–supplement 1.

– The figure legend is missing.

Thank you for pointing this out. This is now Figure 2—figure supplement 3. We have added the appropriate legend for this figure. Sorry for this mistake.

– Figure 2–supplement 1B indicates pole–to–pole distances of > 8µm for each spindle, with an average around 10.5 µm. However, Table 1 reports spindle pole distances of ~7, 10, and 9 µm. The authors should clarify this discrepancy.

We have corrected this.

Figure 3

– Line 140 in the text reports a KMT packing density of 0.07 KMT/µm2, and Table 3 reports similar KMT packing densities (0.06–0.09 KMT/µm2). However, Figure 3–supplement 1E reports KMT densities in the range of 25–75 KMTs/µm2. The correlation coefficient on lines 137–8 also doesn't match the correlation coefficient on Figure 3–supplement 1D.

We have corrected this.

– Authors should clarify the motivation for comparing inter–kinetochore distance and the number of MTs at the kinetochore, and what previous evidence might suggest a correlation (Figure 3C).

Our motivation here was simply to check if a stretch between kinetochore pairs has an impact on the number of attached KMTs as this would influence the average number of KMTs per k-fiber. We just wanted to rule this out. This point should be clearer now in the revised version of our manuscript.

– Authors should define "neighborhood KMT–KMT" in the figure legend for Figure 3–supplement 1F.

This refers to the average KMT-to-KMT distance at the kinetochore in each k-fiber. We have changed this in the figure legend.

Figure 4

– The authors make several conclusions about the composition of k–fiber bundles, for example, that k–fiber bundles are made up of varying KMT lengths. However, they only present gross KMT data. To directly conclude that individual bundles are made up of varying KMT lengths, they should show their KMT data grouped by k–fiber bundle.

We agree on this point and have added a new figure (Figure 4—figure supplement 2) in which we show the length distribution of the KMTs for the analyzed k-fibers. We have also grouped the k-fibers according to their position on the metaphase plate. Essentially, all k-fibers of all three groups show a high variation in KMT length.

– Relating to Figure 4–supplement 2N, the authors could explain the significance of finding more KMT minus–ends at spindle poles in central k–fibers compared to peripheral k–fibers, expanding on what the motivations were for this analysis and what might it say about global k–fiber organization. The authors could also consider plotting KMT length versus kinetochore region.

Yes, this is a good suggestion. We did this additional analysis for individual k-fibers by showing the variation in the length distribution of KMTs (Figure 4—figure supplement 3). In addition, we present this analysis in the context of the defined three kinetochore regions (now called central, intermediate and peripheral).

– The color of the outer kinetochore region does not match the colors of the images or plots, similarly in Figure 5.

We have corrected this and adapted the color coding. Thanks for pointing this out.

Figure 5

– The authors could expand on their motivations for studying tortuosity of KMTs, and speculate on what their findings could imply about spindle organization.

Thanks. We realized that we should elaborate on this point. Briefly, the tortuosity of the spindles was previously reported by the Tolic lab. We simply wanted to check whether this bending of the MTs as observed by LM is also obvious in our 3D reconstructions, which we could confirm by EM. A simple explanation for this tortuosity in spindles could be that most of the internal bending is caused by MTs that align relative to each other, possibly by some combination of molecular motors and/or passive crosslinkers (see also our parallel study by Conway et al. for our consideration of spindles as liquid crystals). We don’t think that the tortuosity of spindles is directly related to the segregation of the chromosomes.

Figure 6

– The polygon area analysis shown in Figure 6–supplement 1D is unclear and difficult to follow. The authors could clarify why this method was necessary.

Our intention is to calculate the cross-section area of k-fibers. We quickly realized that such an analysis can’t be done by simply fitting a circle, and this is why we thought that the polygon area measurements would be much more precise. We added a comment on this in the results.

– Line 229 confusingly states that the polygon area of the k–fiber was 5–fold lower at the pole–facing end of the fibers. It is unclear whether this is relative to the mid–position or to the kinetochore.

Sorry for being unclear here. This refers to the mid position. We have clarified this issue in our revised version.

Figure 7 and Figure 8

– Some of the text in Figure 7 is too small to read.

Good point. We have changed this and checked all figures for clarity and readability.

– The authors could condense and clarify these figures, as well as compare their findings to previous work on KMT and non–KMT minus–end distributions (O'Toole et al. 2020).

We have intentionally focused our presentation on the patterns of the KMT/non-KMT interactions. Another goal was to show the complexity of the 3D data. Essentially, we did not find signs of bundles of non-KMTs or other clear patterns of non-KMTs in the vicinity of k-fibers. In our paper, we simply want to be careful about this proposed bundling of non-KMTs as proposed by the Tolic lab. The fact that we didn’t find such bundles in our analyses is certainly not a proof for their nonexistence. Our interpretation, however, is that the KMT/non-KMT interactions are statistically distributed all over the spindle but this needs additional analysis. We believe that this is an interesting extension of the present work, which would be best suited for a future publication. However, the complex 3D pattern should be presented here. To illustrate this complexity, we applied our new 3D tool to show the interaction of selected k-fibers with surrounding non-KMTs. We have added new supplementary figures here (Figure 8—figure supplements 1 and 3; Figure 9—figure supplement 1). In this context, we also mention the data presented by O’Toole et al., 2020. Thanks for this hint.

– The authors could discuss more on the key differences found between kMTs and non–kMTs, specifically how the distributions of these two populations are related to their lifetime, organization in the spindle, and mechanistic differences.

We now discuss the implications of our work for the model of spindle organization that has been explained in more detail in the accompanied publication by Conway et al.

– This overall section would benefit from a general summary in the text and model figure(s).

Is this comment related to the paragraphs covering Figures 7 and 8? We have expanded the discussion on this issue.

Reviewer #3 (Recommendations for the authors):

I would recommend a number of additions. Potentially too many for this paper. The most important are the error analysis and the K–fiber identification issue, whilst the interpretation of Figure 8 needs clearing up. Adding more context/discussion and showing tomograph images to support your analysis would be very helpful to your readers.

We have added a paragraph on error analysis in the Experimental Procedures. While we agree that information on this issue should be added to this particular publication, we would like to point out that our 3D reconstruction pipeline has been described in detail in previous publications. An extended analysis on the efficiency and accuracy of template matching for MT segmentation has been published in Weber et al., 2012. Recently, we have also presented a tool to evaluate the accuracy of MT stitching across serial section borders (Lindow et al., 2021). In this new paragraph we consider issues of possible errors during 3D reconstruction and mainly refer to the appropriate publications from our lab. We also worked on the presentation of Figure 8 (now Figure 9), re-wrote the discussion and showed more tomographic slices (see new Figure 2—figure supplement 1).

Additions to support analysis claims:

1. Measurement error analysis and discussion. The manuscript fails to address any issue with respect to errors – all biological data has errors, the question is how much and if it is biased (errors on average not zero). A discussion of accuracy and cautions for interpretation is thus essential.

As mentioned above, a number of error analyses have been done in the context of previous publications, and we didn’t want to be repetitive here. The stitching of MTs over section borders has been described in detail in Lindow et al., 2021. However, we have added a new paragraph to the Experimental Procedures – Error analysis, in which we mention the accuracy in MT segmentation and stitching across section borders. We have also added a new figure (Figure 3—figure supplement 1) that shows the exact tracing of MT across several sections and also visualizes the distribution of stitched MTs over all serial section interfaces.

The key issues are whether:

a. MTs are tracked accurately and along their full length. In particular are microtubules cut prematurely. This could be addressed by analysis of the location of identified MT ends in the sections, in particular errors are more likely at the boundaries of the 300nm slices. Thus, if end density is uniform across the section this provides some reassurance that sectioning (and image morphing) is not causing an error in declaring a MT end when there is none. Since sectioning of the 3 cells is likely to have different orientations with respect to the spindle axis, error rates across sections could be assessed with regard to MT orientation.

As for MT segmentation, an analysis specifically on the ends at section borders has been done extensively in a previous publication (see: Automated stitching of microtubule centerlines across serial electron tomograms, Weber et al., 2014). Using exactly the same computational approach, it is stated: “In our experiments, 95% of the computed connections agreed with an expert's opinion, but 4% (X. laevis) and 1% (C. elegans) connections disagreed.” We would like to point out here that each automatic stitching event in our reconstructions (caused by ‘ends’ of the same MT at section borders, termed ‘MT connection’ in Weber et al., 2014) is checked and (if necessary upon visual inspection) corrected manually.

In our manuscript we now write: "We expect to find approximately the same density of MT endpoints along the Z-direction of each serial-section tomogram. This distribution is visualized in the Serial Section Aligner tool previously presented (Lindow et al., 2021)."

Secondly, can MTs be lost between sections – what is the invisible volume width between sections?

There is indeed a ‘smeared region’ at the top and the bottom of each tomogram. These regions, however, were generated during reconstruction of the tomograms, later used for flattening and then removed before stitching. These regions do not contain MTs. As for the accuracy in the stitching of MT ends, please see our comment above.

Thirdly, examine both the + and – ends and ascertain if they are consistent with MT ends in EM. Since + ends at KTs are curved, it would be good to determine if all + ends in the spindle are curved; otherwise, there may be a signature of an erroneously declared end. Please show examples from the EM. Why wasn't end structure used to determine which are the + and – ends?

In parallel to this study, we have analyzed the end-morphologies of MT ends in the context of untreated and MCRS1-depleted HeLa cells. This analysis will be published as an additional study. The data will also be submitted to ELife and will be available via bioRxiv very soon. Of course, the end morphologies as visualized by electron tomography match exactly the end structures as observed previously by thin-section EM. We have shown this in a number of earlier publications (e.g., see O’Toole et al., 2003; Redemann et al., 2017)! Briefly, the plus ends of the KMTs at kinetochores are all open (mostly) flared, and we see both open (blunt) and closed (capped) minus ends at the spindle poles. Only by visualizing the end morphology, it is not possible for all MTs to annotate ends as either plus or minus. This is particularly true for the blunt ends. Therefore, we refer here to pole-proximal and -distal ends, thus implying that we talk here about MT minus and -plus ends, respectively. This is in full agreement with our previous publications.

b. Are MT ends located accurately, and can you estimate the accuracy?

We are very confident that MT ends are located accurately in our reconstructions. Each MT (including each KMT) in our tomographic reconstructions was manually checked for a correct segmentation at both ends! In Amira, we always check the segmentation of each MT end in 3D (allowing an inspection of each end in an optimal orientation for viewing). We were very careful about this, as the accuracy in the segmentation process is absolutely crucial to this ultrastructural study.

c. Are there lost volumes within sections, or rips, where the sample was destroyed/distorted by the slicing procedure. This would give blind spots in the analysis. What proportion of cell volume is lost and how is it handled in the analysis? Are MT ends called near these problematic volumes?

Of course, we used only perfectly sectioned ribbons of serial sections for our large-scale reconstructions! Serial sectioning is routinely established in our EM lab.

2. Confirm basic statistics with other modalities. To reassure the reader, quantities such as intersister distances, spindle length, KT number, sister–sister twist (wrt metaphase plate), metaphase plate width, kinetochore size, etc could be shown to be consistent with live imaging of the Kyoto HeLa cell line. Perhaps in a Table. It was good to see in Conway et al. the polarisation microscopy comparison.

On purpose, we have moved all light microscopic observations to our parallel manuscript presented by Conway et al. To our mind, the best argument that the EM and LM data are in agreement is the fact that we could fully recapitulate the length distribution of the KMTs by combining both imaging modalities for biophysical modeling. We thought that the data obtained from electron tomography and LM combined with stochastic simulations show remarkable similarity. We strongly believe that both publications have to be read in parallel.

3. Show EM/tomographs to illustrate results. Given this data has 2nm resolution, there is a lack of illustrations with the imaging data. Only examples of KMT + ends are shown in Figure 2 Supplement 2. A sequence of cross sections through a 'K–fibre bundle' would be helpful, marking the KMTs and nonKMTs. This would also help visualise the 'area' and KMT density quantification. An image (sequence) showing an example MT along its length might also be useful. These would allow the reader to see the MT/bundle environment. High resolution sections and/or movies through the spindle moving from the metaphase plate to pole would be good to see, annotated with KMTs in pseudo–colour for instance. Adding this ability to their visualisation tool might be helpful, and taking an idea from Google maps – flip between tomograph section image and analysis would be great. This could be made 3D showing MT orientations as a vector field.

The problem with complex 3D data is that it is very difficult to simultaneously illustrate both the overall structure and the details of certain regions. However, we have added a gallery of tomographic slices to better illustrate the spindle (see new Figure 2—figure supplement 1). The spindle is extremely ‘crowded’ and can be analyzed best in 3D reconstructions. We have added a video (Figure 9-video 2) to illustrate the complexity of the 3D organization in the zone between the spindle pole and the metaphase plate. In this video, MT-MT interactions with an association distance of up to 35 nm are shown. Our primary motivation for presenting the new visualization tool was to give the interested reader the freedom to look at the reconstructions at any desired 3D feature of the spindle at any desired perspective/angle. Compared to the limitations accompanied with previously submitted supplementary videos, we think this is a significant improvement in presenting and visualizing the data.

The Google maps approach is certainly a good idea, and this has been on our to-do-list for quite some time. As a first step towards a better visualization of the tomographic data, we present here (as mentioned above) our new visualization tool. We thought that this is a step in the right direction. More improvements will follow in the near future but this requires much more work and has to be subject to future studies.

Additional analyses, which this data should be amenable to, and likely add to the paper's conclusions:

4. Identify K–fiber bundles. You seem to identify the K–fiber with the bundle of KMTs. I don't think it can be used in this limited way. We know that K–fibres are mechanically distinct MT bundles attached to the KT, bent by forces created by KT attachments (rebounding when cut), MTs in the bundle are crosslinked and K–fibers are cold stable. Hence, can the authors identify nonKMTs that join the bundle (K–fibre) or demonstrate they are not there. These should be parallel to the KMTs with a long association length and be physically close to KMTs. You could use your transverse circle around KMTs to also compute the density of MTs – is that density constant despite loss of KMTs. Movies/image series along the bundle center line could then be constructed showing the bundle tomography image section with distance. Going beyond the KTs would also enable visualisation of bridging fibers, if any – this should complement the analysis of O'Toole et al. on mcMTs. You could then separate MTs into KMTs, mcMTs, and neither (you mention another paper on interdigitating MTs but this paper is weakened without addressing this point). If you find bridging fibers, what is typical geometry of merger to K–fibre and distance from KT?

We only partially agree with this comment. What is the ‘correct’ definition of a k-fiber, and which of the numerous surrounding non-KMTs have to be considered as being associated with the KMTs to establish a k-fiber? For the purpose of this paper, we ‘fished out’ the KMTs from our spindle 3D reconstructions by defining MTs with their putative plus ends associated with the chromosomes as KMTs. We consider these bundled KMTs as the ‘core’ of the k-fibers, and we state this now in the main text of the manuscript. Following this initial characterization, we have considered the non-KMTs in the vicinity of the KMTs. For further analysis and to avoid any bias here, we have chosen different ‘interaction distances’ to analyze the association of the non-KMTs with the KMTs. Using the newly provided computer tool, we now present such interactions in additional supplementary figures (Figure 8—figure supplements 1 and 3; Figure 9—figure supplement 1). The interested reader is encouraged to visualize the interaction pattern of KMTs with non-KMT. Certainly, we don’t want to exclude non-KMTs from our analyses but we need a ‘hard criterium’ to extract those non-KMTs from the population of about two thousand MTs that built the k-fibers. We have added a paragraph on this issue to the discussion. We discuss this core structure of k-fibers now in the context of a maturing of the k-fibers.

5. Quantify + ends. There must be a substantial number of + ends of KMTs in the spindle. It would be good to confirm this. This could be used to examine if MT ends could be generated by breaking MTs – are there + and – ends in close proximity and along the spindle MT orientation, in particular do the KMTs – ends have a + end nearby?

Per definition, KMT plus ends have to be associated with the kinetochores, otherwise we have to classify them as non-KMTs. We are planning on a separate study to show the position of non-KMT plus ends in the spindle. This will be complemented with a detailed analysis of non-KMT length distribution in the context of spindles in which specific proteins, such as augmin and others, have been depleted. This is Best suited for a follow up study.

6. The analysis of peripheral and central KTs (I don't like the word inner and outer) you do for tortuosity can be extended to other statistics – length, fraction KMTs meeting the pole, splay etc. It seems evident that peripheral KMTs will be longer and more likely to fail to reach the spindle pole.

Of course, we could add more analyses on the tortuosity of k-fibers. In the interest of the length of this paper, we are afraid that additional analyses have to be subject to a future publication.

7. You could analyse the angles of interaction of MT end–MT lattice interactions (within 35 nm). Your length association would suggest these are parallel.

Again, in the interest of the length of this paper, we didn’t want to add even more analyses to this paper.

8. You don't account for the change in MT density as you move towards the spindle poles. For instance, the increased MT associations towards the pole can reflect simply this increased MT density. It might also be useful to ascertain the angular dependence of the MTs around the spindle pole (at 1.53 microns). Is it homogeneous as one moves from the pole–pole axis and behind the pole – I suspect not? Is there evidence of clusters (possibly use a statistical test here). It might also be helpful to illustrate the density of MTs. I calculated that MTs would be separated at the spindle pole sphere on average by 148nm (if homogeneous), whilst your tightest bundling of KMTs is 60nm at KTs. Distances are thus very similar at 0.7 microns, close to the peak of the minus end density.

As mentioned in our response to reviewer #1, we are now considering the density of the surrounding MTs in our analysis. We now present data that is normalized against the MT density.

Add more context. The results are not discussed in context of existing literature, including relating results to

i) super–resolution studies, e.g. the twist and handedness of HeLa spindles (Tolic papers, twist appears weak or absent in spindles #1–3),

We have added more context to the observation of spindle tortuosity. We have added a section to the discussion.

ii) live cell imaging such as the EB tracking (Yamashita et al. 2015). The detected EB spots are far lower than the number of MTs detected here. Can this be explained? How many + ends (away from poles) have you in the spindle bulk, not associated with KTs.

Light microscopy analysis of EB1 typically only counts well defined, easily visualized “spots”. This will only include EB1 comets that remain in focus for extended periods of time and which are well resolved from other EB1 comments in the spindle. We believe that this is the primary reason that light microscopy misses so many of the MTs in the spindle. The fact that EB1 only associates with growing ends may also be a contributing factor.

iii) There is also no discussion of bridging fibres; this has been in the literature for a decade and a confirmation/quantification (number MTs) would be very welcome. This of course would entail examining non–KMTs, as suggested above.

On purpose, we avoided a statement on this issue. A possible bundling of non-KMTs similar to KMTs and thus visible as ‘bridging fibers’ (as proposed in the Tolic papers) is not obvious in our large-scale tomograms in metaphase. We just wanted to be careful here. The fact that we didn’t find such a bundling does not exclude such a pattern per se. We simply didn’t find evidence for it. BTW, we did a number of computational experiments to analyze patterns of non-KMTs with KMTs (in fact, we have two figures on this). We certainly need additional ways to analyze such bundling of non-KMTs before a strong statement can be made about this issue. However, the existence of bridging fibers should be much more obvious in anaphase spindles when these proposed fibers are proposed to associate specifically with k-fibers, thus promoting the segregation of chromosomes. This, however, is also on the list of future analyses on the ultrastructure of mitosis.

iv) You have 40% of minus ends away from the spindle poles. It would be good to have your interpretation of the processes that nucleate MTs, both nonKMT and KMT, away from the poles? Does this number make sense or is this evidence of poor MT tracking?

The issue raised above is certainly not related to the accuracy in MT tracing (see also our comments on the accuracy of MT segmentation and the manual correction of tracings). The correlation of MT nucleation and minus-end positioning is tricky as MTs can be moved within spindles. In the manuscript submitted in parallel (Conway et al.) we argue that the KMTs are nucleated at the kinetochore and that the growing MTs are guided towards the spindle poles by the surrounding non-KMTs. A more detailed analysis of the non-KMTs will be the subject of a future manuscript.

Data release.

Tomography data: It is fantastic that the tomography data is released. I would however suggest that there is guidance on which free software can load the Amira files, or release in alternative formats.

We can certainly add additional information about our released data sets. We released all data sets in “.am“ Amira format. This file format allows to open such big files (also on older PCs). All tomographic data is also now available in “.tif“ format, which can be opened with either the ImagJ Fiji or the IMOD open-source software packages. However, these data sets are huge (50-80Gb each), therefore we cannot guarantee that everyone one will be able to open these files.

Tracks: it would be good if the MT traces were released as well. This would enable many people to analyse the networks without the high cost of analysing the tomography data themselves.

The MT-track files containing information about the segmented MTs were already released in binary and ASCII format, allowing anyone to read them. To make this task easier to potential users, the ASGA open-source software, which is part of this publication, is supplied with small scripts written in R language, which allows users to read the ASCII format into array (https://github.com/RRobert92/ASGA/blob/main/R/bin/Utility/Load_Amira.R).

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

The manuscript has been greatly improved but there are some remaining points raised by the reviewers that the authors should consider before acceptance:

Reviewer #1 (Recommendations for the authors):

Kiewisz et al. have done a heroic job of revising their manuscript for resubmission. I appreciate the labor involved in recalculating all the images and interaction distances. Although the distances didn't change much, the images are a significant improvement, and the new data on near–neighbor MT–MT spacings are now more likely to stand the test of time. The revised neighbor distribution curves that are normalized for MT density are also a real improvement. All in all, this paper is now an excellent contribution to the literature and should be published as soon as possible. Below I mention a few issues that still strike my eye, but most of them are simple clarifications and so little work will be needed to make this manuscript a classic.

Thank you for your nice comments on our revised manuscript. We are happy that we could address all critical issues. We have addressed your additional points as follows:

Critique

Ln 1300 Figure 8 is potentially an important figure, but I find two problems with its current version: the gray MTs on a black background are essentially invisible, and the dots in panels C and E are unexplained. This may be my display, but the authors should consider the points.

Yes, we do agree with this statement. We addressed it in the modified new figure.

Figure 8 supplements. The lines representing MTs are so thin that they are hard to see on my screen, even when I blow each sub–image up to fill the screen. In your displays of whole spindles, it is clear why you must use narrow lines, but in these figures with only a few MTs displayed, you could increase the clarity of the images by just making each line a bit wider. Again, dots on the graphics are unexplained.

As stated above, we fixed this issue in the supplements to Figure 8.

In 8Sup1, all I am seeing is KMTs in different colors. There don't seem to be any non–KMTs, and there are no sites of interaction displayed. I gather that this figure shows simply the trajectories of the KMTs that do interact, not the interactions themselves. Do you think this is the best way to show your point?

As suggested, we have thickened the lines representing the MT trajectories. The whole purpose of this figure is to demonstrate the power of ASGA 3Dviewer software and to motivate the reader to display MT interactions by using this newly developed software package.

In 8Sup3, similar to Sup1. I think these figures would be more informative if you would show the interacting non–KMT and particularly the site of interaction. Simply coloring the whole MT erases that information.

Thank you for pointing this out. Again, the visualization as shown here was generated by using the ASGA_3DViewer. Again, this supplementary figure was added to encourage the reader to use the new software. Due to the interactive nature of this software tool, it should be easy to observe directly in the 3D models where MTs interact with each other. In the current version, the visualization of the interaction zones is not possible. However, this is a very good suggestion, and we will work on incorporating of interaction zones to have this feature in the next release of the software.

Ln 331 You are right, of course, that the major peak in Figure 8, Sup2 G shows a major peak near the pole, like all the other associations, but the secondary peak farther from the pole is very noticeable in this display, and given the evidence from other groups that this kinetochore–proximal region may be an important site for interactions between the ends of non–KMTs and the walls of KMTs, I think this really deserves mention.

We included this information in the revised version of our manuscript.

Figure 9, these MT–representing lines barely show up on my screen. A little thicker?

We have changed this according to your suggestion. Thank you for raising this point.

The legends for the Figure 9 supplement Figuresneed attention. The boxes are not referred to or explained, and again the sites of interaction are not clear. Supple. 2 legend text, "Number of KMTs plotted against the number of associations with other MTs in the spindle per individual KMT" doesn't match the labeling on those axes, so it's not clear what is being shown in these graphs.

Thank you for pointing this out. We have corrected this.

Ln 371 and following, you state that the number of associations was 10.6, but it is not clear what this number means. Number/KMT, per k–fiber or what?

We clarified this in the text. This number referred to an average number of individual interactions with KMT.

Ln 384 and following. I understand that the reworking of your images and numbers to accommodate the reviewers' suggestion of expanding the collapsed sections was a major amount of work, and probably pretty painful/annoying to do. Thus, adding this paragraph to the discussion is understandable, but as a reader coming to this version with a fresh point of view, I don't think it is necessary. You describe what you are going to do near the beginning of the paper, and you describe very nicely what you did in the methods section. It seems to me mentioning it again in the discussion over–emphasizes the point to, but this is for the authors to decide.

We removed this as suggested.

Ln 516 The statement that these and related data show that KMTs nucleate predominantly at kinetochores is true only for metaphase cells, and this limitation must be stated, otherwise it is misleading.

Thanks for pointing this out. We have added this to the manuscript.

The addition of https://cfci.shinyapps.io/ASGA_3DViewer/ as a viewer tool is a major step in data sharing. Many thanks to the authors for developing this, because the Amira package is expensive. This addition will make their hard work much more useful to others.

Thanks for this comment. This was exactly our intention: an AMIRA-independent software tool for viewing of our 3D models. The plan is to add more and more spindles to this visualization platform.

Reviewer #2 (Recommendations for the authors):

The authors provide a substantially improved manuscript. We support publication. However, a number of issues remain and should be addressed before publication.

Thank you for supporting the publication of our manuscript. We have addressed your additional points as follows:

– Intro: The authors describe the three models of KMT–pole connections, but should situate known mammalian spindle structure work in the context of these models. More was known prior to this work than what was acknowledged.

As requested, we have added more references to each model of the KMT-pole connections.

– Figure 5B, 5S2B: legend and plot in 5B says centrosome interaction area was defined as a half–width of a peak from the center, but text lines 195 and 408 say "two fit half–widths from the center of the fit peak".

Thank you for pointing this out. We have corrected this.

– Figure 5D: How can the MT–centrosome interaction area be highlighted in gray, if this distance is 1.7 µm but the P–KT length of each k–fiber is different? (i.e. the x–axis of this plot is a relative measurement, but MT–centrosome interaction distance is absolute).

We apologize for being unclear here. As for the relative position of the MT-centrosome interaction area, this area indicates an approximated interaction zone on the pole-to-kinetochore axis. This is now addressed in the main text, in the Experimental Procedures and also stated in each figure legend.

– There is no Figure 5E.

Thank you for pointing this out. We have corrected this.

– Figure 5G: Discrepancy with Figure 5A and 5G legend, where P2 is at a relative position of 1.00 vs. 1.2.

Thank you for pointing this out. We have corrected this.

– Figure 4B, 4S1B, 5B, 5F, 5G, 9S2B, 9S2D: What criteria were used to decide which nKMTs to include? The total number from all three spindles is 16,256, based on Table 1, but these plots all include only 9957 (more than any individual spindle but far less than all three).

This discrepancy is related to the fact that some MTs (KMTs and non-KMTs) were not fully covered in the volume. For instance, if a single KMT from a k-fiber could not fully be reconstructed, we removed this whole fiber from the length distribution analysis. Similarly, non-KMTs not entirely reconstructed in the volume were marked as uncompleted and not considered in our analyses of length distribution, end distributions, curvature, etc. In the case of the MT-MT interaction analysis, this was indeed not correct. We apologize for this mistake. The text and the figure legends have been corrected to include now 16,256 non-KMTs.

– Figure 5S4B legend does not match plot.

Thank you. We have corrected the figure legend.

– Line 1254: What is meant by "A tortuosity of 1.1 is length."?

We deleted this phrase.

– Line 1255: What is meant by "The gray line indicates indicated by a dashed line."?

This line of text was rewritten in for a clarity.

– Figure 6E–F: Color codes are reversed. Red corresponds to higher tortuosity in E but lower tortuosity in F, and vice versa with gray.

We are sorry about this. We have corrected this both in the text and in the figure.

– Lines 231–236: A different motivation is needed for the tortuosity analysis. Tortuosity reports on microtubule curvature, but NOT twist–it doesn't tell us anything about 3D helicity that is consistent along a microtubule's length. It also seems that Figure 6 should have its own heading in the Results text, rather than being combined under the heading "K–fibers are broadened at spindle poles," since the correlation between tortuosity and spindle axis position is very weak and there is no other evidence in Figure 6 to support this statement.

Correct, this was confusing in our previous version. Therefore, we re-wrote the introduction to this paragraph. paragraph. Hopefully, our motivation for the tortuosity analysis is clearer now.

– Figure 7S1D: They did not address our comment that the polygon area analysis is never motivated or explained, and is unclear.

Thank you for raising this point. As suggested, Figure 6 now has its own heading.

– Figures 8–9: They did not change figures 8–9 (formerly 7–8) very much, as we suggested. Expanding their introduction to these figures in the text helps a little, but it's still hard to tell how these figures and sub–figures are making unique points.

As requested, we have changed (condensed) figures 8 and 9 and tried to better explain our motivation to perform the analyses on MT tortuosity. Hopefully, this is clearer now.

– Figure 9A: This cartoon should be moved to Figure 9S2, because interaction length is not quantified in Figures 9 or 9S1.

Cordially, we don’t agree with this specific point. We show this schematic drawing to simply illustrate how interactions in the spindles were detected, specifically how the number and length of interactions was measured. Although Figure 9 is focusing only on the number of interactions, we wanted to help the reader to understand our analysis. It is correct that Figure 9 sup2 then shows the quantification of the length of interactions. We think that this schematic drawing should remain to be shown in Figure 9.

– Figure 9S1: It's unclear what is being shown here or how it relates to Figure 9. Line 1375 says "This 3D model illustrates the association of KMT lattices with other KMT lattices minus ends". What are all the non–KMTs shown in these images? Are we looking at associations with lattices, with minus ends, or microtubules that interact for extended distances? Line 1376 says "The types of interactions are shown by color–coding," but what is the color code?

We apologize for this error. We fixed this and address the above comment in the figure legend. Following the suggestion from Reviewer #1, we also thickened the MT trajectories.

– Lines 497–498: What correlations is this sentence referring to? No correlations are shown in Figures 8 or 9.

We agree with this comment. This correlation refers to the correlation now shown in Figure 9—figure supplement 2C-D. We address this in the text.

https://doi.org/10.7554/eLife.75459.sa2

Article and author information

Author details

  1. Robert Kiewisz

    Experimental Center, Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany
    Present address
    1. Biocomputing Unit, Centro Nacional de Biotecnologia (CNB-CSIC), Darwin, 3, Campus Universidad Autonoma, 28049 Cantoblanco, Madrid, Spain
    2. Simons Machine Learning Center, New York Structural Biology Center, New York, United States
    Contribution
    Conceptualization, Resources, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing
    For correspondence
    robert.kiewisz@gmail.com
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-2733-4978
  2. Gunar Fabig

    Experimental Center, Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany
    Contribution
    Formal analysis, Validation, Methodology, Writing – review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3017-0978
  3. William Conway

    Department of Physics, Harvard University, Cambridge, United States
    Contribution
    Data curation, Formal analysis, Validation, Visualization
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-7532-4331
  4. Daniel Baum

    Department of Visual and Data-Centric Computing, Zuse Institute Berlin, Berlin, Germany
    Contribution
    Validation, Writing – review and editing
    Competing interests
    No competing interests declared
  5. Daniel Needleman

    1. Department of Physics, Harvard University, Cambridge, United States
    2. Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
    3. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, United States
    4. Center for Computational Biology, Flatiron Institute, New York, United States
    Contribution
    Conceptualization, Formal analysis, Writing – original draft, Writing – review and editing
    Competing interests
    No competing interests declared
  6. Thomas Müller-Reichert

    Experimental Center, Faculty of Medicine Carl Gustav Carus, Technische Universität Dresden, Dresden, Germany
    Contribution
    Conceptualization, Supervision, Funding acquisition, Writing – original draft, Project administration, Writing – review and editing
    For correspondence
    mueller-reichert@tu-dresden.de
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-0203-1436

Funding

Deutsche Forschungsgemeinschaft (MU 1423/8-2)

  • Robert Kiewisz
  • Gunar Fabig
  • Thomas Müller-Reichert

Horizon 2020 Framework Programme (675737)

  • Robert Kiewisz
  • Thomas Müller-Reichert

Harvard University

  • William Conway
  • Daniel Needleman

Nick Simons Foundation (1764269)

  • William Conway
  • Daniel Needleman

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

Acknowledgements

The authors thank Dr. Tobias Fürstenhaupt (Electron Microscopy Facility at the MPI-CBG, Dresden, Germany) for technical support. We are also grateful to Drs. Reza Farhadifar, Stefanie Redemann, Alejandra Laguillo Diego and Isabelle Vernos for a critical reading of the manuscript. We also thank Felix Herter for implementing a module in the ZIB extension of Amira that we used in this paper for visualizing different cross-section plains of KMT ends. Research in the Müller-Reichert laboratory is supported by funds from the Deutsche Forschungsgemeinschaft (MU 1423/8–2). RK received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 675737 (grant to TM-R). This work was supported by the NSF-Simons Center for Mathematical and Statistical Analysis of Biology at Harvard (award number #1764269), and the Harvard Quantitative Biology Initiative.

Senior Editor

  1. Anna Akhmanova, Utrecht University, Netherlands

Reviewing Editor

  1. Adèle L Marston, University of Edinburgh, United Kingdom

Reviewer

  1. J Richard McIntosh, University of Colorado, Boulder, United States

Publication history

  1. Received: November 10, 2021
  2. Preprint posted: November 13, 2021 (view preprint)
  3. Accepted: July 24, 2022
  4. Accepted Manuscript published: July 27, 2022 (version 1)
  5. Version of Record published: August 10, 2022 (version 2)
  6. Version of Record updated: August 15, 2022 (version 3)

Copyright

© 2022, Kiewisz 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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  1. Robert Kiewisz
  2. Gunar Fabig
  3. William Conway
  4. Daniel Baum
  5. Daniel Needleman
  6. Thomas Müller-Reichert
(2022)
Three-dimensional structure of kinetochore-fibers in human mitotic spindles
eLife 11:e75459.
https://doi.org/10.7554/eLife.75459
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    Tricia T Nguyen, Gia K Voeltz
    Research Article Updated

    Mitochondria are dynamic organelles that undergo cycles of fission and fusion at a unified platform defined by endoplasmic reticulum (ER)-mitochondria membrane contact sites (MCSs). These MCSs or nodes co-localize fission and fusion machinery. We set out to identify how ER-associated mitochondrial nodes can regulate both fission and fusion machinery assembly. We have used a promiscuous biotin ligase linked to the fusion machinery, Mfn1, and proteomics to identify an ER membrane protein, ABHD16A, as a major regulator of node formation. In the absence of ABHD16A, fission and fusion machineries fail to recruit to ER-associated mitochondrial nodes, and fission and fusion rates are significantly reduced. ABHD16A contains an acyltransferase motif and an α/β hydrolase domain, and point mutations in critical residues of these regions fail to rescue the formation of ER-associated mitochondrial hot spots. These data suggest a mechanism whereby ABHD16A functions by altering phospholipid composition at ER-mitochondria MCSs. Our data present the first example of an ER membrane protein that regulates the recruitment of both fission and fusion machineries to mitochondria.

    1. Cell Biology
    2. Immunology and Inflammation
    Jazlyn P Borges, Ragnhild SR Sætra ... Benjamin Ethan Steinberg
    Short Report

    First recognized more than 30 years ago, glycine protects cells against rupture from diverse types of injury. This robust and widely observed effect has been speculated to target a late downstream process common to multiple modes of tissue injury. The molecular target of glycine that mediates cytoprotection, however, remains elusive. Here, we show that glycine works at the level of NINJ1, a newly identified executioner of plasma membrane rupture in pyroptosis, necrosis, and post-apoptosis lysis. NINJ1 is thought to cluster within the plasma membrane to cause cell rupture. We demonstrate that the execution of pyroptotic cell rupture is similar for human and mouse NINJ1, and that NINJ1 knockout functionally and morphologically phenocopies glycine cytoprotection in macrophages undergoing lytic cell death. Next, we show that glycine prevents NINJ1 clustering by either direct or indirect mechanisms. In pyroptosis, glycine preserves cellular integrity but does not affect upstream inflammasome activities or accompanying energetic cell death. By positioning NINJ1 clustering as a glycine target, our data resolve a long-standing mechanism for glycine-mediated cytoprotection. This new understanding will inform the development of cell preservation strategies to counter pathologic lytic cell death.