To overcome the limitations of confocal microscopy and explore the relationship between different classes of microtubules within the crowded metaphase plate area, we performed stimulated emission depletion (STED) superresolution imaging (Hell and Wichmann, 1994; Klar and Hell, 1999) of microtubules within the bipolar metaphase spindles of human cells (Figure 1A–B, Figure 1—figure supplement 1). This enabled us to easily distinguish between k-fibers that start at kinetochores and midplane-crossing microtubules that pass through the central part of the spindle. HAUS6 or HAUS8 components of the augmin complex were depleted by siRNA in hTERT-RPE1 (hereafter referred to as RPE1) cells stably expressing CENP-A-GFP and immunostained for tubulin (Figure 1A, Figure 1—figure supplement 1). Augmin depletion was confirmed using immunocytochemistry and western blot analysis (Figure 2—figure supplement 1A-CFigure 2—source data 1).

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In control cells, the vast majority of midplane-crossing microtubule bundles laterally attached to a pair of sister k-fibers and formed a bridging fiber between them, consistent with previous findings (Kajtez et al., 2016; Vukušić et al., 2017). These bridging fibers were nearly-parallel with respect to one another and the spindle axis. Additionally, a small portion of midplane-crossing microtubules formed a secondary connection between a k-fiber on one side and a non-sister k-fiber on the other side (O’Toole et al., 2020). In comparison with untreated cells, midplane-crossing microtubules after HAUS6 or HAUS8 depletion extended at a variety of angles, and were wavy and disordered, particularly in the inner part of the spindle close to the pole-to-pole axis. Strikingly, midplane-crossing microtubules less often formed bridging fibers that connect to sister k-fibers in cells depleted of HAUS6 or HAUS8. Instead, they formed more complex arrangements, primarily consisting of one or more connections between various k-fibers within the metaphase spindle. This was contrary to k-fibers which, even though often missing a bridge between them, appeared relatively similar to those in control cells (Figure 1B, Figure 1—figure supplement 1). Taken together, augmin is vital for the proper organization of midplane-crossing microtubules into uniformly arranged bridging fibers that connect two sister k-fibers and extend nearly-parallel to the spindle axis.

The appearance of disordered midplane-crossing microtubules in the metaphase plate area of spindles without augmin prompted us to investigate whether these microtubules affect mitotic fidelity. Augmin depletion has previously been linked to higher incidence of segregation errors (Almeida et al., 2022; Viais et al., 2021; Wu et al., 2008), but their origin remained largely unexplored due to extensive mitotic delays in augmin-depleted cells (Wu et al., 2008). To avoid mitotic delays, we performed live-cell confocal imaging for which we codepleted the checkpoint protein Mad2 together with HAUS6 to induce anaphase onset, and used Mad2-depleted cells (Mayr et al., 2007), which have only a few segregation errors, as a control (Figure 2A, Videos 1 and 2). To explore the mechanistic origin of segregation errors, we divided them into three distinct groups: misaligned chromosomes in which both kinetochores were found outside the metaphase plate just before anaphase onset, lagging chromosomes in which the kinetochore is visibly stretched and positioned in the central part of the spindle while other kinetochores are already separating, and other less common and diverse errors (Figure 2A–B, See Materials and methods).

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Figure 2—source data 1

Immunoblot analysis of HAUS6 siRNA treatment efficiency in RPE1 cells stably expressing CENP-A-GFP and Centrin1-GFP.

Full unedited blots of all three independent experiments are shown.

https://cdn.elifesciences.org/articles/83287/elife-83287-fig2-data1-v2.pdf

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Video 1

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Video 2

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The treatment with Mad2 siRNA resulted in a total of 1.5±0.2 segregation errors per cell (all data are given as mean ± SEM). However, the effect was significantly more severe when Mad2 was codepleted with HAUS6, resulting in a total of 5.7±0.8 segregation errors per cell (Figure 2B). Tracking of sister kinetochores in live-cell videos revealed that the number of misaligned kinetochore pairs per cell was similar in both Mad2 depletion and Mad2/HAUS6 codepletion (Figure 2B), which is why we presume they appeared due to Mad2 depletion independently of HAUS6 depletion. Nevertheless, they were much more likely to missegregate in cells without HAUS6, where 80 ± 9% of kinetochore pairs jointly segregated into the same cell, compared to only 20 ± 13% in control cells (Figure 2B). Interestingly, lagging kinetochores were both more frequent and more likely to missegregate in cells with Mad2/HAUS6 codepletion, in which there were 2.6±0.4 lagging kinetochores per cell, and 45 ± 6% of all lagging kinetochores ultimately missegregated. In contrast, there were only 0.8±0.2 lagging kinetochore pairs per cell in Mad2 depletion, and 77 ± 8% of them segregated correctly (Figure 2B). Finally, errors classified as others were more frequent in cells with Mad2/HAUS6 codepletion when compared to those with Mad2 depletion, but not more prone to missegregation (Figure 2B).

As misaligned chromosomes appeared equally frequently in Mad2 depletion and Mad2/HAUS6 codepletion, but differed in their ability to correctly segregate, we used them as a tool to isolate the role of augmin in resolving segregation errors during anaphase. Consistent with previous findings (Uehara et al., 2009), both poleward movement of kinetochores during anaphase A and spindle elongation during anaphase B were reduced following Mad2/HAUS6 codepletion (Figure 2—figure supplement 1D-F). To analyze in detail the movement of misaligned kinetochore pairs, we tracked both kinetochores with respect to the proximal and distal pole, that is the pole which is closer to the misaligned kinetochore pair or the pole which is further away from it, respectively. The kinetochore closer to the proximal pole approached the proximal pole during anaphase A both after Mad2 depletion and Mad2/HAUS6 codepletion, thereby moving towards the pole to which it should segregate in both cases (Figure 2C). However, the kinetochore further away from the proximal pole usually remained stagnant for a short period of time, and afterwards typically moved towards the distal pole and accurately segregated as a ‘lazy’ kinetochore (Sen et al., 2021) in Mad2-depleted cells. In contrast, the kinetochore further away from the proximal pole experienced a short stagnation period and then typically moved away from the pole to which it should segregate, thereby missegregating in Mad2/HAUS6-codepleted cells (Figure 2D, Figure 2—figure supplement 1G-H). As the interkinetochore distance of both correctly and incorrectly segregating misaligned kinetochore pairs in Mad2/HAUS6-codepleted cells was similar (Figure 2E), the absence of biorientation is unlikely to be the cause of missegregation for these kinetochores. Instead, missegregation likely occurs due to k-fibers with fewer microtubules (Almeida et al., 2022; Uehara et al., 2009; Zhu et al., 2008) creating insufficient force to move the kinetochore towards the distal pole (Dudka et al., 2018), against the movement of neighboring kinetochores and the corresponding chromosome mass which travel towards the proximal pole (Figure 2A, Video 2).

Whereas lagging chromosomes have been previously observed following augmin depletion (Almeida et al., 2022; Viais et al., 2021; Wu et al., 2008), their origin remains unknown. Because we observed that disorganized midplane-crossing microtubules were often concentrated in the inner part of the mitotic spindle near the main spindle axis upon augmin depletion (Figure 1B, Figure 1—figure supplement 1), we decided to investigate the spatial distribution (Figure 2F) of lagging kinetochores in Mad2-depleted and Mad2/HAUS6-codepleted cells to see if their increased number might be connected to this phenotype. In Mad2-depleted cells, all lagging kinetochore pairs were situated in the outer half of the spindle just before anaphase onset. Remarkably, in Mad2/HAUS6-codepleted cells, 19 ± 5% of all lagging kinetochore pairs were situated in the inner part of the spindle just before anaphase onset (Figure 2F), where disordered midplane-crossing microtubules most frequently appeared. Thus, organization of midplane-crossing microtubules into bridging fibers might play an important role in mitotic fidelity.

To further explore how this compromised spindle geometry affects lagging kinetochores, we measured their interkinetochore distance just before anaphase onset. The lagging kinetochore pairs in Mad2/HAUS6-codepleted cells had an interkinetochore distance of 0.89±0.03 µm, which was significantly smaller than the interkinetochore distance of 0.98±0.02 µm measured in error-free kinetochore pairs (Figure 2G). This was not the case for lagging kinetochore pairs in Mad2-depleted cells which had an interkinetochore distance of 1.10±0.05 µm, similar to the interkinetochore distance of 1.05±0.02 µm measured in error-free kinetochore pairs (Figure 2G). Distinctly reduced interkinetochore distance of lagging kinetochore pairs following Mad2/HAUS6 codepletion suggests that they appear due to compromised spindle architecture being unable to maintain adequate kinetochore tension.

As sister k-fibers in the disorganized spindle region were sometimes diagonally positioned with respect to the pole-to-pole axis, we decided to test if this tilt is also connected to the appearance of segregation errors by measuring the angle that either lagging or error-free kinetochores form with the spindle axis just before anaphase onset. As for the interkinetochore distance following Mad2/HAUS6 codepletion, lagging kinetochore pairs were different from error-free kinetochore pairs, the tilt of which was 19.7±1.6° and 10.9±0.8°, respectively (Figure 2H). In contrast, in Mad2-depleted cells with preserved spindle geometry there was no difference between lagging kinetochore pairs with the tilt of 8.2±1.5° and error-free kinetochore pairs with the tilt of 8.9±0.6°, which was also similar to the tilt of 10.9±0.8° measured for error-free kinetochore pairs following Mad2/HAUS6 codepletion (Figure 2H). The tilt of kinetochores inversely correlated with the interkinetochore distance in augmin depletion, but not in control cells (Figure 2I). These data indicate the importance of nearly parallel configuration of kinetochore pairs during metaphase for mitotic fidelity, and points to the augmin-specific cause of lagging kinetochores that likely arise due to compromised and tilted bundle architecture facilitating the formation of merotelic attachments. Indeed, we found merotelic attachments in HAUS6-depleted cells imaged using STED microscopy, with most kinetochores forming an attachment with the microtubule from the opposite side of the mitotic spindle, while missing a proper bridging fiber (Figure 2J). To further test the nature of the observed attachments, we combined STED microscopy with cold treatment to remove midplane-crossing microtubules and preserve only kinetochore microtubules (DeLuca et al., 2006; Sacristan et al., 2018; Silkworth et al., 2012), which allowed us to confirm their true merotelic nature (Figure 2K). Interestingly, our live-cell imaging experiments reveal that augmin is required not only to prevent the formation of merotelic attachments in metaphase, but also to resolve them in anaphase, as a larger percentage of lagging kinetochore pairs ends up missegregating in Mad2/HAUS6 codepletion than in Mad2 depletion (Figure 2B). This suggests that the insufficient force provided by k-fibers with fewer microtubules (Dudka et al., 2018), which is responsible for missegregation of misaligned kinetochore pairs following augmin depletion, also leads to inability to resolve merotelic attachments during anaphase.

Altogether, we propose that augmin ensures mitotic fidelity through the joint action of bridging and k-fibers. While augmin-nucleated bridging fibers prevent merotelic attachments by creating a nearly parallel and highly bundled spindle geometry unfavorable for creating additional attachments, augmin-nucleated k-fibers produce robust force required to resolve any potentially appearing errors during anaphase (Figure 2L).

As our visual assessment revealed that spindles without augmin have disorganized arrangements of midplane-crossing microtubules and often lack proper bridging fibers (Figure 1B), which were also missing at kinetochore pairs that formed merotelic attachments (Figure 2J), we set out to analyze how augmin-dependent microtubule nucleation contributes to the formation of bridging fibers in immunostained RPE1 cells imaged using STED microscopy (Figure 3A–B). Bridging fibers were strictly defined as midplane-crossing microtubules that connect two sister k-fibers, whereas k-fibers were defined as microtubules that start at kinetochores (Figure 3C). We measured tubulin signal intensity of randomly selected bridging (I_b) and k-fibers (I_k) which had no other microtubules in their immediate neighborhood, in a small square region between two kinetochores or at the pole-side of kinetochore, respectively (Figure 3C, see Materials and methods). By using the resulting tubulin signal intensities, we first estimated the number of microtubules in the bridging fiber in untreated RPE1 cells. Electron tomography of spindles in RPE1 cells showed that k-fibers consist of n_k = 12.6 ± 1.7 microtubules (O’Toole et al., 2020). Thus, the bridging fiber consists of n_b = I_b × n_k ⁄ I_k = 3.8 ± 0.4 microtubules (for the explanation of I_b and I_k calculations, see Materials and methods). The accuracy of this calculation was additionally tested by measuring the intensity of astral microtubules, which presumably consist of single microtubules (McDonald et al., 1992). Indeed, using the number of microtubules in the k-fiber, our measurement of astral microtubule intensities showed that the astral microtubules consist of n_a = 1.0 ± 0.1 microtubules (Figure 3D).

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Quantification of STED images further revealed that HAUS6 depletion resulted in 68 ± 8% reduction of the bridging fiber signal intensity and 24 ± 6% reduction of the k-fiber signal intensity, with similar results obtained by HAUS8 depletion (Figure 3D–E). These data indicate that augmin depletion affects not only k-fibers, but even more so bridging fibers. The contribution of augmin to the nucleation of k-fibers was independently tested by measuring their intensity in spindles exposed to cold treatment in which bridging fibers are removed (Figure 3F). HAUS6 depletion resulted in a 37 ± 5% reduction of the k-fibers (Figure 3G), which is consistent with a previous study (Zhu et al., 2008) and comparable to values under non-cold conditions. Based on the measurements under non-cold conditions, we estimate that after HAUS6 depletion bridging fibers consist of 1.2±0.7 microtubules and k-fibers of 9.6±1.5 microtubules, which we interpret as microtubules nucleated in an augmin-independent manner. Thus, 2.6±0.7 microtubules in the bridging fiber and 3.0±0.9 microtubules in the k-fiber are nucleated in an augmin-dependent manner.

Remarkably, 41 ± 4% of all kinetochore pairs in HAUS6-depleted cells had no detectable bridging fibers, defined as those with the tubulin signal below the background signal (see Materials and methods), and consistent with results obtained using visual inspection (Figure 3—figure supplement 1A). The majority of kinetochore pairs without bridging fibers were located in the inner part of the mitotic spindle, where as much as 50 ± 5% of all kinetochore pairs had undetectable bridging fibers after augmin depletion, compared to only 27 ± 5% in the outer part (Figure 3H), thus pointing to an irregular and more complex spatial distribution of bridging fibers in the inner part of the spindles following augmin depletion. Similar results were obtained from superresolution imaging after HAUS8 depletion (Figure 3H). To further validate our results, we performed live-cell confocal imaging with SiR-tubulin (Lukinavičius et al., 2014) and analyzed the spindles by two independent methods (Figure 3—figure supplement 1A–H, See Materials and methods). Altogether, these results reveal that the augmin complex is a major nucleator of bridging fibers, whereas its contribution to the formation of k-fibers is significant but less prominent.

The compromised microtubule nucleation following augmin depletion led to the impairment of overall spindle geometry, creating a unique system where three main types of interactions between k-fibers and bridging fibers can be found within the same spindle: (1) sister k-fibers attached to bridging fibers, (2) sister k-fibers without a bridging fiber, and (3) solitary, long, interpolar bundles without associated kinetochores. This is in contrast with control cells, where the first group dominates and the other two groups are rarely found (Polak et al., 2017). To gain insight into the contribution of each of these functionally distinct microtubule bundles to the maintenance of spindle geometry, we traced the outermost bundles in HAUS6 siRNA-treated RPE1 cells imaged using STED microscopy and fitted a circle to the bundle outline (Figure 3—figure supplement 1, see Materials and methods). Whereas the bundles without kinetochores in HAUS6 siRNA-treated cells had a significantly longer contour when compared to all other bundle types (Figure 3—figure supplement 1J), k-fibers without bridging fibers in augmin-depleted cells had a significantly larger radius of curvature than any of the other bundle types in augmin-depleted or control cells (Figure 3—figure supplement 1K). Taken together, the outer interpolar bundles without associated kinetochores are excessively long and make the spindle wider, whereas k-fibers lacking a bridging fiber are overly straight, ultimately resulting in a diamond-like shape of the spindle. This change in spindle shape in the absence of proper bridging fibers is consistent with the prediction of our theoretical model (Kajtez et al., 2016) and previous experiments (Jagrić et al., 2021).

In addition to spindle architecture, compromised microtubule nucleation following augmin depletion also affected spindle dynamics, as poleward flux in U2OS cells stably expressing CENP-A-GFP, mCherry-tubulin and photoactivatable-GFP-α-tubulin was significantly reduced (Figure 3—figure supplement 1L-M), in agreement with findings in Indian Muntjac cells (Almeida et al., 2022). Recent speckle microscopy experiments in RPE1 cells, which were able to separate the effect of augmin on poleward flux of bridging and k-fibers, revealed that both k-fibers and the remaining bridging fibers were significantly slowed down (Risteski et al., 2022). Bridging fibers fluxed faster than k-fibers in control and augmin-depleted cells (Risteski et al., 2022), supporting the model in which poleward flux is largely driven by sliding apart of antiparallel microtubules (Brust-Mascher et al., 2009; Mitchison, 2005; Miyamoto et al., 2004). We propose that augmin depletion results in slower flux of bridging fibers because the remaining bridging microtubules are likely nucleated at the poles, where microtubule depolymerization mechanisms might curb poleward flux speed (Ganem et al., 2005). In contrast, PRC1 depletion does not affect the flux (Risteski et al., 2022; Steblyanko et al., 2020) even though it reduces bridging fibers (Kajtez et al., 2016; Polak et al., 2017), possibly because the remaining bridging microtubules are generated away from the poles via augmin and can thus flux freely. In sum, augmin ensures proper architecture and dynamics of the metaphase spindle largely through the nucleation of bridging fibers, which link sister k-fibers and ensure their proper shape and function.

Our finding that bridging fibers were more severely perturbed in the inner part of the spindle after augmin depletion prompted us to examine the spatial distribution of these midplane-crossing microtubules and their overlap regions throughout the spindle. We used protein regulator of cytokinesis 1 (PRC1) as a marker because it preferentially crosslinks overlap microtubules (Li et al., 2018; Mollinari et al., 2002), thus providing a specific label for bridging fibers (Polak et al., 2017). By taking a standard ‘side view’ of the spindle and rotating the 3D image stack of the spindle into an ‘end-on’ view, we were able to gain insight into the redistribution of bridging microtubules throughout the spindle cross-section in HeLa (Kajtez et al., 2016) and RPE1 (Asthana et al., 2021) cells stably expressing PRC1-GFP with and without MG-132 treatment (Figure 4A–B, Figure 4—figure supplement 1A). To compare their distribution to that of tubulin, we also rotated the 3D image stacks of the spindles in RPE1 cells stained with SiR-tubulin (Figure 4A–B, Figure 4—figure supplement 1B; Novak et al., 2018).

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The signal intensity of PRC1-GFP bundles in RPE1 cells was reduced by 55 ± 4% following augmin depletion (Figure 4C). Consistently, the number of PRC1-labeled overlap bundles measured in an end-on view of spindles was almost halved; from 28±1–16±1 distinct bundles in control and HAUS6-depleted RPE1 cells, respectively (Figure 4D). Comparable trends were also observed in HeLa cells after depletion of HAUS6 or HAUS8 (Figure 4—figure supplement 1C-G).

The augmin-depleted cells showed a specific barrel-like distribution of the PRC1-GFP labeled bundles, with more overlap bundles being present around the perimeter of the spindle and fewer in the central part (Figure 4A ‘end-on view’ and 4D, Figure 4—figure supplement 1H-I). However, DNA was uniformly distributed throughout the spindle cross-section, both in augmin-depleted and control cells (Figure 4A ‘end-on view’). In agreement with this result, kinetochores and tubulin signal were also found uniformly distributed over the spindle cross-section (Figure 4A ‘end-on view’ of RPE1 cells). This observation indicates that k-fibers are present and roughly uniformly distributed throughout the spindle cross-section and is in agreement with our finding that augmin primarily affects bridging fibers, while k-fibers are less perturbed (Figure 3).

To explore the role of the observed overlap repositioning in defining the overall spindle geometry, we measured spindle width, the diameter of the metaphase plate, spindle length, and overlap length in RPE1 and HeLa cells (see Materials and methods). Despite the spindles being wider in both cell lines, the diameter of the metaphase plate was not larger, as the spindles widened due to the long, curved bundles without kinetochores (Figure 4—figure supplement 1J). While the spindles in RPE1 cells shortened following augmin depletion, those in HeLa cells were longer (Figure 4—figure supplement 1J), consistent with previous observations on Drosophila S2 cells and Xenopus egg extracts (Goshima et al., 2007; Petry et al., 2011). This difference in spindle length might be due to the overlaps remaining the same length after augmin depletion in RPE1 cells, while being longer and thereby able to push the spindle poles further apart in HeLa cells (Figure 4—figure supplement 1K). When both spindle length and overlap length were taken into account, the relative length of overlaps with respect to spindle length increased in RPE1 cells from 48±1%–57 ± 2% following augmin depletion (Figure 4F), comparable to the increase in HeLa cells (Figure 4—figure supplement 1L-M). Altogether, these results suggest that augmin regulates both the width and length of metaphase spindles, while also restricting the portion of spindle length occupied by overlap microtubules.

Interestingly, the long curved bundles characteristic for augmin depletion (Goshima et al., 2008; Uehara et al., 2016; Wu et al., 2008; Zhu et al., 2008) exhibited PRC1 signal along most of their length, suggesting that they consist of antiparallel microtubules, even though contrary to bridging fibers, they form away from the k-fibers and kinetochores (corresponding to long, curved bundles in Figure 1A and Figure 3—figure supplement 1). These bundles likely arose either due to PRC1 crosslinking excessively long astral microtubules that were now able to reach the spindle midzone or due to PRC1 activity combined with the excess of free tubulin present as a consequence of less tubulin being incorporated in bridging and k-fibers. Altogether, the data suggest that there was an overall redistribution of PRC1 within the spindle from a large number of relatively short overlaps to a small number of relatively long overlaps. These results were further corroborated by PRC1-antibody staining in unlabeled HeLa cells, which also showed a reduced number of elongated PRC1 signals along the curved outer bundles after augmin depletion (Figure 4—figure supplement 1F). Thus, without augmin, the spindles are wider and contain fewer overlaps, which occupy a larger portion of spindle length and tend to accumulate at the spindle periphery.

The interkinetochore distance, which is a readout of interkinetochore tension (Waters et al., 1996), decreases after augmin depletion (Uehara et al., 2009; Zhu et al., 2008). Our measurements on RPE1 and HeLa cells also showed a reduced interkinetochore distance in augmin-depleted cells (Figure 5—figure supplement 1A). This reduction of interkinetochore tension may be due to weaker k-fibers (Uehara et al., 2009; Zhu et al., 2008). However, we noticed that the interkinetochore distance was smaller in the inner part of the spindle in augmin-depleted cells (Figure 5A–D, Figure 5—figure supplement 1B), where bridging fibers were most severely impaired (Figures 3H and 4A). This was not the case in control cells, which showed no difference in interkinetochore distance between the inner and the outer part of the spindle (Figure 5D, Figure 5—figure supplement 1B). These findings motivated us to investigate a potential link between the lack of proper bridging fibers and the interkinetochore tension. We thus divided kinetochore pairs in STED images into two groups: (1) those with a bridging fiber (i.e. signal intensity of the bridging fiber above the background signal), and (2) those with undetectable signal intensities at the expected locations of bridging fibers, which we for simplicity refer to as kinetochore pairs without bridging fibers (Figure 5B–C). Remarkably, kinetochore pairs without bridging fibers had a significantly smaller interkinetochore distance than kinetochore pairs with bridging fibers (Figure 5E).

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Although this result suggests a role of bridging fibers in regulating interkinetochore distance, this effect may be indirect and arise due to k-fibers, askinetochore pairs that lacked a bridging fiber typically had thinner k-fibers than those with a bridging fiber in augmin-depleted cells (Figure 5—figure supplement 1C). Hence, we used several approaches to separate the contribution of bridging and k-fibers to the interkinetochore tension. First, we found that although the interkinetochore distance correlated both with bridging and k-fiber intensity after augmin depletion, the correlation with bridging fiber intensity was stronger (Figure 5—figure supplement 1D-E). Such correlations were absent in control cells (Figure 5—figure supplement 1D-E). To explore a specific contribution of k-fibers to the interkinetochore tension, we divided the kinetochore pairs in augmin-depleted cells into two subsets, those with and without bridging fibers, and found that the interkinetochore distance did not correlate with k-fiber intensity within each group (Figure 5F), which argues against the k-fiber intensity as a sole determinant of interkinetochore tension. In agreement with this, when we selected two subsets of kinetochore pairs with either very strong or very weak k-fiber intensity but with comparable bridging fiber intensities (Figure 5—figure supplement 1F-G), we found no difference in the interkinetochore distance between these subsets (Figure 5—figure supplement 1H). Finally, to examine a specific contribution of bridging fibers, we identified two subsets of kinetochore pairs with similar k-fiber intensity values, one of which had bridging fibers and the other which did not (Figure 5—figure supplement 1). We found that the interkinetochore distance was larger in the subset with bridging fibers than without (Figure 5G), indicating a specific effect of bridging fibers on interkinetochore tension. Analysis of live-cell confocal images of RPE1 cells yielded similar results (Figure 5—figure supplement 1J-M). Based on these data, we conclude that augmin has a significant role in regulating interkinetochore tension through the nucleation of bridging microtubules.

Experiments were carried out using unlabeled human HeLa-TDS cells from the High-Throughput Technology Development Studio (MPI-CBG, Dresden); human HeLa-Kyoto BAC cells stably expressing PRC1-GFP (Poser et al., 2008), courtesy of Ina Poser and Tony Hyman (MPI-CBG, Dresden, Germany); human HeLa cells stably expressing CENP-A-GFP and Centrin1-GFP (Gasic et al., 2015), which were a gift from Emanuele Roscioli and Andrew McAinsh (University of Warwick, Coventry, UK); human HeLa-TDS cells stably expressing GFP-α-tubulin as described in our previous work Kajtez et al., 2016; human hTERT-RPE1 (hTERT immortalized retinal pigment epithelium) cells stably expressing CENP-A-GFP and human hTERT-RPE1 (hTERT immortalized retinal pigment epithelium) cells stably expressing both CENP-A-GFP and Centrin1-GFP (Magidson et al., 2011), a courtesy of Alexey Khodjakov (Wadsworth Center, New York State Department of Health, Albany, NY, USA); human RPE1 CRISPR-Cas9 cells stably expressing PRC1-GFP (Asthana et al., 2021), a gift from Thomas Surrey (Centre for Genomic Regulation, Barcelona, Spain); and human U2OS cells stably expressing CENP-A-GFP, mCherry-α-tubulin and PA-GFP-α-tubulin (Barisic et al., 2014), a gift from Marin Barišić (Danish Cancer Society Research Center, Copenhagen, Denmark).

All cell lines were cultured in flasks in Dulbecco’s Modified Eagle’s Medium with 1 g/L D-glucose, pyruvate and L-glutamine (DMEM, Lonza, Basel, Switzerland), supplemented with 10% (vol/vol) heat-inactivated Fetal Bovine Serum (FBS, Sigma Aldrich, St. Louis, MO, USA) and penicillin (100 IU/mL)/streptomycin (100 mg/mL) solution (Lonza, Basel, Switzerland). For the selection of U2OS CENP-A-GFP mCherry-α-tubulin PA-GFP-α-tubulin, HeLa PRC1-GFP, HeLa CENP-A-GFP Centrin1-GFP and Hela GFP-α-tubulin cell lines, 50 μg/ml geneticin was added to the medium (Life Technologies, Waltham, MA, USA).

All cells were kept at 37 °C and 5% CO₂ in a Galaxy 170 R humidified incubator (Eppendorf, Hamburg, Germany). They have also been regularly tested for mycoplasma contamination by examining the samples for extracellular DNA staining with SiR-DNA (100 nM, Spirochrome, Stein am Rhein, Switzerland) and Hoechst 33342 dye (1 drop/2 ml of NucBlue Live ReadyProbes Reagent, Thermo Fisher Scientific, Waltham, MA, USA) and have been confirmed to be mycoplasma free.

At 80% confluence, DMEM medium was removed from the flask and cells were washed with 5 ml of PBS. Then, 1 ml 1% trypsin/EDTA (Biochrom AG, Berlin, Germany) was added to the flask and cells were incubated at 37 °C and 5% CO₂ in a humidified incubator for 5 min. After the incubation, trypsin was blocked by adding 2 ml of DMEM medium. For RNAi experiments, the cells were seeded to reach 60% confluence the next day and cultured on 35 mm uncoated dishes with 0.16–0.19 mm (1.5 coverglass) glass thickness (MatTek Corporation, Ashland, MA, USA) in 2 mL DMEM medium with previously described supplements. After one day of growth, cells were transfected with either targeting or non-targeting siRNA constructs which were diluted in OPTI-MEM medium (Life Technologies, Waltham, MA, US) to a final concentration of 20 nM for HAUS6 and HAUS8 in medium with cells. HAUS6 and HAUS8 siRNA transfections were performed 48 hr prior to imaging and cotransfection with 100 nM Mad2 siRNA was additionally performed 24 hr prior to imaging using Lipofectamine RNAiMAX Reagent (Life Technologies, Waltham, MA, US) according to the instructions provided by the manufacturer. After four hours of treatment, the medium was changed to the previously described DMEM medium. The constructs used were human HAUS6 siRNA (L-018372-01-0005, Dharmacon, Lafayette, CO, USA), human HAUS8 siRNA (L-031247-01-0005, Dharmacon, Lafayette, CO, USA), human Mad2 siRNA (L-003271-00-0010, Dharmacon, Lafayette, CO, USA) and control siRNA (D-001810-10-05, Dharmacon, Lafayette, CO, USA). Mad2 was chosen instead of MPS1 inhibitors as it induces less segregation errors per cell in control cells, as well as to avoid a biased approach in which the inhibitor would likely be added at a different time point during an hours-long error correction process that occurs in augmin-depleted cells.

When microtubules were visualized during live cell-imaging in cell lines without stable expression of tubulin, staining was performed to a final concentration of 100 nM with a far-red silicon rhodamine (SiR)-tubulin-670 dye (Spirochrome, Stein am Rhein, Switzerland), 45 min to 2 hr prior to imaging. As for DNA, either SiR-DNA or SPY-555-DNA (Spirochrome, Stein am Rhein, Switzerland) were used to a final concentration of 100 nM, 20 min to 2 hr prior to imaging. In order to avoid dye efflux, a broad-spectrum efflux pump inhibitor verapamil (Spirochrome, Stein am Rhein, Switzerland) was added at a final concentration of 0.5 μM to RPE1 cells along with tubulin and/or DNA dyes. As an additional control for metaphase cells, MG-132 (Sigma Aldrich, M7449-1ML, MO, USA) was added to the cells used for the measurement of spindle size for 30 min prior to imaging at a final concentration of 20 µM.

For confocal imaging, HeLa cells stably expressing PRC1-GFP were grown on glass-bottom dishes (14 mm, No. 1.5, MatTek Corporation) and fixed by 2 ml of ice-cold methanol for 1 min at –20 °C. Following fixation, cells were washed three times for 5 min with 1 ml of PBS and permeabilized with 0.5% Triton-X-100 in water for 15 min at a room temperature. This step was repeated twice when tubulin staining was performed. To block unspecific binding, cells were incubated in 1 ml of blocking buffer (1% normal goat serum (NGS)) for 1 hr at 4 °C. Cells were then washed three times for 5 min with 1 ml of PBS and incubated with 250 µl of primary antibody solution overnight at 4 °C. The primary antibodies used were as follows: rabbit polyclonal PRC1 (diluted 1:100, sc-8356, Santa Cruz Biotechnology, RRID:AB_2169665), rabbit polyclonal HAUS6 (diluted 1:250, ab-150806, Abcam), rabbit polyclonal HAUS8 (diluted 1:100, PA5-21331, Invitrogen, RRID:AB_11153508) and rat monoclonal tubulin (diluted 1:100, MA1-80017, Invitrogen, RRID:AB_2210201). After the incubation with a primary antibody, cells were washed 3 times for 5 min with 1 ml of PBS and then incubated with 250 µl of secondary antibody for 45 min at a room temperature. Alexa Fluor 488 and 594 (Abcam, ab150073, ab150076, ab150156) were used as secondary antibodies at a 1:1000 dilution for PRC1 staining, 1:500 dilution for HAUS6 and 1:250 for HAUS8 and tubulin staining. DAPI (1 µg/mL) was used for chromosome visualization.

For STED imaging, RPE1 cells stably expressing CENP-A-GFP were grown on glass-bottom dishes (14 mm, No. 1.5, MatTek Corporation), cell medium was removed, and cytoskeleton extraction buffer was added for 20 s to remove the components of the cytoplasm. Following extraction, cells were fixed in 3% paraformaldehyde and 0.1% glutaraldehyde solution for 10 min. To reduce the background fluorescence, quenching (100 mM glycine in PBS) and reduction (0.1% sodium borohydride in PBS) solution were added for 7 and 10 min, respectively. To prevent non-specific binding, cells were incubated in blocking/permeabilization buffer (2% normal goat serum and 0.5% Triton-X-100 in PBS) for 2 hr at 4 °C. Microtubules were then stained using a rat anti-tubulin primary antibody solution (diluted 1:500 in blocking/permeabilization buffer, MA1-80017, Invitrogen) with a 4 °C overnight incubation. The next day, cells were washed with PBS three times for 5 min. After washing, a secondary antibody Alexa Fluor 594 (dilution 1:1000, Abcam) was added and incubated for 1 hr at room temperature. Additionally, DAPI (1 µg/mL) was added and incubated for 15 min at room temperature to visualize chromosomes. Cells exposed to cold treatment were incubated with cold media on ice for 13 min prior to extraction of cytoplasmic components.

RPE1 cells stably expressing CENP-A-GFP and Centrin1-GFP were grown on six-well plates (Greiner Bio-one) and subjected to HAUS6 or HAUS8 siRNA treatment as indicated before. Following transfection, cells were lysed in RIPA buffer (R0287, Sigma) containing 1 x protease inhibitor (5892970001, Roche), 1 x phosphatase inhibitor (4906837001, Roche) and 1 mM PMSF by two cycles of freezing and thawing in liquid nitrogen. Protein extracts were mixed with 2 x Laemlli sample buffer (S3401, Sigma) and heated at 95 °C for 10 min prior to SDS-PAGE. After protein transfer onto the nitrocellulose membrane (IB23002, Invitrogen) and blocking with blocking solution (5% bovine serum albumin and 0,1% Tween 20 in PBS) for 1 hr, membranes were incubated overnight at 4 °C with primary antibodies diluted in blocking solution. The primary antibodies used were as follows: rabbit polyclonal HAUS6 (diluted 1:1000, ab-150806, Abcam), rabbit polyclonal GAPDH (diluted 1:1000, ab9485, Abcam, RRID:AB_307275). Rabbit polyclonal HAUS8 antibody (diluted 1:1000, PA5-21331, Invitrogen, RRID:AB_11153508, and NBP2-42849, Novus Biologicals, RRID:AB_2665500) resulted in no detectable bands under these conditions. Membranes were washed with 0.1% Tween 20 in PBS, incubated for 1 hr with anti-rabbit HRP-conjugated secondary antibodies (dilution 1:10,000, ab6721, RRID:AB_955447) and visualized on the C-DiGit blot scanner (LI-COR, Bad Homburg, Germany) with WesternSure PREMIUM Chemiluminescent Substrate (926–95000, LI-COR).

STED microscopy of fixed cells and live-cell imaging of anaphase were performed using an Expert Line easy3D STED microscope system (Abberior Instruments, Göttingen, Germany) with the 100 x/1.4NA UPLSAPO100x oil objective (Olympus, Tokio, Japan) and an avalanche photodiode (APD) detector. The 488 nm line was used for excitation in both cases, with the addition of the 561 nm line for excitation and the 775 nm laser line for depletion during STED superresolution imaging. Images were acquired using the Imspector software. The xy pixel size for fixed cells was 20 nm and 6 focal planes were acquired with 300 nm distance between planes were acquired. For confocal live-cell imaging of anaphase, the xy pixel size was 80 nm and 16 focal were acquired, with 1 µm distance between the planes and 30 s time intervals between different frames.

Other confocal images and videos were acquired using a previously described microscope setup (Buđa et al., 2017), consisting of a Bruker Opterra Multipoint Scanning Confocal Microscope (Bruker Nano Surfaces, Middleton, WI, USA), mounted on a Nikon Ti-E inverted microscope with a Nikon CFI Plan Apo VC 100 x/1.4 numerical aperture oil objective (Nikon, Tokyo, Japan). During live-cell imaging, cells were kept at 37 °C and 5% CO₂ in Okolab Cage Incubator (Okolab, Pozzuoli, NA, Italy). To excite Hoechst, GFP, mCherry or SiR fluorescence, a 405 nm, 488 nm, 561 nm or 647 nm laser lines were used, respectively. Opterra Dichroic and Barrier Filter Set 405/488/561/640 enabled the separation of excitation light from the emitted fluorescence. Images were acquired using Evolve 512 Delta Electron Multiplying Charge Coupled Device (EMCCD) Camera (Photometrics, Tuscon, AZ, USA), with camera readout mode of 20 MHz. The xy pixel size was 83 nm. In all experiments where the whole spindle stack was imaged, z-stacks were acquired with unidirectional xyz scan mode at 37 focal planes and 0.5 μm distance between the planes. Photoactivation was performed perpendicular to pole-to-pole axis of metaphase spindles using a 405 nm laser diode (Coherent, Santa Clara, CA, USA) and a line pattern of 12 equally distributed points, with each point representing one laser hit. The interval between the points was 0.05ms and photoactivation area was set to 0.5 µm for each point. The interval between successive frames was set to 10 s and one central z-plane was imaged.

In cells where HAUS6 or HAUS8 were silenced only bipolar metaphase spindles were imaged and analyzed, even though multipolar spindles were observed as reported previously (Lawo et al., 2009). All images were analyzed in Fiji/ImageJ (National Institutes of Health, Bethesda, MD, USA, RRID:SCR_003070). Raw images were used for quantification. In representative immunofluorescence images of augmin depletion (Figure 2—source data 1), all signals were adjusted equally in control and treated cells. However, due to severe reduction of bridging fibers in augmin-depleted spindles, the contrast in images for representation on figures was not always equally adjusted, as this led to important spindle structures being either highly oversaturated or barely visible. It was instead adjusted so that astral microtubules are similarly visible in control and augmin-depleted spindles in STED microscopy, or that all present bridging fibers are visible in confocal microscopy. These adjustments did not result in any structures being omitted or otherwise modified in a way that could lead to misrepresentation. MatLab (MathWorks, Natick, MA, USA, RRID:SCR_001622) was used for calculations and plotting and Rstudio (R Foundation for Statistical Computing, Vienna, Austria, RRID:SCR_000432) to transform the cells into an end-on view. Figures were assembled in Adobe Illustrator CS5 (Adobe Systems, Mountain View, CA, USA, RRID:SCR_010279).

For the analysis based on small square regions which was performed on both STED and confocal images, tubulin intensity in bridging and k-fibers was measured using either a 25x25 or 5x5 pixel Square tool (ImageJ) on STED and confocal images, respectively. To measure bridging fibers, the square was positioned on the fiber spanning the area between two kinetochores. K-fibers were measured right next to the kinetochores. The average intensity of the two sister k-fibers was used for further analyses. The background was measured using the same tool at several empty areas within the spindle and its average was subtracted from bridging (I_b = I_b+bcg – I_bcg) and k-fiber intensities (I_k = I_k+bcg – I_bcg). 10 randomly positioned empty areas were taken into account while calculating background for STED imaging, whereas 2 empty areas just above and below bridging fiber were taken into account while calculating background for confocal imaging due to different nature of the acquired images. All measurements were performed on randomly selected bundles in single z-planes, after determining that no other microtubules were crossing the area of measurement. In STED images, the intensity of astral microtubules was additionally measured using the 25x25 pixel Square tool (ImageJ). Their background was measured using the same tool in the empty area between the two astral microtubules and it was subtracted from astral microtubule intensity (I_a=I_a+bcg-I_bcg).

On top of that, tubulin intensities of the bridging fiber and k-fiber region in confocal images were measured in a single z plane using the Segmented Line tool by drawing a 5 pixel line (ImageJ) along the contour of k-fibers and the corresponding bridging fiber. Background was measured in the same z plane by drawing the 5 pixel thick line along the length of the metaphase midzone, as this represents the background signal caused by the presence of neighboring microtubules. The minimum value of the midzone intensity profile was subtracted from the intensity profiles of bundle contours. The minimum value of the mean tubulin intensity profile was set as a distance of zero μm and was selected as the center of the bridging fiber. The final intensity of a bridging fiber (I_b) was calculated as the mean value of intensities in the area 500 nm around the center of the bridging fiber. The final intensity of a k-fiber region (I_bk), which also includes the bridging fiber, was calculated as an average of two mean values of intensities in the area 500 nm around the distance of 1.5 μm away from the center of the bridging fiber. The intensity value of k-fibers alone (I_k) was then calculated as I_k = I_bk – I_b.

For the comparison of SiR and GFP-tubulin signal in HeLa cells stably expressing GFP-α-tubulin, the previously described analysis was used. Tubulin intensity of the bridging fiber and k-fiber region was measured in a single z plane using the Segmented Line tool in ImageJ by drawing the 5 pixel line along the contour of k-fibers and the corresponding bridging fiber. Due to high noise, only outermost bundles were taken into analysis and the reduction was not calculated. The background was measured in the same z plane by drawing the 5x5 pixel square in the cytoplasm and was subtracted from the bundle intensity profiles. The minimum value of the intensity profile was set as a distance of zero μm and was selected as the center of the bridging fiber.

To calculate the interkinetochore distance, two points were put on the centers of signal in each kinetochore pair using a Point tool in ImageJ. Additionally, two points were put on spindle poles and two points on the upper and lower edge of the metaphase plate. Interkinetochore distance and distance from spindle axes were calculated using a home-written MatLab script. Two-dimensional analysis was applied when all tracked kinetochore pairs resided within 2 μm around the central z-plane. Three-dimensional analysis was used when all kinetochore pairs in the spindle were taken into account, regardless of their position. In 3D analysis, the exact distance from the long spindle axis (c) was calculated using the Pythagorean theorem, where a=projected distance of a middle point between two sister kinetochores in a particular z-plane from the long spindle axis, b=distance between the central z-plane and the z-plane of the kinetochore pair x 0.81 (correction factor for the oil objective only, see Transformation of spindles into an end-on view). Kinetochore pairs were defined as those in the inner or the outer part of the spindle if their distance to the pole-to-pole axis was smaller or larger than the average distance of all tracked kinetochore pairs to the pole-to-pole axis, respectively. Additionally, kinetochores with visible bridging fibers and kinetochores with no visible bridging fibers were separately tracked and analyzed in confocal images of RPE1 cells stably expressing CENP-A-GFP and Centrin1-GFP, where the presence of bridging fibers was determined by measuring intensity profiles of the tubulin signal between two kinetochores.

Z-stacks of the mitotic spindles that were positioned horizontally were transformed into the end-on view using a home-written R script, based on the original version (Novak et al., 2018). Prior to transformation, a single-channel grayscale z-stack was rotated using ImageJ to make the long axis of the spindle parallel to the x-axis. Signal intensity at each pixel was used to obtain an end-on view of the spindles by applying the following transformation: I' (i · pixel size, j · pixel size, k · z-distance)=I (k · z-distance, I · pixel size, j · pixel size). A correction factor of 0.81 was used for the z-distance to correct for aberrations caused by the different refractive index mismatch of aqueous samples and immersion oil (Novak et al., 2018).

The number of bundles in HeLa and RPE1 PRC1-GFP cells was determined in an end-on view of the spindle by using sum intensity projections of 10 central z-planes covering 0.83 µm along the long spindle axis.

Spindle length, width and metaphase plate diameter were measured on maximum intensity projections of the side view z-stack of spindles. Spindle length was determined as a distance between the two poles. The position of the poles was determined as either the center of Centrin1 signal or the outermost points of the tubulin or PRC1 signal at the spindle pole. Spindle width was measured as the distance between two lines parallel to the long axis of the spindle and encompassing the outermost PRC1- or tubulin-labeled bundles. Additionally, in RPE1 cells stably expressing CENP-A-GFP and Centrin1-GFP the metaphase plate diameter was measured as the distance between the outermost kinetochore pairs, whereas in HeLa PRC1-GFP it was measured as the distance between the outermost chromosome ends.

Overlap length was measured on sum intensity projections of 2–4 z-planes covering the entire bundle of interest, using ImageJ Segmented line tool by drawing a pole to pole line along the contour of PRC1-GFP and acquiring an intensity profile. The overlap length was defined as the length of the base of the PRC1-GFP intensity peak (Polak et al., 2017).

PRC1 intensity was measured in sum intensity projections of 10 central z-planes of the spindle. Total PRC1 signal in the cell was marked by using Polygon selection tool (ImageJ) and 5x5 Square tool was used to determine the background in the cytoplasm. The final intensity values were obtained using the following formula: PRC1 intensity = Integrated Density of the spindle – (Area of selected cell x mean fluorescence of background). Intensity profiles of PRC1-GFP were measured on the sum intensity projections of 10 central z-planes in an end-on view of the spindle by drawing a 50 pixel wide Straight line tool across the diameter of the spindle.

The shape of spindles was determined in ImageJ using a Point tool. Ten points were distributed throughout the bundle, with the first and last point positioned at the spindle poles. The images were rotated to make the long spindle axis parallel to the x axis. In control cells, only the outermost bundle was tracked. In HAUS6 siRNA-treated cells, three different groups of outermost bundles were tracked: bundles with visible bridging fibers, bundles with no visible bridging fibers and curved bundles extending far from the metaphase plate. Shape and curvature were calculated using a home-written MatLab script by fitting a circle to the tracked points along the bundle. Contour lengths of the bundles were measured by calculating the cumulative distance between the first and the last point of the tracked bundle.

For measuring the poleward flux rate, 10-pixel wide line was drawn from pole to pole along the bundle with photoactivation signal that lasted at least 5 time frames (40 s), using the Segmented Line tool in ImageJ. The position of photoactivated mark in each time frame was determined as the distance between the peaks of intensity profiles in photoactivation and SiR-tubulin channels for photoactivation mark and closer spindle pole, respectively. The analysis was performed on images processed with Gaussian Blur filter with Sigma set to 2 to improve the definition of the intensity profile peaks.

Three types of segregation errors were analyzed in Mad2-depleted and Mad2/HAUS6-codepleted anaphase spindles: misaligned kinetochores, lagging kinetochores and other errors. Misaligned kinetochores were defined as those in which both kinetochores of the pair were situated outside the metaphase plate 30 s before anaphase onset. Lagging kinetochores were defined as those in which the CENP-A signal was visibly stretched and the kinetochore was situated in the central part of the spindle, outside the kinetochore mass that was moving towards the pole during anaphase. Finally, segregation errors classified as others included various kinetochores, precise classification of which was impossible using only CENP-A signal. These included kinetochores situated outside the moving kinetochore mass without stretched CENP-A signal, kinetochore pairs that remained completely unseparated for the whole duration of anaphase, as well as kinetochore pairs in which both kinetochores remained non-stretched and in the central part of the spindle despite the initial separation. Segregation errors were further divided based on their distance to the pole-to-pole axis into those in the inner and the outer part of the spindle. The distance of the kinetochore pair from the pole-to-pole axis was determined in 3D using a home written Matlab script, and the obtained value was then normalized to spindle half-width determined using maximum intensity projections in ImageJ. All kinetochores situated in the area less than 0.5 from the spindle axis 30 s before anaphase onset were defined as those in the inner part of the spindle and all kinetochore pairs in the area equal to or above the value of 0.5 were defined as kinetochores in the outer part of the spindle. All kinetochore pairs were manually tracked in time from just before anaphase onset until entering the daugther cell by using the Point tool in ImageJ. In images acquired using STED microscopy, merotelic attachments were defined as those in which one kinetochore forms attachments with microtubules from the opposite side of the spindle, with no visible microtubule signal just below or above the kinetochore.

To measure anaphase A speed, the coordinates of kinetochores and poles were tracked in time using the Point tool in ImageJ. The speed was calculated from the time point when the distance between the kinetochore and its closer pole started gradually decreasing. The slope of a line equation obtained from the linear fitting of distances over time was determined for every kinetochore as the anaphase A speed. Anaphase B speed was calculated in a manner similar to anaphase A, but instead of kinetochores, the positions of poles were tracked in time with the first time frame determined as the frame when the distance between two poles started gradually increasing.

Anaphase onset was determined in a frame just before the interkinetochore distance of the tracked kinetochore pair started gradually increasing. The coordinates of kinetochore pairs that ended up as errors and of error-free kinetochore pairs were tracked along with the coordinates of spindle poles. The angle that the kinetochores form with the long spindle axis was calculated using a home written Matlab script.

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

We thank Alexey Khodjakov, Ina Poser and Tony Hyman, Thomas Surrey, Emanuele Roscioli, Andrew McAinsh, Mariola Chacon and Marin Barišić for the cell lines. We also thank Marko Šprem and Abberior team for help with developing microscopy protocols, Ivana Štimac and Marko Šprem for help with creating the MatLab and R scripts, Josip Čačković and Arian Ivec for technical assistance with the initial experiments and calculations, all members of Tolić and Pavin groups for discussions and advice, Ivana Šarić for the drawings. Funding This work was funded by the European Research Council (ERC Consolidator Grant, GA number 647077 and ERC Synergy Grant, GA number 855158), Croatian Science Foundation Cooperation Programme with Croatian Scientists in Diaspora “Research Cooperability” (HRZZ Project PZS-2019-02-7653), as well as QuantiXLie Centre of Excellence (Grant KK.01.1.1.01.0004) and IPSted (KK.01.1.1.04.0057) projects cofinanced by the Croatian Government and European Union through the European Regional Development Fund - the Competitiveness and Cohesion Operational Programme.

1. Preprint posted: September 10, 2020 (view preprint)
2. Received: September 7, 2022
3. Accepted: September 26, 2022
4. Accepted Manuscript published: October 21, 2022 (version 1)
5. Version of Record published: November 7, 2022 (version 2)

© 2022, Štimac, Koprivec et al.

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