Previous analyses of meiotic spindle microtubules using EM tomography were based on partial, rather than full, reconstructions of the spindle. This made it impossible to measure the total length of microtubules composing the spindle since most microtubules extend beyond the tomographic volume. We obtained the spindle ultrastructure of C. elegans oocytes by serial section electron tomography, which allows the reconstruction of whole spindles in 3D with single-microtubule resolution (Redemann et al., 2017). We reconstructed two meiotic spindles in metaphase I (T0243.5 and T0243.7), as well as four spindles at early (T0243.4), mid (T0208.1), and late stages of anaphase I (T0275.10 and T0369.8; Figure 1A, Figure 1—videos 1, 2; Figure 3—video 1) for meiosis I (Table 1). In addition, we reconstructed two metaphases (T0186.1 and T0209.7), one early anaphase (T0186.3), and one mid anaphase (T0234.6) stage of meiosis II oocytes (Figure 1B, Table 2). We had previously analyzed the modes of microtubule attachment to chromosomes (end-on vs. lateral) and discussed the resulting role of microtubules in chromosome segregation during anaphase using the meiosis I metaphase (T0243.5), early anaphase (T0243.4), mid anaphase datasets (T0208.1), (Redemann et al., 2018) and late anaphase (T0275.10) (Yu et al., 2019) of the first meiotic division. Here, we used those datasets, together with newly generated additional datasets of meiosis I metaphase (T0243.7), and late anaphase (T0369.8), and two meiosis II metaphases (T0186.1, T0209.7), early anaphase (T0186.3), and mid anaphase (T0234.6), to quantitatively characterize the spindle structure and microtubule rearrangements during female meiosis.

For this, we compiled summary statistics that characterize spindle morphology. In Tables 1 and 2, we report the spindle length, the number of microtubules, the number of microtubules that are located within 150 nm from the chromosome surface, the average microtubule length, the maximum microtubule length, the total polymer length (added length of all microtubules), and the dimension of the tomogram and spindle dimensions for each stage of meiosis I (Table 1) and II (Table 2). We also indicated new and previously analyzed datasets in this table.

We first sought to characterize the overall spindle structure. Female meiotic spindles could be constructed mainly from long microtubules, reaching from near the spindle pole to chromosomes (as in C. elegans mitotic spindles; Redemann et al., 2017), or from short ones distributed throughout the spindle volume, as suggested by Srayko et al., 2006, and, for instance, meiotic Xenopus spindles (Brugués et al., 2012; Burbank et al., 2006; Yang et al., 2007).

Our data show that throughout meiosis I and meiosis II, roughly 40–50% of microtubules are shorter than 500 nm (Figure 1D). In contrast, the fraction of microtubules that are at least half spindle length or longer is only 10%. Throughout meiosis, the mean length of microtubules is approximately 20% of the spindle length (Tables 1 and 2).

Furthermore, we determined the position of the pole-proximal ends of microtubules along the spindle axis. In metaphase, these putative microtubule minus-ends were found throughout the spindle (Figure 1E), with no marked preference for the poles. In anaphase, about 60–70% of microtubules are found within a distance of 150 nm from the chromosomes, and the others are distributed throughout the spindle (Figure 1F).

Together, these findings directly confirm that the acentrosomal female meiotic C. elegans spindle is an array of short microtubules, more similar to meiotic Xenopus spindles than to mitotic spindles in C. elegans, as previously inferred by others based on light microscopy (Brugués et al., 2012; Burbank et al., 2006; Yang et al., 2007). We conclude that the distance between poles in metaphase (5 µm) and chromosomes in anaphase (3–4 µm) is bridged by an array of short overlapping microtubules rather than long ones spanning the entire distance. This is an overall interesting finding as C. elegans meiotic spindles are rather short in comparison to Xenopus meiotic spindles and could easily generate microtubules long enough to bridge the entire spindle length, which is much harder to achieve in a 60 µm Xenopus spindle.

We next sought to understand the role of microtubule movements and dynamics in the structural changes observed during the transition from metaphase to anaphase. Since electron tomography generates static snapshots, we investigated this question by light microscopy. Using fluorescence recovery after photobleaching (FRAP), we first measured microtubule turnover and motion in metaphase I spindles. By photobleaching a small stripe near the center as well as close to the poles of metaphase spindles (Figure 2A, arrows, Video 1), we observed a half-time of microtubule recovery in metaphase of 4.9 s ± 3.4 s (n = 6) in the spindle center and 4.1 s ± 2.7 s (n = 6) at the spindle poles (Figure 2B). In addition, we observed that the photobleached stripes close to the spindle poles showed a rapid poleward movement with a rate of 8.5 ± 2.2 µm/min (n = 6, Figure 2C).

We conclude that microtubules in C. elegans meiosis turn over rapidly and show substantial poleward motion. This is notably different from the first mitotic division in the early C. elegans embryos, where microtubule motion was not detected in similar experiments (Labbé et al., 2004; Redemann et al., 2017). Thus, in female meiosis, both nucleation/depolymerization and microtubule motion might be involved in shaping the spindle structure. Similar microtubule dynamics have been described in Xenopus meiotic spindles using fluorescent speckle microscopy (Burbank et al., 2006; Yang et al., 2007; Burbank et al., 2006; Yang et al., 2007).

To better understand the role of microtubule polymerization dynamics, we next asked whether the number of spindle microtubules changed during spindle rearrangements. From our reconstructions, we detected 3662 and 3812 microtubules in metaphase of meiosis I (3013 and 3808 in meiosis II), 7011 microtubules in early anaphase of meiosis I (5572 in meiosis II), 3317 in mid anaphase of meiosis I (2246 in meiosis II), and 1511 and 1306 microtubules in late anaphase of meiosis I (Tables 1 and 2). This shows that the number of microtubules almost doubles between metaphase and early anaphase. To get a more spatially resolved picture, we also measured the number of microtubules along the spindle axis in our datasets. This measurement showed that the number of microtubules increases by more than twofold in the center of the spindle from metaphase to early anaphase, while the number of microtubules at the spindle poles only slightly increases from metaphase to early anaphase and then decreases throughout anaphase (Figure 3A). During anaphase, the number of microtubules decreased on the poles and almost halved in the spindle center (Figure 3A, B). Thus, we conclude that changing the number of microtubules is correlated with the structural spindle rearrangements that occur during meiosis.

We next sought to gain insight into the mechanisms that drive the observed changes in microtubule numbers. We first asked whether changes in nucleation rate alone could explain the data. If this were the case, microtubule growth, shrinkage, and severing rates would remain the same, and the average length of the microtubules would remain unchanged throughout meiosis. However, the total polymer amount, the length of all microtubules added together, would change in step with the microtubule number.

Interestingly, we found the opposite result: the total polymer length of microtubules remained almost constant from metaphase to anaphase even though the number of microtubules increases twofold (Tables 1 and 2). Furthermore, during the same time, the average length of microtubules went down by a factor of 2 (Figure 1D, Tables 1 and 2). Only in late anaphase, as the spindle continued to elongate, did the number of microtubules and the total polymer length start to decrease. Therefore, the observed changes in spindle morphology were not caused by changes in nucleation rates alone, but also by changes in microtubule disassembly. In principle, this could be caused by local or global changes in microtubule severing, changes in microtubule growth dynamics, or a combination thereof. In the following, we will try to disentangle these possibilities.

We next investigated whether changes in microtubule length were uniform along the spindle axis by quantifying the average microtubule length along the spindle axis. This analysis revealed that, during the transition from metaphase to early anaphase, the average length of microtubules decreased everywhere in the spindle (Figure 3C, D). However, the magnitude of the decrease in length varies as a function of position. The average length of microtubules in the middle of the spindle decreased nearly twice as much as the average length of microtubules near the spindle poles (Figure 3C, D). The analysis of average microtubule length along the axis also showed that in all spindles, in metaphase and anaphase, the average length of microtubules is shorter near the spindle poles (Figure 3C, D), which in anaphase is located at the inner surface of the chromosomes.

We more closely mapped the position of microtubules according to their length (Figure 4A–G) by plotting the number of microtubules that are 500 nm and shorter as well as the number of microtubules between 0.5–1 µm and 1–1.5 µm along the spindle axis (Figure 4H–N). This analysis showed that short microtubules, 500 nm and below, are localized closer to the spindle poles, while longer microtubules, between 0.51 and 1.5 µm, are localized to the spindle center. We also found that the number of short microtubules increased from approximately 35% of all microtubules in metaphase to 50% of all microtubules in anaphase (Figure 4A–G).

Throughout anaphase, we noticed that there were more short microtubules in the spindle half closer to the cell cortex (Figures 3 and 4). This difference was most apparent in early and mid anaphase, where the average microtubule length in the cortical spindle half was 1.00 µm ± 0.6 (p=3.6 E-6) and 1.17 µm ± 0.8 in the cytoplasmic half, and in early anaphase with an average length of 0.91 ± 0.53 (p=0.002) in the cortical half and 1.04 µm ± 0.6 in the cytoplasmic half. We do not know at this point what causes this asymmetry.

Together, our data suggest that microtubule dynamics change throughout the spindle during spindle rearrangements. While the magnitude of this effect is spatially varying, throughout the spindle nucleation and turnover rates increase.

We next sought to better understand the processes that drive the observed microtubule length changes during spindle rearrangements. For this, we constructed a mathematical model that solves for the expected microtubule length distribution given their growth velocity ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', their rate of undergoing catastrophe r, and the rate at which microtubules are cut per unit time and length ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl',. The stability of microtubule plus ends created by cutting is encoded in the parameter ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl',, which interpolates between the two extreme cases, where newly created plus ends immediately depolymerize (∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', = 0) and where newly created plus ends are indistinguishable from preexisting ones (∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', = 1; see Figure 5). The mathematical details of this model are given in Material and methods. In spirit, it is very similar to the model proposed in Kuo et al., 2020.

We used this mathematical model to infer the relative importance of microtubule cutting and changes in microtubule nucleation. Using Markov Chain Monte Carlo sampling (Foreman-Mackey et al., 2013; MacKay, 2003), we infer that the most likely values for the dimensionless ratios ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', and ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', predict the location of the average microtubule lengths ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl',, given the experimentally determined microtubule length distribution (see Materials and methods). Importantly this inference scheme only uses the experimentally measured microtubule length distribution as input and allows us to quantify the relative importance of cutting to turnover ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', independently of direct measurements of turnover rates and microtubule growth velocities, which are hard to do in these very small spindles. We note that additional experiments like FRAP allow us to give absolute time units since it directly measures the turnover rate. The results of the inference scheme are however independent of the FRAP measurements. For details, we refer the reader to Materials and methods.

Using this approach, we first sought to infer the relative importance of turnover to cutting throughout the spindle. In Figure 6, we show the inferred posterior probabilities of model parameters based on the data (Figure 6A–D, Figure 6—figure supplement 1A–D). These plots give the most likely values of the model parameters given the data, 95% confidence intervals for each of the parameters, and 2D error plots for each pair of parameters under the assumption that the third is at its most likely value. We also compared the predictions of the model parameterized by the expectation values of all parameters to our data (Figure 6E–H, Figure 6—figure supplement 1E–H).

We asked whether the transition of spindle structure from metaphase to early anaphase can be explained by microtubule turnover, which here means changes in growth rate and catastrophe, or microtubule cutting. We report our results in terms of the non-dimensionalized turnover rate ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', and the non-dimensionalized cutting rate ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl',, where ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', is the average microtubule length. Most importantly, the ratio of these two quantities ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', gives the length (in units of average MT length) a microtubule has to reach for it to be more likely to get severed than to undergo catastrophe. This quantifies the relative importance of turnover to cutting; for example, if ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', is much smaller than 1, then this indicates a length distribution that is dominated by cutting; if ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', is much larger than 1, it indicates a length distribution that is dominated by catastrophe and turnover. In metaphase (Figure 6A, B, E, F, Figure 6—figure supplement 1A, B, E, F) and early anaphase (Figure 6C, G, Figure 6—figure supplement 1C, G), we find that the non-dimensionalized turnover rate ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', is equal to 1.0, while the non-dimensionalized cutting rate ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', is about 0.1. Here, ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', is the average microtubule length. These numbers imply that the length at which a microtubule is more likely to be cut than to undergo catastrophe is ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl',, that is, cutting is a relatively rare event. In fact, there are no microtubules in metaphase that are longer than 10 times the average microtubule length (i.e., 10 µm) and only one microtubule was larger than 10 times the average length (i.e., 5 µm) in early anaphase. This also implies that the change in the microtubule length observed from metaphase (∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', = 1 µm) to early anaphase (∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', = 0.5 µm) is a consequence of either the microtubule turnover rate or changes in microtubule growth velocity. For error estimates and detailed likelihood plots of the inferred parameters, see Figure 6 and Figure 6—figure supplement 1, which give 95% confidence intervals and likelihood surfaces for all parameters. Note also that given that cutting occurs very rarely the inference is not informative on the parameter α, which describes the stability of newly cut microtubules.

We next use our estimate for the ratio ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', to infer the microtubule growth velocity in meiotic metaphase spindles. For this, we took the measured FRAP half-life in metaphase (see Figure 2B) of about 5 s as an estimate for microtubule turnover time 1/r and determine the average microtubule length of about 1 µm (Tables 1 and 2). Using these values, we estimated that the microtubule growth velocity (vg) during metaphase was close to 12 µm/min. Interestingly, this agrees with growth velocity estimates based on microtubule flux, and it is similar to values reported for microtubule growth rates in the dense regions of mitotic C. elegans spindles, reaching from 16 to 20 µm/min (Redemann et al., 2017). Notably, this value is slower than the growth rates reported for astral microtubules (44 µm/min) growing away from centrosomes reported by Redemann et al., 2017 and Srayko et al., 2005. This suggests that microtubule growth velocities are under spatial and temporal control within the cytoplasm, as was previously described by Geisterfer et al., 2019 and Walczak et al., 2016.

The drastic change in the average microtubule length from metaphase to anaphase could be due to a decrease in microtubule growth velocity to half its metaphase value (6 µm/min). Alternatively, it could also be caused by an increase in microtubule turnover rate. Given the large relative errors of the FRAP measurements in the very small meiotic spindles, we cannot definitely answer whether microtubule growth speed, turnover rate, or both are under biochemical control at this stage. In toto, our data argue that the transition from metaphase to early anaphase is best explained by modulating microtubule growth and polymerization dynamics, and not by increased microtubule cutting. Note that a role for katanin in amplification of microtubule mass and number has been suggested in vitro, where severing activity can result in the incorporation of GTP tubulin into the microtubule lattice, thus increasing the rescue frequency and stability of newly emerging microtubule ends (Vemu et al., 2018).

We finally asked the same question for the transition from early to mid anaphase. We find that later in anaphase the relative importance of cutting increases with ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', = 0.3 and ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', = 0.9 (see Figure 6D, H). This means that, at this later point, the length at which a microtubule is more likely to be cut than to undergo catastrophe decreases to 3 ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl',, which would be approximately 3% of the microtubule population.

Thus, our data suggest that the initial steps of the transition from metaphase to anaphase are due to changes in microtubule turnover rate and growth and not mediated by katanin-dependent severing. This is surprising since earlier work clearly demonstrated the importance of severing during spindle assembly (Srayko et al., 2006; McNally and McNally, 2011; McNally et al., 2014; Connolly et al., 2014; Joly et al., 2016). Estimates of the number of katanin-mediated cutting events by counting lateral defects in partial EM reconstructions of meiotic spindles at earlier stages had found a large number of cutting events in wildtype spindles (Srayko et al., 2006). To test the predictions of our inference scheme, we decided to look for similar cutting sites in our datasets.

Analyzing the frequency of lateral defects in our tomographic data indicated a very low abundance (1.1% of microtubules in metaphase #2, 2.5% in early anaphase, and 1.8% in mid anaphase). We could also not detect an increased occurrence of lateral defects in longer microtubules or at distinct positions within the spindle. This is notably fewer events than what was reported for earlier spindles. We conclude that the initial steps of the transition from metaphase to anaphase are due to changes in microtubule turnover rate and growth and not mediated by katanin-dependent severing.

Our finding that global rearrangements of the spindle structure are mainly caused by changes in nucleation and turnover dynamics made us wonder about the role of katanin-mediated cutting in these spindles. To investigate this, we separated out microtubules in close contact to chromosomes (defined as being closer than 150 nm) (Figure 7A, B) and analyzed them separately using our inference scheme. The results are shown in Figure 8 and Figure 8—figure supplement 1. In metaphase spindles, the fraction of microtubules in close contact to chromosomes is small. We found 13, 25, 16, and 23% for our four metaphase spindle datasets, respectively. However, in contrast to the global population, they showed strong evidence of cutting and ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', > 1 in all four examples. Furthermore, the length distribution of these microtubules, as depicted in Figure 7C, Figure 8E,,F, and Figure 8—figure supplement 1E, F, is clearly not exponential in metaphase, which is also indicative of cutting.

In contrast, in anaphase, the majority of microtubules (about 70%) are in close contact to chromosomes. Despite this, even microtubules in close contact with chromosomes showed a nearly exponential length distribution (Figure 7D, Figure 8G, H, and Figure 8—figure supplement 1G, H), and our inference scheme yields the same results for microtubules near chromosomes and the global microtubule population. The plots for microtubules that were located further than 150 nm are comparable to the plots for all microtubules (Figure 6) and are shown in Figure 8—figure supplement 2.

Together, these data suggest a role for cutting in maintaining the metaphase spindle. In particular, we hypothesize that katanin selectively cuts microtubules that are in close contact with chromosomes. This mechanism seems to be suppressed in late anaphase.

We next sought to investigate the role of katanin on microtubule turnover in the metaphase spindle. As null mutants of the C. elegans katanin homologs MEI-1 and MEI-2 do not assemble bipolar spindles (Mains et al., 1990), we decided to work with the FM13 mei-2(ct98) strain, which has an overall lower expression of MEI-2 (Srayko et al., 2000; O'Rourke et al., 2011) and reduced microtubule-severing activity (McNally et al., 2006; McNally et al., 2014). We used FRAP experiments to measure the effect of katanin mutation on microtubule turnover using the FM13 mei-2(ct98) strain (Figure 9A, B, Video 2). We found that the characteristic time scales for recovery were not significantly affected (4.5 s ± 1.8 s [n = 7] in control and 2.8 s ± 3.4 s [n = 11] in mei-2(ct98), p=0.2434). However, strikingly we observed a significant decrease in the fraction of fluorescence recovery of microtubules in the mei-2(ct98) embryos (Figure 9C). While in wildtype embryos 87% ± 10% of the fluorescent tubulin signal recovers, this is significantly reduced to 52% ± 26% (p=0.0039) in the katanin mutant. This suggests the presence of a population of stabilized microtubules in katanin-depleted spindles. In line with other authors (Brinkley and Cartwright, 1975; Rieder, 1981; Bakhoum et al., 2009), we thus speculate that microtubules in close contact to chromosomes get stabilized by interacting with the chromosomes. Katanin keeps these microtubules from growing too long by cutting these microtubules, and thus, effectively enhances turnover in spindles. In line with this model, our inference data (Figure 8) suggests the new plus ends of newly cut microtubules are mostly unstable. In line with this model, our inference scheme predicts values for ∂tψ=-∂lvgψ-r+Κlψ+Κ1+α∫l∞dl'ψl', that are smaller than 0.5 for chromosome-proximal microtubules in all four metaphase spindles. However, given the small number of microtubules in close contact to chromosomes, some significant uncertainty on this number remains.

Data analysis was performed using either the Amira software package or by exporting the geometric data of the traced microtubules followed by an analysis using MATLAB (MATLAB and Statistics Toolbox Release 2012, The MathWorks). In our analysis of spindle structure, the following errors were considered (Redemann et al., 2017). Briefly, during the data preparation and the imaging process, the tomograms are locally distorted. Furthermore, the exposure of the electron beam causes a shrinking of the sample. During the reconstruction of the microtubules, however, the most important errors occur in the tracing and matching process. In addition, the data is again distorted in all directions to align the tomograms. We assumed that this distortion primarily compensates the distortion of the imaging process. For the tracing, the error was previously analyzed for reconstructions of C. elegans centrosomes (Weber et al., 2012). We assumed that the error lies in the same range of 5–10%. In addition, the traced microtubules were manually verified. It is more difficult to estimate the error of the matching algorithm (Weber et al., 2014) since it depends on the local density and properties of the microtubules. The quality of our analysis should be influenced only by minor 3D distortions.

We seek to not over-constrain our search space and thus use a so-called uninformative prior. This means that we assign all models within the parameter ranges r¯>0, κ¯>0 and 0<α<1 the same a priori likelihood.

To test our inference scheme, we generated datasets from known distributions. We generated datasets that have comparable numbers and length of distributions as our experimental data and ran our inference scheme. In Figures 10 and 11, we show the results of this procedure and compare against ground truth for one case without and one case with cutting.