To measure microtubule dynamics during anaphase, we constructed S. pombe strains expressing Alp7 tagged with 3xGFP at the C-terminus from its endogenous locus. Alp7 is the S. pombe orthologue of mammalian Transforming Acidic Coiled-Coil (TACC) (Sato et al., 2004), and forms a complex with the XMAP215 orthologue Alp14, a microtubule polymerase (Al-Bassam et al., 2012). The Alp7/Alp14 complex localises to Spindle Pole Bodies (SPBs) and microtubule plus ends (Sato et al., 2004). Additionally, our strains expressed the SPB marker Sid4-GFP (Figure 1A and B). Live-imaging of these cells during anaphase B using Structured Illumination Microscopy (SIM) produced movies where microtubule plus ends could be resolved (Video 1). From such movies, we constructed kymographs where the duration and velocity of microtubule growth and shrinkage events can be measured (Figure 1C and D). Given that in S. pombe all the minus ends of interpolar microtubules are located at the SPBs (Ward et al., 2014; Ding et al., 1993), microtubule length can be measured as the distance between the plus end and the pole located opposite to the direction of growth (Figure 1D). Note that vertical comets in kymographs (Figure 1C) do not correspond to non-growing microtubules, but rather to microtubules that grow roughly at the sliding speed: their minus ends are at the SPBs, which move away from the plus end in the kymograph. Finally, some comets superimpose, so not all growth events could be resolved, and we could not count the total number of microtubules. Additionally, for some growth events it was not possible to determine exactly where rescue or catastrophe happened, but the positions of SPBs and microtubule tip could be determined without ambiguity, and thus the growing speed could be measured reliably. Such events were more common at late stages of anaphase B (Figure 1C, filled arrowhead).

Video 1

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We then proceeded to measure the parameters of microtubule dynamics from kymographs. We used spindle length as a proxy for anaphase B progression, as spindle elongation is very stereotypical in S. pombe (Figure 1—figure supplement 1A). Three phases can be observed corresponding to prophase (I), metaphase/anaphase A (II), and anaphase B (III) (Figure 1A and B, Figure 1—figure supplement 1A). We found that the duration of microtubule growth events did not change during anaphase B and was on average 52 ± 23 s (Figure 1—figure supplement 1B, C). Microtubule shrinking speed did not change during anaphase either (Figure 1—figure supplement 1D), and was on average 3.55 ± 1.62 μm/min (Figure 1—figure supplement 1E). On the other hand, microtubule growth velocity decreased during anaphase B (Figure 1C and E). Furthermore, this decrease was not gradual, and we observed two populations of microtubules (fast and slow growing) characteristic of early and late anaphase. In some cells, all microtubules seemed to switch to the slow growing phase simultaneously (Figure 1C), while in others fast and slow growing microtubules co-existed (Figure 2A). A good way to visualise the two populations is to plot microtubule growth speed as a function of the distance between the plus end and the closest pole at the time of rescue (Figure 1D and F). This distance increases for all microtubules as the spindle elongates, and is higher for microtubules that are rescued closer to the center for a given spindle length, hence providing a reference frame aligned with the spindle. On such a plot, the data points visibly cluster in two separate clouds and the variation of growth speeds can be fitted by an error function (Figure 1F), which is characteristic of a system in which a transition between two states occurs at a given distance to the pole. The microtubule growth velocities of these two states, extracted from the fit, were 1.60 μm/min and 0.67 μm/min. This representation captures the fact that at early anaphase B microtubules rescued at the spindle center grow fast (empty arrowhead in Figure 1C), while later in anaphase fast and slow growing microtubules coexist, but those closer to the center grow slower (empty arrowheads in Figure 2A). Therefore, it is not anaphase progression nor position with respect to the center that best captures this behaviour, but a parameter that combines both. Consequently, fitting error functions to microtubule growth velocity vs. (1) position of rescues with respect to spindle center, (2) spindle length and (3) position of rescue with respect to the closest pole yielded $R^2$ values of 0.02, 0.39, and 0.47 respectively, indicating that position of rescue with respect to the closest pole is the best predictor of microtubule growth speed. Hence, we used this parameter for the rest of our analysis.

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In our dataset, most microtubule rescues occurred near the spindle midzone. This is likely due to the fact that Cls1 (CLASP), a MAP required for microtubule rescue, is recruited to the midzone by Ase1 crosslinkers (Bratman and Chang, 2007). To describe the rescue distribution, we measured the positions of rescues with respect to the spindle center, considering the orientation of the microtubule to define negative and positive positions (Figure 1D). This revealed that rescues did not occur uniformly along the midzone, since 93% of the rescues happened at positive positions (Figure 1G). Moreover, the positions where most rescues happened coincided with the edge of the midzone, measured from Cls1-3xGFP signal in another strain (Figure 1G and Figure 1—figure supplement 1F–G).

To confirm that Alp7-3xGFP can be reliably used to measure microtubule dynamics, we performed the same measurements in strains expressing GFP-Mal3 (orthologue of EB1), a protein that tracks the tips of growing microtubules, promoting microtubule growth and recruiting MAPs to the tip (Busch and Brunner, 2004). Cells expressing GFP-Mal3 have similar microtubule dynamics during interphase when compared to cells expressing labelled $\alpha$-tubulin (Busch and Brunner, 2004), and GFP-tagged EB proteins are common microtubule makers (Muroyama and Lechler, 2017; Rieckhoff et al., 2020; Reber et al., 2013). We found that the duration of microtubule growth events was the same in cells expressing GFP-Mal3 and Alp7-3xGFP (Figure 1—figure supplement 2A, C), while in cells expressing GFP-Mal3, microtubule growth speed was slightly lower and rescues occurred slightly closer to the center than in cells expressing Alp7-3xGFP (Figure 1—figure supplement 2D, E). These differences are minor, so we concluded that Alp7-3xGFP is a reliable marker for microtubule dynamics.

Notably, GFP-Mal3 signal was lost from the spindle at late anaphase B (Figure 1—figure supplement 2A), making it impossible to track plus ends. This was not due to bleaching, as the GFP-Mal3 signal was not observed even if imaging was started at late anaphase B (data not shown). In contrast, Alp7-3xGFP remains at microtubule plus ends at late anaphase, making it a better marker for microtubule dynamics during anaphase. On the other hand, GFP-Mal3, unlike Alp7-3xGFP, strongly labels interphase microtubules, so we used GFP-Mal3 to compare microtubule dynamics in anaphase B and interphase (Figure 1—figure supplement 2A, B). We found that both microtubule growth event duration and speed were lower during anaphase B (Figure 1—figure supplement 2F, G). For the growth speed, we compared all interphase events with early anaphase B fast growing events (distance to the closest pole at rescue <2.5 μm, Figure 1—figure supplement 2D).

In summary, our novel imaging approach shows that microtubule dynamics in anaphase and interphase are different. Additionally, at mid-anaphase microtubules transition from a fast growing state to a slow growing state. Finally, microtubule rescues happen with the highest probability at the midzone edge.

To investigate this intriguing transition from fast to slow microtubule growth velocity seen in anaphase B, we next examined various candidate MAPs associated with spindle microtubules that have been shown or proposed to regulate microtubule dynamics during anaphase B.

Bim1 (Orthologue of Mal3/EB1 in S. cerevisiae) is phosphorylated at late anaphase by Aurora B, which reduces its affinity for microtubules (Zimniak et al., 2009). In addition, Bim1 mutants that cannot be phosphorylated delay spindle disassembly (Zimniak et al., 2009). In S. pombe, Mal3 is also phosphorylated in a cell-cycle-dependent manner (Iimori et al., 2012), and mutant Mal3 constructs mimicking this phosphorylation have lower microtubule growth promoting activity in vitro than wild-type Mal3 (Iimori et al., 2012). This, combined with our observation that GFP-Mal3 leaves the spindle at late anaphase B (Figure 1—figure supplement 2A) made it plausible that a combination of phosphorylation and unbinding of Mal3 could lead to the decrease in microtubule growth speed. To test this possibility, we used cells deleted for mal3. As expected, considering that Mal3 promotes microtubule growth (Busch and Brunner, 2004), mal3Δ cells exhibited lower microtubule growth speed throughout anaphase B (Figure 2B and G). However, a reduction of microtubule growth could still be observed with anaphase progression, and normalised microtubule growth velocities were distributed similarly in wild-type and mal3Δ cells (Figure 2H), suggesting that Mal3 is not required for the reduction of microtubule growth speed in anaphase B.

S. cerevisiae Kip3 (kinesin-8) is a plus end directed motor that localises to the anaphase B spindle and suppresses microtubule dynamics in a length-dependent manner (Gardner et al., 2011; Rizk et al., 2014). In S. pombe interphase, the kinesin-8 heterodimer Klp5/Klp6 accumulates at plus ends in a length-dependent manner, promoting catastrophe (Tischer et al., 2009), so Klp5/Klp6 could trigger the transition from fast to slow microtubule growth during anaphase. We tested this hypothesis by deleting klp5 and klp6. As expected, klp5Δklp6Δ cells exhibited slightly longer microtubule growth events (Figure 2—figure supplement 1). However, the distribution of microtubule growth speed as a function of distance from the plus end to the closest pole at rescue was not very different from wild-type cells (Figure 2C, I), indicating that the decrease in microtubule growth speed is independent of Klp5/Klp6.

We next tested the human CLASP orthologue Cls1, a MAP that is recruited to the spindle midzone by the crosslinker Ase1. Cls1 is required for microtubule rescues to occur during anaphase in S. pombe (Bratman and Chang, 2007), and it decreases microtubule growth speed in a dose-dependent manner (Bratman and Chang, 2007; Al-Bassam et al., 2010). We measured Cls1 levels on the spindle and found that they remained constant throughout anaphase B (Figure 2—figure supplement 2A). However, as the number of microtubules in the spindle decreases with anaphase B progression (Ward et al., 2014; Ding et al., 1993), the density of Cls1 on microtubules increases (Figure 2—figure supplement 2B), and this might reduce growth speed. Cls1 is an essential gene and cannot be deleted (Grallert et al., 2006). To study its potential role in regulating microtubule growth, we altered the levels of Cls1 by placing the gene under the control of a P81nmt1 promoter (cls1^off), which reduced the amount of Cls1 on the spindle by approximately 60% (Figure 2—figure supplement 2A, B), or a P1nmt1 promoter (cls1^OE), which led to a more than fourfold increase in the amount of Cls1 on the spindle (Figure 2—figure supplement 2C, D). Consistent with its growth suppression activity (Bratman and Chang, 2007; Al-Bassam et al., 2010), reducing Cls1 levels slightly increased microtubule growth speed, and overexpression slightly reduced it (Figure 2—figure supplement 2E, F). However, these changes in microtubule growth speed were minor compared to the differences on Cls1 density (Figure 2—figure supplement 2B, D). Additionally, as in mal3Δ cells, the normalised growth speeds were distributed similarly to wild-type in both cls1^off and cls1^OE cells (Figure 2J, Figure 2—figure supplement 2G). In other words, the transition of microtubule growth speed occurred across a wide range of Cls1 levels, arguing against a role of Cls1 in this transition.

Finally, we tested the role of Klp9 (kinesin-6), the main driver of microtubule sliding during anaphase B (Fu et al., 2009). Klp9 promotes microtubule growth in vitro and is required for the elongation of bundles of parallel microtubules present in monopolar spindles that undergo metaphase to anaphase transition (Krüger et al., 2021). Notably, the bundle elongation velocity matches the microtubule sliding speed in bipolar spindles, suggesting that Klp9 might set both microtubule growth and sliding speed in bipolar spindles. To test this hypothesis, we measured microtubule growth velocity during anaphase in cells deleted for klp9. As expected (Fu et al., 2009), klp9 deletion reduced spindle elongation velocity (Figure 2—figure supplement 3A). Interestingly, the decrease in microtubule growth velocity was delayed in klp9Δ cells with respect to wild-type (Figure 2—figure supplement 3B, C), while the distribution of microtubule growth speed as a function of the distance from the plus end to the closest pole at rescue was similar (Figure 2E and K). This could indicate that the transition in microtubule growth velocity depends primarily on the position of the plus end of the microtubule when it is rescued. Alternatively, klp9 deletion could delay the activation of a regulatory network that decreases microtubule growth speed. In any case, Klp9 is not required for the transition in microtubule growth speed to occur.

Recruitment of Klp9 to the spindle midzone relies on the dephosphorylation of its Cdk1 phosphosites at anaphase onset (Fu et al., 2009). This dephosphorylation occurs through two independent pathways involving the phosphatase Clp1 (orthologue of Cdc14) (Fu et al., 2009; Wolfe and Gould, 2004; Esteban et al., 2004), and the XMAP215 microtubule polymerase Dis1 (Krüger et al., 2021). Hence, microtubule growth speed could be regulated by Dis1 itself or by downstream effectors of Dis1 or Clp1. clp1Δ and dis1Δ cells had an identical phenotype to klp9Δ cells: their spindle elongation velocity was slower during anaphase, but distribution of microtubule growth speed as a function of distance from the plus end to the closest pole at rescue was similar to wild-type (Figure 2F and L, Figure 2—figure supplement 3D), indicating that neither the dephosphorylation of Cdk1 phosphosites mediated by Clp1 nor the activity of Dis1 are required for the transition from fast to slow microtubule growth velocity to occur during anaphase B.

Finally, the positions of microtubule rescues were clustered as in wild-type across all conditions (Figure 2—figure supplement 4). In mal3Δ and klp5Δklp6Δ cells, the average position of rescues with respect to the spindle center was markedly higher than in wild-type (Figure 2—figure supplement 4A, B). For klp5Δklp6Δ this might be due to longer midzones, as in budding yeast deletion of kinesin-8 increases midzone length (Rizk et al., 2014). It is possible that mal3Δ cells have longer midzones, or a broader distribution of overlap lengths between microtubules. Alternatively, given that Ase1 binds to Bim1 (Mal3) in budding yeast (Thomas et al., 2020), it is possible that this interaction is important for restricting rescues to a narrower region. Ultimately, none of the conditions perturbed the overall organisation of rescues.

In summary, our experiments show that the transition from fast to slow microtubule growth during anaphase occurs in the absence of multiple MAPs associated with the mitotic spindle known to affect microtubule dynamics in a different context or organism. Interestingly, the distribution of microtubule growth speed as a function of the distance from the plus end to the closest pole at rescue is maintained even in cells where spindle elongation is slower, suggesting that microtubule growth velocity during anaphase B could be affected by spatial cues associated with the spindle.

Recent reports provide increasing evidence of a cross-talk between the spindle midzone and the nuclear membrane bridge that forms after the dumbbell transition in closed mitosis (Figure 1A; Dey et al., 2020; Expósito-Serrano et al., 2020; Lucena et al., 2015). Imaging strains expressing the nuclear membrane marker Cut11-mCherry (Figure 3A), we noticed that the slow growing microtubules were the ones inside the nuclear membrane bridge (Figure 3B and C). To verify this, we measured microtubule growth speed in wild-type cells, cells overexpressing Klp9 (klp9^OE), and cells expressing the cell-cycle mutant allele cdc25-22, which all have different sizes and spindle elongation dynamics (Krüger et al., 2019). klp9^OE cells were longer than wild-type cells, and their spindle elongation velocity was higher, while cdc25-22 cells were bigger than wt and klp9^OE cells, and displayed an intermediate spindle elongation velocity (Figure 3—figure supplement 1A–C). Wild-type, klp9^OEand cdc25-22 nuclei underwent dumbbell transition at different spindle lengths (Figure 3—figure supplement 1D), and their distribution of microtubule growth speed as a function of time, spindle length or distance from the plus end to the closest pole at rescue were different (Figure 3—figure supplement 1E–H). However, regression analysis showed that if we categorised microtubule growth events depending on whether they occurred ‘before’ the dumbbell transition, and ‘inside’ or ‘outside’ the nuclear membrane bridge (cartoons in Figure 3D), microtubule growth velocity in each category was not different for wt, klp9^OE and cdc25-22 cells (Figure 3D). In fact, a linear model taking into account only this categorisation, explained 48% of the variability (see Statistical Analysis). The 13% decrease in growth speed observed between ‘before’ and ‘outside’ events was minor compared to the 60% reduction when comparing ‘before’ and ‘inside’ (Figure 3D). This categorisation clarifies our plots of microtubule growth speed as a function of the distance from the plus end to the closest pole at rescue (Figure 1F), as this distance is equivalent to the distance from the plus end to the nuclear membrane bridge edge (Figure 3E).

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From this direct imaging we conclude that microtubules grow slower when they enter the nuclear membrane bridge formed by the dumbbell transition. The wild-type microtubule dynamics are summarised in Table 1.

To check whether the nuclear membrane bridge is indeed causing microtubules to grow slower at mid-anaphase, we prevented the nuclear membrane dumbbell transition in two different ways.

First, we inhibited Aurora B using an analogue sensitive allele (ark1-as3) (Hauf et al., 2007), which often led to failed chromosome segregation (Petersen et al., 2001), and spindles that elongated without undergoing dumbbell transition (Figure 4B). To distinguish the direct effects of Aurora B inhibition from the effects of preventing the dumbbell transition, we added the analogue 1NM-PP1 and imaged cells immediately. Some of the cells were in anaphase B when the analogue was added, and displayed normal chromosome segregation (‘ark1-as3 normal’), others failed chromosome segregation and did not undergo dumbbell transition (‘ark1-as3 abnormal’). In wild-type and ‘ark1-as3 normal’ cells, microtubules grew slower inside the nuclear membrane bridge (Figure 4I, Appendix 1—table 2), but in ‘ark1-as3 abnormal’ cells microtubule growth velocity was not significantly different (p-value 0.38, see Statistical Analysis) outside or inside the nuclear membrane tubes formed at the spindle poles (Figure 4F, I Figure 4—figure supplement 1B). This data shows that the transition from fast to slow microtubule growth can happen upon Aurora B inactivation, but not if chromosome segregation fails and the dumbbell transition is prevented.

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Next, we examined cells treated with the fatty acid synthetase inhibitor cerulenin, which reduces cellular membrane availability, dramatically decreasing spindle elongation, and prevents dumbbell transition (Figure 4C; Yam et al., 2011). Treating cells with 10 µM of cerulenin prevented dumbbell transition, and abolished the decrease in microtubule growth speed (Figure 4C and G, Figure 4—figure supplement 1C). Furthermore, out of the 23 cells treated with cerulenin, we observed a clear bimodal growth velocity distribution only in two cells that underwent dumbbell transition despite the treatment (growth events in the ‘inside’ and ‘outside’ categories in Figure 4J, and Figure 4—figure supplement 1E). By reducing cerulenin concentration to 5 µM, we observed two additional cells in which a reduction of microtubule growth speed after abrupt dumbbell transition was evident (Figure 4H, Figure 4—figure supplement 1D, F).

In summary, our data shows that microtubule growth speed can remain unchanged for a period of time as long as wild-type anaphase B if the dumbbell transition is prevented (Figure 4F and G). This suggests that the decrease in microtubule growth speed observed in wild-type cells is not regulated by a ‘timer’ mechanism, but instead occurs when the nuclear membrane bridge encloses the midzone.

To further understand whether an interaction between the nuclear membrane bridge and the spindle affects microtubule growth, we studied the effect of les1 and nem1 deletions on microtubule growth during anaphase (Figure 4—figure supplement 2A–C). Les1 forms stalks at the edges of the nuclear membrane bridge that restrict nuclear membrane disassembly to the center of the bridge and may constitute sites of close interaction between the nuclear membrane and the spindle (Dey et al., 2020). nem1 deletion causes an increase in nuclear size (Kume et al., 2019), which leads to membrane ruffling (Figure 4—figure supplement 2D) and prevents the formation of Les1 stalks (Dey et al., 2020). We found that in both les1Δ and nem1Δ cells microtubule growth speed inside the nuclear bridge was faster than in wild-type cells, while the microtubule growth speed outside the nuclear bridge was unaffected (Figure 4—figure supplement 2E–F, Appendix 1—table 5, Appendix 1—table 6). This data suggests that the formation of Les1 stalks (which potentially promote close interaction of spindle microtubules with the nuclear envelope) is required for the normal decrease of microtubule growth speed when microtubule plus ends enter the nuclear membrane bridge.

Preventing the decrease in microtubule growth speed by cerulenin treatment or Aurora B inhibition did not compromise spindle stability nor overall microtubule organisation. This suggested that the way microtubule sliding and growth are coordinated is robust against deviations from the normal microtubule growth speed evolution. In fact, since rescues occur most often at midzone edges (Figure 1G), microtubules are stable from pole to midzone, and only their distal parts including the plus ends alternate between assembly and disassembly phases (Figure 7A). Therefore, promoting rescues at the midzone edges could be sufficient for the spindle to maintain a constant midzone length while sustaining sliding. We initially set out to test this mechanism experimentally by deleting ase1, a microtubule crosslinker that organises the midzone (Loiodice et al., 2005; Yamashita et al., 2005) and recruits the rescue factor Cls1 (Bratman and Chang, 2007). As expected (Loiodice et al., 2005; Yamashita et al., 2005; Bratman and Chang, 2007), in cells where ase1 was deleted the characteristic distribution of rescues was lost (Figure 5B and E) and spindles collapsed due to loss of microtubule overlaps before reaching the typical final length (Figure 5B–D Figure 5—figure supplement 1).

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We next examined the microtubule growth speed in ase1Δ cells. Approximately half of ase1Δ cells (30 out of 63) did not reach sufficiently long spindle lengths to undergo dumbbell transition, but we restricted our analysis to ase1Δ cells that did undergo dumbbell transition. Interestingly, we observed that the microtubule growth speed was higher throughout anaphase in ase1Δ when compared to wild-type, but also that the decrease in microtubule growth between ‘before’ and ‘inside’ categories was ∼25%, half of the ∼50% decrease observed in wild-type cells (Figure 5F, Appendix 1—table 4). Plotting the microtubule growth speed as a function of distance to the closest pole at rescue (Figure 5G) showed that this effect was stronger that the conditions tested in Figure 2.

To better understand the effect of Ase1 on microtubule growth speed, we compared strains expressing mCherry-ase1 from the ase1 endogenous promoter or P1nmt1 (mCherry-ase1^OE), which resulted in a more than 10-fold increase of mCherry-Ase1 levels on the spindle (Figure 5—figure supplement 2A–F). Microtubule growth speed in mCherry-ase1^OE cells was similar to wild-type at early anaphase, but decreased more sharply with distance to the pole (Figure 5—figure supplement 2G). We next reduced mCherry-ase1 levels using a P81nmt1 promoter, but the signal was undistinguishable from noise (data not shown). As an alternative, we quantified the levels of GFP-Ase1 in strains expressing GFP-ase1 either from its endogenous promoter or P81nmt1 (GFP-ase1 ^off). GFP-Ase1 levels on the spindle were approximately threefold lower in GFP-ase1 ^off cells (Figure 5—figure supplement 3C, D). We then measured microtubule growth velocity in cells expressing unlabelled ase1 from a P81nmt1 promoter (ase1^off, Figure 5—figure supplement 3B). ase1^off cells exhibited a slight increase in microtubule growth (Figure 5—figure supplement 3E) throughout anaphase, but normalised growth speed as a function of distance from the plus end to the closest pole at rescue was similar to wild-type (Figure 5—figure supplement 3F). These results are reminiscent of those obtained when altering Cls1 levels (Figure 2, Figure 2—figure supplement 2), so they may be partially due to altered recruitment of Cls1 by Ase1. However, like for Cls1, we observed a similar ratio between growth speed at early and late anaphase across a wide range of Ase1 levels (10x to 1/3), arguing against a direct effect of Ase1 on microtubule growth. The strong effects in ase1Δ may indicate that Ase1 is required for the nuclear membrane bridge to have an effect on microtubule growth (see Discussion). Conversely, we cannot rule out that deletion or complete inactivation of cls1 may have a comparable effect to deletion of ase1, but this cannot be tested, as it leads to the immediate disassembly of the spindle at anaphase onset (Bratman and Chang, 2007).

In summary, Ase1 is required for rescue organisation and for microtubule growth speed to decrease normally during anaphase B.

Our observations showed that anaphase B spindles were robust against perturbations on microtubule growth (Figure 4), but sensitive to rescue distribution (Figure 5). Therefore, we asked whether restricting rescues to the midzone edges is sufficient to coordinate microtubule sliding and growth. We developed a minimal mathematical model (see Materials and methods) to compare scenarios that differ in how rescue is promoted inside the midzone. In our model, the spindle is initially composed of nine antiparallel microtubules (Figure 6A) that undergo dynamic instability. For simplicity, we do not specifically simulate motors and MAPs, but we assume a constant spindle elongation speed and define the midzone as a region of the space of fixed length. Based on the fact that Cls1 is recruited by Ase1 (Bratman and Chang, 2007) and that Cls1 levels remain constant during anaphase (Figure 2—figure supplement 2A), we assume that a fixed amount of rescue factor ($R$) is distributed along the overlap between microtubules inside the midzone. The rescue activity is either uniform along the midzone, or distributed according to a beta distribution with parameters $\alpha$ and $\beta$. Increasing $\alpha$ localises the rescue activity at the midzone edges to higher degrees, while keeping the total rescue factor constant (Figure 6A). All the model parameters were derived from experimental measurements, except for $R$, $\alpha$ and $\beta$ (Table 2). $R$ was scanned and tuned to fit the experiments (see below). We explored $\alpha$=$\beta$=1, corresponding to a uniform distribution, and $\alpha$ = 4, 8, 12 with $\beta$=2, representing increasingly skewed distributions towards the midzone edge (Figure 6A). We initially set the microtubule growth velocity to 1.6 μm/min (early anaphase speed, Figure 1F), and aimed to reproduce the experimental distribution of positions of rescue and catastrophe at early anaphase (spindle length <6 μm, Figure 6B), measured from kymographs (Figure 1C), and the total tubulin intensity as a function of spindle length (Figure 6C), measured in cells expressing fluorescent $\alpha$-tubulin (Figure 1—figure supplement 1F). Fluorescent tubulin intensity is proportional to polymerised tubulin (Ward et al., 2014; Loiodice et al., 2019), so it can be compared to the total polymerised tubulin in a simulation by using a scaling factor (Figure 6C, see Materials and methods).

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A good agreement with the experimental data was obtained with $\alpha$=4, $R$=55 μm/min (Figure 6B–D, Figure 6—figure supplement 1D). For higher values of $R$, the spindle was stable (Figure 6E) but, due to the higher microtubule stability, the total polymerised tubulin increased steadily, unlike in the experiment, where it remained more or less constant throughout anaphase (Figure 6C). Importantly, the distributions of rescues and catastrophes were similar to the experimentally observed when the rescue factor was uniformly distributed along the midzone (Figure 6—figure supplement 1E) because even in that case, the most likely place to have a rescue is the first position where it can happen.

For microtubule growth speed characteristic of early anaphase (1.6 μm/min), the spindle stability was not affected by the distribution of rescue rate within the midzone (Figure 6E). In contrast, if we kept $R$ as in Figure 6B–D, but decreased the microtubule growth speed, we observed that spindles with skewed rescue distributions were more stable (Figure 6F). When growth velocity is low, a rescued microtubule might not exit the midzone before undergoing catastrophe, and therefore ‘miss’ a fraction of the midzone with rescue activity. Increasing the rescue rate close to the midzone edge makes it more likely that plus ends of rescued microtubules are outside the midzone by the time they undergo catastrophe, which maximises their chances to be rescued again.

In summary, this simple model shows that promoting rescues at midzone edges is sufficient to maintain the microtubule overlap and sustain sliding across a wide range of microtubule growth speeds (Figure 7A). Within our limited exploration, it suggests that accumulating the rescue activity at the midzone edges might represent an optimal localisation of this activity, in the context of anaphase B.

Figure 7

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Because Cls1 levels on the spindle remain constant during anaphase (Figure 2—figure supplement 2A), our model assumes that a fixed amount of rescue factor $R$ distributes along the midzone overlap, which makes spindles increasingly stable as they lose microtubules (Figure 7B). This mechanism might operate in cells, since anaphase spindles can last for up to 40 min if spindle disassembly is delayed (Figure 2—figure supplement 3A). Additionally, assuming that a fixed amount of rescue factor distributes along overlaps makes rescue rate proportional to the number of neighbours of a microtubule (Figure 7C). Therefore, when a microtubule fully depolymerises, its neighbours oriented in the opposite direction lose one neighbour, while the microtubules in the same orientation as the lost one keep the same number of neighbours. This simple effect promotes even loss of microtubules from both poles (Figure 7D), which is necessary to prevent spindle collapse during anaphase B in S. pombe. To show that indeed microtubules are lost evenly from both poles in cells, let us consider a representative spindle that has nine microtubules at anaphase B onset. By the end of anaphase, approximately five microtubules will remain (Ward et al., 2014). Thus, roughly 1/2 of the microtubules are lost. Assuming that this probability of being lost (1/2) is the same for all microtubules, for a spindle with nine microtubules at anaphase onset (four from one pole and five from the other pole), the probability of losing all microtubules from either pole by the end of anaphase would then be $\sim {\frac{1}{2}}^4+{\frac{1}{2}}^5$, so approximately 10% of spindles would collapse because of this. In contrast, spindles do not collapse in our simulations, where a mechanism driving even loss of microtubules operates. In 500 simulations with parameters as in Figure 6B and C, where spindles start anaphase with nine microtubules, and have on average five microtubules after 15 min (the typical duration of anaphase B) we observed no spindle collapse (Figure 6F). Therefore, this simple mechanism is remarkably effective.

Finally, we tested whether the loss of rescue organisation observed in ase1Δ cells (Figure 5E) could be partly responsible for spindle collapse (Figure 5C and D). We modified the model so that the total amount of rescue factor was distributed all along microtubules, and the rescue rate was the same anywhere on the spindle. By scanning the parameter representing the total rescue factor ($R$), we found that most spindles collapsed due to loss of antiparallel overlap of microtubules in 20 min of simulated time, even for values of $R$ way higher than those required to maintain stability in spindles with midzone (Figure 6E). This is similar to what happens in ase1Δ cells, where interpolar microtubules coming from opposite poles often lose their connection prior to reaching the typical final spindle length (Figure 5C and D). For $R$=34 μm/min, this modified model closely reproduced the distribution of spindle length at collapse observed in ase1Δ cells (Figure 6G and H, Figure 6—figure supplement 1F), suggesting that in these cells a combination of lower rescue rate and loss of rescue organisation leads to spindles collapsing prior to reaching the typical final spindle length.

In animal cells, microtubule dynamics are increasingly suppressed during anaphase B by kinesin-4 (Hu et al., 2011; Nunes Bastos et al., 2013; Asthana et al., 2021). We have found that in S. pombe, which lacks kinesin-4, microtubule growth speed also decreases during anaphase B (Figure 1E). Microtubules exist in two states (fast and slow growing) characteristic of early and late anaphase (Figure 1F). The transition between these states occurs independently of several motors and MAPs that regulate microtubule dynamics (Figure 2), and happens when plus ends enter the nuclear membrane bridge formed after the dumbbell transition (Figure 3). Furthermore, microtubules do not switch to the slow growing state if bridge formation is prevented by cerulenin treatment or Aurora B inhibition (Figure 4). Our data suggests that microtubule growth speed is mainly governed by spatial cues, rather than a ‘timer’ (Figure 2K, Figure 2—figure supplement 3B), which is reminiscent of recent studies showing that late mitotic events respond to spindle length and not time (Afonso et al., 2014; Afonso et al., 2019).

It is tempting to speculate on mechanisms that could decrease microtubule growth speed when plus ends enter the nuclear membrane bridge. ase1 and les1 deletions reduce the decrease in growth speed associated with internalisation of microtubules in the nuclear membrane bridge (Figure 5F, Figure 4—figure supplement 2) while also perturbing the sorting of nuclear pore complexes to the center of the nuclear membrane bridge (Expósito-Serrano et al., 2020; Dey et al., 2020). It is therefore possible that proteins recruited to the center of the membrane bridge might directly reduce microtubule growth speed. Alternatively, close contact of microtubules with the nuclear membrane or its associated proteins might physically hinder growth (Dogterom and Yurke, 1997; Tischer et al., 2009). Finally, since there is no diffusion between the nuclear membrane bridge and the daughter nuclei (Lucena et al., 2015; Boettcher et al., 2012), the availability of tubulin dimers or another factor could limit microtubule growth when plus ends enter the bridge. Consistent with this last possibility, in S. cerevisiae the nuclear bridge acts as a diffusion barrier between daughter nuclei only in the presence of Ase1 (Boettcher et al., 2012). It would be interesting to test whether microtubule growth speed also decreases during anaphase in the closely related fission yeast S. japonicus, which does not form a nuclear membrane bridge during anaphase (Yam et al., 2011). Importantly, membranes also tightly wrap around the spindle in other systems, such as the midbody in animal cells (Hu et al., 2012), or the phragmoplast in plants (Steiner et al., 2016), and may affect microtubule dynamics. Nevertheless, at least in fission yeast, we could not here assign a biological function to this decrease in microtubule growth speed, as completely preventing it (Figure 4), delaying it (Figure 3—figure supplement 1E) or reducing its extent (Figure 4—figure supplement 2) did not compromise spindle stability nor overall microtubule organisation.

We saw no evidence of cross-talk between microtubule sliding and growth. Klp9 has no noticeable effect on microtubule growth speed, despite its growth promoting activity in monopolar spindles (Krüger et al., 2021). We have not seen growth-limited sliding in unperturbed spindles either: although microtubule growth speed decreases by ∼60% (Figure 1F), spindle elongation speed remains constant throughout anaphase B (Figure 1—figure supplement 1A). In S. cerevisiae and Drosophila, deletion or depletion of Kinesin-8, which decreases catastrophe rate (Wang et al., 2010; Rizk et al., 2014), increases sliding speed and final spindle length (Wang et al., 2010; Rizk et al., 2014). This could indicate that sliding is growth-limited in these organisms. On the other hand, in S. cerevisiae, deletion of kinesin-8 kip3 also delays spindle disassembly (Woodruff et al., 2010). Other mutations that delay spindle disassembly (like cdh1Δ, which prevents the degradation of midzone crosslinkers) produce hyperelongated spindles, similarly to kip3 deletion (Woodruff et al., 2010). In both kip3Δ and cdh1Δ, spindle elongation only stops when spindles are cut by the cytokinetic ring (Woodruff et al., 2010), suggesting that no mechanism exists to stop sliding during anaphase B other than the disassembly of the midzone, and the same has been observed in S. pombe (Lucena et al., 2015). Growth-limited sliding does not seem to occur in HeLa cells either, as depletion of kinesin-4 does not affect spindle elongation velocity (Vukušić et al., 2021). Ultimately, measuring microtubule dynamics in these systems will reveal their impact on microtubule sliding. Nevertheless, growth-limited sliding is widely conserved, and may contribute to spindle stability in S. pombe when microtubule dynamics are perturbed, such as during starvation (Tanabe et al., 2020).

The microtubule rescue factor Cls1 (CLASP) is recruited to the midzone by the crosslinker Ase1 (PRC1) in several species (Liu et al., 2009; Bratman and Chang, 2007; Kitazawa et al., 2014), and it had been previously proposed that this would restrict rescues to the midzone (Bratman and Chang, 2007). Indeed, we observed that rescues occur most frequently at midzone edges (Figure 1G). Thus, spindle microtubules remain stable from the pole to the midzone edge, and only their distal parts including the plus ends alternate between assembly and disassembly (Figure 7A). Simulations show that promoting microtubule rescue at midzone edges is sufficient to maintain the overlap between microtubules and sustain sliding across a wide range of microtubule growth speeds (Figure 6F), indicating that this mechanism is robust against perturbations on microtubule growth. Our study suggests that S. pombe cells adopted this mechanism to ensure spindle integrity, rather than a precise regulation of microtubule growth. This is supported by the fact that deletion of Ase1 (Loiodice et al., 2005; Yamashita et al., 2005) and inactivation of Cls1 (Bratman and Chang, 2007) lead to spindle collapse, while perturbing the normal microtubule growth speed evolution during anaphase B has no effect on spindle stability or organisation (Figure 4). In animal cells, the situation is likely more complex: in HeLa cells, depletion of kinesin-4 leads to highly dynamic interpolar microtubules (Hu et al., 2011), but spindles still elongate with normal speed during anaphase B (Vukušić et al., 2021), indicating that a precise regulation of microtubule growth is not required. However, depletion of PRC1/Ase1 does not lead to spindle collapse during anaphase B either (Vukušić et al., 2021; Pamula et al., 2019), suggesting that if microtubule rescue organisation is required for spindle stability, it may rely on a mechanism other than recruitment of CLASP by PRC1. It would be important to understand the relative contribution to spindle stability of these mechanisms, and others not present in yeast during anaphase B, like microtubule nucleation (Uehara et al., 2009; Uehara and Goshima, 2010).

We do not know the molecular mechanism by which rescues happen more often at midzone edges. We can speculate that this might be related to the fact that protofilaments curl outwards when microtubules shrink (McIntosh et al., 2008). Indeed, the distances between adjacent microtubules in the midzone are comparable to the radius of curling protofilaments (McIntosh et al., 2008; Ward et al., 2014), such that steric collisions alone could promote protofilament straightening, enhancing rescue similarly to what has been proposed for kinetochore protein Dam1 (Franck et al., 2007; McIntosh et al., 2008). Recent in vitro studies have combined PRC1, CLASP and dynamic microtubules (Hannabuss et al., 2019; Mani et al., 2021), so it would be interesting to see whether in a reconstitution resembling the yeast spindle rescues also happen at the edges, which would indicate that this is an inherent property of PRC1/CLASP systems.

In summary, a mechanism to coordinate microtubule sliding and growth relying on rescue localisation is robust against perturbations in polymerisation speed and allows for an array of antiparallel microtubules with a given overlap to continuously elongate. Given the diversity of sizes and morphologies of spindles, and the fact that growth limited sliding is widely conserved, other mechanisms are likely to be discovered in the future.

All used strains are isogenic to wild-type 972 and were obtained from genetic crosses, selected by random spore germination and replicated on plates with corresponding drugs or supplements. Gene deletion and tagging was performed as described previously (Bähler et al., 1998), following Kawai et al., 2010. All strains, oligonucleotides and plasmids used, and how they were made are described in the Supplementary file 1.

All S. pombe strains were maintained at 25 °C in YE5S plates and refreshed every third day. One day before the microscopy experiments, cells were transferred to liquid YE5S culture, and imaged the next day at exponential growth. For all experiments except for Figure 3, the cells were grown overnight in YE5S liquid medium at 25 °C. For experiments in the absence of thiamine (used to induce overexpression of klp9, Figure 3), cells were pre-grown in liquid YE5S, then washed three times with deionised water, transferred to EMM supplemented with adenine, leucine and uracil, and incubated 18–22 hr at 25 °C prior to the microscopy experiment. For cerulenin treatment, cells were incubated for 1 hr in liquid medium with the indicated cerulenin concentration prior to the experiment (Sigma-Aldrich, stock solution was 10 mM in DMSO), the same volume of DMSO was added in control. For Aurora B inactivation, 5 µM of 1NM-PP1 was added to both wild-type and ark1-as3 cells (Sigma-Aldrich, stock solution was 5 mM in DMSO), and cells were imaged immediately.

For live-cell imaging, cells were mounted on YE5S agarose pads, containing 4% agarose (Tran et al., 2004). For the experiments in Figure 4, the drug or DMSO was added at the same concentration in the agarose pad as in the liquid medium. Movies used for kymographs were acquired with Structural Illumination Microscopy (SIM).

Imaging of data from figures Figure 1, Figure 1—figure supplement 1, Figure 2 (mal3, cls1, klp9 and their corresponding wt) and Figure 5—figure supplement 3 (ase1^off and its corresponding wt) was performed at 27 °C with a Nikon Eclipse Ti inverted microscope, equipped with a Nikon CFI Plan Apochromat 100x/1.4 NA objective lens, a Nikon Perfect Focus System (PFS), a Mad City Labs integrated Nano-View XYZ micro- and nano-positioner, a Gataca Systems LIVE-SR SIM module, a Yokogawa Spinning Disk CSU-X1 unit, a Photometrics Prime 95B sCMOS camera, controlled by MolecularDevices MetaMorph 8.0. For GFP and mCherry imaging, solid-state lasers of 488 nm (100 mW) and 561 nm (50 mW) were used.

The rest of the imaging was performed at 27 °C with a Nikon Eclipse Ti2 inverted microscope, equipped with a Nikon CFI Plan Apochromat 100x/1.4 NA objective lens, a Nikon Perfect Focus System (PFS), a Mad City Labs integrated Nano-View XYZ micro- and nano-positioner, a Gataca Systems LIVE-SR SIM module, a Yokogawa Spinning Disk CSU-W1 unit, a Photometrics Prime 95B sCMOS camera, controlled by MolecularDevices MetaMorph 8.0. For GFP and mCherry imaging, solid-state lasers of 488 nm (150 mW) and 561 nm (150 mW) were used.

Movies for kymographs were acquired as follows: in the GFP channel, images were acquired as stacks of 5 planes spaced 0.5 μm without binning every 4 s during 15 min (except for mCherry-Ase1 movies, where the images were acquired every 5 s). Exposure was 100ms (Gain 3). In the mCherry channel, for Cut11-mCherry images were acquired as single stacks, every 16 s without binning during 15 min. For mCherry-ase1, images were acquired as stacks of 5 planes spaced 0.5 μm without binning every 8 s during 15 min. Exposure was 200ms (Gain 3). Movies where intensity measurements were made were acquired as stacks of 11 planes spaced 0.5 μm without binning every minute during 90 min. Exposure was 100ms (Gain 3) in all channels. The remaining movies were acquired as stacks of 7 planes spaced 1 μm without binning every minute during 90 min. Exposure was 100ms (Gain 3) in all channels.

To minimise the inter-experiment variance, all the data shown within the same plot was acquired in parallel. In the case of movies used for kymographs this meant that samples of the conditions tested were alternated on the microscope. In the case of one minute interval movies, positions corresponding to all conditions were imaged simultaneously.

All statistical analysis was performed using MATLAB. In the main text, values are reported as mean ± standard deviation. To avoid pseudo-replication and use the right degrees of freedom to calculate statistical significance we used linear mixed models (see Lazic et al., 2018; Aarts et al., 2015 for detailed explanation), and degrees of freedom were estimated with Satterthwaite approximation. In essence, linear mixed models include random effects to account for the fact that multiple measurements from the same experiment or cell are not independent. This is important for our nested data where several measurements of a given magnitude (e.g. microtubule growth) are taken from various cells in several experiments. Additionally, in some cases these measurements are classified in categories (before, outside, inside).

To study the fixed effect of a ‘condition’ (genetic background or drug treatment) on a given response variable $y$ for binned data (such as Figure 2G–L) or univariate distributions (Figure 1—figure supplement 2C, F, G), we took into account the random effects associated with cell and experiment variability. The data was fitted to the following mixed-effects model (in MATLAB / R notation): y ∼ condition + (condition|experiment) + (1|cell:experiment) In this model, (condition|experiment) accounts for the fact that the effect of ‘condition’ may vary between experiments, and (1|cell:experiment) accounts for cell variability, nested within the experiment. The term (1|cell:experiment) is not used in cases where there is only one measurement per cell (Figure 5D, Figure 3—figure supplement 1A, C, D) or when comparing interphase and anaphase cells (Figure 1—figure supplement 2F, G).

To study the fixed effect of ‘condition’ (genetic background or drug treatment) and ‘position’ (before / outside / inside, see cartoons in Figure 4) on microtubule growth speed, we took into account the random effects associated with cell and experiment variability. The data was fitted to the following mixed-effects model (in MATLAB / R notation): growthspeed ∼ condition * position + (condition|experiment) + (position|cell:experiment) In this model, (condition|experiment) accounts for the fact that the effect of ‘condition’ may vary between experiments, and (position|cell:experiment) accounts for the fact that the effect of ‘position’ may vary between cells (which are nested within an experiment). These mixed effects models were used to generate the summary statistical tables in the supplementary. For calculating the mean and confidence intervals of the mean, we used MATLAB’s predict function. To calculate the percentage of variability that is explained by the categorisation ‘before’, ‘inside’ and ‘outside’ in Figure 3 (mentioned in main text) we fitted the data to a conventional linear model (speed ∼ position), and reported the $R^2$ as the percentage of variability explained by the categorisation. To compare microtubule growth speed ‘outside’ and ‘inside’ in ‘ark1-as3 abnormal’ cells (see main text) we reported a p-value obtained with MATLAB’s coefTest function, which evaluates the significance of the difference between means for any pair of categories in the model. We provide our MATLAB analysis script in the supplementary files (Source Code File 1, statistical_analysis.m) to reproduce this statistical analysis. The values of standard deviation reported in the main text and in Table 1 are the average of the standard deviations of individual experiments.

All feature detections, kymographs and length measurements were done in maximal projections of fluorescence microscopy images. Intensity measurements were performed on summed projections.

The simulation is written in Python and available under an open source license https://github.com/manulera/simulationsLeraRamirez2021.

We consider a one-dimensional model in which all microtubules are straight and aligned with the X axis, with the origin corresponding to the spindle center. The spindle poles, which contain the microtubule minus ends, are positioned symmetrically around the origin. Microtubules growing from one pole are orientated towards the opposite pole (Figure 6A). Their positions in the YZ plane are recorded by an index representing their position on a transverse chequerboard lattice (Figure 6—figure supplement 1A). This index may change when the spindle ‘reorganises’ (Figure 6—figure supplement 1A, and see below). For simplicity, we do not simulate crosslinkers or other MAPs, and we assume that the midzone is a region of the space centered at the origin that has a constant length ($L_m$). In each simulation, $L_m$ is drawn randomly, sampling from a fit of the midzone length data shown in Figure 1G to a normal distribution (Figure 6—figure supplement 1C). Each microtubule has its own length, and can exist in a growing or shrinking state. Microtubule growth, shrinkage and sliding occur at constant speeds (v_p, v_d, v_s Table 2). The duration of microtubule growth events is sampled from a fit of the cumulative distribution of duration of microtubule growth events shown in Figure 1—figure supplement 1C to:

This function represents the probability of $n$ events occurring in an interval of time $t$, if they are independent and occur with a constant rate $\theta$. For $\theta$=3.17 min^–1 and $n$=8.53 (see Table 2), we obtained a good agreement with the data (Figure 6—figure supplement 1D). This suggests that catastrophe is not a single step process, agreeing with what was proposed in Gardner et al., 2011. We assume for simplicity that a growing microtubule reaching the spindle pole immediately undergoes catastrophe. Shrinking microtubules may be rescued if their plus end is inside the midzone. Based on the fact that Cls1 is recruited by Ase1 (Bratman and Chang, 2007) and that Cls1 levels remain constant during anaphase (Figure 2—figure supplement 2A), we assume that a fixed amount of rescue factor is distributed along the overlap between microtubules. Therefore, the integral of rescue rate ($r$) along the overlap length of the midzone is constant, and given by ${\displaystyle R=N{\int }_{l=0}^{l=L_m}rdl}$, where N is the number of microtubule pairs in the square lattice. The rescue rate of a microtubule with $n$ neighbours is given by the following expression:

$P(x,\alpha ,\beta )$ is the probability density of a beta distribution with parameters $\alpha$ and $\beta$ as a function of $x$, a reduced coordinate that maps the position of microtubule plus ends in the midzone from zero to one, with zero corresponding to the midzone edge closest to the spindle pole (Figure 6A). The beta distribution offers differently shaped distributions of rescue activity while keeping $R$ constant. The spindle can reorganise when a microtubule is lost by complete depolymerisation. We assume that another microtubule can rearrange in the YZ plane to maximise antiparallel connections, as these are the arrangements observed by electron microscopy (Ward et al., 2014; Ding et al., 1993). Microtubules move to another position of the square lattice, of the same orientation, to increase the compactness of the structure. This can happen in two cases, as shown in Figure 1—figure supplement 1A. (1) A microtubule is lost and another one moves in its place (2) A neighbour of the lost microtubule moves to another available position. The moves only occur if they increase the number of antiparallel connections.

Simulations are initialised with a 4 μm long spindle, with 9 microtubules of 3 μm of length arranged in a square lattice as shown in Figure 6A. Initially they all start in a growing state. The system is evolved using a time step $h$ of 0.01 min. The new positions of spindle poles are calculated as $x_{t+h}=x_t+v_{s}h$, and microtubule lengths are updated similarly. Catastrophe and rescue are stochastic events simulated using the kinetic Monte Carlo method. At the beginning of the simulation, and whenever a microtubule rescue occurs, the time until the next catastrophe for a given microtubule (${\tau }_c$) is sampled from the probability distribution in Equation 4. At every time point, $h$ is subtracted from the ${\tau }_c$ of each growing microtubule, until ${\tau }_c$ is smaller than zero, at which point the microtubule switches to shrinkage. Shrinking microtubules can only be rescued inside the midzone, and at every time point the rescue rate ($r$) is given by Equation 5. The probability to be rescued during $h$, $1-e^{-rh}$ is tested against a random number, uniformly distributed in [0,1]. At every time point, we check if the spindle ‘collapses’ by testing whether the longest microtubules of each pole are too short to overlap. The simulation finishes if the spindle breaks or when it reaches 20 min of simulated time.

The simulations of ase1 spindles are performed similarly, but the rescue rate is the same anywhere on the spindle and is given by $r=R/2L_t$, where $L_t$ is the total length of microtubules. In this model, we assume that a fixed amount of rescue factor is distributed all along microtubules and not along the overlap between neighbours. The factor 2 in the denominator ensures consistency between both models. The fitting parameters for Equation 4 in these simulations are $\theta$=6.8 min^–1 and $n$=2.5 (Table 2).

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

We thank Lara Katharina Krüger and Serge Dmitrieff for discussions and critical reading of the manuscript. We thank Chuanhai Fu (University of Science and Technology of China), Stefania Castagnetti (LBDV, Sorbonne Université), Jonathan Millar (University of Warwick), Ken Sawin (University of Edinburgh), Sylvie Tournier (Université de Toulouse), Rafael R Daga (Universidad Pablo de Olavide, Sevilla) and Gautam Dey (EMBL Heidelberg) for kindly providing strains and plasmids used in this study. We thank Vincent Fraisier and Lucie Sengmanivong for the maintenance of microscopes at the PICT-IBiSA Imaging facility (Institut Curie), a member of the France-BioImaging national research infrastructure. We thank the Japan National BioResource Project – Yeast Genetic Resource Center (Osaka City University, Osaka University and Hiroshima University) for providing strains. Funding Manuel Lera-Ramirez was supported by a PhD fellowship from the European Union ITN-Divide Network, Marie Sklodowska-Curie Actions (grant number: 675737 s). This work and François Nédélec were supported by the Gatsby Charitable Foundation https://www.gatsby.org.uk/. This work is supported by grants from INCa, Fondation ARC, and La Ligue National Contre le Cancer - Ile de France. The Tran lab is a member of the Labex CelTisPhyBio, part of IdEx PSL.

© 2022, Lera-Ramirez et al.

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