Benjamin Lacroix
email: benjamin.lacroix@ijm.fr

Gaëlle Letort

Laras Pitayu

Jérémy Sallé

Marine Stefanutti

Gilliane Maton

Anne-Marie Ladouceur

Julie C Canman

Paul S Maddox

Amy S Maddox

Nicolas Minc

François Nédélec
email: nedelec@embl.de

Julien Dumont
email: julien.dumont@ijm.fr

Microtubule Dynamics Scale with Cell Size to Set Spindle Length and Assembly Timing

Successive cell divisions during embryonic cleavage create increasingly smaller cells, so intracellular structures must adapt accordingly. Mitotic spindle size correlates with cell size, but the mechanisms for this scaling remain unclear. Using live cell imaging, we analyzed spindle scaling during embryo cleavage in the nematode Caenorhabditis elegans and sea urchin Paracentrotus lividus. We reveal a common scaling mechanism, where the growth rate of spindle microtubules scales with cell volume, which explains spindle shortening. Spindle assembly timing is however constant throughout successive divisions. Analyses in silico suggest that controlling the microtubule growth rate is sufficient to scale spindle length and maintain a constant assembly timing. We tested our in silico predictions to demonstrate that modulating cell volume or microtubule growth rate in vivo induces a proportional spindle size change. Our results suggest that scalability of the microtubule growth rate when cell size varies adapts spindle length to cell volume.

Introduction

Eukaryotic cells range in size over six orders of magnitude. Regardless of size from the smallest unicellular eukaryote Ostreococcus tauri (<1 µm) to long motor neurons (>1 m long), all cells contain a common set of organelles and subcellular structures. This requirement mandates a strict scaling between these intracellular components and cell size. One striking example of this scaling is the progressive decrease in cell volume that occurs during cleavage of early embryos. Early embryonic development usually occurs without an increase in the overall embryo volume. Each round of cell division halves the size of blastomeres, so blastomere volume can decrease by two orders of magnitude from single celled-zygotes to multicellular gastrulae (O'Farrell et al., 2004). Thus, intracellular structures and organelles must adapt to this wide range of cell dimensions by adjusting their spatial distribution and/or size to remain functional [START_REF] West | The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization[END_REF]. Organelles known to exhibit size adaptation to cell volume variations include nuclei, cilia, endoplasmic reticulum, and cytoskeletal assemblies like the metaphase spindle (reviewed in Chan andMarshall, 2010, 2012;[START_REF] Levy | Mechanisms of intracellular scaling[END_REF]Marshall, 2015b;[START_REF] Reber | Intracellular Scaling Mechanisms[END_REF].

The metaphase spindle is a bipolar structure composed of highly dynamic microtubules.

Adapting spindle length to cell volume enables accurate chromosome segregation and spindle orientation to accommodate different scales (Dumont and Mitchison, 2009a;[START_REF] Holmfeldt | Aneugenic activity of Op18/stathmin is potentiated by the somatic Q18-->e mutation in leukemic cells[END_REF][START_REF] Lancaster | Mitotic rounding alters cell geometry to ensure efficient bipolar spindle formation[END_REF]. Spindle length scaling among different organisms can occur through biochemical variations in cytoplasmic content. For example, a single amino-acid change in the microtubule-severing protein katanin primarily accounts for the spindle length difference observed between oocytes from Xenopus laevis and the smaller closely related frog Xenopus tropicalis [START_REF] Brown | Xenopus tropicalis egg extracts provide insight into scaling of the mitotic spindle[END_REF][START_REF] Loughlin | Katanin contributes to interspecies spindle length scaling in Xenopus[END_REF]. In contrast, the biochemical composition of different sized blastomeres from a given species is assumed to be constant (Mitchison et al., 2015). During cleavage of the large X. laevis embryo, spindle length remains constant for the first five divisions and then decreases linearly with blastomere radius for the next 5-7 divisions [START_REF] Wuhr | Evidence for an upper limit to mitotic spindle length[END_REF]. In contrast, the smaller C. elegans embryo shows spindle length proportional to cell length from the first division throughout cleavage [START_REF] Decker | Limiting amounts of centrosome material set centrosome size in C. elegans embryos[END_REF]Hara andKimura, 2009, 2013). Seminal experiments using artificially encapsulated extracts from X. laevis oocytes or embryos demonstrated that spindle length directly corresponds to the size of the encapsulating droplet [START_REF] Good | Cytoplasmic volume modulates spindle size during embryogenesis[END_REF][START_REF] Hazel | Changes in cytoplasmic volume are sufficient to drive spindle scaling[END_REF]. These experiments accurately recapitulated the spindle scaling observed in intact embryos with a linear relationship between spindle length and droplet radius in small droplets and an upper limit to spindle length in large droplets. Intrinsic spindle mechanisms, such as balancing force between opposed motors, may account for the upper limit of spindle length scaling (Dumont and Mitchison, 2009a, b;[START_REF] Reber | Intracellular Scaling Mechanisms[END_REF]. In contrast, spindle extrinsic mechanisms, such as component limitation, have been proposed to explain how different cytoplasm volumes with a given composition may produce different spindle lengths [START_REF] Goehring | Organelle growth control through limiting pools of cytoplasmic components[END_REF]Marshall, 2015a;Mitchison et al., 2015;[START_REF] Reber | Intracellular Scaling Mechanisms[END_REF][START_REF] Reber | Emergent Properties of the Metaphase Spindle[END_REF]. In C. elegans early embryos, decreasing spindle length correlates with a progressive reduction in the amount of centrosomal components and with a decaying gradient of the microtubule-associated protein TPXL-1 (ortholog of TPX2) along spindle microtubules [START_REF] Greenan | Centrosome size sets mitotic spindle length in Caenorhabditis elegans embryos[END_REF]. Experiments performed in Xenopus egg or embryo extracts suggest that titration of tubulin heterodimers, limited amount/activity of the microtubule polymerase XMAP215, or cortical sequestration of Importin α, the negative regulator of the microtubule depolymerase KIF2A, could participate in spindle length scaling [START_REF] Reber | XMAP215 activity sets spindle length by controlling the total mass of spindle microtubules[END_REF][START_REF] Wilbur | Mitotic spindle scaling during Xenopus development by kif2a and importin alpha[END_REF]). Yet, it remains unclear how the limited supply of these factors controls spindle size.

The limited supply or local inactivation of key factor(s) could directly regulate spindle microtubule dynamics to efficiently control spindle length [START_REF] Andersen | Spindle assembly and the art of regulating microtubule dynamics by MAPs and Stathmin/Op18[END_REF][START_REF] Andersen | Mitotic chromatin regulates phosphorylation of Stathmin/Op18[END_REF][START_REF] Desai | Microtubule polymerization dynamics[END_REF][START_REF] Goshima | Length control of the metaphase spindle[END_REF]Picone et al., 2010;[START_REF] Tournebize | Control of microtubule dynamics by the antagonistic activities of XMAP215 and XKCM1 in Xenopus egg extracts[END_REF][START_REF] Verde | Control of microtubule dynamics and length by cyclin A-and cyclin B-dependent kinases in Xenopus egg extracts[END_REF]. Both in vitro and in vivo, microtubules alternate between phases of growth and shrinkage in a process called dynamic instability (Mitchison and Kirschner, 1984).

Four parameters define these dynamic properties of microtubules, the velocities of growth and shrinkage and the frequencies of transitions between these two states called catastrophe and rescue [START_REF] Kirschner | Beyond self-assembly: from microtubules to morphogenesis[END_REF][START_REF] Walker | Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies[END_REF]. Typically, long interphasic microtubules display low catastrophe and high rescue frequencies [START_REF] Belmont | Real-time visualization of cell cycle-dependent changes in microtubule dynamics in cytoplasmic extracts[END_REF][START_REF] Verde | Control of microtubule dynamics and length by cyclin A-and cyclin B-dependent kinases in Xenopus egg extracts[END_REF][START_REF] Verde | Regulation of microtubule dynamics by cdc2 protein kinase in cell-free extracts of Xenopus eggs[END_REF]. Microtubules in this state are "unbounded" and continuously elongate over time. In contrast, microtubules shorten upon mitotic entry, due to a sharp increase in catastrophe frequency and a significant decrease in rescue events. In this "bounded" regime, microtubules tend to disassemble, and their average growth velocity, termed J, is negative. A steady population of microtubules can only be maintained because a finite fraction is continuously nucleated de novo (Mitchison et al., 2015;[START_REF] Verde | Control of microtubule dynamics and length by cyclin A-and cyclin B-dependent kinases in Xenopus egg extracts[END_REF]. This regime establishes a distribution of microtubule lengths to dictate a steady state spindle size. Therefore, precise control of microtubule dynamics during mitosis in cleaving embryos becomes an attractive candidate to adjust spindle length for blastomere size. However, the functional link between microtubule dynamics and spindle length scaling as a function of cell volume during embryo cleavage remains unknown.

Results

Microtubule Dynamics are Modulated During C. elegans Embryo Cleavage

We first determined the potential relationship among metaphase spindle length, cell volume, and microtubule dynamics from the 1-to the 16-cell stage in cleaving C. elegans embryos. We combined high-temporal single plane confocal microscopy and 2-photon 3Dvolumetric reconstructions of live embryos expressing GFP-tagged microtubules or a plasma membrane marker respectively (Figure 1A and S1A,B). In line with previous studies, we found that spindle length and cell volume progressively decreased in a sub-proportional manner across early embryogenesis in C. elegans (Figure S1C-F) [START_REF] Decker | Limiting amounts of centrosome material set centrosome size in C. elegans embryos[END_REF][START_REF] Greenan | Centrosome size sets mitotic spindle length in Caenorhabditis elegans embryos[END_REF]Hara andKimura, 2009, 2013). To determine if microtubule dynamics vary concomitantly with spindle length and cell volume, we generated kymographs of individual microtubules from our high frame-rate, single-plane confocal series of embryos expressing GFP-tagged β-tubulin (Figure 1B). This approach allowed us to identify phases of elongation and shortening and to measure the rate and duration of individual phases for all analyzed microtubules. We observed that microtubule growth rates and durations were significantly higher for astral microtubules than spindle microtubules in all blastomeres from the 1-to the 16-cell stage, in agreement with published results for the one-cell stage (Figure 1C) [START_REF] Srayko | Identification and characterization of factors required for microtubule growth and nucleation in the early C. elegans embryo[END_REF]. In addition, we found that microtubule dynamics' parameters for both types of microtubules varied throughout development. While we found a notable but mild decrease in shrinkage duration between the 1and the 16-cell stage, the most striking variation across divisions was the continuous and significant decrease in microtubule growth rate for both astral and spindle microtubules (Figure 1C). Importantly, we obtained similar rates and frequencies using a different promoter to drive expression of our GFP-tagged β-tubulin reporter or mCherry-tagged β-tubulin (Figure S2 and Table S1). These results suggest that microtubule dynamics vary throughout early embryonic divisions, with a distinct decrease in the microtubule growth rate associated with decreased blastomere volume.

To investigate a potential link between these variations in microtubule dynamics and spindle length, we first determined if the length of metaphase spindles reached a steady state or if they were limited by the duration of the cell cycle and the time available before anaphase onset.

Indeed, cell divisions in cleaving embryos of most species are particularly rapid, and spindle length increases continuously from nuclear envelope breakdown (NEBD) to anaphase onset (Mitchison et al., 2015). However, delaying anaphase onset in C. elegans embryos using a proteasome inhibitor did not induce spindle elongation above the normal metaphase spindle length at any analyzed stage (Figure 1D,E) [START_REF] Labbe | The forces that position a mitotic spindle asymmetrically are tethered until after the time of spindle assembly[END_REF]. Moreover, the measured microtubule dynamics parameters indicate that all microtubules are in the "bounded" regime (J<0) at every stage of embryo cleavage, which is compatible with a steady state (Figure S2B and Table S1A,C) [START_REF] Verde | Control of microtubule dynamics and length by cyclin A-and cyclin B-dependent kinases in Xenopus egg extracts[END_REF]. These results suggest that mitotic spindles in early C. elegans embryos reach a steady state length before anaphase onset that is independent of the duration of mitosis. Overall, our results demonstrate that microtubule dynamic instability evolves during embryo cleavage with the microtubule growth rate continuously decreasing in parallel with the progressive reduction of steady state spindle length.

Spindle Microtubule Growth Rate Adapts to Cell Volume in C. elegans

We next asked if variations in microtubule dynamics parameters during early embryogenesis were either a direct consequence of cell size changes or under the control of a developmental program. Therefore we analyzed the direct correlation between cell volume and microtubule dynamics parameters (Figure 2A,B). This analysis revealed that the growth rate of spindle microtubules most significantly correlated with cell volume (Figure 2B). So, we tested if the decrease in cell volume of dividing blastomeres solely accounted for this relationship or if cell fate patterning and developmental timing also contributed. Since C. elegans zygotes divide asymmetrically, patterning is already established at the 2-cell stage by asymmetric distribution of cell fate determinants (Nance, 2005;[START_REF] Rose | Early patterning of the C. elegans embryo[END_REF]. The first division of the C. elegans zygote produces a large anterior AB blastomere from which most somatic tissues emerge and a small posterior P1 blastomere from which the germline originates (Figure 2A) [START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF]. We used a fast acting temperature sensitive (ts) mutant of formin CYK-1 to induce cytokinesis failure in the zygote (Figure 2C) [START_REF] Canman | Inhibition of Rac by the GAP activity of centralspindlin is essential for cytokinesis[END_REF][START_REF] Davies | High-resolution temporal analysis reveals a functional timeline for the molecular regulation of cytokinesis[END_REF]. In control 2-cell stage embryos, AB and P1 blastomeres display shorter spindles than the 1-celled zygote, which correlates with slower microtubule growth in both blastomeres (Figure 2D). At the restrictive temperature (25°C), cyk-1(ts) mutant zygotes exhibit cytokinesis failure and form abnormal one-cell embryos that kinetically correspond to 2-cell stage embryos but possess the cytoplasmic content and cell fate determinants of both AB and P1 blastomeres. These abnormal embryos assembled tetrapolar spindles with microtubules that grew at a rate indistinguishable from normal one-cell zygotes (Figure 2C,D). Thus cell fate determinants and developmental timing do not make a major contribution to set the spindle microtubule growth rate in cleaving C. elegans embryos. To further demonstrate the effect of cell volume on spindle microtubule growth rate, we generated abnormally large zygotes. We generated embryos depleted of the fucosyltransferase C27D9.1, which does not have any known direct effect on microtubules and leads to the formation of abnormally large embryos [START_REF] Hara | Cell-size-dependent spindle elongation in the Caenorhabditis elegans early embryo[END_REF][START_REF] Sonnichsen | Full-genome RNAi profiling of early embryogenesis in Caenorhabditis elegans[END_REF]. In these extra-large zygotes, we found longer spindles and a significantly higher growth rate of spindle microtubules than in control normal-sized zygotes (Figure 2C,D). Altogether, these results show that the observed progressive reduction in the growth rate of spindle microtubules is directly linked to cell volume during embryonic cleavage and independent of developmental timing or cell fate.

Spindle Length Scales with Microtubule Growth Rate in C. elegans

We then asked if variations between dynamics parameters of astral and spindle microtubules and cell volume could underlie spindle length scaling during early embryogenesis.

Strikingly, we found that the growth rate of both astral and spindle microtubules was the only parameter exhibiting a distinct, continuous and linear relationship with spindle length throughout cleavage (Figure 3A-C). This observation suggests that modulating the growth rate of one or both microtubule populations could be a key determinant for spindle length adaptation in cleaving embryos. However, analysis of this scaling in C27D9.1-depleted extra-large zygotes revealed that only spindle microtubule growth rate increased with spindle length (Figure 3B), while astral microtubule growth rate remained similar to controls (Figure 3C and Figure S1G,H) (0.41±0.08 µm/s versus 0.40±0.09 µm/s, p=0.087 unpaired t-test). These results suggest that spindle, but not astral, microtubule dynamics determine spindle length in cleaving embryos.

As the growth rate of spindle microtubules decreased progressively with cell volume during embryo cleavage and concomitant with spindle length, we hypothesized that modulating this parameter is sufficient to scale spindle length to cell volume during embryo cleavage. We calculated the average length <L> predicted from microtubule dynamics parameters (Figure 3D, S2B,C and Table S1) [START_REF] Verde | Control of microtubule dynamics and length by cyclin A-and cyclin B-dependent kinases in Xenopus egg extracts[END_REF]. In control embryos, <L> scaled linearly with our experimentally measured spindle lengths from the 1-to the 16-cell stage. This scaling implies that spindle length is a multiple of <L> and that the multiplicative factor remains relatively constant as cell size evolves. Interestingly, the predicted average length <L> of spindle microtubules in C27D9.1-depleted embryos fitted well with the abnormally long spindles in these extra-large zygotes. Thus, spindle length varies proportionally to the overall microtubule dynamics in cleaving embryos. Since rescue frequency is low but catastrophe frequency and shrinkage rate are almost constant in cleaving C. elegans embryos, our results demonstrate that <L> is primarily determined by the microtubule growth rate (Figure 3B,D and Table S1). Our results support the idea that spindle microtubule growth rate is a key regulator to scale spindle length to cell volume.

To directly test this hypothesis, we experimentally reduced spindle microtubule growth rate in zygotes and measured spindle length. We analyzed zygotes partially depleted of the microtubule-associated protein (MAP) CLS-2 (ortholog of CLASP, Figure 3A-C) [START_REF] Cheeseman | The CENP-F-like proteins HCP-1 and HCP-2 target CLASP to kinetochores to mediate chromosome segregation[END_REF]Espiritu et al., 2012), since CLS-2 promotes microtubule assembly in vitro and in vivo (Maton et al., 2015). Consistent with this, in partial cls-2(RNAi) conditions, spindle microtubules displayed a significantly reduced growth rate compared to in control zygotes (0.25±0.06 versus 0.3±0.07 µm/s, p<0.001 unpaired t-test) (Figure 3B and Table S1). Rescue frequency also slightly increased, while catastrophe frequency and shrinkage rate remained unaltered. As we predicted, abnormally short but functional spindles assembled under this condition. Strikingly, both the average theoretical length of microtubules <L> and spindle length in these depleted zygotes were concomitantly reduced to levels corresponding to that of 4-cell stage control blastomeres (Figure 3B-D). Taken together, our results show that microtubule dynamics parameters, specifically the growth rate of spindle microtubules, vary proportionally to cell volume and are key factors that control spindle length during C. elegans embryo cleavage.

Spindle Length and Microtubule Growth Rate Scale with Cell Volume in the Sea Urchin P. lividus

We next wondered whether the scaling relationship among cell volume, spindle length, and microtubule growth rate identified in C. elegans also takes place in other species. Sea urchin (Paracentrotus lividus) embryos are approximately 20 times larger in volume than C. elegans embryos. P. lividus zygotes are spherical and divide symmetrically and synchronously until the 8-cell stage (Figure 4A) [START_REF] Agrell | A mitotic gradient as the cause of the early differentiation in the sea urchin embryo[END_REF]Parisi et al., 1978). First, we microinjected P. lividus eggs with fluorescently labeled tubulin (ATTO 565-tubulin, Figure S3A-F), which then underwent fertilization. We examined the first six rounds of embryonic cleavages by live confocal microscopy (Movie S1 and S2). Consistent with previous reports for other echinoderms [START_REF] Crowder | A comparative analysis of spindle morphometrics across metazoans[END_REF], spindle length and cell volume progressively decreased across early embryogenesis in P. lividus (Figure S3G-H and Table S2). Spindle lengths measured in ATTO 565-tubulin injected live embryos were indistinguishable from those in control non-injected fixed embryos (Figure S3B,D). To determine if microtubule dynamics also varied concomitantly with spindle length and cell volume, we generated kymographs of individual microtubules to measure spindle microtubule dynamics parameters. In line with our results from C. elegans embryos, microtubule dynamics parameters varied during P. lividus cleavage, but the overall microtubule dynamics remained in the bounded regime at every stage (Figure 4B and Table S2).

We observed a continuous and significant decrease in the growth rate of spindle microtubules across P. lividus embryo cleavage (Figure 4B). This decrease correlated with the progressive reduction in blastomere volume and spindle length (Figure 4C,D). We observed similar spindle lengths and growth rates using another fluorescent microtubule probe (the 3XmCherry-tagged ensconsin microtubule-binding domain, 3XmCherry-EMTB (Faire et al., 1999), Figure S3A-F).

These results suggest that microtubule growth rate is a key determinant of spindle length in cleaving sea urchin embryos. Importantly, both spindle length and spindle microtubule growth rate were comparable in vegetal micromeres (which result from strong asymmetric division at the 8-cell stage and inherit a fate determining polar domain [START_REF] Angerer | Animal-vegetal axis patterning mechanisms in the early sea urchin embryo[END_REF][START_REF] Davidson | Specification of cell fate in the sea urchin embryo: summary and some proposed mechanisms[END_REF]) and in 32-cell stage blastomeres at the animal pole (p=0.85 unpaired ttest, Figure 4A,B). Thus, cell volume, but not cell fate or developmental timing, appears to dictate spindle microtubule growth rate and consequent spindle size in cleaving P. lividus embryos, as we found for C. elegans. We conclude that this scaling principle operates across a 500-fold change in cell volume and could potentially represent an evolutionarily conserved feature of cleaving embryos.

3D Simulations Reproduce Spindle Length Scaling with Microtubule Growth Rate

To directly test if modulating only microtubule growth rate is sufficient to explain the observed spindle length scaling, we utilized computer simulations. Using the cytoskeletal simulator Cytosim to develop a three-dimensional spindle model, we examined the contribution of the microtubule growth rate on spindle size in a dose-dependent manner in silico (www.cytosim.org;Nedelec F, 2007). We modeled each spindle pole as an aster composed of a preset number of microtubules that can grow, shrink, and stochastically undergo catastrophe and rescue (Figure 5A and S4, see detailed parameters in Table S3 and Methods). We constructed two asters by distributing a subset of these microtubules evenly and then confining the remaining microtubules within a cone to account for the higher microtubule density directed toward the metaphase plate in C. elegans spindles. We represented the metaphase plate itself using a fixed discoid volume in the center of the cell that microtubules cannot enter. Using our experimental measurements, we scaled cell volume, metaphase plate thickness and spindle width linearly with respect to the input growth rate (Table S2B). Microtubules are confined inside the cell volume, and growing plus-ends contacting the cell boundaries can create pushing forces leading to aster centration. Similarly, growing microtubules emanating from the two centrosomes, and contacting the metaphase plate, can generate forces that would push spindle poles apart leading to spindle elongation. To ensure that spindle pole movements would strictly occur through growing microtubules pushing on the cell cortex or on the metaphase plate, we omitted microtubule motors from this model. We analyzed the effects of modulating the microtubule growth rate as a function of cell volume, while keeping the three other microtubule dynamics parameters constant. We tested the physiological range of microtubule growth rates that we measured in vivo in C. elegans (Table S1). In this first set of simulations, the spindle length (pole-to-pole distance) trended toward a plateau over time for every tested microtubule growth rate (Figure 5B and Movie S3). Consistent with our hypothesis, the steady state spindle length decreased concomitantly with the microtubule growth rate (Figure 5C). Overall, the spindle lengths calculated in silico were in good agreement with our experimental measurements (Figure 5C), which confirms that this simple model accurately recapitulated the in vivo relationship between microtubule growth rate and spindle length.

Since our experimental data suggested that spindle length correlates with spindle but not astral microtubule dynamics, we tested if a simulation devoid of cell boundary and astral microtubules could reproduce the relationship between spindle length and microtubule growth rate (Figure 5D). With this modified model, we tested a range of microtubule growth rates, while keeping all other parameters constant (Figure 5E and Movie S4). We did find that spindle length plateaued over time at a length that increased with microtubule growth rate that yielded similar values and scaling slopes as in our experiments (Figure 5F). This model exhibited the correct multiplicative factor between <L> and spindle length, which suggests that this scaling factor only depends on the geometrical dimensions of the system (i.e. cell size and/or dimensions of the metaphase plate) included in the simulation. Together, these findings suggest that modulating spindle microtubule growth rate is sufficient to scale spindle size with cell volume in cleaving embryos.

Spindle Assembly and Microtubule Growth Rates Proportionally Correlate with Constant

Spindle Assembly Timing During Embryo Cleavage

An interesting finding from our 3D simulations was that spindle length reached steady state within a timeframe that was independent of microtubule growth rate or final spindle size (Figure 5B, E and S4D). So, our simulations predict that shorter spindles would not assemble faster than longer ones. To test if this occurred in vivo, we compared spindle lengths at various stages of C. elegans cleavage with the timing of spindle assembly (Figure 6A and Movie S5).

Since spindle length continuously increases from NEBD to anaphase onset in C. elegans embryos, we approximated spindle assembly timing as the duration between NEBD and anaphase onset. We found that the timing of spindle assembly was independent of the initial distance between centrosomes or final spindle length (Figure 6B). Although spindle assembly took slightly longer in the 1-celled zygote than in subsequent stages, spindle assembly durations stayed relatively constant over the first five rounds of embryonic division, despite the progressive decrease in spindle length at each division. We also observed a progressive decrease of the spindle assembly rate, which strongly correlated with the decreasing spindle length and microtubule growth rate across early embryonic divisions (including in the zygote, Figure 6C and D). These results agree with the predictions from our simulations. Therefore, the progressive decrease of the microtubule growth rate is sufficient to regulate the constant timing of spindle assembly in cleaving embryos.

Discussion

In summary, we have explored the dynamic properties of microtubules as cell size decreases in early cleaving embryos. Using the nematode C. elegans and the sea urchin P. lividus, our results establish that the growth rate of spindle microtubules in both species is the primary parameter of dynamic instability that decreases proportionally to cell volume and concomitantly with spindle length. Using an in silico 3D spindle model, we demonstrate that decreasing the microtubule growth rate proportionally to cell volume is sufficient to control spindle size and recapitulates the principal features of spindle scaling observed in vivo. Our results suggest a simple mechanism to adjust spindle length with varying cell volume, as typically found in early embryonic development. Importantly, our results elucidate how spindle assembly timing is constant among different blastomere sizes in early embryos. This mechanism may be crucial to prevent chromosome segregation defects [START_REF] Holmfeldt | Aneugenic activity of Op18/stathmin is potentiated by the somatic Q18-->e mutation in leukemic cells[END_REF][START_REF] Lancaster | Mitotic rounding alters cell geometry to ensure efficient bipolar spindle formation[END_REF]Mitchison et al., 2015).

Microtubule Dynamics and Cell Volume

Parameters of microtubule dynamics scaled similarly across cleavages in C. elegans and P. lividus but had different absolute values in the two species. C. elegans embryos are ~20 times smaller in volume than sea urchin embryos, but their microtubules grow significantly faster at every stage of cleavage (Figure 7A). These results indicate that microtubule growth rate is not an absolute predictor of spindle length (Figure 7B-D). In contrast, the average theoretical microtubule length <L>, calculated from the four parameters of dynamic instability, followed a linear and similar trend in both species when plotted against cell volume (Figure 7F). Strikingly, blastomeres of comparable volumes displayed very similar values of <L> regardless of their species of origin (C. elegans 2-cell stage blastomeres and P. lividus 32-cell stage blastomeres display volumes of 10.6 and 9.28 pl respectively and <L> of 2.48 and 2.42 µm respectively).

<L> is a readout of the overall microtubule dynamics, which suggests that microtubule dynamics vary to set an average microtubule length that scales with cell volume. Furthermore, since spindle length is roughly proportional to <L>, microtubule dynamics are modulated to scale spindle length with cell volume.

However, we note that <L> is not equal to the spindle half-length nor do we suggest that spindle length is solely determined by microtubule length. Spindle assembly requires other factors (Dumont and Mitchison, 2009b;Mitchison et al., 2015;[START_REF] Reber | Emergent Properties of the Metaphase Spindle[END_REF][START_REF] Walczak | Mechanisms of mitotic spindle assembly and function[END_REF][START_REF] Waters | Pathways of spindle assembly[END_REF]. We also provide evidence for this premise, as <L> did not always scale linearly with spindle length in P. lividus (Figure 7E). Specifically, 1-and 2-cell stage sea urchin blastomeres deviated from the linear scaling trend followed by other cells, and assembled spindles that were shorter than predicted by values of <L>. Several non-exclusive causes could account for the discrepancy between <L> and spindle length: microtubules may bend, detach from the centrosomes or be severed [START_REF] Brangwynne | Microtubules can bear enhanced compressive loads in living cells because of lateral reinforcement[END_REF][START_REF] Crowder | A comparative analysis of spindle morphometrics across metazoans[END_REF]Dumont and Mitchison, 2009a;[START_REF] Gadde | Mechanisms and molecules of the mitotic spindle[END_REF]Goshima et al., 2005a;Maiato et al., 2004;McBeath and Fujiwara, 1990;[START_REF] Reber | Emergent Properties of the Metaphase Spindle[END_REF][START_REF] Redemann | C. elegans chromosomes connect to centrosomes by anchoring into the spindle network[END_REF][START_REF] Wuhr | Evidence for an upper limit to mitotic spindle length[END_REF]. We also note that theoretically, the microtubule growth rate should regulate microtubule mass within the spindle rather than the spindle length itself (Mitchison et al., 2015;[START_REF] Reber | XMAP215 activity sets spindle length by controlling the total mass of spindle microtubules[END_REF]. So, when microtubule length and spindle length scale linearly together, total microtubule mass in the spindle may also scale. But in larger blastomeres, an excess in microtubule mass, due to the increased growth rate, could be compensated either by an increase in density, or by a change in spindle width rather than length.

Consistent with the later possibility and previous observations done in other species [START_REF] Crowder | A comparative analysis of spindle morphometrics across metazoans[END_REF][START_REF] Hara | An allometric relationship between mitotic spindle width, spindle length, and ploidy in Caenorhabditis elegans embryos[END_REF], we observed a significant change in the spindle length to width ratio and in the centrosome radius in P. lividus among cleavages, which correlated with proportionally wider spindle poles at earlier stages (Figure S3H and Table S2).

Microtubule Dynamics and Spindle Length

Our analysis revealed that the microtubule growth rate and spindle length decrease concomitantly and sub-proportionally to cell volume across reductive divisions in early C. elegans and P. lividus embryos. This contrasts with previous work comparing stage 3 and 8 Xenopus embryo extracts. These studies found no major variation in the microtubule growth rate, but a threefold increase in the microtubule catastrophe frequency correlated with smaller spindles [START_REF] Wilbur | Mitotic spindle scaling during Xenopus development by kif2a and importin alpha[END_REF]. It is possible that different mechanisms may exist across phylogeny that would produce similar effects on spindle length, thus reflecting evolutionary diversity.

However, we note that Xenopus blastomeres (at both stages 3 and 8) are significantly larger than C. elegans or P. lividus embryos, which could favor one spindle scaling mechanism over the other. Moreover, stage 8 blastomeres utilize a linear scaling regime, where spindle length scales linearly with cell size, while stage 3 blastomeres remain in the 'large-cell' regime, in which spindle length reaches an upper limit that is independent of cell size [START_REF] Wilbur | Mitotic spindle scaling during Xenopus development by kif2a and importin alpha[END_REF][START_REF] Wuhr | Evidence for an upper limit to mitotic spindle length[END_REF]. The difference in the catastrophe frequency between stage 3 and 8 could thus be related to the transitioning from 'large-cell' to linear scaling regime rather than reflecting a cell size-dependent spindle scaling mechanism. Finally, results obtained with Xenopus egg extracts could also reflect the removal of membrane confinements. In the 'large-cell' regime, spindle length is controlled through spindle intrinsic mechanisms such as autocatalytic microtubule nucleation [START_REF] Decker | Autocatalytic microtubule nucleation determines the size and mass of Xenopus laevis egg extract spindles[END_REF][START_REF] Ishihara | Physical basis of large microtubule aster growth[END_REF]Mitchison et al., 2015). It is therefore possible that in the 'small-cell' regime, modulation of the microtubule nucleation rate similarly contributes to spindle length scaling. However, our results demonstrate that regulation of the microtubule growth rate is sufficient to account for spindle length adaptation to cell volume in small cells.

We still must determine the specific factors that control microtubule growth rate with respect to cell volume. The limiting component hypothesis proposes that one or several factors critical for spindle assembly have a limited supply, so their absolute quantity per cell diminishes upon embryo cleavage (Mitchison et al., 2015;[START_REF] Reber | Intracellular Scaling Mechanisms[END_REF]. Tubulin is the most obvious candidate, as its concentration does determine the rate of microtubule elongation in vitro [START_REF] Walker | Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies[END_REF]. However, several in vitro and in vivo studies argue against tubulin being the sole limiting component. In Xenopus egg extracts or in the presence of crowding agents in vitro, the growth rate of microtubules is not linearly dependent on the available tubulin concentration (Parsons and Salmon, 1997;[START_REF] Wieczorek | Macromolecular Crowding Pushes Catalyzed Microtubule Growth to Near the Theoretical Limit[END_REF], as robust spindle length scaling occurred in lipid droplets even after artificially increasing the amount of tubulin [START_REF] Good | Cytoplasmic volume modulates spindle size during embryogenesis[END_REF]. In sea urchin embryos, a 5-fold excess of tubulin is present in a soluble non-polymerized form, and can be artificially mobilized into the spindle upon treatment with crowding agents indicating that tubulin itself is not limiting in this system [START_REF] Inoue | Cell motility by labile association of molecules. The nature of mitotic spindle fibers and their role in chromosome movement[END_REF][START_REF] Raff | Microtubule protein pools in early development[END_REF][START_REF] Raff | Soluble microtubule proteins of the sea urchin embryo: partial characterization of the proteins and behavior of the pool in early development[END_REF][START_REF] Rebhun | Regulation of the in vivo mitotic apparatus by glycols and metabolic inhibitors[END_REF]. Quantitative western blotting allowed us to estimate the tubulin concentration to approximately 22 µM in C. elegans embryos, which is similar to Xenopus embryos (Figure S5 and Methods) [START_REF] Belmont | Real-time visualization of cell cycle-dependent changes in microtubule dynamics in cytoplasmic extracts[END_REF]. Based on a recent study providing the first complete electron tomographic reconstruction of the mitotic spindle in the C. elegans zygote [START_REF] Redemann | C. elegans chromosomes connect to centrosomes by anchoring into the spindle network[END_REF], we estimated that the total amount of tubulin heterodimers should be sufficient to assemble 2-3 zygotic mitotic spindles (see Methods). Thus, tubulin seems unlikely to be the only limiting factor for spindle length scaling. Another possibility is that specific microtubule-associated proteins (MAPs) that regulate microtubule growth rate are also limiting. Consistent with this, we found that reducing levels of the CLS-2 protein in C. elegans zygotes modulated microtubule growth rate and spindle length proportionally. Furthermore, by performing a temporal dilution experiment through progressive RNAi depletion of CLS-2 in the C. elegans one-cell embryo, we found that spindle length was proportional to CLS-2 protein level (Figure 8A-E). Together, these results are in agreement with the limiting amount of one or several MAPs restricting microtubule dynamics and spindle length in early embryos (Figure 8F,G). To explain how the absolute amount of MAPs could become limiting and thus control spindle length scaling, we favor a model where a progressive mismatch is established across successive divisions between the number of available MAPs and the number of spindle microtubules (Figure 8G). The CLS-2 and TPXL-1 proteins are good candidate factors for acting as limiting components [START_REF] Greenan | Centrosome size sets mitotic spindle length in Caenorhabditis elegans embryos[END_REF]. However, MAPs influence several microtubule dynamics parameters, which complicates the identification of the key factor(s) that coordinates spindle length with cell size in early embryos in vivo [START_REF] Bowne-Anderson | Regulation of Microtubule Growth and Catastrophe: Unifying Theory and Experiment[END_REF]. We must also point out that the limiting component model cannot account for the spindle-scaling mismatch observed between oocytes and zygotes of most species, and that cell volume is not an absolute predictor of spindle length. Indeed, although they assemble in an identical volume of the same cytoplasm, oocyte spindles are usually smaller than their zygotic counterpart. Meiotic-specific and volume-independent mechanisms can usually account for the discrepancy between cell volume and spindle length in oocytes [START_REF] Clandinin | Genetic studies of mei-1 gene activity during the transition from meiosis to mitosis in Caenorhabditis elegans[END_REF][START_REF] Clark-Maguire | Localization of the mei-1 gene product of Caenorhaditis elegans, a meiotic-specific spindle component[END_REF]Lu et al., 2004;[START_REF] Srayko | MEI-1/MEI-2 katanin-like microtubule severing activity is required for Caenorhabditis elegans meiosis[END_REF].

Microtubule Dynamics and Spindle Assembly Rate

In addition to spindle size, we also found that the rate of spindle assembly (spindle length/time of assembly) scaled with cell size in C. elegans embryos. Our simulations combined with our in vivo measurements suggest that this scalability occurs through the proportional relationship between microtubule growth rate and steady state spindle length. This property could be key in early embryos that undergo rapid cell divisions with a weak spindle assembly checkpoint (Encalada et al., 2005). Indeed, C. elegans embryos respond to unattached kinetochores by inducing a small delay in mitosis but do not arrest their cell cycle progression. In this context, adapting the microtubule growth rate to the final spindle length would ensure efficient chromosome bi-orientation and avoid sister chromatid mis-segregation. Fast-assembling microtubules in large blastomeres reach further and search more space to ensure timely chromosome capture during the short mitotic time window. As cleavage progresses and spindle length decreases, slowing down microtubule assembly may negate the simultaneous connection of individual kinetochores to both spindle poles, which would promote merotely and gross chromosome mis-segregation if not corrected. From these observations, we envision that decreasing the microtubule growth rate permits the embryo to not only scale down its spindles, but also globally optimize chromosome segregation during embryogenesis. Previous work in C. elegans embryos demonstrated that the rate of spindle elongation during anaphase [START_REF] Hara | Cell-size-dependent spindle elongation in the Caenorhabditis elegans early embryo[END_REF] and the rate of cortical ring constriction during cytokinesis [START_REF] Carvalho | Structural memory in the contractile ring makes the duration of cytokinesis independent of cell size[END_REF] also decreased as cell volume decreased, which makes the time needed for anaphase spindle elongation and for cytokinetic ring constriction independent of cell size. Future studies should examine whether the rates of other cell division processes also exhibit intrinsic scalability and whether this is a general principle that dictates how cell biological processes scale with cell size. Maton, G., Edwards, F., Lacroix, B., Stefanutti, M., Laband, K., Lieury, T., Kim, T., Espeut, J., Canman, J.C., and Dumont, J. (2015). Kinetochore components are required for central spindle assembly. Nat Cell Biol 17, 697-705.

McBeath, E., and Fujiwara, K. (1990). Microtubule detachment from the microtubule-organizing center as a key event in the complete turnover of microtubules in cells. Eur J Cell Biol 52, 1-16. tests: p<0.0001), except between the 16-cell micromeres, the 32-cell and the >44-64-cell macromeres (p>0.5 in all cases). However, the 16-cell micromeres and the 32-cell macromeres, as well as the 32-cell and the >44-64-cell macromeres differ significantly using a Student t-test (p=0.0004 and 0.0039 respectively), but the 16-cell micromeres do not when compared to the >44-64-cell macromeres (p=0.85). All parameters including sample size, mean and SD are listed in Table S2. ( Growth rate color-coded as in (E). Experimental data in grey. elegans. All parameters including sample size, mean and SD listed in Table S2. (F) A limiting component model explains microtubule growth rate and spindle length scaling with respect to cell volume [START_REF] Decker | Limiting amounts of centrosome material set centrosome size in C. elegans embryos[END_REF][START_REF] Goehring | Organelle growth control through limiting pools of cytoplasmic components[END_REF][START_REF] Good | Cytoplasmic volume modulates spindle size during embryogenesis[END_REF][START_REF] Hazel | Changes in cytoplasmic volume are sufficient to drive spindle scaling[END_REF]Mitchison et al., 2015;[START_REF] Schmoller | The Biosynthetic Basis of Cell Size Control[END_REF]. In this model, one or several positive regulators of spindle microtubule growth (such as CLS-2) bind to microtubule (+)-ends. The microtubule growth rate depends on the number of (+)-end-bound regulators.

Across successive divisions, the concentration of regulators remains constant but the absolute number of regulator molecules decreases with cell volume. If in parallel, the number of spindle microtubules remains constant or decreases in a sub-proportional manner across divisions, the number of regulators becomes progressively limiting relative to the number of microtubule (+)ends. The limited number of regulators in turn restricts spindle microtubule growth rate.

(G) Schematic evolution of spindle microtubule and regulator number as cell size decreases. As cells get smaller, microtubules are shorter but their number remains constant (or decreases slower than the number of regulators). In contrast, the absolute number of regulator molecules is directly proportional to cell volume. If the regulator stimulates microtubule growth (such as CLS-2), microtubule growth rate will progressively decrease as cell volume decreases across successive divisions.

STAR METHODS

Detailed methods are provided in the online version of this paper and include the following:

• KEY RESOURCE TABLE • CONTACT FOR

KEY RESOURCE TABLE CONTACT FOR REAGENT AND RESOURCE SHARING

Further information and requests for resources and reagents should be directed to and will be fulfilled by the Lead Contact, Julien Dumont (julien.dumont@ijm.fr). Requests related to the simulations should also be addressed to Francois Nedelec (nedelec@embl.de).

EXPERIMENTAL MODEL AND SUBJECT DETAILS

Caenorhabditis elegans

C. elegans are small, transparent hermaphroditic soil worms with rapid, invariant and fully characterized development [START_REF] Sulston | Post-embryonic cell lineages of the nematode, Caenorhabditis elegans[END_REF][START_REF] Sulston | The embryonic cell lineage of the nematode Caenorhabditis elegans[END_REF]. Spindle assembly has been extensively studied in C. elegans (Muller-Reichert et al., 2010), primarily because many key proteins and mechanisms are highly conserved with other metazoans. All C. elegans strains were maintained at 23°C or at 16°c for the cyk-1(ts) mutant strain (JCC49 and JDU156) and cultured using standard procedures [START_REF] Brenner | The genetics of Caenorhabditis elegans[END_REF]. Different strains were obtained either by stable single insertion by MosSCI [START_REF] Frokjaer-Jensen | Single-copy insertion of transgenes in Caenorhabditis elegans[END_REF] or by crossing with pre-existing strains. C. elegans worm strains and genotypes are listed in the Key Resources Table.

Paracentrotus lividus

Paracentrotus lividus sea urchins were purchased from the Roscoff Marine Station (Station Biologique de Roscoff, CNRS-UPMC, France) or from the EMBRC-France (European Marine Biological Resource Center, Banyuls-sur-mer, France). Adult individuals were maintained in large Plexiglas tanks filled with artificial seawater at 16°C under constant oxygenation and recurrent volume exchange. Water constants (temperature, phosphates, sulfates, carbonates, nitrogen…) were controlled on a daily basis and maintained within range compatible with sea urchin physiology. Sea urchins were fed with a mix of frozen algae in agar. P. lividus have no sexual dimorphism and sex could only be determined during spawning for gamete collection.

Sex of imaged embryos was therefore not determined.

METHOD DETAILS

RNA-mediated interference (RNAi) and drug treatment in C. elegans

Depletion of C27D9.1 and of CLS-2 (R107.6) in Figure 8 were done by feeding as described by [START_REF] Kamath | Effectiveness of specific RNA-mediated interference through ingested double-stranded RNA in Caenorhabditis elegans[END_REF]. For L1 larvae synchronization, adult worms were bleachtreated (1.2% NaOCl, 250 mM KOH in water; [START_REF] Stiernagle | Maintenance of C. elegans[END_REF] to release embryos. Embryos were allowed to hatch and left to starve in M9 buffer (22 mM KH 2 PO 4 , 42 mM Na 2 HPO 4 , 86 mM NaCl). Synchronized L1 hermaphrodite larvae were grown on regular NGM plates seeded with the OP50 bacterial strain for 44 hours (until they reached the adult stage), and then adult worms were transferred on RNAi feeding plates for at least 24 hours for C27D9.1 and for an increasing time (from 6 to 24h) for CLS-2 respectively. RNAi feeding was performed on NGM plates containing 50 µg/ml ampicillin (Euromedex) and 1 mM IPTG (Isopropyl β-Dthiogalactopyranoside, Euromedex) and seeded with the HT115(DE3) bacterial strain transformed with the empty L4440 vector (control) or containing the C27D9.1 target sequence (corresponding to nt179-1366 of the genomic sequence). Depletion of CLS-2 in Figure 3 was performed by microinjection of the corresponding dsRNA in L4 hermaphrodite larvae as previously described (Fire et al., 1998). The dsRNA targeting cls-2 was synthesized from a purified PCR product (corresponding to nt164-1081 of the genomic sequence, QIAquick PCR purification, Qiagen) that contained the T3 and T7 phage RNA polymerase promoter sequences (T3: taatacgactcactatagg ; T7 : aattaaccctcactaaagg) in 5' and 3', respectively, using the MEGAscript T3 and T7 transcription kits (ThermoFischer Scientific). Single stranded RNAs were purified using the MEGAclear Transcription Clean-Up kit (ThermoFischer Scientific).

Sense and antisense single stranded RNAs were mixed in equimolar concentrations and annealed at 68°C for 10 min followed by 37°C for 30 min. DsRNAs were aliquoted, snap-frozen in liquid nitrogen and stored at -80°C until use. The dsRNA targeting cls-2 was injected in L4 hermaphrodites at a concentration of 1.8 µg/µl. Partial depletion of CLS-2 as obtained 25 to 27 h post-injection at 23°C (Maton et al., 2015). PTR-2 (C32E8.8) depletion was performed in a humid chamber by soaking 25 to 30 L4 hermaphrodite larvae in a 5 µl drop of the corresponding dsRNAs (synthesized as previously and corresponding to nt1886-2904 of the genomic sequence) supplemented with 2.86 mM spermidine (Sigma) and 0.05 % gelatin (Sigma). L4 larvae were soaked at 20°C for 24 hours, then washed twice in M9 medium and transferred on NGM plates for another 24 hours at 20°C before observation. PTR-2-depleted embryos are defective in eggshell formation and are therefore permeable and amenable to drug treatments. To induce a metaphase arrest in zygotes, PTR-2-depleted adult worms were dissected in 20 µM clastolactacystine β-lactone (CLβL, Merck Millipore) in L-15 blastomere culture medium [0.5 mg/mL Inulin (Sigma); 25 mM HEPES pH 7.5; 3 mL Leibowitz L-15 Media and 20% (vol/vol) Heat-Inactivated FBS (Life Technologies)] with 1% DMSO (Euromedex) final concentration.

18.6 and 24.8 µM (molecular weight of α-tubulin = 50,000 g/mol). C. elegans microtubules are composed of 11 protofilaments on average [START_REF] Chalfie | Structural and functional diversity in the neuronal microtubules of Caenorhabditis elegans[END_REF], and tubulin heterodimers are 8 nm long (Nogales et al., 1998). If we assume an average tubulin heterodimer concentration of 22 µM, a C. elegans embryo contains enough tubulin heterodimers to build 21.2 cm of microtubules in total. The metaphase spindle in the 1-celled zygote is composed of around ~20,000 microtubules, which are on average 4 µm long [START_REF] Redemann | C. elegans chromosomes connect to centrosomes by anchoring into the spindle network[END_REF]. This average microtubule length also corresponds to the theoretical average microtubule length <L> calculated from the dynamics parameters in the 1-celled zygote (Table S1). Therefore, in the 1-celled zygote in metaphase, spindle microtubules reach a total length of about 8 cm (20,000 x 4 µm).

We thus concluded that the C. elegans zygote contains enough tubulin heterodimers to build between 2 and 3 mitotic spindles.

Estimation of CLS-2 protein level following RNAi-mediated depletion in the C. elegans embryo by quantitative western blot

Control or RNAi treated gravid C. elegans were collected and washed into M9 buffer containing 0.1% Triton X-100. Worms (100 worms per 100 µl) were then lysed into 1x Laemmli sample buffer (80 mM Tris-HCl pH 6.8, 140 mM 2-Mercaptoethanol, 2.5% SDS, 10% glycerol) by vortexing in presence of 0.7 mm diameter Zirconia beads (BioSpec Products) 3X5 min at 4°C with pauses of 5 min. Lysis efficiency was assessed using a dissection scope. Samples were then incubated 5 min at 95°C before loading on a SDS-PAGE gel. The equivalent of 10 worms were loaded on a SDS-PAGE gel (8%, 37.5:1 acrylamide:bisacrylamide). Proteins were transferred onto a nitrocellulose blotting membrane Protran 0.45 µm (Amersham, GE Healthcare) by liquid transfer. The membrane was incubated with a rabbit polyclonal custom-made anti-CLS-2 antibody (C2a14) diluted at 1µg/ml and then with a DM1α antibody (Sigma) diluted 1/1000 in 5% fat-free milk in Tris-buffered saline (TBS: 50 mM Tris pH 7.5, 150 mM NaCl). Protein bands were revealed with an HRP-labeled goat anti-rabbit (CLS-2) or anti-mouse (DM1α) IgG 1:10,000 (GE Healthcare) and chemoluminescence (ECL Prime, Amersham). Detection was performed on a luminescence image analyzer LAS-4000 (Fujifilm). Band intensities were analyzed using ImageJ.

Tubulin preparation and fluorescent labeling

Tubulin was obtained from pig brains following cycles of polymerization and depolymerization [START_REF] Castoldi | Purification of brain tubulin through two cycles of polymerization-depolymerization in a high-molarity buffer[END_REF]. Tubulin was then labeled with NHS-ester-ATTO 565 (ATTO-TEC) and further purified through two polymerization/depolymerization cycles [START_REF] Hyman | Preparation of marked microtubules for the assay of the polarity of microtubule-based motors by fluorescence[END_REF].

Two-photon live microscopy of C. elegans embryos

Embryo and blastomere volume measurements were made from Z-stacks of 1-to 16-cell stage embryos expressing a GFP-tagged membrane marker (OD58 strain that expresses the GFP-PHdomain under a pie-1 germline promoter). Gravid worms were dissected in a 5 µl drop of egg salt buffer (ESB, 25 mM HEPES pH 7.3, 118 mM NaCl, 48 mM KCl, 2 mM CaCl 2 , 2 mM MgCl 2 ). Embryos were then transferred between two 3% agarose pads to prevent compression and to minimize refractive index mismatch. The montage was then placed on a glass slide, sealed with paraffin. A well of Valap (petroleum jelly:lanolin:paraffin, 1:1:1) was made around it and filled with water for imaging in immersive conditions. An upright two-photon microscope with a Zeiss Plan APO 20x/NA1.0 water objective was used (Lavision Biotec). GFP was excited with a were fertilized 20 min after ATTO 565-tubulin microinjection (2 mg/ml) by adding a few drops of activated sperm. Live imaging was done using a spinning disk (CSU-W1, Yokogawa) confocal microscope (Leica Microsystems) coupled to an ORCA-Flash4.0 V2 CMOS camera (Hamamatsu). Embryos were maintained and imaged between 18°C and 20°C during and in between acquisitions. All acquisition parameters were controlled by MetaMorph 7 software (Molecular Devices). Images were acquired on a single channel (561 nm excitation) every 1 sec with a single z-plan using a Leica Plan APO 63×/NA1.2 water objective.

Immunostainning of sea urchin embryos

Freshly collected eggs were fertilized in a 140 mm diameter glass container and allowed to develop at 18°C (same as for live imaging). Embryo cleavage and NEBD were monitored by transmitted light on a dissection scope. At NEBD, embryos were fixed following previously described procedures (Foe and von Dassow, 2008;[START_REF] Tanimoto | Shape-motion relationships of centering microtubule asters[END_REF]. Fixation was performed in bulk in 15 ml polypropylene conical tubes. Embryos were first fixed for 70 min in 100 mM Hepes, pH 6.9, 50 mM EGTA, 10 mM MgSO4, 2% formaldehyde, 0.2% glutaraldehyde, 0.2% Triton X-100, and 400 mM dextrose. They were then rinsed three times for 10 min in PBS and placed in freshly made 0.1% NaBH4 in PBS for 45 min. Embryos were rinsed again with PBS and PBS O.1% Triton X-100 (PBT). For microtubule immunostaining, embryos were incubated overnight at 4°C with a primary anti-α-tubulin antibody (DM1α, Sigma-Aldrich) at a 1:5000 dilution, and washed 3 times for 30 min in PBT. Embryos were then incubated overnight in secondary antibody (goat anti-mouse DyLight 550, Jackson ImmunoResearch) at a 1:1000 dilution in PBT. Chromatin was stained using DAPI at a 1:5000 dilution in PBS. Embryos were then mounted in 0.5% n-propyl gallate in a 9:1 solution of glycerol/1M TRIS ph8.0.

Image analysis

Two-photon acquisitions of GFP-PH (membrane marker) during C. elegans embryonic development were analyzed using Imaris software (Bitplane). C. elegans blastomere volumes were extracted after semi-automated surface reconstruction. P. lividus blastomere volumes were estimated from experimentally measured blastomere diameters. Spinning-disk confocal images were analyzed using the Fiji package (http://fiji.sc/; https://imagej.nih.gov/ij/). Spindle length was estimated as the aster-to-aster distance [START_REF] Crowder | A comparative analysis of spindle morphometrics across metazoans[END_REF] on GFP-tubulin images.

Metaphase plate thickness and centrosome radius were measured on segmented mCherry-histone and GFP-β-tubulin images in C. elegans embryos or ATTO 565-tubulin images in P. lividus embryos. At each cleavage stage in C. elegans embryos, a 10% or 40% grey level threshold were applied on mCherry-histone or GFP-β-tubulin images respectively. In P. lividus embryos, a 30% grey level threshold was applied on ATTO 565-tubulin images for centrosome radius measurements. These thresholds were selected to obtain the sharpest limit between the metaphase plate histone signal or the centrosome and the cytoplasmic background with minimal erosion of the signal. Measured values were used in Cytosim simulations to build in silico spindle 3D models.

Analysis of microtubule dynamics

Individual embryos were imaged at a single stage of cleavage and for less than 10 min to avoid photoxicity-induced bias [START_REF] Lacroix | Microtubule dynamics followed through cell differentiation and tissue biogenesis in C. elegans[END_REF][START_REF] Lacroix | Identification of microtubule growth deceleration and its regulation by conserved and novel proteins[END_REF]. Kymographs were traced from time-lapse sequences using the 'Multi kymograph' plugin (http://imagej.net/Multi_Kymograph) in Fiji. Polymerization and depolymerization rates, as well as catastrophe and rescue frequencies, were extracted from these kymographs by manual tracking and semi-automated parameter extraction using homemade macros in Fiji and Excel (Microsoft) software. Catastrophe and rescue frequencies were defined as the inverse of the average growth time or shrinkage time, respectively [START_REF] Desai | Microtubule polymerization dynamics[END_REF][START_REF] Komarova | Life cycle of MTs: persistent growth in the cell interior, asymmetric transition frequencies and effects of the cell boundary[END_REF][START_REF] Walker | Dynamic instability of individual microtubules analyzed by video light microscopy: rate constants and transition frequencies[END_REF]. Although this method could potentially overestimate catastrophe and rescue occurrences (which would be identical in all tested experimental conditions), it allows estimating both parameters independent of microtubule pausing, moving out-of-focus during live imaging or entering in the fluorescence-saturated centrosome area.

Cytosim simulations

All simulations were performed in 3D using Cytosim (www.cytosim.org;Nedelec F, 2007).

Cytosim simulations have already been used to show how polymerization forces and thus microtubules dynamics could affect centrosome positioning [START_REF] Letort | Centrosome centering and decentering by microtubule network rearrangement[END_REF]. Following this approach, we aimed for a minimal model in which spindle length, corresponding to the distance between two asters, would be influenced by microtubules dynamic behavior. A detailed list of Cytosim parameters for each object in the simulations is presented in Table S3. Spindle poles were modeled using microtubules radiating radially from a sphere (asters). The surface of the sphere contains a preset number of nucleation sites, at which microtubules are anchored at their minus-ends constraining their position and orientation. The minus-ends are static, while the plusends may grow or shrink, stochastically switching between these states following the usual phenomenological model of dynamic instability. The metaphase plate was represented as a fixed and rigid disc positioned orthogonally at the center of the "cell". Although microtubules were excluded from inside this plate, microtubule-associated molecules (called "singles", each made of one "hand") anchored on this disc and capable of tracking growing microtubule ends were used to mimic the chromokinesins present on chromosomes, as well as the capture of microtubules by pro-metaphase kinetochores. The primary function of these microtubuleassociated molecules is to prevent microtubules from sliding on the surface of the "metaphase plate". At the start of every simulation, the two asters were positioned symmetrically 2 µm away from the "metaphase plate" on each side.

The input growth rate (! 0 ) varied within the range of experimental measurements made in C. elegans embryos from 1-to 16-cell stage. The effective microtubule growth rate was set to decrease exponentially under an opposing force as

! ! = ! 0 ! -! ! !
, where ! 0 is the input growth rate and!! ! is the force at which microtubule polymerization stalls (Dogterom and Yurke, 1997).

Consequently, microtubules encountering the metaphase plate grew dramatically slower, in agreement with in vivo measurements at the kinetochore (Maddox et al., 2003;[START_REF] Tirnauer | EB1 targets to kinetochores with attached, polymerizing microtubules[END_REF]. Further, in the first simulation that contained both astral and spindle microtubules, a force-dependent increase in the catastrophe rate

! !"# = ! !"# !"#$$ 1!+! ! !"# !"#$$ ! !"# 0 !-1 !! ! ! 0
(see also Table S3)

induced microtubule shrinking soon after cortical or metaphase plate contact. This forcedependent microtubule shrinking was not implemented in the second simulation (with only spindle microtubules). So, the effective average growth rate of microtubules in our simulations represented the mean rate of free growing microtubules and stalled microtubules at the metaphase plate (or at the cortex) (Figure S4A).

Two different spindle models were tested, as described below. (Figure 5A-C): This model included 500 microtubules per aster. 400 microtubules were allowed to grow uniformly in space, and 100 microtubules per aster were constrained in a cone directed toward the metaphase plate to mimic the higher microtubule density observed in vivo in the spindles of C. elegans embryos. C. elegans blastomeres were represented by 3D ellipsoids. Cell volume, metaphase plate thickness and radius were scaled together with respect to the input microtubule growth rate using realistic values extrapolated from our experimental measurements (TableS2B). Scaling to the input growth rate was done assuming a linear proportionality between microtubule growth rate and other dimensions. Due to their initial proximity to the metaphase plate, spindle microtubules were more likely to be stalled and therefore displayed a lower effective average growth rate than astral microtubules (Figure S4B). This was particularly true for higher initial rates and was reminiscent of the difference in the growth rates we measured in vivo between astral and spindle microtubules. This mild difference in the astral and spindle effective growth rates was sufficient to induce a significant deviation of the average microtubule length reached by the two populations (Figure S4C). The average length difference was not evident at low initial growth rates but was particularly clear for rates above 0.3 µm/sec. This result is in agreement with the evolution of <L> for astral and spindle microtubules calculated from in vivo measured parameters, which became closer between the two types of microtubules as cells get smaller (Table S1). The faster decrease of the average length of astral compared to spindle microtubules is likely due to increasing cortical surface to cell volume ratio as cleavage progresses. Indeed, the cortical surface decreases slower than the cell volume, so that astral microtubules are more likely to encounter the cortex and shrink, as blastomeres get smaller. Our simulation therefore accurately recapitulates two key features of the dynamic behavior of astral and spindle microtubules in vivo during embryonic cleavage: 1) spindle microtubules grow slower and are, on average, shorter than astral microtubules during early cleavages and 2) these differences tend to fade as blastomeres become smaller (Figure S4B,C). (B) Formulas used for the calculation of J (estimated average growth velocity of a microtubule population) and <L> (estimated microtubule average length) from [START_REF] Verde | Control of microtubule dynamics and length by cyclin A-and cyclin B-dependent kinases in Xenopus egg extracts[END_REF].

D E

(C) Average theoretical microtubule length <L> calculated using the formula in (B) and plotted over the experimentally measured average spindle length in the indicated conditions (GFP-tagged β-tubulin under mex-5: red, mCherry-tagged β-tubulin under pie-1: purple, error bars, SD). Since microtubules were in a bounded state (J<0) under all conditions, <L> could be calculated.

  Dogterom, M., and Yurke, B. (1997). Measurement of the force-velocity relation for growing microtubules. Science 278, 856-860. Dumont, S., and Mitchison, T.J. (2009a). Compression regulates mitotic spindle length by a mechanochemical switch at the poles. Curr Biol 19, 1086-1095. Dumont, S., and Mitchison, T.J. (2009b). Force and length in the mitotic spindle. Curr Biol 19, R749-761. Encalada, S.E., Willis, J., Lyczak, R., and Bowerman, B. (2005). A spindle checkpoint functions during mitosis in the early Caenorhabditis elegans embryo. Mol Biol Cell 16, 1056-1070. Espiritu, E.B., Krueger, L.E., Ye, A., and Rose, L.S. (2012). CLASPs function redundantly to regulate astral microtubules in the C. elegans embryo. Dev Biol 368, 242-254. Faire, K., Waterman-Storer, C.M., Gruber, D., Masson, D., Salmon, E.D., and Bulinski, J.C. (1999). E-MAP-115 (ensconsin) associates dynamically with microtubules in vivo and is not a physiological modulator of microtubule dynamics. J Cell Sci 112 ( Pt 23), 4243-4255. Fire, A., Xu, S., Montgomery, M.K., Kostas, S.A., Driver, S.E., and Mello, C.C. (1998). Potent and specific genetic interference by double-stranded RNA in Caenorhabditis elegans. Nature 391, 806-811. Foe, V.E., and von Dassow, G. (2008). Stable and dynamic microtubules coordinately shape the myosin activation zone during cytokinetic furrow formation. J Cell Biol 183, 457-470.Lu, C.,Srayko, M., and Mains, P.E. (2004). The Caenorhabditis elegans microtubule-severing complex MEI-1/MEI-2 katanin interacts differently with two superficially redundant beta-tubulin isotypes. Mol Biol Cell 15, 142-150. Maddox, P., Straight, A., Coughlin, P.,Mitchison, T.J., and Salmon, E.D. (2003). Direct observation of microtubule dynamics at kinetochores in Xenopus extract spindles: implications for spindle mechanics. J CellBiol 162, 377-382. Maiato, H., Rieder, C.L., and Khodjakov, A. (2004). Kinetochore-driven formation of kinetochore fibers contributes to spindle assembly during animal mitosis. J Cell Biol 167, 831-840. Marshall, W.F. (2015a). How Cells Measure Length on Subcellular Scales. Trends Cell Biol 25, 760-768. Marshall, W.F. (2015b). Subcellular size. Cold Spring Harb Perspect Biol 7.

  Mitchison, T., andKirschner, M. (1984). Dynamic instability of microtubule growth. Nature 312, 237-242.Mitchison, T.J.,Ishihara, K., Nguyen, P., and Wuhr, M. (2015). Size Scaling of Microtubule Assemblies in Early Xenopus Embryos. Cold Spring Harb Perspect Biol 7, a019182.Muller-Reichert, T.,Greenan, G., O'Toole, E., and Srayko, M. (2010). The elegans of spindle assembly. Cell Mol Life Sci 67, 2195-2213. Nance, J. (2005). PAR proteins and the establishment of cell polarity during C. elegans development. Bioessays 27, 126-135. Nedelec F, F.D. (2007). Collective Langevin dynamics of flexible cytoskeletal fibers. New J Phys 9, 427-427. Nogales, E., Wolf, S.G., and Downing, K.H. (1998). Structure of the alpha beta tubulin dimer by electron crystallography. Nature 391, 199-203. O'Farrell, P.H., Stumpff, J., and Su, T.T. (2004). Embryonic cleavage cycles: how is a mouse like a fly? Curr Biol 14, R35-45. Parisi, E., Filosa, S., De Petrocellis, B., and Monroy, A. (1978). The pattern of cell division in the early development of the sea urchin. Paracentrotus lividus. Dev Biol 65, 38-49. Parsons, S.F., and Salmon, E.D. (1997). Microtubule assembly in clarified Xenopus egg extracts. Cell Motil Cytoskeleton 36, 1-11. Picone, R., Ren, X., Ivanovitch, K.D., Clarke, J.D., McKendry, R.A., and Baum, B. (2010). A polarised population of dynamic microtubules mediates homeostatic length control in animal cells. PLoS Biol 8, e1000542.

  FIGURE LEGENDS

Figure 2 .

 2 Figure 2. Astral and Spindle Microtubule Dynamics Vary with Cell Volume During C.

Figure 3 .

 3 Figure 3. Spindle Length Scales with Spindle, but not Astral, Microtubule Growth Rate

Figure 4 .

 4 Figure 4. Spindle Length Scales with Cell Volume and Microtubule Growth Rate During

  Horizontal bars, means; error bars, SD; n(cells/stage)≥5, n(microtubules/stage)≥55). (C) Mean growth rate for spindle microtubules plotted at each cleavage stage (1-to >44-64-cell stage) over the average corresponding cell volume. (Error bars, SD). (D) Mean spindle length plotted at each stage (1-to >44-64-cell stage) over the corresponding average spindle microtubule growth rate. Dotted blue line and black lines represent the linear regression and 95% confidence interval respectively. Pearson correlation coefficient (r 2 ) is indicated at the top of the graph because p ≤ 0.01. (Error bars, SD).

Figure 5 .

 5 Figure 5. Microtubule Growth Rate Scales Spindle Length in Computational 3D Spindle

Figure 6 .

 6 Figure 6. Spindle Assembly Rate Scales with Spindle Microtubule Growth Rate During C.

Figure 7 .

 7 Figure 7. Microtubules and Spindle Length Adaptation to Cell Volume in P. lividus and C.

  (B) Mean growth rate for spindle microtubules plotted at each cleavage stage over the corresponding average spindle length. (Bars, SD). (C) Mean growth rate for spindle microtubules plotted at each cleavage stage over the average corresponding cell volume. (Bars, SD). (D) Mean spindle length plotted over the cube root of the average cell volume on a log 2 -log 2 scale. (Error bars, SD). (E) Average theoretical microtubule length <L> plotted over the experimentally measured spindle length. (Error bars, SD). (F) (Left) Average theoretical microtubule length <L> plotted over the average cell volume. (Right) Magnification of the graph for the smaller cells (volume<125 pL). (Error bars, SD).

Figure

  Figure 8. A Limiting Component(s) Model for Microtubule Growth Rate and Spindle

  REAGENT AND RESOURCE SHARING • EXPERIMENTAL MODEL AND SUBJECT DETAILS o Caenorhabditis elegans o Paracentrotus lividus • METHOD DETAILS o RNA-mediated interference (RNAi) and drug treatment in C. elegans o Estimation of the tubulin heterodimer concentration in the C. elegans embryo by quantitative western blot o Estimation of CLS-2 protein level following RNAi-mediated depletion in the C. elegans embryo by quantitative western blot o Tubulin preparation and fluorescent labeling o Two-photon live microscopy of C. elegans embryos o Spinning-disc live microscopy of C. elegans embryos o Injection and Imaging of sea urchin embryos o Immunostainning of sea urchin embryos o Image analysis o Analysis of microtubule dynamics o Cytosim simulations • QUANTIFICATION AND STATISTICAL ANALYSIS • DATA AND SOFTWARE AVAILABILITY o Cytosim

  Figure 2

  Figure 5 A B

  Figure S1

  Figure S3

Figure S3 .

 S3 Figure S3. Probing the Allometric Relationship Between Microtubule Dynamics, Spindle Length/Width and Cell Volume in the P. lividus Embryo. Related to Figure 4

Spindle MT growth rate (µm/s) in P. lividus using different probes

	Spindle length (
		ATTO 565-tubulin		3XmCherry-EMTB
	stage	mean (µm/s)	SD	N	mean (µm/s)	SD	N
	1-cell	0.25	0.04	276	0.24	0.04	381
	2-cell	0.23	0.04	391	0.23	0.05	83
	4-cell	0.18	0.04	187	0.17	0.03	173
	8-cell	0.15	0.03	500	0.16	0.03	136
	16-cell	0.13	0.03	341	0.14	0.03	182

µm) in P. lividus embryos using different probes

		fixed embryos		ATTO 565-tubulin		3XmCherry-EMTB
	stage	mean (µm)	SD	N	mean (µm)	SD	N	mean (µm)	SD	N
	1-cell	22.75	1.34	9	21.61	2.02	13	22.28	1.72	29
	2-cell	18.36	2.11	20	19.68	2.02	9	20.33	1.14	8
	4-cell	16.74	1.77	4	17.87	2.77	7	18.72	1.52	16
	8-cell	16.27	1.45	16	16.14	2.05	17	17.21	0.6	14
	16-cell	-	-	-	13.99	3.92	7

14.191.12

ACKNOWLEDGMENTS

We thank all members of the Dumont lab for support and advice, and Kimberley Laband for critical reading of the manuscript. We are grateful to Patricia Moussounda for providing technical support. We thank Life Science Editors for editing assistance. We acknowledge the ImagoSeine core facility of the Institut Jacques Monod, member of IBiSA and France-BioImaging (ANR-10-INBS-04) infrastructures. We thank Nicolas Tissot (ImagoSeine) for his help with the 2-photon microscopy. We thank Julie Ahringer (The Gurdon Institute, University of Cambridge, UK) for the generous gift of the JA1559 C. elegans strain, and George Von Dassow, University of Oregon) for providing recombinant 3xmCherry-EMTB. Some strains were provided by the CGC, which is funded by NIH Office of Research Infrastructure Programs (P40 OD010440). EMBRC-France is supported by the Investments of the Future program under reference ANR-10-INBS-02. We thank Pascal Romans (UPMC, Banyuls-sur-Mer, France) and Anaëlle Pierre (IJM, Paris, France) for technical assistance with sea urchins. We thank Dmitry Ershov (IJM, Paris, France) for his help with MATLAB. We are grateful to Jean-Claude Labbe (IRIC) for initial technical support and discussions. B.L. was originally supported by a postdoctoral fellowship from the Fondation pour la Recherche Médicale (FRM ARF20140129055). JS and NM are supported by the European Research Council (CoG Forcaster N° 647073). This work was supported by CNRS and University Paris Diderot and by grants from the Agence Nationale pour la Recherche (ANR-16-CE13-0020-01), the Mairie de Paris (Emergence) and the Fondation pour la Recherche Médicale (FRM DEQ20160334869) to J.D.

Data availability

All data presented in this manuscript are available upon request to the lead author (julien.dumont@ijm.fr).

DECLARATION OF INTERESTS

The authors declare no competing interests.

Estimation of the tubulin heterodimer concentration in the C. elegans embryo by quantitative western blot

C. elegans early embryos (1-to ~64-cell stage) were extracted from synchronized adult N2 worms by bleaching as described earlier in the "RNA-mediated interference (RNAi) and drug treatment in C. elegans" method section. Embryos were then resuspended in M9 buffer. The number of embryos per volume and their approximate number of blastomeres (stage) were estimated under a dissection scope (Nikon). Embryos were then lysed into 1x Laemmli sample buffer (80 mM Tris-HCl pH 6.8, 140 mM 2-Mercaptoethanol, 2.5% SDS, 10% glycerol) by vortexing in presence of 0.7 mm diameter Zirconia beads (BioSpec Products) 3 times 5 min at 4°C with pauses of 5 min. Lysis efficiency was assessed using a dissection scope. Samples were then incubated 5 min at 95°C before loading on a SDS-PAGE gel. The equivalent of ~1120 or ~2240 embryos were loaded on a SDS-PAGE gel (10%, 37.5:1 acrylamide:bisacrylamide) together with increasing amounts of porcine brain tubulin purified as described in "Tubulin preparation and fluorescent labeling" (Figure S5). C. elegans and porcine brain tubulin samples were treated similarly. Proteins were transferred onto a nitrocellulose blotting membrane Protran 0.45 µm (Amersham, GE Healthcare) by liquid transfer. Membrane was incubated with DM1α antibody (Sigma) diluted 1/1000 in 5% fat-free milk in Tris-buffered saline (TBS: 50 mM Tris pH 7.5, 150 mM NaCl). Protein bands were revealed with an HRP-labeled goat anti-mouse IgG 1:10,000 (GE Healthcare) and chemoluminescence (ECL SuperSignal West Pico, ThermoScientific). Detection was performed on a luminescence image analyzer . Band intensities were analyzed using ImageJ. The amount of α-tubulin contained per embryo was estimated to be between 2.04 and 2.73x10 -11 g. This amount corresponds to a concentration of 0.93 to 1.24 g/L (Embryo volume = 2.2x10 -11 L, Figure S1 and Table S1) or pulsed laser at 920 nm. Emission at 535 nm was collected with a GaAsP detector (Lavision Biotec). The entire embryo was imaged with 1 µm Z-sectioning and 190 nm lateral sampling.

Spinning-disc live microscopy of C. elegans embryos

Gravid worms were dissected in egg salt buffer (ESB, see above). Embryos were transferred on a 3% agarose pad between a glass slide and a coverslip. The montage was then sealed with Valap.

Live imaging was done using a spinning-disk (CSU-X1, Yokogawa) confocal microscope (Roper Scientific) coupled to a CoolSnap HQ2 CCD camera (Photometrics) and all acquisition parameters were controlled by MetaMorph 7 software (Molecular Devices). For microtubule dynamics parameter extraction, images were acquired on a single channel (491 nm excitation) every 0.5 sec with a single z-plan using a Nikon CFI APO LBDA S 60x/NA1.4 oil objective with no binning. To measure spindle assembly timings, images were acquired on two channels sequentially (491 and 561 nm excitations) every 5 sec with 11 z-plan at 1 µm intervals using a Nikon CFI APO LBDA S 40×/NA1.25 water objective with no binning. Maximal projections are presented.

Injection and Imaging of sea urchin embryos

Gametes were collected by intracoelemic injection of 0.5M KCl. Eggs were washed several times in fresh seawater, kept at 12-14°C and used within 24h. Sperm were kept concentrated for several days at 4°C. Upon use, the sperm suspension was diluted 1000 times in fresh seawater and activated by vigorous aeration. Freshly collected P. lividus eggs were dejellied by pouring through a 80 µm pore Nitex mesh (Sefar). Dejellied eggs were immobilized on a protamine (Sigma) treated 60 mm diameter glass-bottom dish for both microinjection and imaging. Eggs (Figure 5D-F): 50 microtubules were constrained in a spindle-shaped cone to reflect the C. elegans embryo spindle geometry (Table S2). Importantly, increasing or decreasing the number of microtubules had no effect on the final outcome of the simulations (data not shown).

The two asters do not include astral microtubules and grow in an infinite space without a cell boundary.

QUANTIFICATION AND STATISTICAL ANALYSIS

All graphs were made in Prism 6 (GraphPad Software). Statistical analyses, including Student ttests, one-way ANOVA multiple comparisons, linear regressions and Pearson and Spearman correlation tests were performed in Prism 6 (GraphPad software). Microtubule dynamics parameters have different variances, so we used the unequal variance unpaired t-test with the Welch's correction for normally distributed populations with unequal standard deviation. Tukey or Dunnett tests were performed for multiple comparisons following one-way ANOVA. In τ vs growth rate Curve fitting Simulations. Related to Figure 5 (A) Simulated effective growth rate of spindle microtubules growing freely in the cytoplasm (triangles), captured at metaphase plate (squares), or the average of both populations (plain circles) plotted over the input growth rate. Color-coding of the input growth rate indicated at the bottom, from magenta (0.42 µm/s) to dark red (0.15 µm/s). See Table S3 and Methods for more details.

(B) Simulated effective growth rate of astral (triangles) and spindle (squares) microtubules plotted over the input growth rate. Color-coding of the input growth rate indicated at the bottom, from magenta (0.39 µm/s) to dark red (0.17 µm/s).

(C) Simulated average astral (triangles) and spindle (squares) microtubule lengths plotted over the input growth rate. Color-coding is the same as in (B).

(D) Spindle assembly timing is independent of the input microtubule growth rate in the computational 3D simulations. (Left) Simulated spindle length plotted over time at various microtubule growth rates for the simulation shown in Figure 5A. Color-coding of the growth rate indicated at the bottom, from magenta (0.39 µm/s) to red (0.17 µm/s). (Center) Example of curve fitting for one input growth rate (0.39 µm/s). In silico data fitted to single exponential functions Forward primer for production of dsRNA against CLS-2 (R107.6) using L4440 feeding vector in HT115 bacteria:

aaatcgtcctcgaacattgg.

https://www.sourcebio science.com/products/ life-scienceresearch/clones/rnairesources/c-elegansrnai-collectionahringer/ SourceBioscience Location III/4J10.

Reverse primer for production of dsRNA against CLS-2 (R107.6) using L4440 feeding vector in HT115 bacteria:

tgatgggttttgacaaacga.