Three-dimensional geometry controls division symmetry in stem cell colonies.

Proper control of division orientation and symmetry, largely determined by spindle positioning, is essential to development and homeostasis. Spindle positioning has been extensively studied in cells dividing in 2-dimensional (2D) environments and in epithelial tissues, where proteins such as NuMA orient division along the cell's interphase long axis. However, little is known about how cells control spindle positioning in 3-dimensional (3D) environments, such as early mammalian embryos and a variety of adult tissues. Here, we use mouse embryonic stem (ES) cells, which grow in 3D colonies, as a model to investigate division in 3D. We observe that at the periphery of 3D colonies, ES cells display high spindle mobility and divide asymmetrically. Our data suggest that enhanced spindle movements are due to unequal distribution of the cell-cell junction protein E-Cadherin between future daughter cells. Interestingly, when cells progress towards differentiation, division becomes more symmetric, with more elongated shapes in metaphase and enhanced cortical NuMA recruitment in anaphase. Altogether, this study suggests that in 3D contexts, the geometry of the cell and its contacts with neighbors control division orientation and symmetry.

elegans embryo divides asymmetrically in size and content, which determines the anterior-posterior axis of the future animal (Gönczy and Rose, 2005). As another example, asymmetric division of neuroblasts in Drosophila and C. elegans allows the generation of a stem cell and a future differentiated cell (Cabernard and Doe, 2009;Ou et al., 2010). Division orientation is also important to cell fate during mammalian development. In particular, division orientation in 8-and 16-cell mouse embryos has been shown to direct cell positioning, and in turn cell signaling and fate (Korotkevich et al., 2017;Maître et al., 2016;Niwayama et al., 2019).
Notably, in early development, cell division often occurs in a 3-dimensional (3D) context, where cells are surrounded by neighbors in all directions. Understanding division orientation and symmetry in 3D is thus crucial to investigate the mechanisms regulating cell fate in development. Yet, the regulation of the orientation and symmetry of cell division have mostly been studied in isolated cells cultured on 2dimensional (2D) substrates or in cells in other 2D contexts, such as epithelial sheets.
In such 2D contexts, division orientation and symmetry depend primarily on the positioning of the mitotic spindle, which relies on cross-talk between the spindle and spindle-positioning proteins at the metaphase cell cortex (McNally, 2013). In many cells types, spindle positioning follows the Hertwig, or "long-axis", rule (Hertwig, and division asymmetry correlate with heterogeneous distribution of the cell-cell junction protein E-Cadherin between the two prospective daughter cells. Finally, we show that at the exit from naïve pluripotency, when cells spread and become responsive to lineage differentiation signals, cell division becomes more symmetric, and that concomitantly, the key regulator of spindle positioning NuMA becomes recruited to the cell cortex at anaphase. Together, our data strongly suggest that the division machinery significantly differs between 2D and 3D environments.

Results
ES cells growing at the periphery of 3D colonies display strong size asymmetries at cell division To investigate spindle positioning and division symmetry in a 3D context, we used mouse ES cells as a model system. When plated on a gelatin substrate in the pluripotency sustaining medium 2i+LIF (Mulas et al., 2019;Ying et al., 2008), ES cells grow in 3D colonies usually a few cells thick (Fig. S1A,B, Movie 1-4), and are able to exit naïve pluripotency similarly to the cells in the peri-implantation blastocyst (Kalkan et al., 2017). To track cell division dynamics, we used an ES cell line expressing histone 2B (H2B) tagged with RFP (Cannon et al., 2015). We tested the ability of this line to contribute to an embryo by injecting H2B-RFP ES cells into a blastocyst of an albino C57BL/6 mouse. We observed that the chimeric mouse coat displayed considerable brown patches, showing that the injected cells integrated well into the blastocyst and significantly contributed to the embryo (See Methods and Fig.   S2A). We then labeled cell membranes using CellMask TM and monitored 3D cellular volume throughout cell division, using a custom plugin that we previously developed Journal of Cell Science • Accepted manuscript (Smith et al., 2016). Our previous work has shown that while single isolated ES cells divide relatively symmetrically, ES cells dividing in 3D colonies can display significant size asymmetry between daughter cells (Chaigne et al., 2020). To test the influence of the 3D environment on cell division, we asked whether the level of asymmetry depended on cell position and on the orientation of the division with respect to the colony (Fig. 1A,B). We defined the division asymmetry ratio as ratio of the volume of the smaller future daughter cell over the volume of the bigger daughter cell 15 min after cytokinesis onset (Fig. S3B).
We found that ES cells where division took place entirely inside the colony divided mostly symmetrically, similarly to isolated ES cells; however, ES cells dividing at the periphery of colonies often displayed significant size asymmetry between daughter cells (Fig. 1A,B, Movie 5,6). The proportion of peripheral divisions depended on the colony size, but even large colonies displayed a significant number of cells dividing at the periphery (Fig. S2C). Cells dividing at the periphery of the colonies with the spindle oriented perpendicular to the colony border ("radial" division orientation) displayed highest size asymmetries between daughter cells (Fig. 1B). For these cells with radial division orientation, there was no preferential direction of the asymmetry; indeed, the smallest of the 2 daughter cells had the same probability to be positioned away from or towards the colony center (Fig. 1C,D, Fig. S2D). Together, these data indicate that cell division introduces significant size heterogeneity in mouse ES cells growing in 3D colonies, and that division asymmetries are highest for cells dividing radially on the surface of the colonies.

Journal of Cell Science • Accepted manuscript
Size asymmetries at division are not the result of cortical contractions We then explored the mechanisms underlying asymmetric division in ES cells. We observed that cells at the colony periphery displayed significant shape instabilities characterized by strong contractions and blebbing (Fig. S3A, Movie 7). Previously, myosin-driven contractions at the cell poles during cytokinesis have been shown to lead to asymmetric division in neuroblasts (Cabernard et al., 2010;Ou et al., 2010).
We thus hypothesized that polar surface contractions and instabilities could be responsible for division asymmetries in ES cells. To assess this hypothesis, we first quantified the occurrence of polar shape instabilities in ES cells dividing at different locations in the 3D colonies. Visual assessment of 3D stacks suggested that 57% of dividing cells showed unstable shapes during cytokinesis (Movie 7). To assess shape instabilities in a more unbiased manner, we further analyzed cell curvature dynamics in 2D, focusing on the midplane of each prospective daughter cell (see Methods). This analysis was consistent with our visual assessment of 3D stacks, with the cells visually classified as unstable displaying significantly more variable contours ( Fig. S3B-D). Cells dividing radially displayed more shape instabilities (Fig.   S3E), and cells displaying significant shape instabilities also displayed higher division asymmetries (Fig. S3F).
We then asked whether the observed shape instabilities might drive division asymmetry. We noticed that Myosin-II accumulated on the outside of ES cell colonies (Fig. S3G,H), suggesting that high levels of myosin at the cell poles could cause polar shape instabilities, as previously reported (Cabernard et al., 2010;Sedzinski et al., 2011). We thus interfered with myosin activity to reduce polar contractions and shape instabilities. We treated cells with 1 M of the myosin-activity inhibitor Blebbistatin, which at such low doses slowed down cytokinesis (Fig. S3I,

Journal of Cell Science • Accepted manuscript
Movie 8) but did not prevent cell division. Blebbistatin treatment considerably reduced cytokinetic cell shape instabilities (Fig. S3J, Movies S8), but did not reduce division asymmetries (measured in 3D, Fig. S3K). Therefore, polar contractions are unlikely to be responsible for division asymmetries in mouse ES cell colonies.
Size asymmetries at division correlate with high spindle mobility in metaphase In order to further investigate how division asymmetries arise in ES cells at the colony surface, we monitored the dynamics of the mitotic spindle, which is key in positioning the cleavage furrow. We used the position and orientation of the mitotic plate in cells expressing H2B-RFP, as a proxy for spindle position. We performed fast 3D live imaging and tracking of the metaphase plate in ES cells dividing at the periphery of or inside colonies ( Fig. 2A,B, Movies S9,10). To quantify spindle dynamics, we calculated the 3D Mean Squared Displacement (MSD, a measure of how much the metaphase plate moves during increasing time intervals) of the position of the center of the metaphase plate in the reference frame of the cell, with respect to the final position of the metaphase plate at anaphase. Metaphase plate position displayed extensive fluctuations in 3D, particularly in cells dividing at the periphery of the colony. Indeed, metaphase plates for cells dividing at the periphery of the colony displayed a linear increase of the MSD in time, consistent with an unconstrained diffusion of the spindle, whereas metaphase plates inside colonies showed a plateau or even a decrease of the MSD with increasing time interval, consistent with constrained spindle diffusion (Fig. 2C). This supports the possibility of decreased regulation of spindle position for cells dividing at the colony periphery. We then quantified metaphase plate angular dynamics in 3D in the reference frame of the colony (Fig. 2D,E). Interestingly, we observed that the metaphase plate also displayed extensive rotations, which significantly decreased in the 10-15 min prior to anaphase in cells dividing inside colonies, but not in cells dividing at the colony periphery ( Fig. 2D,E). We did not notice any difference in spindle radial motility between cells dividing radially and orthoradially (Fig. 2E). Differences in cell or spindle volumes could lead to differences in available space for movement, which could in turn affect spindle dynamics. However, we found no difference in either cell or spindle volumes between cells dividing inside colonies or at the periphery of colonies (Fig. 2F), and the asymmetry ratio between daughter cells showed no correlation with cell volume in metaphase (Fig. 2G). Furthermore, we verified that, as described in other cell types (Cadart et al., 2014;Son et al., 2015;Zlotek-Zlotkiewicz et al., 2015), ES cells display volume swelling at the beginning of cell division, and observed that the relative volume change was comparable in cells dividing inside or at the periphery of the colony (Fig. 2H,I). Finally, we tested that the increased mobility of the spindle in cells dividing peripherally was not simply due to enhanced division duration or delays in the satisfaction of the spindle assembly checkpoint (SAC). We measured division duration (from nuclear envelope breakdown to anaphase onset) and found no significant difference between cells dividing inside or at the periphery of colonies (Fig. 2J,K, DMSO). We then treated cells with 100 nM of the SAC inhibitor Reversine. As expected, Reversine treatment lead to an increase in the number of cells dividing with lagging chromosomes (Fig. 2J,L) and an overall shortening of division duration (Fig. 2K). However, we found no difference in division duration between Reversine-treated cells dividing inside and at the periphery of colonies (Fig. 2J,K), suggesting that SAC-independent phases of cell division proceed with similar dynamics in the two configurations. Together, these experiments strongly suggest that there are no delay in SAC activation in cells Journal of Cell Science • Accepted manuscript dividing peripherally. Altogether, these results show that cell division asymmetry correlates with high spindle mobility and suggest that enhanced spindle mobility at the colony periphery is not simply caused by differences in cell geometry, division duration or SAC satisfaction.
Size asymmetries at division correlate with asymmetrically distributed E-Cadherin cell-cell contacts We then hypothesized, based on our observation that asymmetric divisions particularly arise at the periphery of colonies (Fig. 1B), that asymmetries in E-Cadherin distribution between prospective daughter cells could be responsible for division asymmetries. Indeed, E-Cadherin accumulates at cell-cell junctions and therefore is more uniformly localized around cells inside colonies than around cells at the colony surface (Fig. S4A,B). We thus plated cells on E-Cadherin-coated substrates, which lead to naïve ES cells spreading in 2D colonies (Fig. 3C, Movie 11,12). Thus, as cells division is oriented parallel to the substrate in 2D colonies, both daughter cells are exposed to comparable levels of E-cadherin throughout division, through contact of their bottom surface with the substrate. We first verified that plating ES cells on E-Cadherin abolished the difference in E-Cadherin cell-cell junction heterogeneities between inner and outer cells; in fact, cells plated on E-Cadherin displayed barely any E-Cadherin at cell-cell junctions, likely because most of their E-cadherins engaged with the substrate (Fig. S4A,B). We then assessed division asymmetries on E-Cadherin substrates. Cells plated on E-Cadherin divided much more symmetrically than cells in 3D colonies (Fig. 3D,E, Movie 12).
Furthermore, cells at the periphery of ES cell colonies on E-cadherin displayed spindles as stable as cells inside 3D colonies (Fig. 3F,G green dots "periphery E-

Journal of Cell Science • Accepted manuscript
Cadherin", Movie 12). Together, these observations suggest that the high spindle mobility and division asymmetry observed at the periphery of 3D ES cell colonies could be mediated by unequal E-cadherin distribution between prospective daughter cells.
Since the geometry of the colony was affected when cells were plated on E-Cadherin, we sought to verify whether colony spreading in 2D could by itself lead to reduced division asymmetries. To do so, we used laminin-coated substrates where ES cell colonies adopt spread morphologies similar to cells on E-Cadherin (Fig. S5A, Movie 13,14). We found that on laminin, ES cells dividing at colony peripheries displayed asymmetries comparable to cells dividing at the periphery of 3D colonies, and higher than in similarly positioned cells dividing on E-cadherin ( Fig. S5B,C, Movie 14). This suggests that reduced spindle mobility and higher cell division symmetry in ES cells plated on E-Cadherin is not simply due to the spreading of the colonies. We verified that cells plated on laminin displayed a similar heterogeneity in E-Cadherin intensity between inner and outer junctions as cells plated on gelatin (Fig. S5A,B).
Reduced division asymmetries on E-cadherin were also not due to smaller cell volumes, which might confine spindle motion, as cells plated on E-Cadherin had volumes measured in 3D comparable to cells in 3D colonies (Fig. S5D). Furthermore, cell division duration for cells on E-Cadherin substrate was shorter than in 3D colonies, mostly due to a shorter time spent in prometaphase and metaphase ( Fig.   S5E-H). This suggests that division asymmetries are not the result of a longer times spent in the phases of division during which the spindle is positioned. Altogether, these results suggest that inhomogeneity in E-cadherin distribution between the prospective daughter cells during cell division at the periphery of 3D colonies may lead to instabilities in spindle position and strong asymmetries in cell size at cell division.
Cell division symmetry increases during exit from naïve pluripotency We then sought to examine whether the levels of division asymmetry are maintained during exit from naïve pluripotency. We induced exit by removing 2i+LIF from the culture medium and assessed division symmetry after 24h and 48h. After 24h, the population should be a mixed population of exited and naïve cells, and most cells will have exited naïve pluripotency at 48h (Kalkan et al., 2017). When ES cells exit naïve pluripotency, they spread on the substrate (De Belly et al., 2019) ( Fig. 4A), making 3D volume measurements from confocal stacks inaccurate in the thinner portions of the cell. Therefore, we used a 2D quantification of cell area as a read-out of cell size.
We observed that cells exiting naïve pluripotency displayed significantly more symmetric divisions compared to their naïve counterparts (Fig. 4A,B).
The spindle positioning protein NuMA becomes enriched at the anaphase cortex during exit from naïve pluripotency To explore the molecular basis for this increase in division symmetry, we focused on the spindle positioning regulator NuMA. Indeed, NuMA can act to specify spindle positioning as part of the NuMA/Gi/LGN complex, but also independently of the complex, through interactions with the proteins 4.1G/R (Kiyomitsu and Cheeseman, 2013). NuMA, Gi, LGN and 4.1R are all expressed in naive embryonic stem cells (Kalkan et al., 2017;Yang et al., 2019). Therefore, we explored NuMA localization as a good proxy for the localization of spindle positioning complexes. We first verified that as expected, in metaphase and anaphase HeLa cells, NuMA accumulated at the Journal of Cell Science • Accepted manuscript spindle poles, where it is known to organize microtubules, and at the cell cortex (Kiyomitsu and Cheeseman, 2013) (Fig. 4C). To quantify NuMA recruitment to the cortex, while accounting for cell-to-cell staining variation, we quantified the cortical NuMA signal as the ratio between NuMA mean intensity at the polar cortex and mean the spindle pole intensity. Strikingly, we observed that while HeLa cells recruit NuMA to the cortex in metaphase, where it contributes to the control of spindle positioning, as previously reported (Kotak et al., 2012;Woodard et al., 2010), naïve ES cells or cells in early stages of naïve pluripotency exit (24h) did not (Fig. 4C,D).
We also observed little cortical enrichment of NuMA in anaphase in naïve ES cells and in cells 24h after triggering exit from naïve pluripotency. However, NuMA became strongly recruited to the anaphase polar cortex in cells at late stages of exit from naïve pluripotency (48h) (Fig. 4C,D). Together, this data suggests that enhanced division symmetry upon exit from naïve pluripotency could be mediated by NuMA recruitment to the anaphase cortex. Interestingly, all three components of the NuMA/Gi/LGN complex are expressed in naïve cells and during exit from naïve pluripotency (Kalkan et al., 2017;Yang et al., 2019). In particular, NuMA expression levels are maintained during exit from naïve pluripotency (Kalkan et al., 2017;Yang et al., 2019) suggesting that the low levels of cortical NuMA in naïve cells that we observe are not due to the absence of the protein but to regulation of its localization.
Enhanced division symmetry is accompanied by NuMA recruitment in anaphase and elongated metaphase cell shapes In order to explore what might control the cortical recruitment of NuMA in anaphase in cells exiting naïve pluripotency, we characterized cellular shape in these cells.
Indeed, interphase cell shape has been proposed to direct metaphase NuMA Journal of Cell Science • Accepted manuscript localization and subsequent division orientation in various cell types (Bosveld et al., 2016;Kiyomitsu and Cheeseman, 2013). We thus measured interphase and metaphase cell elongation in cells >30 hours after induction of naïve pluripotency exit and asked if it correlated with the angle of cell division. We found that while interphase shape was more elongated than metaphase shape (as expected since cells round up for mitosis, Fig. 5A), the cells did not divide along their interphase long axis (Fig. 5B, black dots; the angle between the division axis and the cell long axis was comparable for cells displaying an elongation >1.2 -82% of the cellsand for cells displaying lower elongation, p=0.34). In contrast, we found that for cells that spindle size scaled at every stage of exit from naïve pluripotency (Fig. 5F). Our data show that recruitment of NuMA to the anaphase cortex correlates with increased cell shape elongation in metaphase and spindle orientation along the metaphase long axis.
NuMA recruitment to the cortex in anaphase is important for controlling division symmetry in HeLa cells (Kiyomitsu and Cheeseman, 2013). In cells exiting naïve pluripotency, NuMA recruitment in anaphase correlated with increased division symmetry and with more elongated metaphase cell shapes. Interestingly, we also noticed that when ES cells were plated on E-Cadherin, where cells divide more symmetrically than in colonies, they exhibited elongated shapes in metaphase ( Fig.   5G,H). Finally, the localization of E-Cadherin itself remained unchanged on all substrates when cells exited naïve pluripotency (Fig. S5A,B), suggesting that the increase of symmetry at exit naïve pluripotency is not due to changes in E-Cadherin localization. Altogether, these data suggest that metaphase cell shape elongation, which is higher in ES cells plated on E-Cadherin and cells exiting naïve pluripotency than in ES cells in 3D colonies, might influence spindle positioning and division symmetry.

Discussion
During early development and homeostasis, robust cell organization relies on a tight control of cell division orientation. While many studies have investigated the control of division orientation and the mechanisms of spindle positioning in isolated cells or epithelia (Anastasiou et al., 2020;Bosveld et al., 2016;Fink et al., 2011;Hart et al., 2017;Nestor-Bergmann et al., 2014;Théry and Bornens, 2006;Théry et al., 2005; Journal of Cell Science • Accepted manuscript Théry et al., 2007;Wyatt et al., 2015), not much is known about the mechanisms controlling spindle orientation and relative daughter cell sizes in cells growing in disordered 3D environments, such as the early mammalian embryo.
Here, we investigate cell division orientation and symmetry in mouse embryonic stem cell 3D colonies. We observe that ES cells display strong size asymmetries between daughter cells, especially for cells dividing at the periphery of the colony ( Fig.s 1,2). Division asymmetry appears to be due to heterogeneous distribution of E-Cadherin at the time of division. In particular, when both daughter cells are in contact with E-Cadherin, either through cell-cell contacts when dividing inside colonies or through substrate contact when dividing on E-cadherin, the spindle is more stably positioned at the center of the cell and division is more symmetric (Fig.   3). However, for cells where only one prospective daughter cell displays substantial contact with the colony, the spindle displays high mobility and divisions are asymmetric in size (Fig.s 1-3). E-Cadherin has been implicated in orienting cell regulators have also been shown to directly control pluripotency (Liu et al., 2017;Michowski et al., 2020).
Finally, we show that in naïve ES cells dividing in 3D, the spindle positioning factor NuMA is expressed and localizes at spindle poles, but is not recruited to the metaphase cell cortex as is observed in HeLa cells or Drosophila epithelia (Kiyomitsu and Cheeseman, 2013;Kotak et al., 2012;Woodard et al., 2010).
Furthermore, in cells exiting naïve pluripotency, NuMA becomes recruited to the cortex, but only in anaphase, suggesting that metaphase and anaphase localization of NuMA are regulated independently of each other. We also find that in cells exiting naïve pluripotency an elongated cell shape at metaphase correlates with enhanced Journal of Cell Science • Accepted manuscript division symmetry and preferential spindle alignment with the metaphase long axis ( Fig.s 4,5). This suggests that NuMA recruitment in anaphase might be instructed by metaphase cell shape, or by the underlying mechanical forces on the cortex (Fink et al., 2011), in contrast to what has been described in cultured cells dividing in 2D and epithelia, where NuMA recruitment in metaphase is instructed by interphase cell shape (Bosveld et al., 2016;Kiyomitsu and Cheeseman, 2013). In addition to spindle positioning, NuMA regulates many other aspects of cell division, including spindle pole focusing and nucleus reformation (reviewed in (Radulescu and Cleveland, 2010)) making direct investigation of NuMA's effects on spindle positioning challenging. As new tools, such as optogenetic targeting constructs, become available, it will be interesting to directly test how e.g. delocalising NuMA from the cortex affects spindle position and division symmetry in ES cells.
Altogether, these observations suggest that spindle mobility and spindle centering by

Conflict of interest
The authors declare no conflict of interest.

Data and materials availability
All raw data and cells used in the analysis are available upon request. This study includes no data deposited in external repositories.

Cell lines, cell culture and drug treatments
Mouse embryonic stem cells were routinely cultured as described in (Mulas et al., 2019) on 0.1% gelatin in PBS (unless otherwise stated) in N2B27+2i-LIF + penicillin and streptomycin, at a controlled density (1.5-3.0 10 4 cells/cm 2 ) on Falcon flasks and passaged every other day using Accutase (Sigma-Aldrich, #A6964). They were kept in 37˚C incubators with 7% CO 2 . Cells were regularly tested for mycoplasma.
In this study, the cells used were: E14 wild type cells and E14 cells stably expressing H2B-RFP (Cannon et al., 2015).
The E14 cells stably expressing H2B-RFP were tested for contribution to chimeras, to verify that they were indeed pluripotent, by the Francis Crick Institute (London, UK) mouse facility. Cells were injected into C57BL/6 blastocysts and gave rise to a viable mouse with good contribution of the H2B-RFP cells as assessed by the color of the mouse (Fig. S3A, the mouse has extensive brown patches even though the host C57BL/6 mice are albino), and via dissection under a fluorescent lamp, which confirmed that the H2B-RFP cells contributed to tissues.

Live imaging
For colony imaging, the cells were typically plated on 35 mm Ibidi dishes (IBI Scientific, #81156) coated with gelatin (unless otherwise stated) the day before the experiment, and imaged on a Perkin Elmer Ultraview Vox spinning disc (Nikon Ti attached to a Yokogawa CSU-X1 spinning disc scan head) using a C9100-13 Hamamatsu EMCCD Camera. Samples were imaged using a 60X water objective (CFI Plan Apochromat with Zeiss Immersol W oil, Numerical Aperture 1.2). Typically, the samples were imaged overnight acquiring a Z-stack with ΔZ = 2 m every 5 minutes.
Shape instability assessment ( Fig S1) and duration of the different phases of division were done by visual assessment.
The mesh deformation was made according to the perpendicular maximal gradient of the signal. The segmentation was stopped when the volume appeared resolved by visual assessment.
For 2D measurements, cell areas were measured by manually drawing the cell contour in the mid-plane of the cell using Fiji (Schindelin et al., 2012). Similarly, cell elongations were measured by drawing the cell contour in the mid-plane of the cell and automatically fitting an ellipse using Fiji and measuring the ratio of the long axis to the short axis.

Shape instabilities assessment
To assess shape instabilities during cell division, we used 4 consecutive frames with a 5-minute bin, the first frame being 15 min after anaphase. We first assessed in 3D which cells displayed shape instabilities over time and which displayed more stable shapes. To validate the visual analysis, we then performed a quantitative analysis of cell shape variability in 2D. We focused on the midplane of each prospective daughter cell, and used the JFilament plugin (Smith et al., 2010) to segment the cell and generate "snakes" representing the outline of the cell (Fig. S4D). We then Journal of Cell Science • Accepted manuscript normalized the snakes for contour length and compared the evolution of the outlines over time, by computing a cell shape variability parameter. Specifically, we measured the curvature at each point, then the variance of this curvature over the whole snake and finally the variance of this curvature variance over the 4 frames assessed. Finally, we used a ROUT test to identify outliers and removed them from the analysis. This led to 20 out of the 168 cells that had been visually assessed, being removed from the analysis (11 cells removed from the "stable" category and 9 from the "unstable" category).
Details of curvature calculations on discretized snakes: First the snakes were scaled so that the distance was in m and then the snakes were discretised into a succession of points separated by ~2um. The curvature (k i ) was then calculated at each point i as the rate of change of the unit tangent vector: where t i was the unit tangent from point i-1 to point i and l i the distance between points i and i-1. The curvature was negative if the cross product between the two unit tangent vectors was negative.
The average curvature was then obtained as the average over all n points in one frame of the snake:

Journal of Cell Science • Accepted manuscript
The variance of the curvature along the snake contour was then calculated as:

∑ 〈 〉
Finally, the cell shape variability parameter is then calculated as the variance of  2 over time.
To measure the cell shape variability for the DMSO and Blebbistatin treated cells, we first excluded every cell that displayed high variability in cell area (cell area variance >100 m -4 ) as those likely represented cells that moved extensively in the Z-direction. We then performed a ROUT test (using Prism (Graphpad)) to exclude outliers (2 outliers for DMSO treatment, 6 outliers for Blebbistatin treatment).

Transfections
Transfections were performed using 5 g of plasmid and 6 L of Lipofectamin, incubated in 250 L OptiMEM for 5 minutes, then mixed and incubated at room temperature for 20 minutes, and added to cells passaged onto Ibidi dishes concomitantly. The medium was replaced with fresh medium after 5 hours and the cells were imaged the next day.
For Myosin-II transfection, we used a MRLC-YFP plasmid (kind gift from Guillaume Charras, LCN, UK). Myosin-II levels quantification was done by measuring the mean grey intensity for each cell in the mid-plane of the cell at the outer, inner cortex and in the cytoplasm in interphase cells. To take into account inhomogeneities, we took 3 measurements per region per cell and averaged them.

Journal of Cell Science • Accepted manuscript
Immunofluorescence For E-Cadherin staining, cells were fixed in Ibidi dishes (IBI Scientific, #81156) in 4% formaldehyde in PHEM buffer with 0.125% Triton, blocked in 3% BSA in PBS and incubated for 2h at room temperature with primary antibodies against E-Cadherin

Spindle and metaphase plate position and size measurement
The position of the metaphase plate (imaged using the H2B-RFP signal) was measured from Z-stacks using the "furrow" option of the 3D mesh plugin (Smith et al., 2016). We confirmed that when the spindle position (using SIR-Tubulin (Tebu-bio #SC002, diluted in media to 20 nM and incubated for 6h)) was measured in the same cell, spindle and metaphase plate followed very similar tracks (data not shown).
Briefly, the plugin allows to position a plane onto the metaphase plate and to define the center of the metaphase plate. The plugin measures the angle of the plate in the reference frame of the 3D image. The coordinates of the center of gravity of the colony is measured using the plugin by drawing a mesh around the colony using the same parameters as for volume measurements. The angle between this center of gravity and the angle of plate is then calculated.
The size of the spindle was measured by measuring the pole-to-pole distance of flat spindles.