Polarized branched Actin modulates cortical mechanics to produce unequal-size daughters during asymmetric division

The control of cell shape during cytokinesis requires a precise regulation of mechanical properties of the cell cortex. Only few studies have addressed the mechanisms underlying the robust production of unequal-sized daughters during asymmetric cell division. Here we report that unequal daughter-cell sizes resulting from asymmetric sensory organ precursor divisions in Drosophila are controlled by the relative amount of cortical branched Actin between the two cell poles. We demonstrate this by mistargeting the machinery for branched Actin dynamics using nanobodies and optogenetics. We can thereby engineer the cell shape with temporal precision and thus the daughter-cell size at different stages of cytokinesis. Most strikingly, inverting cortical Actin asymmetry causes an inversion of daughter-cell sizes. Our findings uncover the physical mechanism by which the sensory organ precursor mother cell controls relative daughter-cell size: polarized cortical Actin modulates the cortical bending rigidity to set the cell surface curvature, stabilize the division and ultimately lead to unequal daughter-cell size.

The control of cell shape during cytokinesis requires a precise regulation of mechanical properties of the cell cortex. Only few studies have addressed the mechanisms underlying the robust production of unequal-sized daughters during asymmetric cell division. Here we report that unequal daughter-cell sizes resulting from asymmetric sensory organ precursor divisions in Drosophila are controlled by the relative amount of cortical branched Actin between the two cell poles. We demonstrate this by mistargeting the machinery for branched Actin dynamics using nanobodies and optogenetics. We can thereby engineer the cell shape with temporal precision and thus the daughter-cell size at different stages of cytokinesis. Most strikingly, inverting cortical Actin asymmetry causes an inversion of daughter-cell sizes. Our findings uncover the physical mechanism by which the sensory organ precursor mother cell controls relative daughter-cell size: polarized cortical Actin modulates the cortical bending rigidity to set the cell surface curvature, stabilize the division and ultimately lead to unequal daughter-cell size.
Many asymmetric cell divisions (ACDs) are characterized by a difference in size of the two daughter cells 1 . From a physical point of view, the generation of unequal daughter-cell size represents a mechanical challenge during cytokinesis. According to Laplace law, if two daughter cells are not identical in size, the smaller daughter would collapse into the bigger daughter during cytokinesis. Indeed, cells, dividing under a global contractile tension at the poles, are expected to exhibit dramatic shape instabilities 2,3 . As daughter cells are never exactly identical, cells must ensure to compensate for such instabilities, which can ultimately lead to cytokinetic failure 2 . Consequently, the precise control of the mechanical properties at the cortical poles is critical during ACD, when cells divide into unequal daughter-cell size. Identifying the mechanisms of daughter-cell size control is also crucial to understand cell function, because the ability to produce asymmetric daughters underlies cellular diversity and can influence proliferation rates 4 and cell differentiation [4][5][6] , which are key for stem cell renewal [7][8][9] .
Previous reports have proposed a role of spindle positioning in determining size asymmetry [10][11][12] . However, recent data suggest that spindle-induced cleavage furrow positioning is not enough to explain cell-size asymmetry (reviewed in ref. 13 ) and cells without spindles can divide with normal daughter-cell size asymmetry 14,15 . Furthermore, this does not resolve how the cell overcomes the mechanical instabilities during cytokinesis mentioned above.
Instead, the actomyosin cortex at the cell poles has been proposed to play a key role in the generation of cell size asymmetry 5,14,15 . These previous studies have mainly focused on the role of contractile actomyosin tension in determining cortical mechanical properties, while the role of other mechanical properties, such as cortical stiffness or Article https://doi.org/10.1038/s41556-022-01058-9 is downregulated, Actin asymmetry is abolished ( Fig. 1g and Extended Data Fig. 2c,d). Conversely, when Formins are inhibited by the SMIFH2 drug [25][26][27] , cortical Actin asymmetry is not affected (Extended Data Fig. 2e,f). Furthermore, both Rac and Cdc42, upstream regulators of Arp2/3 (ref. 28 ), are enriched in the posterior cortex (Extended Data Fig. 3a-d), but not Diaphanous, which is the main Formin known to nucleate Actin at the cell cortex and to be involved during cytokinesis 21,[29][30][31] (Extended Data Fig. 3e,f). Additionally, only Filamin (a large, flexible crosslinker arranging Actin into a meshwork) 32,33 is found enriched at the cortical poles, but not Fascin, α-Actinin or Fimbrin, all of which organize F-Actin into bundles [34][35][36] (Extended Data Figs. 3g-j and 4a,b). Therefore, Actin asymmetry seems to be dominated by branched Actin in SOPs.
In other ACDs, enrichment of cortical Myosin has been shown to correlate with the smaller daughter cell 5,14,15 . We then set up to study and manipulate contractility factors (such as Myosin and bundler proteins) in SOPs (Extended Data Fig. 4a-l). For instance, Myosin-II is found enriched at the cell cortex, but no asymmetry could be detected (Extended Data Fig. 4c-e). Therefore, asymmetric cell size in SOPs might arise from an alternative mechanism, where the asymmetric accumulation of branched cortical Actin, instead of Myosin, determines relative daughter-cell sizes. To investigate this, we next studied the functional relationship between cortical Actin asymmetry and unequal daughter-cell size.

Actin asymmetry coupled with PAR complex and daughter size
Cell size asymmetry during ACD can be controlled through polarity cues organized by the PAR complex 37 . We thus studied cortical Actin in SOPs expressing a phospho-defective lgl mutant version (lgl 3A ) known to impair PAR complex activity 38 .
While in control SOPs the polarity marker Pon is restricted to the anterior cortex by the PAR complex 39 (Figs. 1a and 2a), in lgl 3A mutants, Pon is found at the cell cortex of both poles 38 (Fig. 2a). Strikingly, in lgl 3A , SOPs divide into two daughters of similar size (Fig. 2b) and exhibit symmetric cortical Actin (Figs. 1g and 2c,d; see also Extended Data Fig. 5a-e for dsh and Gβ13F phenotypes). This indicates that the mechanism underlying the posterior accumulation of Actin is under the control of the PAR complex. To further study the relationship between Actin and size asymmetry, we next uncoupled Actin polarity from the position of the mitotic plane.

Polar Actin asymmetry levels correlate with daughter size
During SOP mitosis, three features align to the anterior-posterior axis: (1) the posterior cortical PAR domain (excluding Pon to the anterior), (2) the mitotic spindle orientation and (3) the posterior cortical Actin domain. A Mud-Dynein complex couples spindle orientation to the PAR domain 40 . Indeed, in mud 4 mutants, the Pon domain is bisected in bending rigidity, is less well understood. For example, during asymmetric neuroblast division in Caenorhabditis elegans and Drosophila, cortical Myosin enrichment in the smaller pole has been proposed to produce unequal-sized daughters by creating an asymmetry of contractile tension 5,14,15 . However, during these divisions, it is unknown how shape instabilities, such as the collapse of the smaller cell pole, which exhibits a larger contractile tension, are prevented 2 . Thus, how cells control and stabilize their shape and relative daughter-cell size during ACD remains an open question. In this Article, we investigate how polar branched Actin at the cell cortex regulates cortical mechanics to robustly achieve asymmetric division into two unequal-sized daughter cells.

Daughter-cell size asymmetry during SOP division
Sensory organ precursor (SOP) cells divide into an anterior PIIB and a posterior PIIA daughter cell. To study the sizes of PIIA and PIIB (Fig. 1a), we analysed the three-dimensional (3D) geometry of dividing SOPs from imaging data ( Fig. 1b and Supplementary Note 1). During cytokinesis, SOP volume remains constant, and, at the end of mitosis, PIIA has nearly twice the volume of PIIB (Fig. 1c,d and Extended Data Fig. 1a-c). The total surface area increases by 20%, as expected for a sphere when it is split into two with volume conservation ( Fig. 1e and Supplementary Information II.I). Using the cleavage furrow as landmark, we found that the increase of total surface area is mainly due to an increase in posterior pole surface (Fig. 1e). To identify the origin of this surface area asymmetry and corresponding cell size asymmetry, we studied the cortical cytoskeleton at the poles.

Cortical Actin asymmetry during asymmetric mitosis
As in other mitotic systems 16,17 , Actin is recruited to the SOP cortex at metaphase onset (Extended Data Fig. 1d) during the mitotic rounding process [18][19][20] . In contrast, in late anaphase, the posterior Actin cortex is enriched by fourfold (Fig. 1f,g, Supplementary Video 1 and Extended Data Fig. 1d-h) and is 40% thicker compared with the anterior cortex (Extended Data Fig. 1i,j). In accordance with this, Actin dynamics in the posterior cortex is slower, as revealed by fluorescence recovery after photobleaching (FRAP) using green fluorescent protein (GFP)-Actin (Extended Data Fig. 1k,l). Similar to the SOP, Drosophila larval neuroblasts also display asymmetric cortical Actin enrichment, with higher levels in the apical pole, which gives rise to the neural stem cell, the larger daughter (Extended Data Fig. 2a,b).
Formins and the Arp2/3 complex drive the polymerization of linear and branched filamentous Actin (F-Actin), respectively [21][22][23] . In SOPs, we show that asymmetric cortical F-Actin probably arises from an asymmetric Arp2/3 activation. Indeed, when Nausicaa, a protein known to regulate branching nucleation and density in Drosophila 24 , Fig. 1 | Daughter-cell size and cortical Actin asymmetry. a, Maximum projection of SOP expressing cytosolic GFP (green) and RFP-Pon (red; a marker of the anterior pole corresponding to the future PIIB cell) under the Neuralized promoter. b, Three-dimensional segmentation of a dividing SOP using the Squassh algorithm (Supplementary Note 1); anterior (violet) and posterior cell poles (orange) are indicated. Green plane, cleavage plane. c, Volume dynamics (total volume and volume of the poles) during mitosis (mean ± standard deviation). Cytokinesis stages are indicated. Volumes have been normalized by the average conserved volume of each cell, respectively (Supplementary Note 1). Poles are defined only after the onset of cytokinesis (at the beginning of anaphase B) by the position of the cleavage furrow. d, Daughter-cell volume. Mean ± s.e.m., t-test two-tailed, P < 0.001. e, Surface area dynamics (total and polar) during mitosis (mean ± standard deviation). Areas have been normalized by the corresponding area from a sphere of volume equals to the total average volume for each cell, respectively (Supplementary Note 1). Poles are defined only after the onset of cytokinesis (at the beginning of anaphase B) by the position of the cleavage furrow. Mann-Whitney rank sum test two-sided (P < 0.001 for posterior and not significant (NS) for anterior). f, Top: time-lapse spinning disk confocal maximum projections of SOP expressing Lifeact-mCherry (red) and GFP-Pon (green) under the Neuralized promoter. Middle: a posterior enrichment of cortical Actin (Lifeact) can be observed in late anaphase (see third timepoint, white asterisk). Bottom: look-up Article https://doi.org/10.1038/s41556-022-01058-9 random locations by the cleavage plane [41][42][43] (Fig. 2e). In this condition, daughter-cell sizes display a broad range from being asymmetric as in wild type to symmetric daughters (Fig. 2b).
Like in control SOPs, the Actin and Pon domains in mud 4 still exclude each other, confirming that Actin is enriched within the PAR domain (Fig. 2e,f), consistent with Par6/Cdc42 interactions as previously reported [44][45][46] . Consequently, not only the Pon domain but also the Actin domain is randomly partitioned between the two poles in mud 4 (Fig. 2e,f). This condition therefore generates a continuum of cortical Actin asymmetry levels that correlate with the degree of cell size asymmetries (Fig. 2g and Extended Data Fig. 5f): low levels of Actin asymmetry give rise to symmetric sizes, while posterior enrichment of Actin leads to wild-type-like asymmetric daughter-cell size. Therefore, the level of Actin asymmetry ultimately forecasts the relative sizes of the two daughters.

Nanobody mistargeting of Actin can invert size asymmetry
In mud 4  independent. To study whether polar Actin can directly control size, we inverted the Actin asymmetry with nanobodies 47,48 while keeping the PAR polarity normal. We co-expressed in SOPs a GFP fusion of WAVE, the major cortical regulator of Arp2/3 (ref. 49 ) (Extended Data Fig. 5g,h), and GFP-binding protein (GBP)-Pon, an anti-GFP nanobody fused to the localization domain of Pon. This way, GFP-tagged WAVE is targeted to the anterior cortex, causing an anterior cortical accumulation of branched F-Actin (Fig. 3a,b and Extended Data Fig. 5i,j) and  daughter-cell size inversion: the anterior daughter becomes larger than the posterior (Fig. 3a,c and Supplementary Video 2). Interestingly, while, in lgl 3A mutant, daughter-cell size is symmetrical, targeting WAVE to one pole by optogenetics (see below for details) in lgl 3A mutant is sufficient to yield this pole larger and can thereby generate asymmetric daughter-cell size (Extended Data Fig. 5k,l). In contrast, targeting Myosin, α-Actinin or Fimbrin (two crosslinkers generating F-Actin bundles [34][35][36] ) by nanobody targeting to the anterior pole leads to a smaller rather than a larger daughter cell (Extended Data Fig. 4f-l and Supplementary Information III.II.2.c). This indicates that the effect of branched Actin on the cell cortex mechanics is distinct from Myosin-mediated contractile tension (see below).
Conversely, we exacerbated Actin asymmetry beyond wild type by targeting WAVE-GFP to the posterior cortex through co-expression of GBP-Baz 48 , a GBP fusion to the Drosophila Par3 orthologue Bazooka. This leads to a more extreme size asymmetry compared with control SOPs (Fig. 3c and Extended Data Fig. 5m,n). These nanobody WAVE experiments suggest that the relative daughter-cell sizes can be directly determined by the cortical Actin asymmetry. In wild type, PAR controls Actin asymmetry and Actin, in turn, determines unequal cell size.
Interestingly, in the inversion experiment in which PIIA becomes smaller than PIIB (Fig. 3a,c), we noticed that bristle length in the adult fly was also reduced (Fig. 3d,e). This bristle cell derives from the lineage of the large PIIA cell, opening the possibility that PIIA/PIIB size asymmetry impacts the final cell sizes in the subsequent lineage and thereby the functions of these mechanoreceptors.

Impairing cortical branched Actin at the cell poles
In the previous experiments, we enriched the cortical Actin in each pole. We next impaired the cortical Actin asymmetrically through targeting of Arpin, AIP1 or Cofilin. Arpin inhibits Arp2/3 (ref. 50 ), while AIP1 or Cofilin sever Actin filaments 51 . Posterior targeting of these factors using GBP-Baz caused embryonic lethality precluding their study at the subsequent pupal stage. To overcome this, we established optogenetics for temporal control based on CRY2/CIB 52 , whose binding is induced by 445/488 nm laser light.
By co-expression of Lifeact-CRY2 FL -mCherry and CIB 1 -GFP-Arpin in SOPs, we recruited Arpin to Actin-rich regions with spatio-temporal control (posterior cortex at anaphase onset) using holographic patterned photo-stimulation microscopy 53 . Under these conditions, the relative Actin asymmetry between the two poles is lost (Fig. 4a-f and Article https://doi.org/10.1038/s41556-022-01058-9 Supplementary Video 3) and daughter-cell sizes become symmetrical (Fig. 4g). As expected, when Arpin is optogenetically targeted to both poles, only the general levels of Actin density are affected and the effect on size asymmetry is observed to a lesser extent (Extended Data Fig. 6a-e). Furthermore, when size asymmetry is abolished by impairing branched F-Actin nucleation at the posterior cortex, cell polarity and, in particular, asymmetric spindle positioning are not affected (Extended Data Fig. 6f-h). This suggests that asymmetric spindle positioning by itself is not enough to drive size asymmetry (see below). Conversely, impairing the cortical Actin meshwork only in the anterior pole by using GBP-Pon and GFP fusions to Arpin, AIP1 or Cofilin led to a small but notable enhancement of daughter size asymmetry (Extended Data Fig. 7a-h). Furthermore, while inhibiting Formins does not affect size asymmetry, downregulating branched Actin nucleation leads to symmetrical daughters ( Fig. 2b and Extended Data Figs. 2c-f and 5e), confirming that it is branched Actin that could modulate the daughter-cell sizes.
Taken together, our results confirm that the relative amount of branched Actin between the two cortices and, in particular, posterior branched Actin enrichment are key to producing size asymmetry.

Polar Actin acts beyond spindle positioning
Cortical actomyosin is known to influence mitotic spindle positioning 54 . The antiparallel microtubule overlap established in metaphase positions the centralspindlin complex, which itself organizes the actomyosin ring in anaphase 55,56 and, hence, the cytokinetic furrow 2,57 .  This could, in turn, determine daughter-cell size. In SOPs, the metaphase plate is asymmetrically positioned towards the anterior pole (Extended Data Fig. 8a-f), yet this asymmetry is not enough to explain the asymmetry of size observed in wild type (Supplementary Information II.II). Furthermore, SOPs treated with Colcemid, to depolymerize all microtubules, still generate two poles with a size asymmetry similar to wild-type SOPs (Extended Data Fig. 8g-i), as previously reported in Drosophila neuroblasts 14,15 . This further supports the fact that asymmetric spindle positioning does not dominate unequal cell size in SOPs. Nonetheless, this prompted us to ask whether the inversion of daughter-cell size observed during the anterior WAVE targeting could be influenced by an Actin-mediated spindle positioning process during metaphase or whether it was only dependent on the polar Actin cortex having an effect on cortical mechanics.
To test this, we used LOV/PDZ optogenetics, where blue illumination opens the LOV domain to expose a PDZ binding domain 58 , at different stages of cytokinesis. We co-expressed three proteins: WAVE-GFP, GBP-LOV and PDZ-Pon (Fig. 5a-d). WAVE-GFP binds GBP-LOV and, upon blue illumination, is targeted to PDZ-Pon in the anterior cortex ( Fig. 5b-d). Photoactivation at any timepoint from metaphase to late anaphase led to cell size inversion through Actin enrichment in the anterior cortex ( Fig. 5b-d and Supplementary Video 4). Importantly, in late anaphase, the positions of the spindle midzone and the actomyosin ring are already committed (Extended Data Fig. 8e,f). Yet, photoactivation in late anaphase still affected daughter size asymmetry (Fig. 5b). Therefore, polar cortical Actin itself can control daughter size asymmetry independently of spindle positioning and relative daughter-cell sizes can still be modified until late stages of cytokinesis. This is consistent with the possibility that cortical Actin directly controls cell size by regulating the material properties and mechanics of the polar cortex itself.
Indeed, mechanical properties between the two poles are different. Blebs are local reporters of cortical tension: their size correlates indeed with cortical tension 59 . At the end of SOP mitosis, blebs are more frequent and larger in the posterior pole (Extended Data Figs. 1e and 9a,b). We also confirmed this cortical tension asymmetry by generating laser-induced blebs by ablation of the cell cortex (Extended Data Fig. 9c,d).

Physics of daughter-cell size asymmetry
We then established a minimal physical model of cortical mechanics to study (1) which mechanical factors, modulated by Actin, are required for asymmetric size, (2) whether differences in cortical Actin asymmetry levels can explain quantitatively the experimental size asymmetries observed and (3) under which conditions are daughter-cell shape geometries mechanically stable. Following experimental observations (Extended Data Fig. 9e,f), our model neglects effects from neighbouring cells.
We considered a minimal model where a spherical cell of radius R divides into two daughter cells, represented by two connected spherical caps 60 (Fig. 6a and Extended Data Fig. 9g) that can have different mechanical surface properties (Supplementary Information III): a contractile cortical tension σ, a bending rigidity κ (cortical stiffness in response to bending deformations) and a cortical spontaneous curvature C 0 (intrinsic tendency to bend). The cortical actomyosin cytoskeleton could modulate these material properties 61,62 , thereby contributing to cortical mechanical responses, cortical curvature and, ultimately, relative daughter sizes.
We explored a mechanism where κ and σ are determined by the cortical Actin density I. For simplicity, both κ and σ increase linearly with I, according to κ = α κ I and σ = α σ I (Supplementary Information III. II.3). In this model, different Actin asymmetry levels between the two caps, for given α κ , α σ and C 0 values, give rise to different force-balanced surface geometries characterized by a size asymmetry ∆a (Fig. 6a). Consequently, we fit our model to the experimentally measured, Actin-dependent PIIA/PIIB cell size asymmetries (R 2 = 0.96; Fig. 6b,c and Extended Data Fig. 9h).
For the fit, only two free parameters need to be determined: (1) the ratio α κ /α σ and (2) C 0 (relative to cell size; Supplementary Information III.II.3). With these two parameters alone, we can quantitatively explain the cell size ratios observed in our experiments, from the asymmetric wild-type scenario and the symmetric mutant conditions to those in which the size ratios are inverted (Fig. 6b,c). Importantly, the fairly large value of α κ α σ R 2 = 7.1 ± 0.8 obtained from the fit suggests that Actin-mediated modulations of cortical bending rigidity, as characterized by α κ , play a crucial role in ACD and that changes in cortical Actin density have a much stronger effect on bending rigidity than on cortical tension (Extended Data Fig. 9i-k). This reveals a critical role of cortical Actin in determining daughter-cell sizes during ACD by providing substantial cortical bending elasticity.
Formin-mediated Actin is considered as a key determinant of cell mechanics 63 through its impact on cortical contractility 64 . We show, however, that branched Actin modulates cortical mechanics to control size asymmetry in SOPs. This uncovers two fundamental aspects in cell mechanics: (1) branched cortical Actin can also play a key role for cell mechanics, and (2) not only contractility but also bending rigidity is important for cell morphogenesis.
Finally, we studied the mechanical stability of the two emerging spherical caps during furrow constriction. If the system is unstable, the furrow slips to one side: the smaller cap collapses into the bigger one. For the fit parameters obtained above, the system is least stable at the beginning of cytokinesis but stabilizes after 25% constriction (Extended Data Fig. 9i and Supplementary Information III.II.2). A reliable constriction during early cytokinesis can be achieved, for example, if constriction is faster than the collapse of the smaller cap or if branched Actin decreases cortical contractility 65 (Extended Data Fig. 9l,m and Supplementary Information III.II.4).

Cortical Actin determines size by modulating local curvature
Our theoretical model suggests that local changes in Actin density modulate the mechanical properties of the cell cortex locally to induce local shape changes of the cell contour. Indeed, when WAVE is mistargeted to the anterior cortex with nanobodies, local enrichment of branched Actin in patches correlates with a local cell contour flattening (Fig. 6d). To investigate this further, we measured the local enrichment of cortical Actin and the local cell curvature in normal conditions (Fig. 6e,f). At the cell poles, Actin density in the cortex correlates with curvature ( Fig. 6f and Extended Data Fig. 9n). This suggests that Actin density itself could tune the cell contour curvature by modulating local cortical mechanics: flattening the cell surface contributes to the emergence of a larger daughter cell.
We then looked at the curvature dynamics while locally targeting WAVE in real time to the cortex though optogenetics (Fig. 6g-j and Supplementary Video 5). Figure 6i shows that cortical flattening upon local branched Actin enrichment happens in only a few minutes. These fast dynamics are compatible with a role of cortical Actin to shape cells during cytokinesis, which occurs at a timescale of about 15 min.

Discussion
Our work shows that polarized cortical Actin produces unequal-size daughters during ACD. In particular, branched Actin modulates the cytokinetic cell shape by locally setting the bending rigidity, and thereby determines the daughter-cell size asymmetry (for summary, see Extended Data Fig. 10a). This is based on the following key observations: (1) In wild type, cortical branched Actin accumulation is observed in the larger posterior pole (Fig. 1f,g) and local Actin density correlates with local curvature (Fig. 6d-f and Extended Data Fig. 9n). (2) When cortical Actin is symmetrical, the SOP divides with symmetric daughter sizes (Figs. 1g, 2b-d    size is inverted (Figs. 3a-c and 5b-d). (4) When cortical branched Actin polymerization is induced locally by optogenetics, the cortex flattens locally (Fig. 6g-j). During SOP division, an asymmetry in bending rigidity is sufficient to achieve asymmetric sizes (Extended Data Fig. 9i-k). Our theoretical approach shows that an Actin dependence of both bending rigidity and tension accounts quantitatively for the observed correlation between cortical Actin density and daughter-cell size in all experimental conditions (Fig. 6b,c). However, our data show that Actin impacts bending rigidity much more strongly than tension: cortical branched Actin hence sets the bending rigidity of the cell cortex. This uncovers a distinctive, fundamental role of bending rigidity, instead of cortical tension, for asymmetric daughter-cell size determination.
In systems such as the Drosophila and Caenorhabditis neuroblasts, cortical tension due to Myosin asymmetries has been proposed as a major player for generating asymmetric daughter-cell sizes 5,14,15 .
Here we propose that the modulation of daughter-cell sizes can be mediated by two mechanisms, each related to a specific population of Actin: linear Actin together with Myosin leading to tension asymmetries and branched and crosslinked Actin leading to bending rigidity asymmetries. However, the control of bending rigidity by branched Actin, which we discovered here, adds to the toolkit to generate stable ACDs with unequal daughter-cell sizes. Finally, our findings may have implications for the understanding of cortical mechanics during stem cell divisions, which are not only important for cell shape and tissue morphogenesis, but also for cell fate assignation and tumour growth.

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Key resources table
Materials, reagents and resources used in this study can be found in Supplementary Table 1.

Experimental model and subject details
Fly handling, fly lines and maintenance. All fly stocks were maintained at 18 °C. Fly crosses were raised at 25 °C, then kept at 16 °C until pupariation, and shifted to different temperature depending on the experiments (25 °C or 29 °C as indicated in Supplementary Table 1). To express genes in the SOPs, the Neuralized promoter together with the UAS-Gal4 system was used. We also used the Gal80 ts protein to reduce the levels of expression. For example, we used Gal80 ts to achieve low levels of Zipper (Myosin Regulatory Heavy Chain) expression to prevent motor aggregates (Extended Data Fig. 4e)  More details on the transgenes used can be found in Supplementary Table 1. Supplementary Table 1.

Detailed genotypes and temperatures. Detailed genotypes and temperatures can be found in
Neuroblast culture. Live imaging was performed as described previously 85 . Briefly, brains were dissected in collagenase buffer and incubated in collagenase for 15 min (0.2 mg ml −1 collagenase, Sigma C0130). Brains were manually dissociated into a culture medium (Schneider's medium supplemented with glucose, fetal calf serum, fly extract and insulin) as in ref. 85 .
Fluorodish was first activated using a plasma cleaner (Harrick Plasma, PDC-32G) for 3 min and then coated with poly-l-lysine. Dissociated brains were transferred onto the activated and coated Fluorodish. Cells were allowed to settle and adhere to the coverslip 30 min before imaging. Neuroblast culture medium composition. The composition of 2.5 ml of Schneider + glucose medium were as follows: 300 µl FBS (10%, Thermo Fisher #10270106), 75 µl fly extract (inactivated and filtered sterilized medium: 100 g of smashed Oregon flies into 680 ml of cold M3 insect medium, Millipore Sigma, #S3652), 3 µl insulin (Sigma 19278) and 30 µl P/S (Gibco 15140).

Plasmids.
Most of the open reading frames cloned by PCR for this study were flanked by FseI and AscI (FA) sites for convenient shuttling between compatible plasmids.
• UAS-GFP::WAVE: For GFP N-ter WAVE cloning, the Drosophila WAVE coding region was digested by FA from the plasmid: pCS2 GFP dWAVE, gift from Alexis Gautreau, and inserted into a Drosophila UAS expression plasmid pUAST4 PC GFP FA blue. • UAS-GFP::Arpin: Similarly, for GFP N-ter Arpin cloning, Arpin coding region was digested by FA from the plasmid pcDNA5 FRT His PC TEV Arpin, gift from Alexis Gautreau 50 , and inserted into a Drosophila UAS expression plasmid pUAST4 PC GFP FA blue. N-terminal GFP tagging of Arpin has been previously shown to be functional. • UAS-GBP::mCherry::LOV: We also cloned the GBP, or so-called GFP nanobody, a lama VHH single-chain antibody against GFP for expression of fusion proteins in the fly with Light Oxygen Voltage Sensing Domain (LOV), a photo-interacting protein able to interact with a PDZ domain from Avena sativa 58 . The GBP nanobody has been previously cloned into a pUAST4 GBP FA blue plasmid as described in ref. 48 . mCherry-LOV, flanked with FA restriction sites, is a synthetic gene to remove unwanted AscI sites inside the sequence (IDT). We also added a flexible linker (glycine-and serine-rich linker) between mCherry and the LOV peptide. It was then inserted in C-ter into pUAST4 GBP FA blue plasmid. For the synthetic mCherry::LOV gene and oligonucleotide sequences used, see Supplementary https://doi.org/10.1038/s41556-022-01058-9 • UAS-GFP::Cdc42: For the Cdc42 protein cloning, Cdc42 was amplified by PCR, flanked with FA digestion sites from the plasmid available from Addgene collection ID 52248 (pUASp YFP Cdc42 WT) and was inserted in C-ter into pUAST4 PC GFP FA plasmid pre-digested by FA for insertion of the Cdc42 FA fragment. All the cloning has been confirmed by sequencing (Fasteris). All synthetic genes have been generated by IDT (G-blocks gene fragment). Injection of plasmids into Drosophila embryos to generate transgenics was performed by BestGene in w 1118 background.

Imaging method details
Fly notum imaging. Fly notum dissection and SOP imaging was performed in clone 8 medium after embedding into a fibrinogen clot in order to diminish tissue movements during fast 3D image acquisition as described 86 . Imaging was performed using a 3i Marianas spinning disk confocal setup based on a Zeiss Z1 stand, a 63× PLAN APO NA 1.4 objective and a Yokogawa X1 spinning disk head followed by a 1.2× magnification lens and an Evolve EMCCD camera (Photometrics). Fast z-stack acquisition of entire SOP cells (0.4 µm steps) was obtained using a piezo stage (Mad City Labs). Single-emitter emission filters were always used to avoid bleed-through, and each channel was acquired sequentially. To increase acquisition speed, we acquired 3D stacks spanning only 16-18 µm along the z axis, which is usually sufficient to contain the entire dividing SOP. To assure linearity and avoid saturation, fluorescent signal was systematically checked to be within the camera dynamic range. Unless stated otherwise, data presented in figure panels correspond to maximum-intensity projections.
SiR-DNA probe. To follow the different mitosis stages, after fibrinogen clot embedding described as above, clone 8 imaging media were supplemented with 1 µM SiR-DNA 87 (Spirochrome) and incubated at least 10 min at room temperature before imaging and left into the imaging media until the end of the experiment. Fig. 1k,l) was performed on the fly genotype w 1118 ; UAS-GFP-Actin 5C/+; Neur-Gal4/+ on the 3i Marianas spinning disk confocal setup based on a Zeiss Z1 stand, a 63× PLAN APO NA 1.4 objective and a Yokogawa W1 spinning disk head followed by a 1.2× magnification lens and an iXon EMCCD Andor camera equipped with Vector Photomanipulation hardware, a high-speed galvanometer-based point scanner, driven by Slidebook 6.0.

FRAP. FRAP of Actin-GFP (Extended Data
Two circular bleaching regions (2 µm diameter) were drawn onto the anterior and the posterior cortex and bleached simultaneously on both poles in late anaphase. Owing to the fast recovery of Actin-GFP (timescale of few seconds), recovery was monitored in 2D (one z plane) to maximize frame rate and ensure acquisition is as fast as possible. The recovery was then monitored by spinning disk confocal imaging at an average frame rate of 4.3 Hz.
For each FRAP experiment, we followed four different regions: (1) Anterior FRAP region of interest (ROI); (2) Posterior FRAP ROI; (3) Photobleaching ROI: cytoplasmic ROI within the same cell to measure the decay in fluorescence due to the acquisition bleaching; (4) Background ROI: ROI outside the cell to measure the offset intensity.
The photobleaching and background curves have been fitted with single exponential functions of the form: Anterior and posterior FRAP curves were first processed for signal background subtraction (with the ROI outside the cell) and for photobleaching correction (with the cytoplasmic ROI within the cell) as follows: where I Pre-FRAP norm and I Pre-photobleaching norm correspond to the average pre-bleaching intensities in the FRAP ROIs and in the photobleaching ROI, respectively.
Additionally, we performed full-scale normalization according to the following formula: where I FRAP double norm (bleach) is the intensity value just after bleaching and I Pre-FRAP double norm the average intensity before bleaching of the double normalized data. Both anterior and posterior normalized FRAP curves were then fitted to a double exponential equation (as previously established for Actin dynamics 89,90 ): In Extended Data Fig. 1l, the represented turnover is the average of τ 1 and τ 2 . For the anterior pole τ 1 = 0.3 ± 0.08; τ 2 = 9.01 ± 0.9 and for the posterior pole τ 1 = 0.8 ± 0.32; τ 2 = 28.31 ± 2.2 and in Extended Data To fully describe the Actin turnovers at the cell cortex, the curves should additionally be corrected for a cytoplasmic diffusive recovery process as described in ref. 91 . Yet, our FRAP experiment aims to compare the anterior and the posterior cortex dynamics, and we assume that this process is similar in both the anterior and the posterior cytoplasm.
Fly notum immunofluorescence. Fly notum staining was performed as previously described 86 : In brief, fly nota were dissected in PEM (80 mM PIPES, 5 mM EGTA and 1 mM MgSO 4 ), then fixed during 20 min in PEM with 4% PFA (Electron Microscopy Science) followed by a 20 min incubation in PEM with 4% PFA and 0.2% Triton X-100. Nota were then processed for immunofluorescence using standard techniques.
For Actin filament visualization, we used Phalloidin 425 (from Sigma) at a 1/40 dilution. Coverslips were mounted in Prolong Gold anti-fade reagent (Molecular Probes). Image acquisition setting was then performed on the 3i Spinning disk confocal microscope W1 setup described above.

Drug treatments.
To inhibit Formins, we incubated our tissue with 40 µM SMIFH2 drug.
To dissasemble spindles during division, we used the microtubule depolymerizing drug Colcemid at 10 µg ml −1 together with Roscovitine (CDK inhibitor) at 25 µM to bypass the metaphase-arrest checkpoint.
Nanobody targeting. In this study, we used the 'nanobody assay' established in ref. 48 , consisting of a GBP (or so-called GFP nanobody), a lama VHH single chain antibody against GFP 47 fused with polarity proteins in the fly (GBP::Pon and GBP::Bazooka). GBP::Pon will segregate in the anterior cortex as the wild-type Pon protein, whereas GBP::Baz will segregate in the posterior cortex.
Flies co-expressing GBP::Pon and WAVE::GFP (Fig. 3a-c) displayed occasional spindle orientation defects reflected by a division plane orthogonal to the polarity. Cells showing such spindle orientation defects were excluded from subsequent analysis.
We also used Gal80 ts to achieve lower levels of GBP-Baz to prevent ectopic expression of Bazooka (Extended Data Fig. 5m,n).

Photo-interacting protein optogenetic experiments.
Whole-cell illumination. Whole-cell photomanipulation in Fig. 5a,b and Extended Data Figs. 6a-d and 8j,k was performed on the 3i Marianas spinning disk X1 setup described above as a stack acquisition with 488 laser at 250-500 ms and 405 laser at 10-20 ms exposure time to promote the interaction between the LOV peptide and the PDZ sequence protein or the CRY2 FL and CIB 1 protein couple.
To target Arpin into cortical Actin-rich regions for branched Actin inhibition upon light illumination, we used w; UAS-CIB 1 ::GFP::Arpin/+; UAS-Lifeact::mCherry::CRY2 FL , Neur-Gal4/+ fly genotype (Extended Data Fig. 6c,d). Fig. 4c-g and Extended Data Fig. 6f-i was performed on a 3i Marianas spinning disk confocal W1 setup described above with 3i Phasor hardware, a spatial light modulator-based computer-generated holography, driven by Slidebook 6.0. We generated a squared ROI centred in the middle of the cell in z englobing the posterior compartment to promote the interaction between the CRY2 FL and CIB 1 protein couple within the posterior pole only. We used the Phasor 445 laser at 15-20% laser power for 500 ms exposure starting in anaphase onset and illuminated the region after each 3D stack acquisition. To target Arpin into the posterior cortex for branched Actin inhibition upon light illumination, we used the w; UAS-CIB 1 ::GFP::Arpin/+; UAS-Lifeact::mCherry::CRY2 FL , Neur-Gal4/+ fly genotype (Fig. 4e-g and Extended Data Fig. 6f-h) or w; UAS-CIB 1 ::GFP::Arpin/UAS-FP670::Pon; UAS-Lifeact::mCherry::CRY 2 FL , Neur-Gal4/+ fly genotype (Extended Data Fig. 6i). Fig. 6g-j was performed on a 3i Marianas spinning disk confocal W1 setup described above with the 3i Vector hardware. We used the vector 488 laser to illuminate a 3 µm circle ROI located in the anterior pole, the illumination ROI was centred in the middle of the cell in z for 50 ms to 100 ms exposure starting at the second timepoint and then performed after each 3D stack acquisition. We always located our ROI regions in the anterior pole for two reasons: (1) to avoid the influence of the posterior Actin enrichment observed in wild type and (2) because, in the smaller anterior pole, the curvature is higher and thus any contribution of branched Actin on the curvature of the cell cortex would have a more dramatic/visible effect in the anterior pole.
Laser ablation. Cortex ablation. Cortical laser ablation was performed on the 3i Marianas spinning disk setup described above (63× NA 1.4 oil objective) equipped with Vector coupled with Ablate! pulsed laser ablation hardware driven by Slidebook 6.0 (Extended Data Fig. 9c,d).
To cut the cortex, laser ablation was performed on SOPs expressing w;; UAS-Lifeact::mCherry, Neur-Gal 4/+. We performed sequential cuts: first in the anterior cortex and then in the posterior cortex. As we observed bigger blebs (innate and laser-induced) in the posterior pole, we always performed ablation of the cortex at the anterior pole first in order to discard the effect of an intracellular pressure release at the first ablation, which could induce bigger blebs. In the quantification, we selected only cells that were not damaged by the ablation (where laser-induced blebs could retract after ablation and SOPs were able to finish cytokinesis). The bleb areas were measured when the bleb sizes reached their maximum size before retraction.
Neighbour cell ablation. Laser ablation was performed on the 3i Marianas spinning disk setup as described above in nota expressing w;; UAS-Lifeact::mCherry, Jupiter::GFP, Neur-Gal 4/+ (Extended Data Fig. 9e,f). We performed tissue ablation on entire pupae as described in ref. 92 . To remove the impact of neighbour cells on the daughter-cell size asymmetry, we performed large cuts in the anterior side of dividing SOPs (in anaphase) to remove neighbour cells. We then measured daughter-cell size once cytokinesis was completed.
Scanning electron microscopy. Flies were killed by exposure to diethyl ether for 20 min, then mounted on scanning electron microscopy holders using double-sided carbon tape (Electron Microscopy Sciences) and subsequently treated with a gold sputter coater ( JFC-1200, JEOL). Imaging was performed using a JEOL JSM-6510LV scanning electron microscope operating in high-vacuum mode using a working distance of 1 mm and an acceleration of 10-15 kV.

Statistics and reproducibility
Unless stated otherwise, measurements are given as mean ± standard error of the mean (s.e.m.). All statistical analyses were performed using SigmaStat 3.5 software (Systat). Normality of variables was verified with Shapiro-Wilk tests. Homoscedasticity of variables was always Nature Cell Biology Article https://doi.org/10.1038/s41556-022-01058-9 verified when conducting parametric tests. In cases where variables failed normality and/or homoscedasticity tests, non-parametric tests were applied.
Micrographs are representative of a set of at least two independent experimental rounds performed on different days and were in all cases reproducible. No statistical method was used to pre-determine sample size. The experiments were not randomized. The Investigators were not blinded to allocation during experiments and outcome assessment. As disclosed above in Methods, SOP cells showing spindle orientation defects were excluded from the WAVE nanobody experiment and, for the dshRNAi experiment, only cells with polarity defects were selected (low phenotype penetrance). For more detail, see Reporting Summary.

Supplementary Note 1
For additional methods, in particular, on quantification and image analysis, please refer to section Supplementary Methods.
For additional information, please refer to section Supplementary Information.
For the theory, please refer to section Supplementary Theory.

Reporting summary
Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability
Source data are provided with this paper. All other data supporting the findings of this study are available from the corresponding author on reasonable request.

Code availability
Custom codes written in ImageJ and MATLAB are available from the corresponding author upon reasonable request. Local curvature has been measured by an adapted MATLAB script from ref. 93 .  Fig. 9a, b). ), for the anterior pole τ 1 = 0.3 ± 0.08; τ 2 = 9.01 ± 0.9 and for the posterior pole τ 1 = 0.8 ± 0.32; τ 2 = 28.31 ± 2.2). Mann-Whitney Rank Sum Test two-sided, P < 0.001. All data are presented as Mean ± SEM unless stated otherwise. For details on genotypes, in this and other figures in this report, see Supplementary  Table 1. n = number of cells from 6, 6, 6, 2, 4, 4, 9, 10 pupae for a, b, c, f, g, h, j, l respectively. Source numerical data are available in source data.