Cell lineage-dependent chiral actomyosin flows drive cellular rearrangements in early development

Proper positioning of cells is important for many aspects of embryonic development, tissue homeostasis, and regeneration. A simple mechanism by which cell positions can be specified is via orienting the cell division axis. This axis is specified at the onset of cytokinesis, but can be reoriented as cytokinesis proceeds. Rotatory actomyosin flows have been implied in specifying and reorienting the cell division axis in certain cases, but how general such reorientation events are, and how they are controlled, remains unclear. In this study, we set out to address these questions by investigating early Caenorhabditis elegans development. In particular, we determined which of the early embryonic cell divisions exhibit chiral counter-rotating actomyosin flows, and which do not. We follow the first nine divisions of the early embryo, and discover that chiral counter-rotating flows arise systematically in the early AB lineage, but not in early P/EMS lineage cell divisions. Combining our experiments with thin film active chiral fluid theory we identify specific properties of the actomyosin cortex in the symmetric AB lineage divisions that favor chiral counter-rotating actomyosin flows of the two halves of the dividing cell. Finally, we show that these counter-rotations are the driving force of both the AB lineage spindle skew and cell reorientation events. In conclusion, we here have shed light on the physical basis of lineage-specific actomyosin-based processes that drive chiral morphogenesis during development.


INTRODUCTION
C. elegans nematode, remains poorly understood. RESULTS We set out to determine the extent of chiral rotatory movements in the actomyosin cell cortex of the first nine cell division in early C. elegans development. We started with investigating the first two divisions, the divisions of the P 0 zygote and the AB cell, and quantified flows from embryos containing endogenously tagged non-muscle myosin-II (NMY-2)::GFP using spinning disc microscopy ( Fig. 1(a), Supplement Video 1,2). We used particle image velocimetry (PIV) to determine cortical flow velocities in two rectangular ROI's placed on opposite sides of the ingressing cytokinetic furrow ( Fig. 1(a)). The velocity component parallel (y-direction) to the plane of cytokinesis (as determined by the cytokinetic ring) was averaged over the area of each box and over a time period of 21s after the onset of furrow ingression, indicating the beginning of cytokinesis. Strikingly, while P 0 does not exhibit counter-rotating flows, AB exhibits counterrotating flows with the two dividing halves spinning in opposite directions during division (Supplement Video 1,2). To quantify the speed and the handedness of these rotary flows, we use the velocities measured in each box (v 1 and v 2 ) to define a chiral counter-rotation flow velocity v c = e z · (e x × v 2 − e x × v 1 ) (akin to [33]), where e x is a unit length base vector pointing from the cytokinetic ring towards the pole, e y is an orthogonal unit length vector parallel to the cytokinetic plane ( Fig. 1(a)), and e z = e x × e y . With this definition, |v c | quantifies the speed of counter-rotating flows and the sign of v c denotes their handedness (see methods and Supplement Fig. 1(a)). Indeed, counter-rotating flows are absent during the division of the P 0 cell with v c = 0.01 ± 0.51 µm/min (mean ± error of the mean at 95% confidence unless otherwise noted), but present during AB cell division with v c = -7.01 ± 0.34 µm/min. We conclude that of first two cell divisions in the developing nematode, one displays counter-rotating actomyosin flows during cytokinesis while one does not.
This raises the question which of the later cell divisions display chiral counter-rotating flows, and which do not. To this end, we quantified chiral counter-rotating flows for the next seven cell divisions as described above. We find that cells of the AB lineage (ABa, ABp, ABar and ABpr) counter-rotate with average velocities of v c = -3.46 ± 0.33 µm/min, -3.68 ± 0.41 µm/min, -1.24 ± 0.19 µm/min and -1.16 ± 0.22 µm/min respectively ( Fig. 1(b)). In contrast, average counter-rotating flow velocities of cells of the P/EMS lineage (P 1 , EMS and P 2 ) are 0.15 ± 0.38 µm/min, 0.03 ± 0.14 µm/min and 0.253 ± 0.19 µm/min, respectively ( Fig. 1(b)). We also observe that cells of the P/EMS lineage, but not those of the AB lineage, exhibit a whole-cell (net-)rotating flow where the cortex in both cell halves move in the same y-direction [43] (Supplement Fig. 2(b), Supplement Video 1-5). To conclude, early cell divisions of the AB lineage, but not of the P/EMS lineage, undergo chiral counter-rotating flows. Note also that the chiral counter-rotating flow velocity in the AB lineage decreases as development progresses and cells become smaller ( Fig. 2(b)).
Together these findings show that both presence and strength of chiral counter-rotating flows are related to the fate of the dividing cell.
We have shown previously that chiral rotating cortical flows are driven by active torque generation that depends on the myosin distribution [33]. Given that chiral counter-rotating flows arise only during AB and not P/EMS cell divisions, we hypothesize that myosin distributions during division of the AB and the P/EMS-lineage cells differ in specific features. To investigate this, we determined the NMY-2 distribution along the long axis of dividing cells (Fig. 1(c)) for the first six cell divisions, and extracted two features: a myosin ratio that characterizes the difference in myosin intensity between the two cell halves and the relative cytokinetic ring position that characterizes the relative position of the myosin peak along the long axis, and the degree of asymmetry of cell division. We find that myosin ratios for the AB, ABa and ABp cells are 1.0 ± 0.13, 0.92 ± 0.29, and 1.00 ± 0.24, respectively, indicating that there is no significant difference in cortical myosin concentration between the two halves of AP lineage dividing cells. In contrast, the myosin ratios in P 0 , P 1 and EMS are 1.67 ± 0.3, 2.07 ± 0.61, 1.68 ± 0.33, respectively ( Fig. 1(e)).
We find that cytokinetic ring position for AB, ABa and ABp cell are at positions of 0.49 ± 0.01, 0.49 ± 0.01 and 0.51 ± 0.02 relative to cell length, respectively. In contrast, the cytokinetic ring position for P 0 , P 1 and EMS cells are at positions of 0.58 ± 0.01, 0.57 ± 0.02 and 0.59 ± 0.01 relative to cell length, respectively ( Fig. 1(d)). To conclude, the early cell divisions of the AB lineage are symmetric in terms of myosin intensity ratio and ring position, while early cell divisions of the P/EMS lineage are asymmetric in these two features.
We next asked if the differences in presence and absence of chiral counter-rotating flows between AB and P/EMS cells can be accounted for by the observed difference in myosin ratio and cytokinetic ring position.
We utilized thin film active chiral fluid theory [33,44] in an isotropic model cell of similar dimension with constant coefficient of friction with respect to the cytoplasm of the cell and the outside environment, and determined the chiral counter-rotating flow velocity v c for different values of myosin ratio and ring position.
We find that a myosin ratio of one and a symmetric ring position at 0.5 results in a maximal v c , while myosin ratios different from one and asymmetric ring position results in lower values of v c (Supplement Fig. 3(d)-(e)). This indicates that the switch between chiral and non-chiral flows between the two lineages could in principle be attributed to the observed difference in myosin ratio, cytokinetic ring position or both.
We note, however, that while thin film active chiral fluid theory can relate at a quantitative level the myosin profile along the long axis of the dividing cell with the chiral y-component of the actomyosin flow-field for AB, ABa, and ABp, this is not possible for the P/EMS lineage (Supplement Fig. 3(a)-(b), Supplement Table 1,2). We suspect this is due to specific features of the overall dynamics that are not included in our theoretical description, such as movements of the midbody remnant particular to the P/EMS linage [45] or possible inhomogeneities in the friction coefficient (e.g. friction with respect to the neighboring cells). This indicates that our understanding of the mechanisms that shape the cortical flow fields in these divisions is still incomplete.
We next focus our attention on the mechanism by which dividing cells assume their correct position inside the developing embryo. Specific rotations of the spindle (termed spindle skews) are thought to be a key mechanism by which dividing cells reposition themselves in the embryo [33,45,46]. One hypothesis is that spindle skews are driven by spindle elongation [32]. In this case spindle elongation causes a skew because the spindle rearranges within an asymmetric cell shape, thus responding to the constraints provided by neighboring cells and the eggshell (Supplement Fig. 4(a)). An alternative hypothesis is that spindle skews are driven by counter-rotating flows of the dividing cell halves [33]. In this case the mechanism is akin to a bulldozer rotating on the spot by spinning its chains in opposite directions [33]. Counter-rotating cortical flows of the two cell halves will lead to a torque and a cell skew in the case that the cell experiences different friction coefficients on different surfaces (e.g. friction with respect to eggshell in comparison with friction with respect to a neighboring cell; Fig. 2(f)). To discriminate between these two hypothesis, we first asked if those cells that undergo spindle skews also exhibit chiral counter-rotating flows. We quantified spindle skews by determining the positions of spindle poles at the beginning and at the end of cytokinesis in embryos expressing TBB-2::mCherry for the first 11 cell divisions (Supplement Video 9). The angle between the lines that join the two spindle poles at the onset and after cell division defines the spindle skew angle (Fig. 2(a)). We find that cells of the early AB lineage undergo an average skew angle of 21.17   Fig. 2(b)). Given that AB lineage cells, but not P/EMS lineage cells, undergo chiral counter-rotating flows, we conclude that cells that exhibit significant chiral counter-rotating flows also undergo significant spindle skews during early development ( Fig. 2(b)).
The results obtained so far are consistent with a scenario in which cell fate determines the presence of chiral counter-rotating flows, and these counter-rotating flows then drive spindle skews. We test for these two causal relationships separately. We first asked if cell fate determines the presence of chiral counter-rotating flows. In this case, we expect that on the one hand, anteriorizing the worm leads to equal and significant counter-rotating flows for the second and third division. On the other hand, we expect that posteriorizing the worm would lead to absence of chiral counter-rotating flows. Consistent with the first expectation, anteriorizing the embryo via par-2; chin-1; lgl-1 (RNAi) [47] results in the second and the third cell division exhibiting chiral counter-rotating velocity with v c values that are not significantly different from one another (-6.53 ± 1.13 µm/min and -6.67 ± 0.8 µm/min, respectively; Supplement Video 6; Fig. 2(c)-(d)). Consistent with the second expectation, posteriorizing the embryo via par-6 (RNAi) [48] results in both the second and the third cell division not exhibiting counter-rotating flows (v c = 0.07 ± 0.71 µm/min and -0.85 ± 1.13 µm/min, respectively; Supplement Video 8; Fig. 2(c)-(d)). Hence, cell fate determines the presence or absence of chiral counter-rotating flows. Note also that switching the cell fate results in a concomitant changes in the spindle skew angle for both the second and third cell division ( Fig. 2(e)). We conclude that cell fate determines both the presence of chiral counter-rotating flows and the degree of spindle skew.
We next tested the second causal relationship, and asked if chiral counter-rotating flows in the cortex drive spindle skews. Changing the speed at which the chains of a bulldozer counter-rotate leads to a change in the speed at which the entire bulldozer rotates. Hence, we evaluated if increasing or decreasing the chiral counter-rotating flow velocity results in increased or reduced rates of spindle skews. We first evaluated if we can increase and decrease counter-rotating flow velocity in the AB cell, by RNAi of RhoA regulators [33].
Weak perturbation RNAi of ect-2 results in a counter-rotating flow velocity of -3.57 ± 0.57 µm/min, which is reduced in comparison to the unperturbed embryo (v c = -6.6 ± 0.37 µm/min; Fig. 3(a)-(b)). Conversely, weak perturbation RNAi of rga-3 increases the chiral counter-rotating flow velocity to v c = -8.71 ± 0.58 µm/min ( Fig. 3(a)-(b)). Note that these perturbations impact only on active torque generation and chiral counter-rotating flows, and do not significantly change on-axis contractility-driven flow consistent with previous findings [33] (Fig. 3(c)). We now use these perturbations to test whether chiral counter-rotating flows determine the rate of spindle skew. We indeed find that decreasing the chiral counter-rotating flow velocity by mild ect-2 (RNAi) leads to concomitant reduction of the rate of spindle skew (average peak rate of spindle skew: 0.59 ± 0.05 • /min (Supplement Video 10) as compared to 1.01 ± 0.1 • /min in control embryos (Supplement Video 11); Fig. 3(d)). Conversely increasing RhoA signaling by mild rga-3 (RNAi) treatment leads to increase of both the chiral counter-rotating flow velocity and the rate of spindle skew (average peak rate of spindle skew: 1.29 ± 0.12 • /min (Supplement Video 12); Fig. 3(d)). Note that the peak rates of spindle elongation remain unchanged as compared to the control for both perturbations ( Fig. 3(d)). We conclude that changing counter-rotating flow velocities results in concomitant changes of the rates of spindle skews without impacting on the dynamics of spindle elongation. Hence, it is unlikely that spindle skews are driven by the spindle elongating in an asymmetric cell shape [13,32], as stated in the first hypothesis above. These results instead lead credence to the second hypothesis, that chiral counter-rotating flows mechanically drive cell and spindle skews.
If chiral counter-rotating flows indeed drive spindle skews, we predict that a complete absence of chiral flows would lead to a complete absence of spindle skews. We test this prediction in the AB cell, by inactivating cortical flows entirely through a fast acting temperature sensitive nmy-2(ts) mutant [49].
Worms were dissected to obtain one-cell embryos and mounted at the permissive temperature at 15 • C, to allow them to develop normally. Approximately 60 s after the completion of the first (P 0 ) cell division, the temperature was rapidly shifted to the restrictive temperature of 25 • C using a CherryTemp system.
Imaging was started as soon as the AB cell entered anaphase. In all nmy-2(ts) mutant embryos (12 out of 12) an ingressing cytokinetic ring was absent and cytokinesis failed after temperature shifting, indicating that NMY-2 was effectively inactivated [50] (Supplement Video 14). Interestingly, while the dynamics of spindle elongation, including the peak rate of spindle elongation and the final spindle length, are essentially unchanged as compared to control embryos at restrictive temperature, the average peak rate of spindle skew was significantly reduced as compared to control embryos (0.33 ± 0.09 • /min as compared 1.43 ± 0.13 • /min in control embryos; Fig. 4(a)-(b); Supplement Video 13,14). This demonstrates that a functional actomyosin cortex with chiral cortical flows is required for spindle skews of the AB cell. In light of our experiments above, we now conclude that spindle skews in the AB cell are independent of spindle elongation, but are instead driven by chiral counter-rotating flows. Finally, we performed temperature shift experiments for the first 11 divisions in the nematode, and found that all cells belonging to the AB cell lineage show a significantly reduced skew in the nmy-2(ts) embryos at restrictive temperatures as compared to the control (Fig. 4(c)). We conclude that a functional actomyosin cortex with chiral cortical flows is required for spindle skews of early AB lineage cell divisions during worm development. Furthermore, spindle skews and cell repositioning of early AB lineage cells are independent of spindle elongation, but are instead driven by chiral counter-rotating flows.

DISCUSSION
Here, we show that lineage-specific chiral flows of the actomyosin cortex drive lineage-specific cell rearrangements in early C. elegans development. Recently, actomyosin flows were demonstrated to be required for determining the initial orientation of the mitotic spindle [17]. We here show that actomyosin cortex drives an active counter-rotation of the two halves of dividing early AB lineage cells, leading to cellular repositioning of these cells during cell division. We suggest that chiral counter-rotating flows represent a general mechanism by which dividing cells can reorient themselves in order to allow their daughters to achieve their appropriate positions.
How does the cell lineage determine the presence or absence of chiral cortical flows? We know that AB lineage cells divide symmetrically, while the early P/EMS lineage cell divisions are asymmetric [51].
Accordingly, we here show that cell divisions in the AB lineage are symmetric in terms of cytokinetic ring positioning and myosin distribution and display chiral counter-rotating flows, while divisions in the P/EMS lineage are asymmetric in these measures and chiral counter-rotating flows are absent ( Fig. 1(b)-(e)). Cell lineage determinants like PAR proteins, instrumental for cell polarity, may therefore control chiral flows by modulating the distribution of molecular motors along the cell division axis [52]. In addition, many cortical constituents polarise along the anteroposterior axis prior to the first division, resulting in the AB cell to inherit higher levels of actin, myosin and its regulators [53][54][55] (Fig. 1(c)). The molecular composition of the cortex may therefore be different in the AB and P/EMS lineage, which is consistent with a recent study showing that both lineages are differentially dependent on the actin nucleator CYK-1/mDia for successful cytokinesis [56]. Together, the combined action of cortex composition and the intracellular distribution of molecular motors may also determine the type of chiral flow behavior (Supplement Fig. 2).
By which mechanism are active torques generated? We showed previously that chiral active fluid theory can quantitatively recapitulate the chiral counter-rotating flows as observed during C. elegans zygote polarization. In this coarse-grained hydrodynamic description, the cortex is treated as a two-dimensional gel that has liquid-like properties and generates active torques. Assuming that the local torque density is proportional to the measured NMY-2 levels, we here show that this theory can quantitatively recapitulate the observed chiral flow behaviour in the dividing AB blastomeres (Supplement Fig. 3(a)-(b)). However, given that many actin-binding proteins (e.g. actomyosin regulators, nucleators and cross-linkers) localise in a pattern similar to myosin, and many of these affect the chirality of actomyosin flows in the polarising one-cell embryo, we cannot exclude that other force generators provide the active torque needed for chiral counter-rotating flows. Interestingly, like myosins [41], diaphanous-like formins are known to generate torque at the molecular level [57,58] and are required for numerous cellular [59] and organismal chiral processes [60][61][62]. Future work will be needed to first identify the molecular torque generator and to subsequently unravel the molecular mechanism underlying active torque generation. What is needed for driving cellular rearrangement by chiral counter-rotating flows, however, is an asymmetry in friction between the dividing cell and its environment ( Fig. 2(f)). We speculate that the dividing cell simultaneously contacts different surfaces (e.g. neighboring cells and the eggshell), which gives rise to an inhomogeneous friction coefficient [17], thus allowing the cell to rotate and reposition.
To conclude, our work shows that chiral rotatory movements of the actomyosin cortex are more prevalent in development than one might have suspected. We report on an intricate pattern of chiral flows during early C. elegans development, leading to dedicated cell skew and cell reorientation pattern. This is interesting from a physical perspective, since together the cells of the early embryo represent a new class of active chiral material that requires an explicit treatment of angular momentum conservation [33,44]. This is interesting from a biological perspective, since cell skews driven by actomyosin torque generation represent a novel class of lineage-specific morphogenetic rearrangements. Together, our work provides new insights into chiral active matter and the mechanisms by which chiral processes contribute to animal development.

MATERIALS AND METHODS
Worm strains and handling: C. elegans worms were cultured on NGM agar plates seeded with OP50 as previously described [63]. The following C. elegans strains were used in this study: (RNAi) conditions, young L4 were transferred to feeding plates 24 hrs before imaging. Embryos used as controls for all RNAi experiments were grown on plates seeded with bacteria containing a L4440 empty vector, and exposed for the same number of hrs as the corresponding experimental RNAi perturbed worms.
The indicated hrs of RNAi treatment reflects the time that worm spent on the feeding plate. All dissections were done in M9 buffer to obtain early embryos. Embryos were mounted on 2% agarose pads for image acquisition for the all cell divisions except 4-6 cell stage [67]. Four cell embryos were mounted using low melt agarose [31,33]. The rga-3 feeding clone was obtained from the Ahringer lab (Gurdon institute, Cambridge, United Kingdom) and the ect-2 feeding clone from the Hyman lab (MPI-CBG, Dresden, Germany). RNAi feeding clones for par-2, par-6, chin-1 and lgl-1 were obtained from Source Bioscience (Nottingham, United Kingdom).
Image Acquisition: All the imagining done in this study was performed at room temperature (22-23 • C) with a spinning disk confocal microscope. Two different spinning disk microscope systems were used for the study. TH155 strain was used to image TBB-2::mCherry together with PH::GFP to determine cytokinetic ring position and spindle skew angle in Fig. 2(b)for 11 cell stages. SWG204 strain was used for temperature sensitive experiments (Fig. 4(a)-(c)). Spindle pole imaging for AB cell (TBB-2::mCherry) was performed by acquiring nine-z-planes (1 µm apart) with a 594 nm laser and exposure of 150 ms on the second system at an interval of 3s. For long term imaging using TH155 strain ( Fig. 2(b)), TBB-2::mCherry together with PH::GFP was imaged in 24 z-slices (1 µm apart) with 594 nm laser and exposure of 150 ms at an interval of 30 s (Supplement Video 9).
Image Analysis: Cortical flow velocity fields in the xy-plane were obtained using a MATLAB code based on the freely available Particle Image Velocimetry (PIVlab) MATLAB algorithm [69]. Throughout the study, we used the 3-step multi-pass with linear window deformation, a step size of 8 pixels and a final interrogation area of 16 pixels.
To determine the average flow fields that were fitted by the chiral thin film theory (Supplement Fig. 3(a)), we first tiled the flow field determined by PIV into 9 sections along the long-axis of cells. Within each section, we averaged the flow field over the entire duration during which flows occur. Since we were only interested in flows that are generated by the cytokinetic ring, we excluded embryos in which we could not differentiate whole body rotation from cytokinesis [43]. From all the imaged cell divisions, a small subset of measurements in which the optical focus on the cortical plane was lost during imaging, was discarded.
From the measured cortical flows, we extracted properties that are later used to quantify their chiral counter-rotating nature in the following way. First, we identified the cleavage plane or the cytokinetic ring by eye. We then defined a region of interest (ROI) on each side of the cytokinetic ring ( Fig. 1(a)). In order to ensure that PIV measurements were not affected by the saturating fluorescence signal from the cytokinetic ring, we placed the inner boundary of each ROI at a distance of 1 µm from the ring. The position of the outer boundary of each ROI (along the long axis) was scaled with the size of the analyzed cells (10 µm, 8.5 µm, 6 µm, 6.5 µm, 6.5 µm, 6.5 µm for P 0 , AB, P 1 , ABa, ABp and EMS, respectively, measured from the position of the cytokinetic ring). For P 2 , ABal and ABpr cells the distance of the outer ROI boundary to the cytokinetic ring varied around 4 µm, depending on the cell surface area visible in the imaging focal plane. For every cell, the width of ROIs was set equal to the length of the cytokinetic ring visible in the focal plane. In each ROI, we averaged the observed flow field over a period of 21 s. Consistent with earlier findings, we observed a whole cell rotation prior to P 0 cytokinesis [43,70]. We discarded a small subset of embryos (4 out of 17), where this whole cell rotation coincided with the time frames in which we performed the flow analysis.
In order to quantify chiral flows, we defined a chiral counter-rotating flow velocity v c together with a handedness as follows. First, we introduce a unit vector that is orthogonal to the contractile ring and points towards the cell pole that is in the direction of the anteroposterior-axis of the overall embryo (e x , see Supplement Fig. 1(a)). A second unit vector e y is used, which is parallel to the cytokinetic ring and orthogonal to e x . We denote the average velocities determined in the two halves of the cell (measured within the ROIs described above) as v 1 and v 2 . With this, we define the chiral counter-rotating flow velocity where e z = e x × e y is the third base vector of a right-handed Finally, in order to determine a flow measure that captures cortical flows along the cell's long axis and into the contractile ring, we define the contractile flow velocity (v contr ) depicted in Fig. 3 For contractile cortical flows into the cytokinetic ring, we have e x · v 1 > 0 and e x · v 2 < 0, and therefore v contr < 0.
Spindle skew and elongation analysis: In order to measure spindle skew angles, z-stacks (nine-planes; 1µm apart at 3s time interval) of the spindle poles were first projected on the plane perpendicular to the cytokinetic ring. For P 0 , AB and P 1 the imaging plane was already perpendicular to the plane of cytokinesis while for the remaining cell divisions the embryos were rotated accordingly using the clear volume plugin [71] in FIJI. Subsequently, the spindle skew angle was defined as the angle between the line that joins the spindle poles at the onset of spindle elongation (anaphase-B) (initial spindle angle) and at completion of cytokinesis (final spindle angle) (Fig. 2(a)). Spindle elongation length was defined as the distance between the two spindle poles during the same time-frames. To measure the dynamics of spindle elongation and skew angle in the AB cell (Supplement Fig. 4 Determining myosin ratio, cytokinetic ring position and fitting myosin profiles: In order to obtain cortical myosin distributions (Fig. 1(c)) we normalized the axis of cell division and calculated the mean myosin intensity in a 20 pixel-wide stripe along this axis for the same timepoints when v c was calculated.
The myosin ratio ( Fig. 1(e)) was determined by dividing the mean intensity at the anterior (0-20% of the normalized cell division axis) by the mean intensity at the posterior (80-100% of the normalized cell division axis) for P 0 , AB, P 1 and EMS. For ABa and ABp the myosin intensity was calculated similarly but along the L/R axis. To determine the position of the cytokinetic ring, we performed midplane imaging using a strain expressing a membrane marker (PH::GFP) and a tubulin marker to label spindle poles (TBB-2::mCherry). The cell division axis was defined as the line through the two opposing spindle poles and was normalized between cell boundaries. The relative cytokinetic ring position was defined as the position where the ingressing ring intersects the normalized cell division axis.
For visualization purposes (Fig. 1(c)), we fitted the myosin distributions using the fitting function The errorfunction erf and the Gaussian represent contributions from the anteroposterior myosin asymmetry and from the contractile ring, respectively. The fitting parameters I P , I A , I R , w and x r , respectively, describe myosin intensities at the posterior pole, the anterior pole and in the cytokinetic ring, as well as the width and position of the ring.
Temperature sensitive experiments: We used the cherry temp temperature control stage from Cherry Biotech for all temperature sensitive experiments in the study. L4 worms carrying tbb-2::mCherry (SWG63, control) and nmy-2(ts); tbb-2::mCherry (SWG204) were grown at 15 • C (permissive temperature for nmy-2(ts) mutants) overnight. During image acquisition temperature was maintained using the cherry temp temperature control stage from Cherry Biotech. For imaging the dynamics of spindle elongation and skew angle in the AB cell for nmy-2(ts) and control embryos, 60 s after the successful completion of the first cell division (P 0 cell division), temperature was raised to 25 • C. Embryos were imaged approximately 5 min after the temperature shift to minimize photo toxicity. Similarly, for later cell stages, the temperature shift was carried out right after completion of cytokinesis of the mother cell. A small subset of embryos in which spindle poles of daughter cells could not be visualized were discarded. Cortical flows in C. elegans embryos have been successfully described using the thin film theory of active chiral fluids [33,40]. We use the fact that cells are approximately axisymmetric, and we assume that the active forces during cell division vary mostly along their symmetry axis, in the following referred to as long axis. In this case, the hydrodynamic equations of a chiral thin film can be formulated as an effectively one-dimensional system of equations, capturing flows parallel (v x ) and orthogonal (v y ) to the long axis: Here, η is the viscosity of the cortex and γ is the friction with surrounding material. Note that the assumption of a homogeneous friction γ is a strong simplification, where we neglect details of the potentially inhomogeneous mechanical interactions between cells, as well as with the extra-embryonic fluid and the egg shell. Gradients of active tension T and active torques τ lead to contractile and chiral flows, respectively.
It has been demonstrated previously that active tension and active torques both dependent on the local myosin concentration in the cortex [33,35,40]. Using the fluorescent myosin intensity I(x) as a proxy for the myosin concentration, we can write in the simplest case T = T 0 I(x) and T = τ 0 I(x).
Denoting the length of the measurement domain by L (approximately the length of the cell's long axis), we can identify three independent parameters in the model Eqs. (S1) and (S2): The characteristic contractile and chiral velocities v T = LT 0 /η and v τ = Lτ 0 /η, respectively, as well as the hydrodynamic length = η/γ.

Fitting cortical flows
For the fitting of cortical flows for given myosin profiles we closely follow our previous work [33]. Briefly, we use experimentally determined myosin profiles I(x) in Eqs. (S1) and (S2) to calculate flows v x and v y .
We then determine the parameters v T , v τ and for which the predicted flows best match the experimental data. To extract unique solutions from Eqs. (S1) and (S2), we use the experimentally measured flow velocities at the boundaries of the measurement domain as boundary conditions. Note that due to imaging    We also considered asymmetrically dividing cells (P 0 , P 1 , EMS) in which, instead of counter-rotating flows (|v c | > 0, v r ≈ 0), mainly net-rotating flows occur (v c ≈ 0, |v r | > 0) (Supplement Fig. 2). Following the same fitting procedure as described in the previous section, we noticed that the chiral thin film theory Eqs. (S1) and (S2) generally could not account quantitatively for the observed cortical flow profiles.
However, using the theory it is still possible to rationalize qualitative properties of the observed cortical flows, as we discuss in the following.

Qualitative properties of myosin distributions and chiral flows
While the chiral thin film theory does not recapitulate all of the experimentally observed flows quantitatively, the theory allows linking qualitative predictions to key properties of observed myosin distributions and chiral flows. In particular, we noticed that the myosin profiles in asymmetrically diving cells consistently featured a rather asymmetrically positioned contractile ring ( Fig. 1(d)). Furthermore, the myosin profiles of asymmetrically dividing cells are asymmetric with respect to the cytokinetic ring and exhibit plateaus towards the anterior cell poles (Fig. 1(c)and Fig. 1(e)). An overview of these qualitative properties for the P/EMS lineage and the AB-lineage is given in Table S2.
Myosin peak position Anterior-posterior myosin Chiral flow properties AB-lineage Centered Symmetric v r ≈ 0, |v c | > 0 P/EMS lineage Off-center Asymmetric |v r | > 0, v c ≈ 0  To establish how a contractile ring and an overall myosin asymmetry generally affect flows predicted by the chiral thin film theory, we generalize the chiral thin film equations [33,40] to curved surfaces and solve them on an ellipsoid using corresponding synthetic torque profiles (Supplement Fig. 3(c)). We find that a symmetrically placed ring pattern yields perfectly counter-rotating flows (v r = 0, |v c | > 0, Supplement Fig. 3(c), left), while an anterior-posterior myosin asymmetry yields net-rotating flows (|v r | > 0, v c = 0, Supplement Fig. 3(c), right). To study the combined effect of a varying position of the contractile ring and a myosin asymmetry, we develop in the following section a simple minimalistic model of the system.

Chiral flow minimal model
In the following, we develop a minimal description of the occurrence of counter-and net-rotating flows based on key characteristics of the myosin profiles discussed in the previous section. We consider a simplified myosin profile in the form Here Here, α = 2γL 2 /η is an inverse dimensionless hydrodynamic length and v τ = Lτ 0 /η the characteristic velocity associated with active torques. The coefficients in Eq. (S6) are given by With these coefficients, Eq. (S6) describes flows v r y resulting from the contractile ring given in Eq. (S4) and flows v ap y resulting from the asymmetric myosin profile given in Eq. (S5). Note that, as expected, flows due to the presence of the contractile ring vanish for I R = 0 and flows due to the presence of a myosin asymmetry vanish if I A = I P . General flow profiles are given as superposition of the two contributions: v y = v r y +v ap y .
Finally, to evaluate these solutions, we define a dimensionless counter-rotating velocityṽ c and the net-rotating velocityṽ r in analogy to the quantities introduced in the main text as Here,ṽ y = v y /v τ and we consider a window of 15 % (∆/L = 0.15) of the total length towards either side of the idealized contractile ring over which the mean flow velocity is determined ( Fig. 1(a), Supplement Fig. 1(a)). Using this minimal model, we can now investigate how the combined contributions of a largescale myosin asymmetry (I ap ) and a varying contractile ring position (I r ) affect the counter-rotating velocitỹ v c and net-rotating velocityṽ r . In particular, we fix for the discussion α = 1 and w/L = 0.1, as well as I R /I P = 2. In this case, the counter-rotating flow velocityṽ c and the net-rotating flow velocityṽ r are only functions of the relative ring position x r /L and the anterior-posterior myosin ratio I A /I P with properties shown in Supplement Fig. 3(d)-(g)and described in the following.
For an anterior-posterior symmetric myosin profile, counter-rotating flows |ṽ c | have a weak maximum in their amplitude if the contractile ring is at a centered position x r /L = 0.5 (Supplement Fig. 3(d)).
Furthermore, a centered contractile ring has no effect on the counter-rotating flow measureṽ c if a largescale myosin asymmetry I A /I P > 1 is introduced (Supplement Fig. 3(e)). However, for an off-centered ring x r /L > 0.5 the presence of a myosin asymmetry will contribute flows that reduceṽ c and can even lead to vanishing counter-rotating flowsṽ c = 0 if I A /I P is sufficiently large. While this matches the qualitative experimental observations listed in Tab. S2, the required asymmetry predicted by the theory is significantly larger than the experimentally measured one.
Also, the behavior ofṽ r in our minimal model is compatible with the qualitative properties listed in Tab. S2. In particular, for a large-scale myosin asymmetry I A /I P > 1, the net-rotation velocityṽ r is negative for any ring position, while it can becomes positive for x r /L > 0.5 if I A = I P (Supplement Fig. 3(f)). Furthermore, net-rotating flows vanish for a symmetric myosin profile I A = I P and a centered contractile ring x r /L = 0.5 (Supplement Fig. 3(g)), which corresponds to the observations made in ABlineage cells. Finally, the presence of large-scale myosin asymmetries I A /I P = 1 is generally expected to contribute to net rotating flows (Supplement Fig. 3(g)). This holds true for essentially arbitrary positions of the contractile ring and indicates that such asymmetries could play an important role for developing a better understanding of net-rotating flows in the P/EMS lineage cells in the future.    orange, ABp) obtained from thin film active chiral fluid theory using NMY-2::GFP gradients measured during cytokinesis. For the AB cell, a representative NMY-2::GFP gradient is shown in Fig. 1(c).