Cortical flow aligns actin filaments to form a furrow

1Cytokinesis begins in late anaphase, triggered by regulatory pathways with feedback from the mitotic spindle that ensure appropriate positioning of the molecular machinery (reviewed in; ). As a consequence, the small regulatory GTPase RhoA and the molecular motor myosin are enriched in an equatorial band. Myosin can directly organize the actin network, and if myosin-based active alignment (e.g. via search-and-capture) or flow-based compression as proposed by White and Borisy drive furrow formation and cytokinesis in eukaryotes remains unclear.

2We set out to address this question in the one cell embryo of the nematode C. elegans which forms two constricting ingressions, first a pseudocleavage furrow during polarity establishment, and then a cytokinetic furrow during cytokinesis (Figure 1—figure supplement 1a, Video 1). Notably, the pseudocleavage furrow is linked to cortical flow and lacks regulatory control from the mitotic spindle. We first characterized the actomyosin cortical network during pseudocleavage and cytokinesis. For this, we generated a Lifeact::mKate2 fluorescent line of C. elegans by coupling the Lifeact peptide to the far-red fluorophore mKate2 that was codon optimized for C. elegans (see Materials and methods and Video 2). This allows us to quantify cortical actin filament orientation in space and time, as well as cortical flow velocity fields by Particle Image Velocimetry (PIV, Figures 1 and 2, Figure 2—figure supplement 1). We find that actin filaments change from a randomly oriented and isotropic gel before cortical flows initiate, into a more circumferentially aligned organization at the future site of furrow ingression during both pseudocleavage and cytokinesis (Figure 1b, Figure 1—figure supplement 1 and Videos 1 and 3). We studied how pseudocleavage and cytokinesis differ in the spatial distribution of molecular regulation and contractility within the equatorial region (Figure 1). Non-muscle myosin II (NMY-2) is the essential molecular motor that drives both cortical flow and cytokinesis, whereas the small GTPase RhoA, when active, is responsible for its local activation. At the onset of cytokinesis, active RhoA and NMY-2 locally increase at the position of the contractile ring, while for pseudocleavage we observed no such increase (Figure 1). Instead, the equatorial region in pseudocleavage corresponds to a transition zone with a gradual decrease of RhoA and myosin between the anterior region of high and the posterior region of low contractility (Figure 1). The actin nucleator formin CYK-1 is downstream of RhoA and follows a similar pattern of localization, and actin bundling via anillin or plastin also does not appear to be increased in the equatorial region during pseudocleavage (Figure 2—figure supplement 5e–f). To conclude, the pseudocleavage furrow ingresses with a circumferential alignment of filaments in the gel, but without a local zone of RhoA activation and the corresponding local increase in myosin and formin density. Since search-and-capture like mechanisms require a localized band of myosin and actin nucleators at the equator to drive myosin-based active alignment, this suggests that actin filaments in pseudocleavage align via flow-based compression and not via active alignment.

3We next sought to test if flow-based compression drives actin filament alignment. To this end, we developed tools for the spatiotemporal quantification of compression by flow, of filament orientation, and of cortex ingression distance within the gel both at the onset of pseudocleavage and cytokinesis (see Appendix as well as Figure 2a and Figure 2—figure supplement 1). We find that the flow compression rate along the antero-posterior direction (AP axis or x axis), given by the spatial gradient of the velocity field (Figure 2b), increases with time during the very early stages of pseudocleavage. The compression rate peaks in the central region of the embryo, with a maximum of ~0.4 min−1. Notably, this peak is stable for several minutes until pseudocleavage flows cease entirely (Figure 2b). For cytokinesis, we find that the early flow also proceeds in a unidirectional manner from the posterior toward the anterior (Figure 2b). Similar to pseudocleavage, the compression rate increases with time over the very early stages of cytokinesis, with the compression profile peaking at the center of the embryo with a maximum rate of ~0.7 min−1 (Figure 2b). We characterized the average actin filaments orientation by a nematic order tensor Q (Figure 2—figure supplement 1a). This analysis relies on the fact that the intensity of the Fourier transformed image encodes geometric characteristics such as its main orientation pattern (see Appendix). We find that vertical (orthogonal to the direction of flow) alignment appears coincidental in space and time with the local increase of the compression rate (Figure 2b, compare column 2 and 3). Notably, changing the direction of flow also changes the direction of alignment: off-site sperm entry leads to flows along the short axis of the egg and actin filaments still align in the direction determined by compression (Figure 1—figure supplement 1d, Video 4 and Appendix). Finally, the ingressing furrow forms in the region where filaments are aligned (Figure 2b, column 4). Our quantifications reveal remarkable similarities between the compression rate fields, the pattern of alignment, and the ingression distance between pseudocleavage and cytokinesis (Figure 2b), suggesting common mechanisms. To conclude, actin filament alignment arises at locations of significant compression by flow.

4If flow-based compression aligns actin filaments for forming an ingression, we would expect compression to precede or to be concomitant with alignment and ingression. The 1D crosscorrelations between compression, filament alignment and ingression distance, calculated for the time that flows are essentially stationary (Figure 2b and Figure 2—figure supplement 1), show that for pseudocleavage both compression rate and alignment peak at about the same location, while the ingression field peaks ~ 3 µm further to the anterior (Figure 2c and Figure 2—figure supplement 2 for the spatiotemporal crosscorrelations). The situation is similar at cytokinesis, except that the compression field peaks furthest to the posterior. We next translated the characteristic distances between peaks in stationary flow to temporal delays between events (see Materials and methods for further explanation). We find that for pseudocleavage, filament alignment is essentially concomitant with compression, while for cytokinesis compression precedes alignment by 0.40 ± 0.16 min (Figure 2d). Furthermore, ingression arises approximately 0.5 min after compression for pseudocleavage and 0.9 min after compression for cytokinesis. To conclude, filament alignment appears to rapidly follow compression while ingression arises with a delay.

5We next sought to provide a physical explanation for flow-based alignment. The cell cortex in this and other systems can be thought of as a gel that forms a thin layer underneath the plasma membrane. Recent advances in physical theory show that this gel is active and generates the forces that drive cell shape changes. We describe the actin cortical layer as a thin film of a nematic gel under shear and compression by flow. In the x-direction, the time evolution of the local nematic order Q depends on advection (first term on the right hand side in Equation 1), compression in gel flow (second term), a process of relaxation to an isotropic configuration possibly via turnover (third term), and a tendency of filaments to align with each other over space (last term, see also Figure 3a)

6The characteristic time for relaxation to an isotropic state via turnover is determined by, while is a dimensionless coefficient that describes how local compression impacts nematic ordering. Finally, is a length scale that determines the distance over which actin filaments tend to point in the same direction. In our experiments, we observe a stationary phase (Figure 2b), and the profile of nematic order Q at steady-state is given by

7We next determined the theoretical alignment field from the experimental flow field and compression field. We used nonlinear least-square fitting to evaluate parameter values for which the theoretical alignment profile best matched the experimental one. There are five unknowns (three parameters that characterize emergent material properties,,, and, as well as two boundary values of nematic order) but three spatial fields, hence the fitting procedure is significantly constrained and the best fit parameters are uniquely defined in most cases (see Appendix and Figure 3—figure supplement 1). For cytokinesis the calculated alignment profile (dashed red lines in Figure 3b) best matches the experimentally measured one for =0.64 (0.548, 0.713) min (unless otherwise noted we indicate the median value together with the standard 68% confidence interval of the distribution of the bootstrap data, see Appendix), = 2.3 (1.89, 2.71) min and = 1.7 (1.37, 2.44) μm (Table 1 and Table 2). For pseudocleavage, was similar (0.6 (0.577, 0.7) min), was determined to be smaller than 0.5 min, and = 4.7 (3.12, 6.09) μm larger (Table 1 and Table 2). We note that in both cases, we obtain good agreement between the theoretical and experimental alignment field, allowing us to conclude that compressive gel flow can account for alignment. Further, we observe a small for pseudocleavage and a larger for cytokinesis, which is consistent with the observation that alignment appears concomitant with compression in pseudocleavage but arises with a short delay during cytokinesis (Figure 2d). We speculate that the changes in physical parameters of the actomyosin cortical layer between pseudocleavage and cytokinesis (higher and smaller ) reflect the fact that the cell forms a strong and more pronounced ring of aligned filaments during cytokinesis. To conclude, our results are consistent with a scenario in which actin filament alignment arises in a disordered network through compression by flow.

8Until now, we have not considered processes of myosin-based active alignment in our theory. This simplification is probably appropriate for pseudocleavage, but this is less clear for cytokinesis given that there is a clear band of myosin enrichment at the equator when the cell divides (Figure 1c,d). We next consider active alignment by myosin, and describe the cortical layer as a thin film of an active nematic gel. For stationary flows the profile of nematic order is now given by

9where the right-most term describes active alignment by myosin molecular motors, with an alignment parameter dependent on the local myosin concentration. In our modified fitting procedure, we now evaluate the respective contributions of myosin-based active and flow-based passive alignment to the stationary Q profile, under the assumption that is proportional to local myosin concentration. We find that considering active alignment does not increase the overall agreement between calculated and measured alignment profiles for both pseudocleavage and cytokinesis (Figure 3—figure supplement 2). Notably, the contribution of active alignment to pseudocleavage is insignificant, while active alignment contributes to enhancing compression-induced alignment during cytokinesis (Figure 3—figure supplement 2b; see Appendix), albeit to a small degree. We conclude that compression by flow and not myosin-based active alignment is the driving force of ring formation in both pseudocleavage and cytokinesis.

10A key prediction from our model is that reducing flow speeds and compression rates should give rise to less filament alignment and a possible inhibition of pseudocleavage furrow formation. To test this prediction, we performed weak-perturbation RNAi experiments of the regulatory myosin light chain of non-muscle myosin (mlc-4(RNAi) to mildly reduce actomyosin flow speeds without significant changes in overall actomyosin organization (Figure 4—figure supplement 1). Short feeding times (5–7 hr) lead to a small reduction in gel flow and compression rates (Figure 4a), but actin filaments still aligned in the central region and the pseudocleavage furrow still formed and ingressed. Consistent with our hypothesis, longer feeding times (7–9 hr) lead to a complete abolishment of cortical flow and a loss of both actin alignment and pseudocleavage furrow (Figure 4b). Actomyosin foci are not required for compression-based alignment since anillin- depleted embryos (ani-1(RNAi), 24 hr) still show significant alignment under compression in the absence of these dense foci (Figure 4c). Reduced flow speeds and compression rates can also account for the absence of alignment and pseudocleavage in nop-1(RNAi) embryos, in which RhoA-dependent processes are affected and pseudocleavage formation abrogated (Figure 4d, Figure 4—figure supplement 1 and 2). Overall, these experiments lead us to conclude that reducing gel flow and compression rates affects alignment in a manner that is consistent with Equation 2. Finally, a complete loss of flow and compression abolishes pseudocleavage entirely (Figure 4b;d and Figure 4—figure supplement 1). Taken together, our results suggest that the pseudocleavage furrow arises as a by-product of compressive flows, mechanically aligning actin filaments into a ring even in the absence of localized RhoA activation.

11In this context we wondered if the cortex is specifically modified to favor ring formation in cytokinesis. We used our fitting procedure to determine the parameters that characterize emergent material properties of the cortex under mlc-4(RNAi). Notably, we observe that 7–9 hr of mlc-4(RNAi) leads to a reduction of the alignment relaxation time scale during cytokinesis. The value obtained is similar to the alignment relaxation time scale during pseudocleavage under non-RNAi conditions (Table 1 and Table 2), leading us to speculate that an increase in myosin activity via Rho signaling is responsible for the observed increase of the characteristic relaxation time in cytokinesis. Importantly, increasing allows the cell to form a pronounced ring of aligned filaments by compressive cortical flow during cytokinesis, as predicted by theory (Figure 3—figure supplement 1).

12Finally, we sought to find support from theory that aligned filaments in the equatorial region drive anisotropic stress generation to form an ingression. By use of a theory that connects anisotropic active stress generation in the active nematic gel to changes in cell shape (see Appendix and Figure 3d) we show that we cannot appropriately account for the observed ingression profiles unless we consider anisotropic active stress generation in an aligned gel (Figure 3e, Figure 3—figure supplement 3). This suggests that anisotropic active stress generation in a network of aligned actin filaments is important for forming an ingression.

13To conclude, we find that compression by flow drives actomyosin ring formation in both pseudocleavage and cytokinesis, as originally proposed by White and Borisy (Figure 5). For this, we provide a general framework for determining emergent material parameters of the actomyosin gel. This characterizes flow-alignment coupling and allows for capturing essential aspects of the mechanics of furrow generation. Our analysis of the pseudocleavage ingression in C. elegans demonstrates that constricting rings can form in the absence of equatorial RhoA activation. This reveals that cortical flow functions as a central organizer of network architecture, mechanically aligning filaments to form a constricting furrow in the equatorial region without a localized increase of actin nucleation (Figure 2—figure supplement 5,f) and myosin contractility (Figure 1b-d). Finally, it will be interesting to investigate if a cortex that is aligned by compressive flow favors the recruitment of specific actin binding proteins such as bundling or motor proteins, comprising an interesting mechanism of positive feedback for stabilizing and enhancing the ring during cytokinesis. Our work highlights that determining emergent material properties of actomyosin is important for understanding cytokinesis, and a challenge for the future is to link emergent material properties at the larger scale with molecular mechanisms.

14Existing reagents did not allow for detailed and long-term imaging of actin filaments in embryos, which is critical for reliably quantifying their orientation. Hence, we generated a new Lifeact transgenetic line with enhanced actin filament labeling (SWG001). A codon optimized for C. elegans far-red fluorophore, mKate2 kindly shared by Henrik Bringman (26 kDa, 588/633 nm) was added to the actin probe with a linker (66 bp) and cloned into MOSCI vector containing unc119 rescue gene (Hyman Lab) under the control of the mex-5 promoter. Stable integration was obtained by bombardment of this plasmid in DP38 strain. This strain was then backcrossed with N2. In this line, we observed within the cortical plane bright actin filament labeling with a high signal-to-noise ratio and little photobleaching. Importantly, overall cortical organization and flow dynamics appeared to not be affected by this reagent, foci lifetime, spacing, cortical flow velocities were similar to previous measurement with other fluorescent lines. A dual colored transgenic line was obtained in order to image simultaneously actin and myosin dynamics by crossing Lifeact::mKate2 strain with LP133 (NMY-2::GFP obtained by CRISPR, SWG007). The RhoA biosensor used for Figure 1 was developed by the Glotzer lab (GFP::AHPH, C. elegans strain MG617, ). This sensor consists of GFP fused to the C-terminal portion of C. elegans anillin, which contain its conserved region (AH) and pleckstrin homology (PH) domain. It lacks the N-terminal myosin and actin-binding domains but retains its RhoA-binding domain. The strains expressing CYK-1:GFP (SWG004) and PLST-1:GFP (SWG005) were obtained by the insertion of a GFP tag at the endogenous locus in their C-terminal region using CRISPR according to Dickinson et al. C. elegans worms were cultured on OP50-seeeded NGM agar plates as described.

15L4 mothers were maintained overnight at 20°C before dissection in M9 buffer. For imaging, one-cell embryos were mounted on 2% agar pads, thereby slightly compressed to increase the cortical surface visible in a confocal plane. Images were acquired with spinning disk confocal microscope (Zeiss C-Apochromat, 63X/1.2 NA or 100X/1.42 NA, Yokogawa CSU-X1 scan head and Hamamatsu Orca-Flash4.0 camera) every 2 s on two or three different planes (one or two at the bottom for a cortical section, and one 12 µm above for a medial section of the embryo). For 3D acquisitions, Z-stacks were acquired every 0.2 μm. We assume the shape to be rotationally symmetrical to the longer axis, thus the outline of one medial section of the embryo reflects faithfully cell shape changes and ingression distance.

16RNAi experiments were performed by feeding. L4 worms were grown at 20°C on feeding plate (NGM agar containing 1 mM isopropyl-β-D-thiogalactoside and 50 μg ml−1 ampicillin) for the required number of hours before imaging.

17Spatiotemporal correlation functions were calculated for all time points during the stationary period, in the 30 μm central region of the embryo. The plot of the spatial correlation only (1D correlation function) is shown in Figure 2c between the compression, alignment and ingression data sets. Peak value positions are obtained by a Gaussian fitting procedure and allow the calculation of positional differences between the different data sets. Because the flow field appears stationary, we expect this distance between peaks of compression, alignment and ingression to arise due to temporal delays between these events in the reference frame co-moving with the cortical flows. We thus translated the characteristic distances between stationary peaks to temporal delays using the average flow velocity in the −10 μm to 0 central region (6.16 ± 1.23 µm/min for pseudocleavage and 4.01 ± 1.92 µm/min for cytokinesis) (Figure 2d).