In order to acutely inhibit myosin activity in live embryos (Figure 1a), we generated an optogenetic tool, ‘Opto-Rho1DN,’ to inhibit Rho1 through light-dependent plasma membrane recruitment of a dominant negative form of Rho1 (Rho1DN). Like other Rho GTPases, Rho1 cycles between an active, GTP-bound state and an inactive, GDP-bound state (Etienne-Manneville and Hall, 2002). Rho1DN bears a T19N mutation, which abolishes the ability of the mutant protein to exchange GDP for GTP and thereby locks the protein in the inactive state (Barrett et al., 1997). A second mutation in Rho1DN, C189Y, abolishes its naive membrane targeting signal (Sebti and Der, 2003; Roberts et al., 2008). When Rho1DN is recruited to the plasma membrane, it binds to and sequesters Rho1 GEFs, thereby preventing activation of endogenous Rho1 as well as Rho1-Rok-mediated activation of myosin (Barrett et al., 1997; Feig and Cooper, 1988).

Opto-Rho1DN is based on the CRY2-CIB light-sensitive dimerization system (Liu et al., 2008; Kennedy et al., 2010; Guglielmi et al., 2015; Figure 1b). The tool contains two components: a GFP-tagged N-terminal of CIB1 protein (CIBN) anchored at the cytoplasmic leaflet of the plasma membrane (CIBN-pmGFP) (Guglielmi et al., 2015), and a fusion protein with Rho1DN, a mCherry tag, and a blue light-reactive protein Cryptochrome 2 (CRY2-Rho1DN). CRY2-Rho1DN remained in the cytoplasm when the sample was kept in the dark or imaged with a yellow-green (561 nm) laser (Figure 1c, T=0). Upon blue (488 nm) laser stimulation, CRY2 undergoes a conformational change and binds to CIBN (Kennedy et al., 2010; Liu et al., 2008), resulting in rapid recruitment of CRY2-Rho1DN to the plasma membrane (Figure 1c and d; Figure 1—video 1). The average time for half-maximal membrane recruitment of CRY2-Rho1DN is 4 s (3.9±2.8 s, mean±s.d., n=5 embryos). Embryos expressing CIBN-pmGFP and CRY2-Rho1DN developed normally in a dark environment and could hatch (100%, n=63 embryos). In contrast, most embryos (>85%, n=70 embryos) kept in ambient room light failed to hatch, reflecting the essential role of Rho1 in Drosophila embryogenesis (Barrett et al., 1997; Magie et al., 1999; Johndrow et al., 2004).

The effectiveness of Opto-Rho1DN on myosin inactivation was validated by stimulating embryos during apical constriction, which resulted in diminishing of apical myosin signal within 60 s (Figure 1e and f; Figure 1—video 2). Rapid disappearance of cortical myosin upon Rho1 inhibition is consistent with the notion that Rho1 and myosin cycle quickly through active and inactive statues due to the activity of GTPase activating proteins (GAPs) for Rho1 and myosin light chain phosphatases, respectively (Munjal et al., 2015; Coravos and Martin, 2016). Our data also provide direct evidence that sustained myosin activity during ventral furrow formation requires persistent activation of Rho1.

In addition to myosin, we found that acute Rho1 inhibition also affects cortical F-actin networks during apical constriction, presumably through inactivation of the Rho1 effector formin Diaphanous (Johndrow et al., 2004; Homem and Peifer, 2008; Mason et al., 2013; Coravos and Martin, 2016). In unstimulated embryo, F-actin is enriched at the apical domain of the constricting cells (Figure 2a, red arrowheads and cyan arrows) and along the lateral membrane in both constricting and non-constricting cells (Figure 2a, yellow arrows and magenta arrows). Apical F-actin disappeared within 1.2 min after Opto-Rho1DN stimulation (Figure 2b). Lateral F-actin in the constricting cells was not immediately affected and only appeared to diminish 4 min after stimulation (Figure 2b). In contrast, lateral F-actin in the ectodermal cells was not significantly affected (Figure 2b). Taken together, our results indicate that Opto-Rho1DN is an effective tool for spatially- and temporally-confined inactivation of apical actomyosin contractility through simultaneous myosin inactivation and actin disassembly.

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Consistent with the actomyosin phenotype, Opto-Rho1DN stimulation before or during apical constriction resulted in prevention or reversal of apical constriction, respectively (Figure 1—figure supplement 1). In addition, Opto-Rho1DN stimulation resulted in an immediate loss of cortical tension at the ventral surface of the embryo during apical constriction (Figure 3), in accordance with the previous finding that the increase in tissue tension in the ventral mesodermal region during apical constriction is due to activation of apical myosin contractility and integration of contractile forces across the constriction domain (Martin et al., 2010). Finally, by stimulating the embryo within a specific region of interest (ROI), we showed that membrane recruitment of CRY2-Rho1DN and inhibition of apical constriction are restricted to cells within the stimulated region (Figure 1g, Figure 1—figure supplement 1c, d).

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Using Opto-Rho1DN, we determined the role of actomyosin contractility at different stages of ventral furrow formation. We first obtained non-stimulated control movies by imaging embryos bearing Opto-Rho1DN on a multiphoton microscope using a 1040-nm pulsed laser, which excites mCherry but does not stimulate CRY2 (Guglielmi et al., 2015). Without stimulation, the embryos underwent normal ventral furrow formation (Figure 4a). The transition from the lengthening phase to the shortening phase (T_{L-S trans}) occurred around 10 min after the onset of gastrulation (9.3±1.6 min, mean±s.d., n=10 embryos), which was similar to the wild-type embryos (8.9±0.8 min, mean±s.d., n=6 embryos) (Figure 4—figure supplement 1a-c). This transition was characterized by a rapid inward movement of the apically constricted cells and could be readily appreciated by the time evolution of distance between the cell apices and the vitelline membrane of the eggshell (invagination depth ‘D,’ Figure 4—figure supplement 1d).

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Cell length measurements for determining lengthening-shortening transition time.

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Next, we examined the effect of Opto-Rho1DN stimulation on furrow invagination (Figure 4b; Figure 4—figure supplement 1e; see Materials and methods). Measuring the rate of furrow invagination (dD/dt) immediately after stimulation revealed three types of tissue responses to stimulation (Figure 4a and b; Figure 4—figure supplement 1f, g; Figure 4—video 1). For most embryos that were stimulated before T=7 min (‘Early Group’ embryos), the constricting cells relaxed immediately. The initial apical indentation disappeared (dD/dt<0). The flanking, non-constricting cells, which were previously apically stretched by neighboring constricting cells, shrunk back, indicating that the apical cell cortex was elastic (Figure 4—figure supplement 2a, b). In contrast, for most embryos that were stimulated after T=7 min (‘Late Group’ embryos), furrow invagination proceeded at a normal rate and dD/dt remained positive. Finally, some embryos stimulated around T=7 min (6.5±1.4 min, mean±s.d., n=4 embryos; ‘Mid Group’ embryos) displayed an intermediate phenotype, where ventral furrow invagination paused for around 5 min (4.7±0.5 min; dD/dt≈0) before invagination resumed. We confirmed that there was no residual apical myosin in Late Group embryos upon stimulation (Figure 4—figure supplement 3a). Furthermore, lateral myosin, which has been shown to facilitate furrow invagination (Gracia et al., 2019; John and Rauzi, 2021), also quickly disappeared after stimulation (Figure 4—figure supplement 3b, c). Overall, furrow invagination in Late Group embryos is not due to myosin activities at the apical or lateral cortices of the mesodermal cells. Taken together, these results indicate that actomyosin contractility is required in the early but not the late phase of furrow formation. The narrow time window when Mid Group embryos were stimulated defined the ‘transition phase’ for sensitivity to myosin inhibition (T_trans), which is immediately before T_{L-S trans} (Figure 4c).

While all Early Group embryos showed tissue relaxation after stimulation, five out of eight of them were able to invaginate after a prolonged delay (Figure 4b; Figure 4—figure supplement 2c-f). The invagination was associated with modest myosin reaccumulation at the cell apices that occurred approximately 10 min after the initial stimulation (Figure 4—figure supplement 2e-f). It is unclear why apical myosin sometimes reoccurred in the presence of persistent membrane localization of CRY2-Rho1DN. Nevertheless, the completion of furrow invagination when apical constriction is partially impaired is consistent with previous genetic studies and suggests that invagination is facilitated by additional mechanical input (Costa et al., 1994; Parks and Wieschaus, 1991).

Because the response of ventral furrow formation to myosin inhibition appears to be binary, we sought to identify morphological features of the progressing furrow that associate with T_trans. Hence, we examined the relationship between D immediately after stimulation (D_s) and the extent by which furrow invagination is affected (assessed by the delay time in furrow invagination, T_delay; see Materials and methods). We found that for stimulated embryos, T_delay was ultrasensitive to D_s, with a steep transition at around 6 μm (Figure 4d). When D_s was above the threshold, T_delay was close to 0. When D_s was below the threshold, T_delay increased to 10 min (9.4±1.4 min, mean±s.d., n=5 Early Group embryos) or longer (fail to invaginate, n=3 Early Group embryos). Therefore, the response to acute myosin inhibition can be well predicted by the tissue morphology associated with the stage of furrow progression.

The binary response of the embryo to acute myosin inhibition led us to propose that the mesoderm during gastrulation is mechanically bistable. In this model, the mesoderm epithelium has two stable equilibrium states: the initial, pre-constricted conformation and the final, fully invaginated conformation (Figure 4e). Energy input from actomyosin-mediated apical constriction drives the transition from the initial state to an intermediate state (T_trans), which has the propensity to transition into the final state without further requirement of actomyosin contractility. If myosin is inhibited before T_trans, the furrow would relax back to the initial state. In contrast, if myosin is inhibited after T_trans, the furrow would continue to invaginate without pause (Figure 4e).

To gain further insights into how cells respond to rapid myosin loss after Rho1 inhibition, we performed three-dimensional cell reconstruction using ilastik (Berg et al., 2019). For each embryo, we examined a single row of cells (cells 1–11) along the medial-lateral axis that include the ventral mesodermal cells (cells ~1–6, ‘constricting cells’), the lateral mesodermal cells (cells ~7–9, ‘non-constricting flanking cells’), and presumably some ectodermal cells (cells ~10 and 11) (Figure 5a and f). Our analysis covered time points with most notable cell shape changes after stimulation (0, 2.2, and 4.4 min for Early Group embryos, and 0, 1.1, and 2.2 min for Late Group embryos). Shorter time windows were used for Late group embryos because of the rapid furrow invagination despite the inhibition of actomyosin contractility.

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As expected, in Early Group embryos, there was a prompt apical area relaxation in the constricting cells and an accompanying apical area reduction in the flanking cells following stimulation (see Figure 5b for a cartoon depiction). A number of features were observed in Early Group embryos. First, there was no substantial cell volume change (±5%, Figure 5—figure supplement 1), similar to the observation for normal ventral furrow formation (Gelbart et al., 2012; Polyakov et al., 2014). Second, the flanking cells that were most apically stretched before stimulation underwent most prominent apical area reduction, which is anticipated (comparing cells 7–9, Figure 5c). Surprisingly, the extent of apical relaxation in the constriction domain was not uniform. In general, cells located at the side of the constriction domain (‘side constricting cells,’ cells 4–6) relaxed more than those located closer to the ventral midline (‘mid constricting cells,’ cells 1–3) (Figure 5c). The lower degree of apical relaxation in the mid-constriction cells was accompanied with less prominent ‘reversal of lengthening’ (Figure 5d, see Figure 5b for a cartoon depiction). Finally, the alteration in apical cell area was associated with changes in cell curvature along the apical-basal axis. Before stimulation, the flanking cells and the side constricting cells were all tilted, with their apical side bending toward the ventral midline (e.g., cyan and orange cells in Figure 5a). After stimulation, the cells straightened up and partially restored their initial, columnar cell shape. This cell shape change is associated with a reduction in the apical-basal cell length and lateral cell area (Figure 5b, d and e; Figure 5—figure supplement 1). The ectodermal cells also showed some unbending, but their shape changes were in general moderate (Figure 5, cells 10 and 11).

Interestingly, despite the drastic tissue level difference between Early and Late groups of embryos, several trends we observed in Early group was also present in Late group, such as the conservation of cell volume (Figure 5—figure supplement 1), the straighten-up of some (but not all) flanking cells (e.g., cell nine in Figure 5j), and the uneven pattern of apical relaxation in the constriction domain (Figure 5h). Despite these similarities, Late Group embryos displayed several prominent features that were distinct from Early Group embryos (see Figure 5b and g for a cartoon depiction). First, the mid constricting cells barely showed any apical relaxation and underwent rapid cell shortening after stimulation (Figure 5h and i, cells 1–3), which were not observed in Early Group embryos but rather resembled the normal cell shortening process (Polyakov et al., 2014). Second, despite undergoing apical relaxation, the side constricting cells bent further toward the ventral midline instead of straightening up as their counterparts in Early Group embryos (Figure 5j, cells 4–6). The behavior of the middle and side constricting cells in Late Group embryos elucidates the cellular basis for the continued deepening of the furrow after Opto-Rho1DN stimulation and explains the tissue level difference between Early and Late Group embryos. Importantly, the observed cell shape change and tissue invagination in Late Group embryos occurred in the absence of actomyosin contractility, suggesting the presence of additional mechanical contributions.

What mechanism may account for the apparent mechanical bistability during mesoderm folding? One possible mechanism is germband extension, a body axis elongation process in Drosophila that occurs soon after the onset of gastrulation (Kong et al., 2017). During germband extension, the ventral and lateral ectoderm undergo convergent extension and converge toward the ventral midline as they extend along the anterior-posterior (AP) axis. If germband extension-mediated ventral movement starts around T_trans, it may account for the binary tissue response to actomyosin inhibition. However, previous literature indicates that germband extension does not start until ventral furrow formation is nearly completed (Lye et al., 2015). Furthermore, germband extension depends on Rho1-mediated activation of actomyosin contractility in the ectodermal cells (Kong et al., 2017). Since we stimulated Opto-Rho1DN in both the mesoderm and the ectoderm in our optogenetic experiment, we anticipate that germband extension would be inhibited. Consistent with this notion, we did not observe AP tissue movement in Opto-Rho1DN treated embryos (Figure 6—figure supplement 2), suggesting that other mechanisms are responsible for the invagination of ventral furrow in Late Group embryos.

Previous biophysical studies demonstrate that the embryonic epithelium in early Drosophila embryos can display an elastic response with a decay timescale of at least 4 min (Doubrovinski et al., 2017). The apparent bistable characteristic of the mesoderm is reminiscent of a compressed elastic beam undergoing snap-through buckling facilitated by a transverse ‘indentation force’ (Figure 6b; Qiu et al., 2004). Based on this analogy, we hypothesized that mesoderm invagination is mediated through tissue buckling enabled by in-plane compressive stresses. We tested this hypothesis by implementing compressive stresses from the ectoderm in a previously published two-dimensional vertex model for ventral furrow formation (Polyakov et al., 2014; Figure 6a; see Materials and methods). In this model, the sole energy input is apical constriction of the ventral cells, whereas the apical, lateral, and basal cortex of cells were represented by elastic springs that resist deformation (Polyakov et al., 2014; see Materials and methods). Note that the elasticity assumption in this model is a simplification of the actual viscoelastic properties of the embryonic tissue. However, this model successfully predicted the intermediate and final furrow morphologies with a minimal set of active and passive forces without prescribing individual cell shape changes (Polyakov et al., 2014; see Materials and methods). It is therefore advantageous to use this model to explore the main novel aspect of the folding mechanics underlying ventral furrow formation and to test the central concept of our hypothesis based on relatively small number of assumptions.

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Computer code for the energy minimization-based vertex model for ventral furrow formation.

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Using this model, we simulated the effect of acute myosin loss by removing the apical contractile forces at different intermediate states of the model (Materials and methods). Remarkably, in the presence of ectodermal compression, the model recapitulated the binary response to loss of apical constriction as observed experimentally (Figure 6c). In particular, the transitional state of the tissue revealed in the simulation is visually similar to that identified in our optogenetic experiments. As a control, in the absence of ectodermal compression, the model always returned to its initial configuration regardless of the stage when apical constriction was eliminated (Figure 6c). Therefore, our simulation indicates that buckling of an elastic cell sheet jointly mediated by local apical constriction and global in-plane compression can well reproduce the observed binary tissue response to acute actomyosin inhibition. Our model also predicts that the presence of ectodermal compression could compensate for partial impairment of apical constriction (Figure 6d), which explains why some Early Group embryos could still invaginate when myosin activity was greatly downregulated.

Interestingly, our simulation predicts that for embryos stimulated after T_trans, the ventral furrow at the final invaginated state would be narrower with fewer cells being incorporated into the furrow compared to control embryos. Our observation in Late Group embryos well matched this prediction (Figure 6c; Figure 6—figure supplement 1a, b). Consistent with our 3D analysis (Figure 5h), we found that stimulation in Late Group embryos induced a mild but noticeable alteration in tissue flow that indicates the occurrence of apical relaxation in the constricted cells (Figure 6—figure supplement 1c, d). These results suggest that maintaining actomyosin contractility after T_trans helps to prevent local relaxation of the apical membranes, thereby allowing more cells to be incorporated into the furrow. This ‘late’ function of actomyosin contractility is dispensable for furrow invagination per se but is important for the complete internalization of the prospective mesoderm.

In the vertex model described above, shortening of the constricting cells is mediated by passive elastic restoration forces generated in these cells as their lateral edges are stretched during cell lengthening (Polyakov et al., 2014). This passive elastic force is not affected by in silico myosin inactivation. However, our experiments show that Opto-Rho1DN stimulation results in rapid diminishing of lateral myosin in the constricting cells, suggesting that Rho1 inhibition may weaken the shortening forces in these cells (Gracia et al., 2019; John and Rauzi, 2021). To account for this effect, we implemented active lateral constriction forces in the ventral cells. In such a scenario, the active and passive lateral forces worked in combination to mediate ventral cell shortening, but only the active force was sensitive to myosin inactivation (Materials and methods). The active and passive lateral forces were given by ${\displaystyle K_{L\mathrm{\_}active}l}$ and ${\displaystyle K_{L\mathrm{\_}passive}(l-l_0)}$, respectively, where ${\displaystyle l}$ and $l_0$ were the current and the resting length of the lateral edge, respectively. As expected, the addition of the active lateral force allows us to reduce the passive lateral force while still generate furrows with normal morphology (Figure 7a, comparing column $K_{L\_active}$=0 with column $K_{L\_active}$=2). The implementation of myosin-dependent active lateral forces allowed us to examine how the binary response would be influenced if myosin inactivation weakens the cell shortening forces in the mesoderm.

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We performed the tests under the conditions where the model generates normal furrow morphology (green shaded region in Figure 7a, $K_{L\_passive}=20$ while $K_{L\_active}$ ranges from 0 to 2, or $K_{L\_active}=2$ while $K_{L\_passive}$ ranges from 0.002 to 20). When $K_{L\_passive}=20$, changing $K_{L\_active}$ has little impact on the response of the model to stimulation (Figure 7b). When $K_{L\_active}=2$, changing $K_{L\_passive}$ did not affect the binary tissue response per se but influenced the final morphology after stimulation (Figure 7c). When the passive lateral force was relatively high ($K_{L\_passive}=$ 20), the model displayed normal binary response with realistic final furrow morphologies. Lowering the passive lateral force by a factor of ten ($K_{L\_passive}=$ 2) did not change the tissue response aside from a mild reduction of the invagination depth ‘D’ (from 61 μm to 51 μm) in Late Group embryos. Strikingly, further lowering $K_{L\_passive}$ to 0.2 resulted in a very shallow furrow and abnormal constricting cell morphology in Late Group embryos (D=30 μm). Taken together, these results demonstrate that the binary response of the model to myosin inhibition still exists when the cell shortening forces in the mesoderm become sensitive to myosin inhibition. However, a minimal level of myosin-independent lateral elastic force ($K_{L\_passive}$>0.2) is required for the model to generate realistic final furrow morphology in Late Group embryos. Interestingly, we found that in real embryos the lateral actin in the constricting cells persisted for several minutes after Opto-Rho1DN stimulation (Figure 2b, yellow arrows), which might provide the lateral elasticity described in our model.

It remains unclear whether compressive stresses exist in the ectoderm during ventral furrow formation in real embryos. No cell division happens in the embryo during ventral furrow formation (Foe, 1989; Edgar et al., 1994), thereby excluding a role for cell proliferation in generating compressive stresses as seen in many other tissues (Nelson, 2016). Interestingly, it has been reported that ectodermal cells undergo apical-basal shortening during gastrulation (Brodland et al., 2010). In theory, this cell shape change could generate compressive stresses in the planar direction if the cell volume remains conserved. To further investigate the extent of ectodermal shortening during gastrulation, we performed 3D tissue volume measurement (Vol_ec) in the lateral ectodermal region of wild-type embryos (ROI: 60°–120° away from the ventral midline and 75-μm long along the AP axis; Figure 8a). We focused our analysis on the lateral ectodermal region since a previous study shows that the dorsal ectoderm does not significantly contribute to ventral furrow formation (Rauzi et al., 2015). We reasoned that if the ectodermal cells undergo apical-basal shortening, there should be a net volume outflux from the ROI, causing a reduction in Vol_ec (Figure 8a). Since cell shortening may not be uniform across the tissue, the change in Vol_ec provides a less noisy measure of the change in average tissue thickness. To measure Vol_ec, we performed 3D tissue segmentation without segmenting individual cells (Materials and methods).

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This analysis led to the following observations. First, Vol_ec increased during the first 10 min of ventral furrow formation (Figure 8c). This observation is consistent with the previous measurement of ectodermal cell length during gastrulation (Brodland et al., 2010). Second, in all cases examined, Vol_ec started to decrease approximately halfway through ventral furrow formation, but the exact time of this transition varied between embryos (11.1±2.3 min, mean±s.d., n=3 embryos; Figure 8c and f, arrowheads). Finally, the percent reduction in Vol_ec from the peak volume to that at the end of ventral furrow formation ranged between 4% and 8%. These observations are consistent with an independent 2D measurement of the cross-section area (as a proxy for tissue thickness) of a lateral ectodermal region that was between 60° and 90° from the ventral midline (~6% reduction; Figure 8—figure supplement 1).

The observed ectodermal shortening could be driven by an active mechanism that reduces cell length or could be a passive response to the pulling from ventral furrow. To distinguish these possibilities, we repeated the Vol_ec measurements in snail mutant embryos. As expected, ventral furrow failed to form in snail embryos (Figure 8g). Strikingly, the reduction of Vol_ec occurred at about the same time as in the wild-type. In addition, the rate of Vol_ec reduction was similar between the wild-type and snail embryos, although the snail embryos on average had a smaller Vol_ec to start with (Figure 8d, f and h). This result indicates that pulling from ventral furrow cannot fully account for the apicobasal shrinkage of lateral ectoderm in the wild-type embryos and suggests the presence of ventral furrow-independent mechanism for ectodermal shortening.

In our vertex model, ectodermal compression was generated by letting all ectodermal cells shorten by 20% (ΔL=20%; Materials and methods). Further analysis demonstrates that a minimum of 5%–10% shortening in all 60 ectodermal cells is critical for generating the binary response, which was greater than the range measured in the actual embryos (4%–8% shortening, measured in ~45% ectodermal cells; Figure 8; Figure 8—figure supplement 2). A number of factors may account for the difference between the model and the actual embryo. For example, we observed residual cellularization in the ectoderm during the first 10 min of gastrulation, but there was no cell growth in our model (Figure 8c). While an apical-basal shrinking of the ectodermal cells can generate in-plane compression, the onset and the effect of this shrinking may be underestimated by volume or length measurement if the cells are growing at the same time. In addition, other morphogenetic processes occurring during gastrulation might also contribute to the generation of tissue compression. For example, Rauzi et al., 2015 found that both the onset of rapid ventral furrow invagination and the onset of ventrally directed movement of the lateral ectoderm are delayed in the mutant that disrupts cephalic furrow formation and posterior midgut invagination (Rauzi et al., 2015). Finally, the difference between an elastic model and the actual viscoelastic embryonic tissue may also contribute to the discrepancy between the measurements and model predictions. While our model recapitulated the major cell morphological features during ventral furrow formation and correctly predicted the binary response to acute actomyosin inhibition, future research is needed to elucidate the mechanism and function of ectodermal shortening in gastrulation. An interesting prediction from the Late Group embryo observation based on our proposed model is that ectodermal shortening does not depend on Rho1 activity, since ventral furrow invagination continued in Late Group embryos in which both the mesoderm and the ectoderm were stimulated (Materials and methods). Consistent with this prediction, we found that Opto-Rho1DN stimulation only had a mild and transient effect on ectoderm thickness change, suggesting that Rho1 inhibition did not directly impact ectodermal shortening (Figure 8—figure supplement 3).

In theory, compression generated by ectodermal shortening should result in displacement of the ectodermal cells toward the ventral region regardless of whether mesoderm invagination occurs. Previous studies have shown that ventral movement of the lateral ectoderm still occurs in mesoderm specification mutants that do not form ventral furrow (Rauzi et al., 2015). Our own observation in the snail mutant is also consistent with this result (Figure 8e). Interestingly, we found that in snail mutant embryos, cells moved toward both ventral and posterior sides as soon as ectodermal shortening began (Figure 8d). This is in sharp contrast to the wild-type embryos, where the onset of the posteriorly directed movement commenced 20–25 min later than the onset of Vol_ec reduction and ventrally directed movement (Figure 8c). The altered pattern of cell movement in snail embryos could be explained by a combined effect of ectodermal compression and lack of ventral furrow invagination (Figure 8f). In this hypothetical scenario, the compression promotes ventral furrow invagination in wild-type embryos, which in turn functions as a ‘sink’ to facilitate (and thereby bias) the movement of the ectoderm in the ventral direction. However, since the snail mutant embryos do not form ventral furrow, an increase in ectodermal compression induces tissue movement in both AP and DV axis simultaneously, albeit slower.

So far, data from ours and others have shown that ventrally directed ectoderm movement still occurs without ventral furrow formation. It remains unclear, however, whether this decoupling of tissue movement can be observed without altering cell fate specification. Our optogenetic approach provided an opportunity for us to test this. First, we examined the ectodermal movement in the Early Group embryos immediately after stimulation. Our measurements confirmed the “reverse” movement of the ventral cells during tissue relaxation and demonstrated that during the same time period the lateral ectoderm moved in the opposite direction, toward the ventral midline (Figure 9a–e). Second, we inhibited Rho1 at the onset of apical constriction to mimic the ventral furrow phenotype of the snail mutants, but without changing mesodermal cell fate (Figure 9f–i). Despite the lack of apical constriction, we observed ventrally directed ectodermal movement similar to that in the snail mutants (Figure 9f–i). These results indicate that the ventrally directed lateral ectoderm movement can occur independent of ventral furrow formation when cell fate specification is expected to be normal. Taken together, our observations suggest that ectodermal shortening may serve as an independent mechanical input that could function together with other mechanical factors to facilitate mesoderm invagination. We propose that apicobasal cell shortening of the ectodermal cells (along with other unknown mechanisms) generates in-plane compression during gastrulation, which functions together with active cell shape changes in the mesoderm to facilitate mesoderm invagination through epithelial buckling (Figure 9j).

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Measurements of velocity of tissue movement as a function of the initial distance from the ventral midline in Early Group embryos.

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Measurements of velocity of tissue movement as a function of the initial distance from the ventral midline in Opto-Rho1DN embryos stimulated before gastrulation.

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To generate the CRY2-mCherry-Rho1DN fusion gene, the Rho1 CDS bearing an ACT to AAT mutation and a TGC to TAC mutation (T19N and C189Y, respectively) was synthesized and inserted to the C-terminal end of pCRY2PHR-mCherryN1 (Addgene, deposited by Chandra Tucker) through Gibson assembly. A 12-aa flexible linker sequence (GGGGSGGGGSGG) was included between the mCherry and Rho1DN sequences. The resulting CRY2PHR-mCherry-Rho1N18Y189 fusion gene was subsequently inserted into pTiger, a transformation vector containing the attB site and 14 upstream UAS GAL4-binding sites (courtesy of S. Ferguson, State University of New York at Fredonia, Fredonia, NY). The resulting pTiger-CRY2-mCherry-Rho1DN construct was sent to Genetic Services for integration into the attP2 site using the phiC31 integrase system (Groth et al., 2004).

Fly lines containing the following fluorescent markers were used: Sqh-GFP (Royou et al., 2002), Sqh-mCherry (Martin et al., 2009), E-cadherin-GFP (Oda and Tsukita, 2001), P4M-mCherry (Chen and He, 2021), and Utrophin-Venus (Figard and Sokac, 2011). To generate snail mutant embryos, we used the halo snail/CyO, Sqh-GFP line (Martin et al., 2009).

Fly lines containing CIBN-pm-GFP (II), CIBN-pm (I) (Guglielmi et al., 2015), or CRY2-Rho1DN (III) (this study, note that CRY2-Rho1DN also contains the mCherry tag) were used to generate the following stocks: CIBN-pm-GFP; CRY2-Rho1DN and CIBN-pm; CRY2-Rho1DN. To generate embryos containing maternally deposited CIBN-pm-GFP and CRY2-Rho1DN proteins, CIBN-pm-GFP; CRY2-Rho1DN females were crossed to males from the Maternal-Tubulin-Gal4 line 67.15 to generate CIBN-pm-GFP/67; CRY2-Rho1DN/15 females (‘67’ and ‘15’ refer to Maternal-Tubulin-Gal4 on chromosomes II and III, respectively [Hunter and Wieschaus, 2000]). To generate embryos containing maternally deposited CIBN-pm (without GFP) and CRY2-Rho1DN proteins, CIBN-pm; CRY2-Rho1DN females were crossed to 67.15 males to generate CIBN-pm/+; +/67; CRY2-Rho1DN/15 females. In both cases, embryos derived from the F1 females were used in the optogenetic experiments. The use of CIBN-pm without a GFP tag was to allow better visualization of GFP-tagged myosin regulatory light chain Sqh. The following Maternal-Tubulin-Gal4 lines were used: (1) 67; 15, (2) 67 Sqh-mCherry; 15 Sqh-GFP, (3) 67 Sqh-mCherry; 15 E-cadherin-GFP, (4) 67 Sqh-GFP; 15, (5) 67 Sqh-GFP; 15 Sqh-GFP, (6) 67 Sqh-mCherry; 15 Utrophin-Venus, and (7) 67 Sqh-GFP; 15 P4M-mCherry. Specifically:

• Figure 1c, d and g, Figure 1—figure supplement 1: CIBN-pm-GFP; CRY2-Rho1DN females were crossed to 67; 15 males.

• Figure 1f: CIBN-pm; CRY2-Rho1DN females were crossed to 67 Sqh-GFP; 15 males.

• Figure 2a: CIBN-pm females were crossed to 67 Sqh-mCherry; 15 Utrophin-Venus males.

• Figure 2b: CIBN-pm; CRY2-Rho1DN females were crossed to 67 Sqh-mCherry; 15 Utrophin-Venus males.

• Figure 3: CIBN-pm; CRY2-Rho1DN females were crossed to 67 Sqh-mCherry; 15 E-cadherin-GFP males.

• Figures 4 and 5, Figure 4—figure supplements 1–2, Figure 5—figure supplement 1, Figure 6—figure supplements 1–2, Figure 8—figure supplements 1 and 3, Figure 9a–e: CIBN-pm-GFP; CRY2-Rho1DN females were crossed to 67 Sqh-mCherry; 15 Sqh-GFP males.

• Figure 4—figure supplement 3a: CIBN-pm; CRY2-Rho1DN females were crossed to 67 Sqh-mCherry; 15 Sqh-GFP males.

• Figure 4—figure supplement 3c: CIBN-pm; CRY2-Rho1DN females were crossed to 67 Sqh-GFP; 15 Sqh-GFP males.

• Figure 9f–i: CIBN-pm; CRY2-Rho1DN females were crossed to 67 Sqh-GFP; 15 P4M-mCherry males.

Embryo viability test was performed by hand selecting cellularizing embryos derived from 67/CIBNpm-GFP; 15/CRY2-Rho1DN female flies in a dark room where the only illuminating light is red light. The selected embryos were randomly divided into two groups and placed on two fresh apple juice plates. One plate was kept in the dark and the other was placed under a beam of white light with moderate intensity. Plates were kept at 18°C for more than 48 hr, after which the hatched and unhatched embryos were counted using a Nikon stereo microscope. Three independent trials were conducted. In total, 60 out of 70 stimulated embryos did not hatch whereas all 63 unstimulated embryos hatched.

To prepare embryos for live imaging, embryos were manually staged and collected from apple juice plates, and dechorionated with ~40% bleach (i.e., ~3% sodium hypochlorite) in a dark room using an upright Nikon stereo microscope. In optogenetic experiments, embryos were protected from unwanted stimulation using an orange-red light filter placed on top of white light coming from the stereo microscope. After dechorionation, embryos were rinsed thoroughly with water, and transferred on a 35-mm glass-bottom dish (MatTek Corporation). Distilled water was then added to the dish well to completely cover the embryos. Live imaging was performed in water at room temperature with one of the following approaches.

To examine the plasma membrane recruitment of CRY2-Rho1DN and its impact on cortical association of myosin (Figure 1c–f), embryos were imaged using a Nikon inverted spinning disk confocal microscope equipped with the perfect focus system and Andor W1 dual camera, dual spinning disk module. A CFI Plan Apo Lambda 60×/1.40 WD 0.13-mm oil objective lens was used for imaging. For membrane recruitment of CRY2-Rho1DN, time-lapse movies were taken for post-cellularization embryos at a single z-plane close to the apical side of the tissue at a frame rate of 0.46 s per frame. For cortical association of myosin, a small Z-stack (five slices, 0.5 μm step size) was taken at a rate of 3.46 s per stack. The image size is 858 by 1536 pixels with a lateral pixel size of 0.11 μm, which corresponds to a 94 μm by 169 μm region. For each embryo, pre-stimulation images were acquired using a 561-nm laser, which did not activate Opto-Rho1DN. Stimulation and post-stimulation imaging were performed simultaneously as we subsequently imaged the embryo with both 488 nm and 561 nm lasers in an alternating pattern using triggered excitation.

To examine the spatial confinement of stimulation (Figure 1g) and the effect of activation of Opto-Rho1DN on apical constriction during ventral furrow formation (Figure 1—figure supplement 1), embryos were imaged on a Leica SP5 confocal microscope with a 63×/1.3 NA glycerin-immersion objective lens. A 2× zoom was used. Twenty confocal z-sections with a step size of 1 μm were acquired every 13 s. The image size is 1024×512 pixels with a lateral pixel size of 240 nm. The total imaged volume is approximately 246×123×19 μm³. First, a single-time-point pre-stimulated image stack was acquired using a 561-nm laser. Next, stimulation was performed by taking a single-time-point image stack using both 488 nm and 561 nm lasers, which took 13 s. Stimulation was followed by post-stimulation acquisition with 561 nm laser for 20 time points (260 s). The stimulation and post-stimulation acquisition cycle were repeated until the end of the movie (i.e., stimulated for 13 s every 273 s).

To examine the rate of tissue recoil after laser ablation (Figure 3), embryos were imaged on an Olympus FVMPE-RS multiphoton system with a 25×/1.05 numerical aperture water immersion objective lens. For unstimulated embryos, a pre-ablation Z-stack was obtained using a 1040-nm laser to image a 512×100-pixel region (171×33 μm², 3× zoom) with a step size of 2 μm, which took approximately 16 s. Laser intensity increased linearly (4%–7%) from the surface of the embryo to 100-μm deep. This pre-ablation Z-stack was used to determine the stage of the embryo. Next, a 10-frame single Z-plane pre-ablation movie was obtained with a 1040-nm laser. A 512×512-pixel region (171×171 μm³, 3× zoom) was imaged, which took approximately 1 s per frame. Next, a 920-nm laser with 30% laser intensity was used to ablate a 3D region from immediately below the vitelline membrane to ~20-μm deep. This was achieved by taking a Z-stack with a step size of 1.5 μm. The ROI of the ablated region is ~3 μm along the AP axis. The purpose of targeting multiple Z-planes for ablation was to ensure that the very apical surface of the ventral cells was ablated. This was particularly important for the stimulated embryos since the ventral cells undergo rapid apical relaxation after Rho1 inhibition. Immediately after laser ablation, a 100-frame single Z-plane post-ablation movie was acquired using both 1040 nm and 920 nm lasers. The same ROI was imaged as the pre-ablation single Z-plane movie with identical image acquisition speed. For stimulated embryos, a stimulation procedure was included before laser ablation. First, a Z-stack was acquired to determine the stage of the embryo, as described above. Then, a 458-nm diode laser with 0.3% laser intensity was used to illuminate the whole embryo under 1× digital zoom for 12 s to activate the optogenetic module. A 3-min wait time was applied after stimulation to ensure the complete inactivation of myosin and disassembly of apical F-actin before laser ablation. Following this wait time, the same laser ablation procedure as used for the unstimulated embryos was applied (pre-ablation single Z-movie, laser ablation, and post-ablation single Z-movie), except that both 1040 nm and 920 nm lasers were used for acquiring the pre-ablation movie.

The analyses of F-actin (Utrophin-Venus) after Opto-Rho1DN activation (Figure 2) and the stage-specific effect of Opto-Rho1DN activation on ventral furrow invagination (Figure 4) were conducted using the following imaging protocol. Embryos were imaged on the Olympus FVMPE-RS multiphoton system with a 25×/1.05 numerical aperture water immersion objective lens. Pre-stimulation images were obtained by using a 1040-nm laser to excite a 512×100-pixel region (171×33 μm², 3× zoom). Continuous imaging was conducted for pre-stimulation imaging. For each time point, a 100-μm Z-stack with step size of 1 μm was obtained with linearly increased laser intensity (4%–7.5%) over Z, which took 34 s. Stimulation was performed at different stages of ventral furrow formation using a 458 nm single-photon diode laser by illuminating the whole embryo under 1× zoom for 12 s with 0.3% laser intensity. A wait period of ~20 s was imposed after stimulation for examining the stage-specific effect. Post-stimulation images were obtained using both 1040 nm and 920 nm lasers. Same setting as pre-stimulation imaging was applied, with an addition of a linear increase in 920-nm laser intensity (0.1%–0.5%) over Z. Stimulation was conducted manually every five stacks during post-stimulation imaging (i.e., stimulation for 12 s every ~200 s) to ensure the sustained membrane recruitment of CRY2-Rho1DN.

To image wild-type and snail mutant embryos for the volume measurement in the lateral ectoderm (Vol_ec, Figure 8), embryos were imaged on the Olympus FVMPE-RS multiphoton system with a 25×/1.05 numerical aperture water immersion objective lens. Z stacks of 120 μm with a step size of 1 μm was acquired continuously over a 512×150-pixel region (256×75 μm², 2× zoom). A 920-nm laser with a linear increase of laser intensity over Z (0.3%–2.5%) was used for imaging. The temporal resolution of the movie was ~54 s/stack. halo snail homozygous mutant embryos were derived from the halo snail/CyO, Sqh-GFP stock and were recognized based on the ‘halo’ phenotype during cellularization.

To examine ectodermal cell movement after Opto-Rho1DN activation (Figure 9f–i), embryos were imaged on the Olympus FVMPE-RS multiphoton system with a 25×/1.05 numerical aperture water immersion objective lens. A pre-stimulation Z stack was acquired using 1040-nm laser to illuminate an ROI (512×150 pixels, 171×50 μm², 3× zoom) with a step size of 1 μm for a total depth of 100 μm. The laser intensity increased linearly over Z (3%–7%). Next, whole embryo stimulation was achieved by illuminating the embryo with a 458-nm laser at 0.3% laser intensity for ~12 s under 1× zoom. Post-stimulation Z stacks were acquired using similar protocol as the pre-stimulation Z stack, except that both 920 nm and 1040 nm lasers were used for imaging. The intensity of the 920-nm laser also increased linearly over Z (0.5%–2.5%). The temporal resolution of the post-stimulation movie was ~41 s/stack. At the end of each experiment, a single frame image of the embryo was acquired at 1× zoom to record the AP orientation of the embryo.

All image processing and analysis were processed using MATLAB (The MathWorks) and ImageJ (NIH).

To quantify the percent membrane recruitment of CRY2-Rho1DN after stimulation (Figure 1d), cell membrane was segmented based on the CIBN-pm-GFP signal using a custom MATLAB code. The resulting membrane mask was used to determine the signal intensity of CRY2-Rho1DN (mCherry tagged) along the cell membrane over time. The intensity of the CRY2-Rho1DN signal in the cytoplasm, which is determined as the average intensity in the cells before stimulation, was subtracted from the measured intensity. The resulting net membrane signal intensity was further normalized by scaling between 0 and 1.

To quantify the rate of tissue recoil after laser ablation (Figure 3), the width change of the ablated region along the AP axis was measured over time from the kymograph using ImageJ. The width change during the first 20 s after laser ablation (when the change over time was relatively linear) was reported to indicate the rate of tissue recoil.

The invagination depth D (i.e., the distance between the vitelline membrane and the apex of the ventral-most cell, e.g., Figure 4b) and the apical-basal length of the ventral cells over the course of ventral furrow formation (Figure 4—figure supplement 1a,b) were manually measured from the cross-section view of the embryos using ImageJ.

To categorize embryo responses to stage-specific Opto-Rho1DN stimulation, first, each post-stimulation movie was aligned to a representative control movie based on the intermediate furrow morphology at the time of stimulation. The purpose of this alignment was to minimize the impact of embryo-to-embryo variation in T_{L-S trans} (Figure 4—figure supplement 1d). The resulting aligned time was used in the analysis because it provided a better measure of the stage of ventral furrow formation than the ‘absolute’ time defined by the onset of gastrulation in each embryo. Next, dD/dt immediately after stimulation is determined by a linear fitting of D over time in the first 4 min after stimulation (Figure 4—figure supplement 1f). Embryos with dD/dt<–0.3 μm/min are defined as Early Group. These embryos undergo tissue relaxation and result in decrease in D over time. Embryos with dD/dt between –0.3 μm/min and 0.3 μm/min are defined as Mid Group. These embryos do not undergo obvious tissue relaxation but display a temporary pause before they continue to invaginate. Embryos with dD/dt>0.3 μm/min are defined as Late Group. These embryos continue to invaginate despite the rapid inactivation of myosin. To quantify the impact of myosin inhibition on furrow invagination (Figure 4d), the delay time in furrow invagination (T_delay) was measured. T_delay is defined as the difference in time for a given stimulated embryo to reach a D of 20 μm compared to a representative control embryo.

To examine the change of apical cell area of the flanking, non-constricting cells in stimulated Opto-Rho1DN embryos (Figure 4—figure supplement 2a, b), a custom MATLAB script was used to generate a flattened surface view of the embryo which accounts for the curvature of the embryo. The apical cell area was measured by manually tracking and outlining flanking cells followed by area measurement using ImageJ.

To segment the mesoderm cells (Figure 5), Carving procedure from ilastik (Berg et al., 2019) was used in combination with manual correction using ImageJ and MATLAB to segment and reconstitute the 3D shape of individual cells. Cell length was calculated by summing up the distance between neighboring centroids at consecutive z planes to account for the curvature of the cell. Apical surface area was calculated based on the intersection area between the curved apical surface of the tissue and the 3D object of the cell. This intersection area was determined using a custom MATLAB code. The lateral surface area was calculated by a subtraction of the apical and basal surface area from the overall cell surface area, which was calculated from the 3D object of the cell. The volume is calculated directly from the 3D object of the cell.

To evaluate the volume flux in the lateral ectoderm region (Figure 8), pixel segmentation procedure from ilastik (Berg et al., 2019) was used to segment a fixed lateral ectoderm region (ROI: from 60° to 120° away from the ventral midline and 75 μm long along the AP axis) in both WT and snail mutant embryos. Segmentation was performed based on Sqh-GFP signal which clearly defines the apical and basal boundaries of the tissue. The tissue was segmented as a continuum without segmentation of individual cells. The volume of the selected ROI (Vol_ex) at each time point was determined based on the segmented 3D tissue object. To measure the movement of lateral ectoderm during gastrulation, the position of a cell initially located 50° away from the ventral midline at the onset of gastrulation was manually tracked over time using ImageJ.

To measure ectodermal shortening from 2D cross-section view of the embryos (Figure 8—figure supplements 1 and 3), the thickness of the lateral ectoderm is reported as the cross-section area of the ectodermal cell layer between 60° and 90° from the DV axis, which provides a good readout of tissue volume redistribution in 3D. A custom MATLAB script was used to facilitate the measurement. Specifically, the apical surface of the tissue was determined by automatic segmentation of the vitelline membrane of the embryo. The resulting curve was subsequently fit into a circle (the outer membrane circle). The basal surface of the tissue was determined by automatic segmentation and tracking of the basal myosin signal, with necessary manual corrections when the basal signal became too dim to be segmented accurately. Tissue thickness was measured as the cross-section area of a section of the ectodermal tissue bounded by the outer membrane, the basal surface, and two radii of the outer membrane circle that are 60° and 90° away from the ventral midline, respectively.

To detect ectodermal cell movement in Early Group embryos after stimulation (Figure 9a–e) and in embryos stimulated at the onset of gastrulation (Figure 9f–i), kymographs were generated from the surface views with the CIBN-pmGFP signal or P4M-mcherry that marks the cell membrane. Individual membrane traces within the first 6 min after stimulation were manually tracked from the kymograph using the line selection tool in ImageJ. The slope of the lines was subsequently measured using ImageJ to calculate the rate of membrane movement, which was then plotted against the position of corresponding membrane relative to the ventral midline at the time of stimulation. The average velocity of tissue movement at ventral mesodermal (from –10 μm to –40 μm and from 10 μm to 40 μm) or lateral ectodermal (from –60 μm to –120 μm and from 60 to 120 μm for Early Group embryos or <–40 μm and >40 μm for embryos stimulated at the onset of gastrulation) regions of the embryos was calculated and tested using one-tailed one-sample t-test against 0.

The 2D vertex model for ventral furrow formation, which considers the cross-section view of the embryo, was constructed as previously described (Polyakov et al., 2014). In brief, the model contains a ring of 80 cells that represent the cross-section of an actual embryo. The initial geometry of the cells in the model resembles that in the real embryo. The apical, basal, and lateral membranes of the cells are modeled as elastic springs that resist deformation, and the cells have a propensity to remain constant cell volume (area in 2D). In the model, apical constriction provides the sole driving force for tissue deformation, which is achieved by allowing the apex of the cells in the ventral region of the embryo to shrink. The resulting morphological changes of the tissue are determined by the stiffness of the apical, lateral, and basal springs, cell volume conservation, and a stepwise reduction of basal spring stiffness (see below).

The energy equation that approximates the mechanical properties of the system is described by the following expression:

The first term in the equation stands for myosin-mediated apical constriction. The term ${\phi }_i{\mu }_i$ defines the spatial distribution of myosin contractility. ${\phi }_i$ equals to one for cells within the mesoderm domain (9 cells on each side of the ventral midline, a total of 18 cells) and 0 for the rest of cells, which ensures that only the mesodermal cells will constrict apically. ${\mu }_i$ is a Gaussian function that peaks at the ventral midline. Specifically,

Here, $i_{mid}$ stands for the cell ID at the ventral midline, ${\mu }_0$ defines the strength of apical constriction, and $\sigma$ defines the width of the force distribution. Note that due to the Gaussian-shaped force distribution, only 12 cells at the ventral most region of the embryo will undergo apical constriction, similar to what occurs in the real embryo.

The second term in the equation stands for the elastic resistance of the membranes. $a_i$ , $b_i$ , and $l_i$ stand for the area (length in 2D) of the apical, basal, and lateral membrane of cell $i$, respectively. $a_0$ , $b_0$ , and $l_0$ are the corresponding resting length, which are set to be their initial length. $k_a$ , $k_b$, and $k_l$ are the spring constant of the apical, basal, and lateral springs, respectively.

The third and fourth terms, $C_{VOL}$ and $C_{YOLK}$ , are constraint functions that describe volume conservation of the cells and the yolk, respectively. These two terms impose penalties when the volume deviates from the resting value. Specifically,

Here, $V_i$ stands for the volume of cell $i$. $V_0$ stands for the initial equilibrium volume of cell $i$. Similarly, $V_{yolk}$ stands for the volume of the yolk. $V_{0,yolk}$ stands for the initial equilibrium volume of the yolk. $K_v$ and $K_{yolk}$ control the deviation of the cell volume and the yolk volume from the initial equilibrium values, respectively.

In the simulation, the basal rigidity of the epithelium ($K_b$) decreases adiabatically, allowing the model to transition through a series of intermediate equilibrium states defined by the specific $K_b$ values. These intermediate states recapitulate the lengthening-shortening dynamics of the constricting cells observed in the real embryos (Polyakov et al., 2014).

To produce an in-plane compressive stress in the ectodermal tissue, we set the resting length of the lateral springs ($l_0$) 20% shorter than their original length. Because of the cell volume conservation constraint, shortening of the ectodermal cells in the apical-basal direction will result in an expansion of cells in the orthogonal direction, which is the planar direction of the epithelium. This expansion provides a mechanism to produce in-plane compressive stress in the epithelial sheet. As shown in Figure 8—figure supplement 2, when the percent reduction of the ectodermal cell length is lowered from 20% to 10%, the binary response to acute actomyosin inhibition is still present, although the final depth of the furrow in the simulated Late Group embryo is reduced. Further lowering the percent reduction to 5% abolishes the binary response.

To simulate the optogenetic inhibition of myosin contractility in the model, we set the program such that the apical contractility term will be reduced to 0 at defined intermediate equilibrium state. This approach allows us to inhibit apical contractility at any intermediate furrow configuration specified by $K_b$ .

In order to simulate the impact of impairing apical constriction on invagination, we modified our model in two different ways. First, to reduce the number of apically constricting cells, we decreased the width of the Gaussian function that defines the spatial distribution of apical myosin contractility. Second, to recapitulate the weakened and uncoordinated apical constriction observed in certain apical constriction mutants, we inhibited apical constriction from every other cell within the ventral 18 cell region.

In order to account for the impact of optogenetic stimulation of Opto-Rho1DN on lateral myosin in the constricting cells, we implemented an active lateral constriction force along the lateral edges of the constricting cells, on top of the passive lateral restoration force described above. In such a scenario, the active and passive lateral forces worked in combination to mediate ventral cell shortening, but only the active force was sensitive to myosin inactivation. For each lateral cortex within the constriction domain, the active lateral constriction force is generated by a spring with a resting length of 0. The lateral shortening force in the constricting cells is determined by:

where $K_{L\_active}$ and $K_{L\_passive}$ are the spring constant of the active and passive lateral springs, respectively, and $l$ and $l_0$ are the current and the resting length of the lateral edges, respectively. As shown in Figure 7, a spring constant of $K_{L\_active}=$ 2 generated the desired furrow morphology under a broad range of passive spring constant ($K_{L\_passive}$=[0.002, 20]). A further increase of $K_{L\_active}$ result in deeper furrows as more cells are incorporated into the neck region of the furrow. To account for the observation that lateral myosin in the constricting cells rapidly diminishes after Opto-Rho1DN activation, $K_{L\_active}$ is set to 0 after in silico myosin inhibition.

List of parameters used in Figure 6c:

*: In the simulation, K_b decreases adiabatically from 2¹⁰ to 2⁰, with a twofold reduction at each step. An energy equilibrium state is reached for each value of K_b . These energy equilibrium states define the intermediate and final furrow morphologies.

**: The model recapitulates the binary response to acute loss of actomyosin contractility under a wide range of μ₀ tested (500 – 50,000).

Sample sizes for the presented data and methods for statistical comparisons can be found in figure legends. p values were calculated using MATLAB ttest2 or rank-sum function.

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

The authors thank members of the He lab and the Griffin lab at Dartmouth College for sharing valuable thoughts during this work; James Moseley and Magdalena Bezanilla for providing constructive suggestions and comments on the manuscript; Ann Lavanway for imaging support. The authors thank the Wieschaus lab and the De Renzis lab for sharing reagents, Oleg Polyakov for sharing the code for the energy minimization-based vertex model, and the Bloomington Drosophila Stock Center for fly stocks. This study is supported by NIGMS ESI-MIRA R35GM128745 and American Cancer Society Institutional Research Grant #IRG-82-003-33 to BH. The study used core services supported by STANTO15R0 (CFF RDP), P30-DK117469 (NIDDK P30/DartCF), and P20-GM113132 (bioMT COBRE).

1. Preprint posted: March 19, 2021 (view preprint)
2. Received: April 3, 2021
3. Accepted: February 22, 2022
4. Accepted Manuscript published: February 23, 2022 (version 1)
5. Version of Record published: March 4, 2022 (version 2)

© 2022, Guo et al.

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