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The interplay of stiffness and force anisotropies drive embryo elongation

The morphogenesis of tissues, like the deformation of an object, results from the interplay between their material properties and the mechanical forces exerted on them. Whereas the importance of mechanical forces in influencing cell behaviour is widely recognized, the importance of tissue material properties, in particular stiffness, has received much less attention. Using C. elegans as a model, we examine how both aspects contribute to embryonic elongation. Measuring the opening shape of the epidermal actin cortex after laser nano-ablation, we assess the spatiotemporal changes of actomyosin-dependent force and stiffness along the antero-posterior and dorso-ventral axis. Experimental data and analytical modelling show that myosin II-dependent force anisotropy within the lateral epidermis, and stiffness anisotropy within the fiber-reinforced dorso-ventral epidermis are critical to drive embryonic elongation. Together, our results establish a quantitative link between cortical tension, material properties and morphogenesis of an entire embryo.


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Morphogenesis and organ formation rely on force distribution and tissue material properties, which 31 are often heterogeneous and evolve over time. Forces are generated through a group of relatively 32 well-conserved molecular motors associated with the cytoskeleton, among which myosin II linked to 33 actin filaments is the most prevalent during epithelial morphogenesis (Vicente-Manzanares, 2009). 34 Myosin II spatial distribution and dynamics greatly influence morphogenetic processes (Levayer and 35 Lecuit, 2012). In particular, the asymmetric distribution of the actomyosin network and its pulsatile 36 behaviour define the direction of extension during Drosophila germband elongation (Bertet, 2004, 37 Blankenship, 2006, Drosophila renal tubule formation (Saxena, 2014) or Xenopus mesoderm 38 convergent extension (Shindo and Wallingford, 2014). Whereas the implication of mechanical forces 39 has been intensively investigated (Zhang andLabouesse, 2012, Heisenberg andBellaiche, 2013), 40 much fewer studies have considered the impact of tissue material properties in vivo, except for their 41 influence on cell behaviour in vitro (Kasza, 2007). 42 C. elegans embryonic elongation represents an attractive model for studying morphogenesis, as it 43 offers single cell resolution and powerful genetic analysis. During its elongation, the embryo evolves 44 from a lima-bean to a typical cylindrical shape with a four-fold increase in length, without cell 45 migration, cell division, or a notable change in embryonic volume (Sulston, 1983, Priess and Hirsh, 46 1986) (figure 1a). This process requires the epidermal actomyosin cytoskeleton, which acts mostly in 47 the lateral epidermis (also called seam cells), while the dorso-ventral (DV) epidermal cells may remain 48 passive (supplementary SI1) (Wissmann, 1997, Wissmann, 1999, Shelton, 1999, Piekny, 2003, 49 Diogon, 2007, Gally, 2009, Chan, 2015, Vuong-Brender, 2016. Indeed, the non-muscle myosin II is 50 concentrated in seam cells; in addition short disorganized actin filaments, which favour actomyosin 51 contractility, are present in seam cells, but not in the DV epidermis where they instead form parallel 52 circumferential bundles (Figure 1b-d) (Gally, 2009, Priess andHirsh, 1986). The actomyosin forces are 53 thought to squeeze the embryo circumferentially, to thereby increase the hydrostatic pressure and 54 promote embryo elongation in the antero-posterior (AP) direction (Priess and Hirsh, 1986) (figure 1e). 55 Although the published data clearly imply myosin II in driving elongation, they raise a number of 56 issues. First, myosin II does not show a polarized distribution (figure 1f-g) nor does it display dynamic 57 pulsatile foci at this stage; hence, it is difficult to account for the circumferential squeezing. Moreover, 58 force measurements are lacking to establish that the actomyosin network does squeeze the embryo 59 circumferentially. Second, a mechanical continuum model is needed to understand how the embryo 60 extends preferentially in the AP direction. 61 To address those issues, we used laser ablation to map the distribution of mechanical stress (i.e the 62 force per unit area) and assess tissue stiffness (i.e. the extent to which it resists deformation) in the 63 embryonic epidermis. We then correlated the global embryonic morphological changes with these 64 physical parameters. Finally, we developed continuum mechanical models to account for the 65 morphological changes. Altogether, our data and modelling highlight that the distribution of forces in 66 the seam cells and the stiffness in the DV epidermis must be polarized along the circumferential axis 67 (or DV axis) to drive elongation. 68 69 70

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Measuring the mechanical stress on the actin cortex through laser ablation 73 To measure the stress distribution on the actin cortex, we used laser nano-ablation, which has now 74 become a standard method to assess forces exerted in cells, to sever the actin cytoskeleton and 75 observe the shape of the opening hole (figure 2a). We visualized actin with a GFP-or mCherry-76 labelled actin-binding-domain protein (ABD) expressed in the epidermis (Gally, 2009) (figure 1b-d). 77 We adjusted the region of interest to cut within one cell, restricting our analysis to the early phase of 78 elongation (≤1.7F; for staging, see figure 1 legend). 79 We observed two types of ablation responses (see Methods). In the first (accounting for > 80% of the 80 cases), the opening hole within the actin cytoskeleton reached equilibrium in less than 10 s, and 81 resealed within less than 2 min ( To compare the response between different conditions, we detected the cut opening shape, which we 93 fitted with an ellipse to derive the shape parameters (see Methods). The laser setup we used did not 94 enable us to image the recoil dynamics within the first second after the cut, which other investigators 95 previously used to assess the extent of mechanical stress (Rauzi and Lenne, 2015, Smutny, 2015, 96 Saha, 2016. To circumvent this issue, we developed a novel analysis method to derive mechanical 97 stress, based on the equilibrium shape of a thin cut in an infinite elastic isotropic plane, subjected to 98 biaxial loading (stress applied in two perpendicular directions) (Theocaris, 1986). The rationale for 99 approximating the epidermis to such a plane is further outlined in the supplementary SI2-SI3. In these 100 conditions, a thin cut will open to form an elliptical hole at equilibrium (figure 2a). The opening of the 101 cut reflects mechanical stress in the direction perpendicular to the cut direction. 102

Stress anisotropy in seam cells correlates with embryonic morphological changes 128
We applied the method described above on three seam cells (head H1, body V3, tail V6; figure 3a), 129 since myosin II acts mainly in seam cells (Gally, 2009), and compared the response with embryonic 130 morphological changes. We focused on the anisotropy of stress between the DV and AP directions 131 (difference of stress along both directions) in a given cell (figure 3b). Indeed, in other systems, such 132 as Drosophila embryos (Rauzi, 2008) and C. elegans zygotes (Mayer, 2010), this parameter is critical. 133 At the 1.3F stage in H1, there was no significant stress anisotropy; however, as the embryo elongated 134 to the 1.5F and 1.7F stages, the stress became anisotropic (figure 3b). In V3, the anisotropy of stress 135 evolved in the opposite direction, with higher stress anisotropy at the 1.3F compared to the 1.5F stage 136 (figure 3b). In V6, the stress was slightly anisotropic at both the 1.3F and 1.5F stages (figure 3b). In all 137 cells, whenever the stress became anisotropic it was higher in the DV direction. Overall, the opening 138 increased as the embryo elongated from the 1.3F to the 1.5F stage and from the 1.5F to the 1.7F 139 stage for H1. 140 To correlate the stress anisotropy with the morphological changes of the embryo, we used markers 141 labelling cortical actin (an ABD) and junctions (HMR-1/E-cadherin). We observed that the head, body 142 and tail diameter (at the level of H1, V3 and V6, respectively) decreased at different rates over time 143 (figure 3c), as also observed by Martin and colleagues (Martin, 2014). The head diameter did not 144 diminish between the 1.3F and 1.5F stages when the stress was nearly isotropic, but decreased 145 significantly between the 1.5F and 1.7F stages as the stress anisotropy increased. Conversely, the 146 body diameter decreased the fastest between the 1.3F and 1.5F stages when the stress was highly 147 anisotropic, then changed at a lower pace beyond the 1.5F stage when the stress became less 148 anisotropic. Finally, the tail diameter decreased nearly linearly between the 1.3F and 1.7F stages, at a 149 lower rate than the body diameter, coinciding with a smaller anisotropic stress in V6. Thus, the local 150 morphological changes within the embryo correlate with locally higher stress in the DV compared to 151 the AP direction. 152 To define whether all cells equally contribute to the diameter change, we quantified the circumferential 153 width of the epidermal cells H1, V3 and their adjacent DV cells (figure 3d-e). At the level of V3, the 154 decrease in body diameter came from both seam (V3) and DV cells, whereas in the head it came 155 mainly from DV cells (figure 3e). Collectively, our results strongly suggest that the stress anisotropy 156 correlates with morphological changes. Furthermore, we found that both seam and DV epidermal 157 cells contribute to the changes in embryo diameter, irrespective of their level of active myosin II. 158

159
The establishment of stress anisotropy depends in part on the spectrin cytoskeleton 160 Taking the H1 cell as an example, we considered some cellular factors that could contribute to the 161 stress anisotropy in seam cells: (i) actin-anchoring proteins, (ii) muscle-induced tension. To ease 162 comparisons, we defined the anisotropy of stress (AS) as 163  Second, we wondered whether muscle contractions, which start after the 1.5F stage, could account 172 for AS changes (figure 3b). Compared to controls, embryos depleted of UNC-112/Kindlin, which 173 mediates sarcomere assembly (Rogalski, 2000), showed a significantly higher opening in both the AP 174 and DV directions at the 1.7F stage, but no change in stress anisotropy (figure 3f-g). This is 175 consistent with their wild-type elongation rate up to the 2F stage ( Thus, AS establishment in the H1 cell after the 1.5F stage is independent of muscle contractions. 177

A mechanical model for seam cell elongation depending on stress anisotropy 179
To define the possible causal relationship between the AS and embryonic shape changes, we aimed 180 at simplifying the shape of the embryo to apply classical physical laws such as the Young-Laplace 181 equation, which predicts the relationship between surface tension and the surface curvature. As 182 illustrated in figure 1, the embryo has a circular section and a cylindrical or conical shape depending 183 on the stage, in which the epidermis is thin (100 nm to 2 µm, depending on areas; 184 www.wormatlas.org) compared to the embryo diameter (25 µm). Within the embryo, the epidermis is 185 subjected to hydrostatic pressure when the section decreases (Priess and Hirsh, 1986). We can thus 186 model the C. elegans embryo as an isotropic thin-wall (the epidermis) vessel with capped ends under 187 hydrostatic pressure, and determine the relationship between the mechanical stress on the epidermis 188 and the embryo shape. 189 First, we calculated the anisotropy of stress on the wall of such a vessel. For an axisymmetric vessel, 190 the AS on the wall depends on the surface curvature and the radius (supplementary SI5), which for 191 simple geometrical configurations can be written as shown in figures 4a-c. Typically, the AS factor, or 192 the DV to AP stress ratio, is equal to 1 for a sphere, equal to 2 for a cylinder and takes an 193 intermediate value between 1 and 2 for an ellipsoid. We can simplify the geometry of C. elegans 194 embryos as a curved cylinder (body), attached to a sphere (head) between the 1.3F and 1.5F stages 195 (figure 4d-e). The head evolves into an ellipsoid between the 1.5F and 1.7F stages (figure 4f). Thus, 196 the AS of the head can be determined easily. We previously observed that the AP stress among the 197 seam cells at a given stage differs by 20% ( figure 3b). Thus, if we approximate the AP stress as a 198 constant at a given stage, the AS in the body will depend on the ratio of the body to head radius 199 To examine whether the AS can dictate embryonic morphological changes, we related the 204 deformation of the vessel wall with the forces applied using the Hooke's law (figure 4h, supplementary 205 SI6A) -for instance Hooke's law states that the one-dimensional deformation of a spring equals to 206 the ratio of the applied force to the spring stiffness. Similarly in a two-dimensional system and for an 207 isotropic material, the deformation is proportional to the mechanical stress (forces) and inversely 208 proportional to the Young modulus (stiffness) along the different loading directions (figure 4h). The 209 resulting equations, which assume that seam cells have an isotropic cortex and are subjected to 210 contractile stress, correctly predict that the seam cell dimension increases along the AP axis (ε AP ) 211 with the AS (figure 4h-j), and decreases along the DV axis (ε DV ). Indeed, consistent with the 212 equations, the head evolves from a sphere to an ellipsoid between the 1.5F to the 1.7F stages as the 213 AS becomes greater than 1 (figure 3b-c). 214 In conclusion, our experimental and modelling data show that the AS induces morphological changes 215 occurring in embryonic seam cells and provide a basis to understand how the embryo elongates from 216 a mechanical standpoint. 217 218

Stiffness anisotropy-based elongation of the DV epidermis 219
As shown in figure 3e, the head diameter reduction primarily involves changes of the circumferential 220 width in the DV epidermis. Since the RhoGAP RGA-2 maintains myosin II activation in these cells at a 221 low level (Diogon, 2007), actomyosin contractility in DV cells cannot account for such changes. Salker, 2016). We thus hypothesized that the circumferential polarized actin distribution in DV 225 epidermal cells could induce higher stiffness in that direction and thereby influences their deformation. 226 To establish whether it is the case, we investigated both stress and stiffness distribution in the 227 epidermal cells dorsal and ventral to the H1 seam cell using laser nano-ablation (figure 5a). Since 228 these cells are the precursors of the HYP7 syncytium, we will denote them HYP7 henceforth. 229 We found that, in the HYP7 cell, the opening in the DV direction was larger than in the AP direction 230 (figure 5b; dorsal and ventral cells behaved similarly after laser cutting), at the 1.5F and 1.7F stages, 231 similarly to the H1 cell (figure 3b). However, the ratio of DV/AP opening in HYP7 was more important 232 than in H1 (figure 5c). Assuming that the HYP7 cell cortex has isotropic material properties like that of 233 H1, our model (figure 4; supplementary SI5) would predict that the DV/AP opening ratio in HYP7 234 depends only on the head axisymmetric shape and is equal to that of H1, and would thus contradicts 235 our observations. Hence, this reductio ad absurdum argument suggests that the HYP7 cell has 236 anisotropic cortical material properties indeed. compressive stress (Bert, 1977). To define which model best applies to the DV epidermis, we used 245 continuum linear elastic analysis (Muskkhelishvili, 1975, Suo, 1990, Theocaris, 1986, Yoffe, 1951) 246 (supplementary SI7) to interpret the laser cutting data on the DV epidermis. We discarded the 247 orthotropic model, as it did not adequately describe our data (supplementary SI8), and focused on the 248 fiber-reinforced plane model, which better accounts for the presence of well aligned actin fibers in DV 249

cells. 250
In a fiber-reinforced material composed of a matrix superimposed with fibers, the contribution of the 251 fibers to the stiffness of the material depends on their orientation. In the direction parallel to the fibers, 252 the Young modulus is much increased, whereas in the direction perpendicular to the fibers this 253 contribution is small. According to our modelling, the Young modulus along the fiber direction, 254 increases linearly with a factor K related to the fiber stiffness and density; whereas the stiffness along 255 the direction transverse to the fibers varies as a hyperbolic function of K and reaches a plateau 256 (supplementary SI7). For fiber-reinforcement in the DV direction, the change in Young modulus along 257 the DV and AP directions predicted by modelling is given in figure 6ab. Cuts perpendicular to the 258 fibers opened similarly to an isotropic material with the matrix Young modulus, because they locally 259 destroyed the fibers (figure 6c; see equation 1 above). By contrast, cuts along the fibers opened with 260 an equilibrium value that depends on the fiber stiffness and distribution through the factor K defined 261 above ( figure 6d, supplementary SI7). 262 Since the H1 seam and the head HYP7 cells are adjacent along the circumference (figure 3d), they 263 should be under the same DV stress due to tension continuity across cell-cell junctions. According to 264 equation (1), if the stress in two cells is the same their opening should vary inversely with their 265 respective Young moduli. Since the DV opening of HYP7 was about 1.5 times smaller than that of H1 266 (figure 7a), we infer that the Young modulus of the HYP7 matrix without fibers was about 1.5 times 267 stiffer than that of H1 (supplementary SI9), suggesting that these cells have distinct material 268 properties. Comparing the DV and AP opening for the HYP7 cell, we found that the factor K increased 8c) were statistically significant, whereas it is not the case in V3 (figure 8d). In the HYP7 cell, actin 295 filaments already acquired a preferential DV alignment at the 1.3F stage (figure 8c), but became 296 increasingly organized along the DV direction as the embryo elongated to the 2F stage, with a highly 297 significant difference between the 1.5F and 1.7F stages ( figure 8c and 8f). These changes correlated 298 with the increase of stiffness anisotropy observed in the HYP7 cell (figure 7c). 299 We have attempted to functionally test how actin organization could affect stress and stiffness by 300 manipulating actin polymerization through two different strategies to express cofilin during early 301 elongation. However, we could not obtain meaningful results. Altogether, we conclude that the pattern 302 of actin distribution showed a good correlation with the observed stress and stiffness anisotropy. It will 303 remain important to define the mechanisms bringing changes in actin distribution, and ultimately 304 whether it is a cause or a consequence of anisotropy. anisotropy by reducing the level of actin fiber alignment. Finally, although myosin II activity is low in 338 DV cells (Diogon, 2007), the remaining activity might create some DV-oriented stress feeding back on 339 seam cells. 340 By modelling the DV cells as a fiber-reinforced material, we reveal how the polarized cytoskeleton in 341 DV cells increases their stiffness to orient the extension in the AP direction, acting like a 'molecular 342 corset'. Related 'molecular corsets' have been described and proposed to drive axis elongation in 343 other systems (Wainwright, 1988). In Drosophila, a network of extracellular matrix fibrils was 344 proposed to help elongate developing eggs (Haigo and Bilder, 2011). In plant cells, the orientation of 345 cellulose microfibrils determines the axis of maximal expansion. In the latter, stiffness anisotropy also 346 helps overcome stress anisotropy (Green, 1962, Baskin, 2005. Importantly, C. elegans embryos 347 reduce their circumference during elongation, while Drosophila eggs and plants increase it. It 348 suggests that to conserve the actin reinforcement properties when the diameter decreases, C. 349 elegans DV epidermal cells should have a mechanism to actively shorten the actin bundles, as 350 observed in a biomimetic in vitro system (Murrell and Gardel, 2012). 351 Our experimental data were consistent with the predictions from Hooke's law. They prove that the 352 actomyosin cortex preferentially squeezes the embryo circumferentially, and that the stress anisotropy 353 is tightly linked to the geometry of the embryo. By quantitatively assessing the contribution of stiffness 354 anisotropy in tissue elongation, we have emphasized its importance relative to the more established 355 role of stress anisotropy. The precise relationship between both anisotropies remains to be 356 investigated. Thus, the juxtaposition of cells with different "physical phenotypes", seam epidermis 357 expressing stress anisotropy and DV epidermal cell showing stiffness anisotropy, powers C. elegans 358 elongation, as previously suggested in chicken limb bud outgrowth (Damon, 2008) or chick intestinal 359 looping (Savin, 2011). We did not mention other potential stress bearing components, like 360 microtubules and the embryonic sheath (Priess and Hirsh, 1986), since the former mainly serves to 361 enable protein transport (Quintin, 2016) whereas the function of the later will be the focus of an 362 upcoming work. 363 In conclusion, our work highlights that tissue elongation relies on two fundamental physical quantities 364 (mechanical stress and tissue stiffness), and provide the most advanced mesoscopic understanding 365 to date of the mechanics at work during the first steps of C. elegans embryonic elongation. 366 confocal Leica SP5 microscope with a 63X oil immersion objective and zoom factor 8. We used a step 410 size of 0.08 µm, a pinhole opening of 0.6 Airy Unit and projected 2 µm around the actin cortex. The 411 embryos were rotated on the scan field to have the same antero-posterior orientation. The acquired 412 images were deconvoluted using the Huygens Essential software from Scientific Volume Imaging 413 (Hilversum, Netherlands). We chose a region of interest (ROI) of 4x4 µm 2 within the seam cell H1 or 414 dorso-ventral epidermal cell HYP7, and of 3x3 µm 2 within the seam cell V3 to perform Fast Fourier 415 Transform (FFT). We used a high-pass filter to remove the low frequencies then did inverse FFT. We 416 found that the high pass filter removed changes in intensity due to unequal labelling or out of focus 417 signals but retain the actin texture. Finally we use an ImageJ plugin "Spectral Texture To make a line cut, a region of interest with a length varying from 3 to 6 µm and a width of 0.08 µm (1 436 pixel width) was drawn. We used a laser wavelength varying from 800 nm to 900 nm, which gave 437 similar ablation responses. The laser power was tuned before each imaging section to obtain local 438 disruption of the cortex response (>80% of the cases, visible opening, no actin accumulation around 439 cell borders in the repair process and the ablated embryos developed normally). Typically the power 440 of the laser was 2000 mW, and we used 50% power at 100% gain. Wounding response (actin 441 accumulation around cell borders in the repair process, embryo died afterwards) was rarely observed 442 at the power used for local disruption, but more often when the power was increased to 60-65%. The 443 first time point was recorded 1.44 s after cutting, which corresponded to the time needed to reset the 444 microscope from a two-photon to a regular imaging configuration. The image scanning time recorded 445 by the software was usually less than 400 ms, so the total exposure time of the chosen ROI to 446 multiphoton laser was less than 1 ms. The cuts were oriented either in the antero-posterior (AP) or 447 dorso-ventral (DV) directions relative to the global orientation of the embryos. After ablation, the 448 embryos were monitored to see if they continued to develop normally or they expressed the desired 449 phenotype. More precisely, we verified whether embryos ablated at 1.3F and 1.5F developed past the 450 2F stage, embryos ablated at 1.7F developed past the 2.5F stage, unc-112(RNAi) embryos and spc-451 1(RNAi) embryos arrested at 2F stage. 452 453 Laser ablation image processing and data analysis 454 The shape of the cut opening was detected using the Active Contour plugin ABsnake (Brenner, 1974). 455 A starting ROI was drawn around the opening as the initiation ROI for ABsnake. After running the 456 plugin, the results were checked and corrected for detection errors. The detected shape was fitted 457 with an ellipse to derive the minor axis, major axis and the angle formed by the major axis with the 458 initial cut direction. The average opening of the five last time points before the repair process began 459 (figure S2, from around 8 to 10 s after cutting) was taken as the opening at equilibrium. The standard 460 error of the mean was shown. 461 The curve fit was performed on the average value of the cut opening (defined as the minor axis/initial 462 cut length) using GraphPad Prism 5.00 (San Diego, California, USA) and the equation of one-phase 463 association: 464 where y 0 is the initial width of the cut opening, Plateau is the minor axis of the opening at equilibrium 465 and γ is the relaxation rate. The standard error of the mean given by the software was shown. 466

Statistical analysis 468
The two-tailed t-test was performed on the average of the last five time points (from about 8 s to 10 s) 469 of the cut opening using MATLAB R2014b (The MathWorks Inc     response in the seam cell H1 between wild-type (WT) and let-502(sb118)/Rho kinase mutant embryos 709 at a stage when muscles start to twitch (around 1.5F). Time zero, moment of the cut; DV and AP 710 show direction of opening. Two-tailed t-test, ***: p=4*10 !! between WT DV and let-502(sb118) DV, 711 p=4*10 !! between WT AP and let-502(sb118) AP; N, number of embryos examined. 712