An ex vivo system to study cellular dynamics underlying mouse peri-implantation development

Summary Upon implantation, mammalian embryos undergo major morphogenesis and key developmental processes such as body axis specification and gastrulation. However, limited accessibility obscures the study of these crucial processes. Here, we develop an ex vivo Matrigel-collagen-based culture to recapitulate mouse development from E4.5 to E6.0. Our system not only recapitulates embryonic growth, axis initiation, and overall 3D architecture in 49% of the cases, but its compatibility with light-sheet microscopy also enables the study of cellular dynamics through automatic cell segmentation. We find that, upon implantation, release of the increasing tension in the polar trophectoderm is necessary for its constriction and invagination. The resulting extra-embryonic ectoderm plays a key role in growth, morphogenesis, and patterning of the neighboring epiblast, which subsequently gives rise to all embryonic tissues. This 3D ex vivo system thus offers unprecedented access to peri-implantation development for in toto monitoring, measurement, and spatiotemporally controlled perturbation, revealing a mechano-chemical interplay between extra-embryonic and embryonic tissues.

Correspondence erzberger@embl.de (A.E.), t.hiiragi@hubrecht.eu (T.H.) In brief Ichikawa et al. establish a 3D ex vivo culture that recapitulates mouse periimplantation embryo development. Lightsheet microscopy reveals dynamic cellular coordination underlying epiblast order emergence. Tension release in the polar trophectoderm allows its development into the extra-embryonic ectoderm, which later guides epiblast growth and patterning through mechanochemical interactions.

INTRODUCTION
Implantation is a unique event in mammalian development whereby an exchange interface is established between the embryo and the maternal tissues (Hemberger et al., 2020;Wang and Dey, 2006). In the first few days following fertilization, the pre-implantation embryo develops into a fluid-filled blastocyst wherein the pluripotent epiblast (EPI) is sandwiched between the outer trophectoderm (TE) and the primitive endoderm (PrE). Upon implantation, the extra-embryonic portion of the embryo, consisting of TE and PrE-derived cells, engages the maternal tissue in a complex interplay that eventually forms the placenta. In the embryo proper, implantation coincides with major changes in tissue architecture as it undergoes gastrulation and body axes specification (Arnold and Robertson, 2009;Rossant and Tam, 2009;Takaoka and Hamada, 2012). Though genetic studies characterized key genes and signaling pathways required for these processes, their underlying cellular mechanisms remain obscured by inaccessibility to the implantation process.
Ex vivo culture provides an experimental setting to monitor, measure, and manipulate embryonic development to glean mechanistic insight. Ex vivo culture of peri-implantation mouse embryos so far relied on embryonic growth on 2D surfaces (Bedzhov and Zernicka-Goetz, 2014;Hsu, 1971Hsu, , 1972Morris et al., 2012;Pienkowski et al., 1974;Tachi, 1992). This culture typically induces adhesion and spread of trophoblast cells over the surface, disrupting embryonic morphogenesis. Therefore, recapitulation of in vivo development is limited with current methods, both in terms of efficiency and physiological relevance.
In toto live-imaging has been carried out for later post-implantation mouse development using light-sheet microscopes (Ichikawa et al., 2013;McDole et al., 2018;Udan et al., 2014;Yue et al., 2020). However, these experimental settings limit the sample number and do not allow quantitative analyses of cellular and tissue morphogenesis or spatiotemporally controlled perturbations. Furthermore, though many studies have introduced new experimental systems focused on the development of embryonic tissues ( Resource Shahbazi et al., 2016;Warmflash et al., 2014;Zheng et al., 2019), the contributions of extra-embryonic or uterine tissues in embryonic development have been relatively overlooked, largely due to technical challenges (Brennan et al., 2001;Christodoulou et al., 2019;Guzman-Ayala et al., 2004;Hiramatsu et al., 2013;Thomas and Beddington, 1996). It remains to be examined how interactions between embryonic and extra-embryonic tissues influence mammalian peri-implantation development.
It is evident that tissue interactions are vital throughout development. Morphogenesis induces spatiotemporally coordinated tissue-tissue interactions that feed back on cellular behaviors such as differentiation and cellular rearrangement, which in turn guide morphogenesis (Bailles et al., 2019;Eiraku et al., 2011;Harland and Gerhart, 1997;M€ unster et al., 2019;Saunders and Gasseling, 1968;Shyer et al., 2015). To study such an interaction between embryonic and extra-embryonic tissues, it is essential to have an experimental system that faithfully recapitulates peri-implantation development ex vivo. Furthermore, the system must be compatible with live monitoring, measurement, and perturbation tools to provide mechanistic insights into relevant processes.
In this study, we developed a 3D culture method for mouse peri-implantation embryos that can couple to in toto light-sheet live-imaging. Quantitative analyses of tissue dynamics at single-cell resolution and biophysical measurements and perturbations revealed a key role for mechano-chemical interactions between embryonic and extra-embryonic tissues during early mammalian development.

RESULTS
Tension release in the trophectoderm enables invagination and formation of the extra-embryonic ectoderm With the goal of recapitulating in utero development ex vivo, we attempted to culture peri-implantation mouse embryos while maintaining their 3D-morphology. Blastocysts developed in utero up to embryonic day 4.5 (E4.5) were recovered and embedded into a mixture of Matrigel and collagen. Their development was compared with embryos in utero at equivalent stages, undergoing implantation and egg cylinder formation. After 24 h of culture, however, this ex vivo condition failed to support proper embryonic development, resulting in disorganized morphology and deterioration of the EPI ( Figure 1A). To improve this culture method, we compared embryos at early stages of culture with corresponding stages of in utero developed embryos. We found that the polar trophectoderm (pTE) cells do not invaginate and thus fail to form the extra-embryonic ectoderm (ExE) after 6 h in culture, unlike E4.75 embryos developed in utero (Figures 1A and S1;Christodoulou et al., 2019;Copp, 1979). Instead, pTE cells in cultured embryos appeared highly stretched, in contrast to the columnar appearance in embryos developed in utero ( Figure 1B). This suggested high tension acting on pTE cells in culture. Accordingly, actin and bi-phosphorylated myosin regulatory light chain (ppMRLC) were enriched at the apical surface of the pTE cells before and during invagination in in utero developed embryos, whereas they were localized at cell-cell junctions in those developed ex vivo (Figures 1C and 1D). Furthermore, direct measurement by micropipette aspiration (Maître et al., 2015) indicated that cortical tension of pTE cells increases during this period ( Figure 1E). Collectively, these findings suggest that pTE cells invaginate from the surface layer by the apical constriction, similar to Drosophila gastrulation (Martin et al., 2009), and that excess tension acting on pTE cells, as induced by this culture method, prevents pTE invagination and subsequent ExE formation.
This hypothesis predicts that tension release may allow pTE cells to undergo apical constriction and invagination. We tested this by using two micromanipulation methods that release TE tension at the boundary between polar and mural TEs and examined their impact at different spatiotemporal scales. First, spatiotemporally controlled infra-red laser pulses (de Medeiros et al., 2020), targeted at the TE apical cortex of the embryos cultured for 6 h, indeed induced apical constriction of pTE cells over the following 20 min ( Figure 1F; Video S1). The pTE cells shortened apically and elongated along their apico-basal axis . Next, to examine the impact of tension release at a longer timescale, we microsurgically excised the mural trophectoderm (mTE) from E4.5 embryos at the mTE-pTE boundary. This rapidly (B) Aspect ratio (width to length) of pTE cells in embryos developed in utero or in 3D gel culture shown in (A). n = 16, 18, and 12, respectively. Three pTE cells per embryo were measured. (C) Representative images of mouse embryos developed in utero (top) in comparison with those cultured in 3D gel from E4.5 (bottom) immunostained for actin, biphosphorylated myosin regulatory light chain (ppMRLC), and DNA. Arrows indicate the apical constriction of pTE cells. n = 24 (E4.5), 34 (E4.75), and 16 (6 h), respectively. (D) Subcellular localization of actin and ppMRLC along the apical surface of pTE cells in embryos shown in (C). Line intensity profiles obtained by tracing along the apical membrane of pTE cells (white broken lines). Peaks indicated by arrowheads in the intensity profiles (bottom) correspond to the cell-cell junctions indicated in the microscope images (top). (E) Cortical tension of pTE cells in E4.5 embryos and embryos after 6 h of culture, measured by micropipette aspiration. n = 41 cells from 16 embryos (E4.5) and 44 cells from 18 embryos (6 h). Yellow broken lines mark the EPI. (F) Time-lapse images of a representative GFP-Myh9 embryo after 6 h of 3D gel culture, ablated with infra-red laser pulses. Ablated point is marked with an asterisk (t = 00:00, top) and arrowheads in enlarged views (bottom). Time, minutes:seconds. (G) Schematic for cell shape analysis of TE cells in (F). (H) Change in the apical width of pTE cells, upon laser ablation. Data presented as mean ± SEM. n = 6. (I) Kymographs of GFP-Myh9 signal along with blue and red lines in (F), and measurement of the apico-basal length of pTE cells upon laser ablation. Data presented as mean ± SEM. n = 6. (J) Time-lapse images of a representative Cdx2-GFP embryo at E4.5 immediately after microsurgical removal of mTE cells, without adhesion and spreading of remaining trophectoderm. An arrowhead indicates the apically constricting pTE cells, an asterisk the invaginated ExE cells. Time, hours:minutes:seconds. n = 4. p values calculated using Kruskal-Wallis ANOVA, followed by multiple Mann-Whitney U test (B) and Mann-Whitney U test (E). Scale bars: 50 mm in (A and C) and 20 mm in (D, E, F, and J). See also Figure S1 and Videos S1 and S2. induced pTE cell constriction, followed by invagination after 2 h ( Figure 1J; Video S2). These results support the hypothesis that pTE cells invaginate by apical constriction during implantation, which requires release of tension acting on TE cells.
We therefore decided to excise the mTE for subsequent 3D culture of peri-implantation mouse embryos. Notably, this finding that mTE removal improves ex vivo culture is in agreement with an earlier observation (Bedzhov et al., 2014), despite the difference between 3D and 2D culture methods. Taken together, these findings show that during mouse peri-implantation development, TE tension increases before its release enables the apical constriction of pTE cells for invagination, growth, and formation of the ExE tissue.
3D-geec recapitulates mouse peri-implantation development We further investigated conditions optimal for robust recapitulation of peri-implantation development ex vivo in a 3D gel environment. We first tested blastocysts recovered at E3.5 and developed ex vivo for 24 h before removing the mTE ( Figure S2A). However, few of these embryos developed into egg cylinders (12%, n = 4 of 33 embryos), due to their inability to recapitulate in utero blastocyst maturation ( Figures S2B-S2H). We therefore used blastocysts recovered at E4.5 and removed their mTE for subsequent 3D culture ( Figure S2I). To establish the robust culture methods, we introduced quantitative measures to define the initial embryonic parameters for successful ex vivo development and to evaluate the outcome after 48 h of culture ( Figure 2). We found that embryos recovered at E4.5 after natural mating exhibit a high degree of variability in their progression of development, with the combined number of cells in the inner cell mass and pTE ranging from 55 to 232 ( Figures S2J and S2K). The success rate of ex vivo culture increases with cell number at E4.5. Therefore, a high sample number and efficient ex vivo development can be achieved in combination when E4.5 embryos are selected for cell numbers greater than or equal to 110 (Figure S2K). Although this introduces an additional step before culture, in which the embryos are labeled with Hoechst and briefly imaged by confocal microscopy to count cell numbers, this does not compromise development ( Figure S2L). Together, cell number is a reliable predictor of successful ex vivo development and ensures consistent and robust experimental outcomes.
With these embryos, we quantitatively evaluated the performance of our 3D ex vivo culture, named 3D-gel embedded embryo culture (3D-geec), in comparison with embryos developed in utero. Over 48 h, development in 3D-geec closely follows in utero developmental changes that occur from E4.5 to E6.0, as judged from embryo morphology and anterior-posterior axis specification ( Figures 3A and S3A). Again, we found that in utero development progresses with considerable variability in embryo size and cell number ( Figures 3B and 3C). The dimensions of 3Dgeec embryos are largely comparable, whereas they exhibit a slightly higher diameter-to-length ratio when compared with their in utero counterparts (Figures 3D,S3B,and S3C). Cell numbers in the EPI and visceral endoderm (VE) show a proportional increase in 3D-geec, with 1.5 days (from E4.5 to E6.0) of in utero development achieved by 48 h in culture. Overall, embryonic development in 3D-geec exhibits a 25% temporal delay based on cell number (Figures 3C,3E,and 3F), and these data offer a faithful and quantitative method to stage mouse peri-and post-implantation embryos upon recovery by cell number (Figures S3D and S3E).
We also introduced additional measures to evaluate the outcome of 3D-geec, based on cell differentiation and embryonic patterning. For this purpose, we analyzed the distribution of anterior visceral endoderm (AVE) cells in the VE after 48 h in 3D-geec. At E6.0, mouse embryos establish the anterior-posterior axis through the migration of distal VE cells to the anterior, forming the AVE (Brennan et al., 2001;Thomas et al., 1998). To quantitatively assess the anterior-posterior axis specification, we defined an AVE asymmetry index based on the 3D distribution of Lefty1-or Cerl1-expressing AVE cells relative to Gata4expressing VE cells at the distal tip of the egg cylinder (Figures 4A and 4B). Using in utero developed embryos as a reference, we found that 3D-geec embryos with an AVE asymmetry index greater than 0.15 can be considered as having successfully established an asymmetric AVE distribution and thus the anterior-posterior embryonic axis ( Figure 4C). Based on this criterion, 67% (n = 12 of 18) of the 3D-geec-derived egg cylinders displayed AVE asymmetry. On the other hand, 74% (n = 17 of 23)  Figure 2. A new 3D ex vivo culture of the mouse peri-implantation embryo Schematic of the 3D-geec workflow (top) and representative DIC images of the embryo (bottom). Mouse embryos from natural mating are recovered at E4.5. After microsurgically removing mTE, the qualified embryos, with cell number 110 or higher (see Figure S2), are embedded in a Matrigel-collagen mix and submerged in IVC medium. Embryo development is evaluated after 48 h of culture by the formation of egg cylinder (see Figure 3) and the asymmetric distribution of AVE (see Figure 4). Scale bars, 50 mm. See also Figure S2.  Figure 3. 3D-geec recapitulates in utero development from E4.5 to E6.0 by 48 h (A) Comparison of 3D-geec embryos from day 0 (D0) to 2 (D2; bottom) with embryos developed in utero from E4.5 to E6.0 (top). Immunofluorescence images of a representative embryo (see Figure S3 for additional stages) stained for Sox2 + or Oct3/4 + EPI, Gata4 + VE, and asymmetrically localized Lefty1 + AVE (yellow arrowheads).
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Live imaging with an inverted light-sheet microscope reveals cellular dynamics Next, we aimed to develop in toto live-imaging microscopy compatible with 3D-geec. Increasing embryo size, photo-sensitivity, and the long gel-filled distance between the imaging objective and the embryo render our system incompatible with most conventional microscopes. We therefore employed an inverted light-sheet microscope (Strnad et al., 2016) to live-image 3Dgeec embryos ( Figure 5). The mTE-removed E4.5 embryos were embedded in gel, submerged in IVC medium, and further covered by mineral oil to prevent evaporation ( Figure 5A). This setting allows for successful live-imaging of mouse peri-and post-implantation embryos under 3D-geec for 48 h without compromising embryonic development, as judged from AVE formation, embryo dimensions, and cell number (Figures 5B-5G; Videos S3 and S4).
Quantitative analysis of cellular dynamics is essential for mechanistic understanding of embryonic morphogenesis and patterning. However, available studies so far have limited their analyses to nuclear tracks and lineages (Ichikawa et al., 2013;McDole et al., 2018;Udan et al., 2014;Yue et al., 2020). To extend the analysis to cell shape changes and cell-cell interactions, we developed a machine-learning-based image-processing pipeline for automatic segmentation of EPI cells based on their plasma membrane signal ( Figures 6A and 6B; Video S5). We focused on the first 24 h of the 3D-geec culture until the embryo forms a pro-amniotic cavity to quantitatively analyze cellular dynamics of the EPI tissue both at the level of overall (Figures 6C-6E and S4G-S4I) and single-cell lineages ( Figures 6F-6H, S4A-S4F, and S4J-S4L). Whereas cell volume exhibits a regular change at each cell cycle ( Figures 6C, 6F, S4A, S4D, S4G, and S4J), many EPI cells undergo elongation, and those elongated cells progressively align radially to form a rosette ( Figures 6D,  6E, 6G, 6H, S4B, S4C, S4E, S4F, S4H, S4I, S4K, and S4L). The apical domain emerges in EPI cells and progressively clusters at the center of the EPI tissue as cells elongate, where the proamniotic cavity eventually forms ( Figures 6L, 6M, and S4M; Video S6). Notably, neighboring cells, but not necessarily cells in the same lineage, become progressively correlated in aspect ratio and alignment, pointing to potential cell-cell interactions assisting in the organization of the EPI tissue ( Figures 6I, 6J, and 6K). Together, quantitative characterization of cellular geometry and polarization reveals their dynamic coordination, suggesting feedback mechanisms underlying maturation of the EPI, in addition to the key role that EPI cell polarization plays in pro-amniotic cavity formation (Bedzhov and Zernicka-Goetz, 2014;Christodoulou et al., 2018).
ExE invagination and growth facilitate EPI growth, morphogenesis, and patterning Whereas the collective behavior of EPI cells may thus drive rosette formation, we noted that EPI cell-cell rearrangement is enhanced upon invagination of pTE cells ( Figure S5A). This suggests possible influence by the neighboring ExE tissue on patterning the EPI. To investigate the impact of ExE on EPI growth, morphogenesis, and patterning, we compared cellular dynamics and morphogenesis between 3D-geec embryos with (see Figure 1) and without mTE (see Figures 2, 3, 4, 5, and 6). As described earlier, the latter recapitulates ExE formation in a manner comparable to in utero development, whereas the former fails to form the ExE, as pTE cells do not invaginate and instead remain a single layer of cells surrounding the EPI (Figure 7A; see also Figure 1A at 6 and 24 h, and 3A at D1). When cell numbers are compared after 18 h of culture, a properly formed ExE has a higher mean cell number than a pTE that failed to invaginate. Furthermore, the EPI consists of a significantly higher number of cells in the presence of an ExE ( Figure 7B). These data suggest that the presence of the neighboring ExE tissue may facilitate growth of the EPI.
To investigate the possible mechanism of this tissue-tissue interaction, we first examined the role of biochemical signaling pathways. Specifically, the expression of Id1 and live-reporter expression of A 7 -Venus and Dusp4-T2A-mVenus were used to examine BMP, Nodal-Foxh1 (Takaoka et al., 2017), and FGF-Dusp4 signaling pathways, respectively. Nodal signaling in the EPI exhibits cell-to-cell heterogeneity regardless of the presence of ExE (Granier et al., 2011; Figure S5B). Id1 expression is enriched in the EPI region in contact with the ExE or pTE, regardless of EPI geometry or the presence of ExE ( Figure 7C), strongly suggesting that BMP is secreted from the ExE or pTE to activate BMP-Id1 signaling in the proximal EPI, as reported for BMP4 signaling at later stages (Winnier et al., 1995). In marked contrast, FGF-Dusp4 signaling shows an activity gradient across the proximal-distal axis in the EPI, and this patterned signaling activity is lost in the absence of ExE ( Figures S5C and S5D). This indicates an essential role for ExE in establishing the FGF signaling landscape in the EPI ( Figure 7D). Collectively, these data suggest that biochemical signaling from the ExE acts paracrine to the neighboring EPI tissue to drive its growth and patterning.
Next, we investigated the possibility of mechanical influence of the ExE tissue on the EPI. We noted that a flat or convex boundary forms between the ExE and EPI tissues during pTE invagination and ExE growth (see Figures 3A, 5B, 6B, 7A, 7C, 7D, and S5A). This is in contrast with development without ExE, in which the EPI is surrounded by a single layer of pTE cells. The boundary between ExE and EPI lacks Collagen IV and is

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Resource therefore distinct from the remainder of the EPI boundary that is enriched with Collagen IV. The presence of Collagen IV enables Integrinb1-mediated adhesion at the basal side of EPI cells (Bedzhov and Zernicka-Goetz, 2014; Figure 7E). We therefore investigated whether this Collagen-free ExE-EPI boundary impacts the self-organization of the EPI tissue, particularly the formation of the pro-amniotic cavity.
We started with a theoretical analysis of the mechanics to delineate the conditions under which the cavity can achieve stable growth (STAR Methods). Lumen formation has been described as a process analogous to the nucleation of a droplet in a new phase (Duclut et al., 2019). Briefly, lumina may grow if the inner pressure P L acting on the lumen-tissue interface is large enough to overcome the resisting interfacial tension: Here, R denotes the lumen radius, a is a dissipative coefficient, and g is the effective surface tension associated with the lumentissue interface. Notably, the resisting surface term scales inversely with the lumen radius; consequently, the size and shape of a lumen determine its growth. Lumina may grow only if their radii exceed the critical threshold R crit = 2g=P L , which is set by the competition of surface and bulk terms. Interestingly, in many physical systems, heterogeneous nucleation-where an external wall or an impurity provides an additional interface for newly forming droplets-dominates over homogeneous nucleation. It is an everyday observation that gas bubbles first form at the surface of a pot of water about to boil. Indeed, the radius of curvature of a nascent droplet adhered to a surface is larger compared with a non-adherent droplet of equal volume (Figures 7F and 7G). Correspondingly, the surface term resisting nucleation is lowered for an adherent droplet (Turnbull, 1950). We hypothesized that the neighboring ExE tissue provides an interface with properties facilitating lumen formation, analogous to heterogeneous nucleation. Assuming that the interfacial tension between the lumen and EPI cells is similar to that between the lumen and the ExE, heterogeneous nucleation may occur as long as the ExE-EPI boundary has a positive interfacial tension. We calculated the parameter regimes in which stable lumen expansion is achieved, and found that our theory predicts more robust lumen formation in the presence of the ExE-EPI boundary ( Figure 7H).
To test this prediction, we examined the formation of the proamniotic cavity in the embryo developing in the presence or absence of the neighboring ExE tissue. More than half (7 of 13) of the embryos developing with an ExE formed a pro-amniotic cavity after 18 h of 3D-geec, comparable with the 7 of 13 in utero developed E5.0 embryos that had a pro-amniotic cavity (Figure 7I). In contrast, the EPI is disorganized in embryos that failed to form an ExE, which is marked by multiple rosettes without a lumen. Regarding the positioning of the nascent pro-amniotic cavity, 38 (90%) of 42 embryos developed in 3D-geec formed the pro-amniotic cavity at the boundary between EPI and ExE tissues (see Figures 5B, 6B,       E5.25), 24 (67%) formed the pro-amniotic lumen at the boundary between EPI and ExE tissues ( Figure S5E), with an additional 4 embryos that had already begun EPI elongation with the lumen connected to the boundary as a fissure-like structure ( Figure 7I; a total of 28 embryos, 78%). Furthermore, time-lapse images of 3D-geec embryos show that the lumen emerges at the ExE-EPI boundary ( Figure 7J), or alternatively, that while rosettes form at multiple locations within EPI tissue, the lumen expands from the ExE-EPI boundary ( Figures S5F and S5G). These data are all in agreement with our calculated prediction that lumen formation is more stable at the ExE-EPI tissue boundary, illustrating the mechanical contribution of the ExE in shaping the EPI. Taken together, these findings strongly suggest that the ExE acts both biochemically and mechanically on the neighboring EPI to facilitate its growth, morphogenesis, and patterning, leading to EPI elongation and ultimately egg cylinder formation.

DISCUSSION
The new 3D-geec methods presented here enable 3D culture and live-imaging of mouse peri-and post-implantation embryos from E4.5 to E6.0 ex vivo over 48 h. A number of quantitative measures, newly introduced for mouse peri-implantation embryos, ensure an efficient success rate and reproducibility. Our findings show that 3D gel culture recapitulates in utero development more faithfully than available 2D methods, in line with a recent study that developed human peri-implantation embryo culture in 3D (Xiang et al., 2020). These 3D gel cultures effectively prevent disruption of embryonic morphogenesis, which has been largely inevitable in the 2D culture methods. Our 3D culture method is also compatible with live-imaging using commercially available light-sheet microscopes (Serra et al., 2019;Strnad et al., 2016), offering sufficient spatiotemporal resolution for automatic image analyses, including cell tracking and membrane segmentation. Notably, these microscopes also accommodate multi-sample imaging and enable spatiotemporally controlled perturbations such as photo-manipulation. The unprecedented access to cellular dynamics during peri-implantation development and the capability for in toto monitoring, measurement, and manipulation will ultimately lead to finer mechanistic understanding of this crucial period in mammalian development.
In this study, we found that releasing TE tension enables pTE cells to invaginate by apical constriction and proliferate to form the ExE. This ExE in turn facilitates the growth and morphogen-esis of the neighboring EPI by establishing BMP and FGF signaling landscapes, consistent with the essential role of BMP signaling in maintaining EPI pluripotency (Di-Gregorio et al., 2007). The reduced growth of EPI in the absence of ExE might also be explained by the role of proprotein convertases, Spc1 and Spc4, secreted by ExE, in activating Nodal signaling in the EPI (Beck et al., 2002). Furthermore, theoretical analysis and biological experiments consistently show that juxta-positioning of the ExE tissue also facilitates luminogenesis and patterned morphogenesis of the EPI tissue. In addition to the direct mechanical effect of the ExE interface, lumen positioning might be facilitated by the radial organization of polarizing EPI cells. This is in line with the findings that whereas embryonic stem cells (Bedzhov and Zernicka-Goetz, 2014) and embryos lacking an ExE (Figures 1, 7, and S5C and S5D) may form rosettes or a pro-amniotic cavity in a simplified geometry, EPI patterning occurs more consistently and robustly in vivo through tissue-tissue interactions.
Overall, our data demonstrate the biochemical and mechanical roles of extra-embryonic tissues in mammalian embryonic development, in addition to their impact on VE morphogenesis, which was reported in a recent study (Christodoulou et al., 2019). As the EPI is known to control the proliferation of the ExE via FGF (Christodoulou et al., 2019;Gardner et al., 1973), our findings suggest that reciprocal interactions between embryonic and extra-embryonic tissues (Brennan et al., 2001) start as early as E5.0.

Limitations of the study
Although 3D-geec offers novel access to mouse peri-implantation development, it also leaves us with new challenges. First, the present methods require removal of the mTE, similar to 2D methods (Bedzhov et al., 2014), to release TE tension and to induce formation of the ExE. Whereas this results in robust ex vivo recapitulation of mouse peri-and post-implantation development from E4.5 to E6.0 in 3D gel, in utero development certainly involves the mTE, which together with the parietal endoderm forms Reichert's membrane (Salamat et al., 1995). When the invasive behavior of mTE cells was experimentally induced by adhesive beads, pTE cells showed constriction with actin enriched at the apical surface, similar to the embryos developed in utero (see Figure 1D), suggesting the role of embryo-uterine interaction in tension release ( Figures S5H-S5K). However, the exact mechanism of how the TE tension is released  in utero and the development of an ex vivo culture method that retains the mTE will be topics of future studies. Second, in utero development to E4.5 blastocyst is necessary for the high success rate of ex vivo culture shown in this study ( Figures  S2A-S2H). This indicates an as-yet uncharacterized chemical or mechanical role of the uterine environment in the blastocyst maturation and currently precludes the in vitro culture of mouse embryos from the zygote through to the post-implantation stage. Finally, the diameter of the 3D-geec embryo is wider than embryos developed in utero ( Figure 3B). This spherical tissue dimension may be driven by pressurized expansion of the proamniotic cavity, similar to blastocyst cavity expansion prior to implantation (Chan et al., 2019;Dumortier et al., 2019;Leonavicius et al., 2018;Niwayama et al., 2019). Moreover, uterine tissue may be necessary to confine this expansion for precise EPI elongation during in utero development.
In all cases, it is highly conceivable that mammalian peri-and post-implantation development requires intimate interactions between embryos and extra-embryonic tissues, as well as a contribution from uterine tissues. Further development of methods to recapitulate these interactions ex vivo, or to study embryonic development in situ inside the uterus (Huang et al., 2020), will be necessary to integrate their respective roles and gain a comprehensive understanding of mammalian development.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following: (F) Theoretical analysis of lumen formation as a nucleation process. The contact angle q of a lumen in contact with an external tissue is governed by the surface tensions g, g W1 , g W2 associated with the different interfaces, as described by Young's equation (see STAR Methods).
(G) The radius of curvature of a lumen in contact with a wall (red line) is always larger than the radius of curvature of a spherical (homogeneous) lumen of the same volume (black line). R Min refers to the radius of the minimal initial spherical lumen of volume V. For g W / g < À1 (in which g W = g W2 À g W1 ), a contact area between lumen and wall is not favored (zero wetting), whereas for g W / g > 1, lumina would undergo complete spreading along the wall (total wetting).
(H) The state diagram shows the parameter regions in which lumina grow or shrink. In the green area, both homogeneous and heterogeneous nucleation events lead to lumen expansion. In the yellow region, only heterogeneous nucleation leads to lumen growth. In the orange region, no lumen growth can be sustained. The hatched regions are outside the regime of partial wetting, where heterogeneous nucleation cannot occur. P Norm = 2g/R Min .
(I) Immunofluorescence of representative embryos developed in utero, or ex vivo for 18 h in the presence or absence of ExE, stained for pERM, actin, and Oct3/4 + EPI. The number of EPI cells in relation to the outcome of EPI patterning (bottom). n = 13, 13, and 8, respectively. Arrowheads and asterisks mark the pERMenriched rosettes and pro-amniotic cavities, respectively. (J) Time-lapse images of a representative H2B-GFP;mT mouse embryo developing ex vivo in the presence of ExE from E4.5 (t = 00:00, hours:minutes). Arrowheads and asterisks mark rosettes and the pro-amniotic cavity, respectively. p values calculated using t test. Scale bars, 50 mm or 20 mm (enlarged views). See also Figure S5.

DECLARATION OF INTERESTS
The authors declare no competing interests.

RESOURCE AVAILABILITY
Lead contact Further information and requests for resources and reagents should be directed to and will be fulfilled by the lead contact, Takashi Hiiragi (t.hiiragi@hubrecht.eu).

Materials availability
All unique/stable reagents generated in this study are available from the lead contact with a completed Materials Transfer Agreement.

Data and code availability
All datasets/codes generated during this study are available upon request.

EXPERIMENTAL MODEL AND SUBJECT DETAILS
Animal work All animal work was performed in the Laboratory Animal Resources (LAR) at the European Molecular Biology Laboratory (EMBL) with permission from the Institutional Animal Care and Use Committee (IACUC) overseeing the operation (IACUC number TH11 00 11). LAR is operated according to the Federation of European Laboratory Animal Science Associations (FELASA) guidelines and recommendations. All mice were maintained in specific pathogen-free conditions with 12-12 hours light-dark cycle and used for experiments at the age of 8 to 35 weeks.

Mouse lines and genotyping
The following mouse lines were used in this study: a F1 hybrid strain between C57BL/6 and C3H (B6C3F1) as wild-type ( were generated in this study. Standard tail genotyping procedures were used to genotype transgenic mice (for primers and PCR product sizes, see Table S1).
To generate Ezrin-mCherry mice, human ezrin coding sequence tagged with mCherry was PCR amplified using pRN3-Ezrin-mCherry plasmid (a gift from Sophie Louvet-Vallé e; Dard et al., 2001) as a template and primers introducing Nhe1 and EcoR1 recognition sites at the ends of the amplicon. The PCR fragment was digested with Nhe1 and EcoR1 and then inserted into pgk-ATG-FRT2-CAG plasmid (a gift from Judith Reichmann, Ellenberg lab in EMBL) cut with the same restriction enzymes. The obtained plasmid contained Ezrin tagged with mCherry under CAG promoter. This plasmid was digested with Pvu1, and the resulting 7018 bp fragment was used for pronuclear injection into C57BL/6 zygotes to generate a mouse with random integration. To generate Dusp4-T2A knock-in alleles, we targeted the stop codon of endogenous Dusp4 locus with one selection and two different reporter cassettes coding for a destabilized triple mCherry and triple mVenus. The reporter cassettes were flanked by loxP-and FRTsites to remove the selection cassette. Thus, the targeting vector was constructed as follows: loxP-T2A-3xmCherry-NLS-PEST-FRT-PGK Neo-loxP-T2A-3xmVenus-NLS-PEST-FRT. Cre-mediated excision resulted in Dusp4-T2A-3xmVenus allele used in this study. Dusp4-T2A-3xmVenus knock-in reporter line was generated by standard gene targeting techniques using R1 embryonic stem cells. Briefly, chimeric mice were obtained by C57BL/6 blastocyst injection and then outbred to establish the line through germline transmission.

Mouse embryos
To obtain mouse embryos, mice were naturally mated, and noon on the day when a vaginal plug was detected was defined as embryonic day 0.5 (E0.5). Recovery of all embryos was performed under a stereomicroscope (Zeiss, StreREO Discovery.V8) equipped with a thermo plate (Tokai Hit) at 37 C. Pre-implantation blastocysts were recovered by flushing dissected oviducts and uteri with globalÒ medium w/ HEPES (LifeGlobal, LGGH-050). Peri-and post-implantation embryos were recovered from dissected uteri in dissection medium (DMEM (Gibco, 11880028) supplemented with 15% heat-inactivated FBS (PAA, A15-080), 2 mM GlutaMAX (Gibco, 35050061), 10 mM HEPES (Sigma, H0887), 25 units/mL Penicillin and 25 mg/mL Streptomycin (Gibco, 15070063)). Blastocysts at E4.5 are either floating in the uterine luminal space or loosely adherent to the uterine luminal epithelium, and can be isolated by opening along with the mesometrial side of the uterus, followed by a gentle touch using fine forceps (Dumont,No.5). Sites of embryo adherence can be identified by locally red and swollen luminal epithelium tissue. Recovery of later post-implantation embryos is as described (Nagy et al., 2003). The Reichert's membrane of the post-implantation embryos was removed using sharp needles (BD eclipse, 305757). Recovered embryos were handled using an aspirator tube (Sigma, A5177) equipped with a glass pipette pulled from glass micropipettes (Blaubrand intraMark 708744) and cultured in an incubator with a humidified atmosphere of 5% CO 2 at 37 C (Thermo Scientific, Heracell 240i).

METHOD DETAILS
3D-gel embedded embryo culture (3D-geec) Gel mix for embedding was prepared on ice, first adding basal medium (advanced DMEM/F-12 (Gibco, 12634010) supplemented with 2 mM GlutaMAX, 25 units/mL Penicillin and 25 mg/mL Streptomycin), growth factor reduced Matrigel (Corning,356230,lot. 7345012), and then rat-tail Collagen I (Corning, 354236, lot. 6053001). Due to lot-to-lot variation of Matrigel and Collagen I, it is recommended to test for culture side-by-side prior to a large purchase. We tested three lots of Matrigel (lot. 7107329, 7202001, and 7543012) and two lots of Collagen I (lot. 5064009 and 6053001) and selected as above based on the rate of successful egg cylinder formation. We also examined different combinations of the final concentration of Matrigel and Collagen I ranging from 0.5 to 5.0 mg/mL and 0 to 0.7 mg/mL, and found 3.0 mg/mL and 0.3 mg/mL resulted in the best performance, respectively. 15 mL gel mix was added in an inner well of the m-Slide Angiogenesis dish (Ibidi, 81506), and then embryos quickly rinsed with the gel mix were carefully embedded in the gel droplet so that they did neither adhere to the surface of the dish nor float at the interface of the gel. After solidification of the gel upon 30 minutes incubation in the incubator, 50 mL pre-warmed IVC1 medium (Bedzhov et al., 2014) was added to fill the upper well. IVC1 medium was exchanged for IVC2 medium (Bedzhov et al., 2014) after 24 hours of culture.
For 3D gel-embedded embryo culture (3D-geec), mural trophectoderm (mTE) was microsurgically removed from E4.5 embryos immediately after recovery using sharp needles under a stereomicroscope. mTE-removed embryos were then embedded as described above. To count the initial number of cells, mTE-removed embryos were incubated in IVC1 containing 5 mg/mL Hoechst 33342 (Invitrogen, H21492) for 30 minutes at 37 C. Embryos were rinsed with IVC1 three times and live-imaged with 405 nm laser on a confocal microscope (Zeiss, LSM880) in a custom-made incubation box set to 5% CO 2 and 5% O 2 at 37 C. To minimise the UV-damage, imaging was achieved within 30 seconds by using Airyscan Fast mode. This additional step before culture ensures the highest quality and consistent experimental outcome without compromising the development ( Figure S2L).

Cortical tension measurement
Micropipette aspiration set-up was used as described previously (Biro and Maître, 2015;Maître et al., 2015) to measure the cortical tension of pTE cells. Briefly, microforged micropipettes coated with Sigmacote (Sigma, SL2) of radius 3-4 mm were coupled to a microfluidic pump (Fluigent, MFCS-VAC). Pressures were increasingly applied in a step-wise manner, until reaching a cortex deformation which has the radius of the micropipette in use (R p ). At steady state, the cortical tension g of the pTE is calculated based on Young-Laplace's law: g = P c /2(1/R p À 1/R c ), where P c is the pressure used to deform the cell of radius R c . Embryos were cultured in suspension by hanging-drop of IVC1 medium for 6 hrs, prior to micropipette aspiration. The surface of the glass-bottom dish was also coated with Sigmacote to prevent the embryos from attachment to the dish. Microscopic inspection of cell membrane deformation ensured aspiration of a single pTE cell.
Images of immunostained embryos were obtained by LSM880 equipped with a C-Apochromat 40x/1.2 NA water immersion objective (Zeiss). ASE-YFP and Dusp4-mVenus signals were imaged by LSM confocal mode. Otherwise, Airyscan Fast mode was used, and raw Airyscan images were post-processed by ZEN black software (Zeiss). E6.0 and D2 embryos in Figure 4B, and embryos after 48 hours of live-imaging in Figure 5C were imaged by an inverted light-sheet microscope (Bruker, Luxendo, InVi SPIM) to illuminate in deep.
Light-sheet live-imaging 3D-geec embryos were live-imaged using InVi SPIM. Up to ten embryos were embedded in a 10 mL gel mix within the V-shaped sample holder covered with transparent FEP foil, carefully positioned so that they are at proximity but do not attach to the FEP foil which would disrupt morphogenesis via adhesion. After gelification, embryos were immersed in 75 mL IVC1 medium and further covered with 200 mL mineral oil to prevent evaporation. IVC1 medium was exchanged for IVC 2 medium after 24 hours of culture. The sample holder was enclosed in an environmentally controlled incubation box with 5% CO 2 and 5% O 2 at 37 C.
InVi SPIM was equipped with a Nikon 25x/1.1NA water immersion detective objective and a Nikon 10x/0.3 NA water immersion illumination objective. The illumination plane and focal plane were aligned before each imaging session and maintained during the imaging. Images were taken every 20 min by a CMOS camera (Hamamatsu, ORCA Flash4.0 V2) with line-scan mode in LuxControl (Luxendo). The imaged volume in case of 48 hours of continuous live-imaging was 425.983425.983400 mm 3 , with a physical voxel size of 0.20830.20831.000 mm 3 , along the X, Y and Z axis, respectively. For the live-imaging shorter than 24 hours, the volume was 212.993212.993200 mm 3 with a physical voxel size of 0.10430.10431.000 mm 3 . The lasers and filters used were 488 nm and BP525/50, 515 nm and BP545/40, 561 nm and LP561, and 594 nm and BP632/60 to image GFP, mVenus, tdTomato, and mCherry fluorophores, respectively. Exposure time for each plane was set to 50 ms. Eighty-one % (n=13 of 16) embryos that expressed both H2B-GFP and mT, alternatively 77% (n=23 of 30) embryos that expressed mT regardless of H2B-GFP, developed into the egg cylinder after 48 hours of live-imaging from 5 independent experiments ( Figure 5B) without substantial change in embryo size and cell number ( Figures 5E  and 5F), suggesting no significant harmful effects of live-imaging on 3D-geec development.

Laser ablation with light-sheet live-imaging
To perform laser ablation of embryos in gel while light-sheet live-imaging, we equipped InVi SPIM with a photomanipulation module (Bruker, Luxendo) (de Medeiros et al., 2020). Specifically, a pulsed infrared (IR) laser at 1040 nm, 200 femtoseconds pulse length and 1.5W (Spectra-Physics, HighQ-2) was coupled with the detection objective. The illumination spot of IR laser was aligned at the focal plane before each experimental session and maintained during the experiment to ensure spatial control of the ablation while avoiding wound response. Viability of ablated embryos was verified by embryo growth at 6 hours of culture after ablation.
Ablation at the cell-cell junction in a TE layer was performed by defining a circular ROI of 0.8 mm in diameter on the GFP-Myh9 enriched cell-cell junction, and using 100% laser power, 100 ms dwell time, 5 times repetitions and 2 pixels spacing in LuxControl. Images were taken every 15 seconds with 5 Z-slices separated by 1 mm. Only those experiments in which laser ablation did not elicit typical wound responses such as cortex blebbing, cell swelling or bursting were considered for analysis ( Figures 1F-1I).

Blastocyst immunosurgery and culture
Blastocysts recovered at E3.5 as described above were treated with 0.5% (w/v) Protease (Sigma, P8811) in an incubator with a humidified atmosphere of 5% CO 2 at 37 C to remove zona pellucida and subsequently cultured for 24 hours in 2ml global medium (LifeGlobal, LGGG-050) drops under mineral oil on 35 mm glass-bottom dishes (MatTek, P35G-1.5-14-C) treated with Sigmacote. The TE layer was ll OPEN ACCESS

Resource
Developmental Cell 57, 373-386.e1-e9, February 7, 2022 e5 removed by from blastocysts by immunosurgery (Ohnishi et al., 2014). Briefly, blastocysts were incubated for 30 minutes in anti-mouse serum antibody (Sigma, M5774) diluted 1:3 in global medium at 37 C, washed in global medium, followed by incubation for 30 minutes in complement sera from guinea pig (Sigma, S1639) diluted 1:3 in global medium at 37 C. Lysed TE cells were removed by mouth pipetting. As the pTE is more tightly attached to the ICM than the mTE, extensive mouth pipetting resulted in complete TE removal, while gentle mouth pipetting left remnant pTE cells. Embryos were then allowed to recover for 30 minutes in IVC1 medium before being embedded for 3D-geec as described above. Embryos were fixed after 24-28 hours of culture and subjected to immunofluorescence staining and imaging.

Microbeads embedding
Heparin-Agarose microbeads (Sigma, H0402) washed in PBS three times, followed by incubation in 0.1% BSA containing PBS overnight at 4 C with gentle agitation were used to establish adhesive contact with mTE cells. Beads were washed in basal medium to remove excess BSA prior to embedding into gel together with embryos and carefully positioned in proximity to embryos. Embryos were fixed after 18 hours of culture, and only those embryos that adhered to beads retained beads while fixation.
Nucleation theory of lumen formation: Heterogeneous versus homogeneous case Fluid-filled cavities can appear within cellular assemblies, and such lumina play important roles during embryonic development (Ryan et al., 2019). Lumen formation has been described as a process analogous to the nucleation of a droplet in a new phase (Duclut et al., 2019), where the competition between a surface-and a bulk term sets a critical radius above which a lumen can grow. In many biological systems, active processes contribute to these terms, i.e., cytoskeleton-generated cellular surface tensions and active pumping of fluid by the cells (Torres-Sá nchez et al., 2021;Le Verge-Serandour and Turlier, 2021). In many physical systems, heterogeneous nucleation -where an external wall or an impurity provides an additional interfacedominates over homogeneous nucleation. In classical nucleation theory, this is explained as a lowering of the free energy barrier that needs to be overcome for nucleation when an additional interface lowers the surface energy of the forming droplet (Turnbull, 1950). Here we investigate the role of an additional tissue in lumen formation. The external tissue acts like a wall on which heterogeneous nucleation can occur. We show how the presence of this additional interface facilitates lumen formation. Critical radius for lumen formation We begin by deriving the critical radius above which a lumen will expand and below which it will disappear. This radius depends on the parameters of the system, i.e., the lumen pressure and the surface tension associated with the tissue-lumen interface. For a spherical lumen, the balance of forces at each point of the tissue-lumen interface is given by the Young-Laplace equation: in which P is the pressure difference across the tissue-lumen interface, g is a positive effective surface tension associated to the tissue-lumen interface, and R is the radius of the lumen. We assume that the pressure equilibrates within the cavity on the timescale of the radius dynamics and can thus be taken to be uniform. In general, P has several contributions, including active pumping terms. We decompose the pressure into a constant term P L and a dissipative term, and write the following constitutive relation: in which a is a dissipative coefficient associated with changes of the lumen radius. Here we do not consider any other dependencies of the pressure on the radius. From Equations 1 and 2, we obtain a differential equation for the lumen radius: that has the traditional form of a nucleation equation with competing bulk and surface terms. The critical radius for lumen growth is given by: Whether lumina of a given size will grow or shrink depends on the parameters g and P L which are actively regulated by the cells through the formation of their apical domains and their pumping activities. A lumen can expand when the bulk term dominates over the surface term, i.e., when active fluid pumping overcomes the cost of increasing the lumen-cell interface.

Presence of a wall
We assume that the system is able to produce initial proto-lumina with a finite initialization volume V -set for example by a characteristic exocytosis volume. The initial proto-lumen radius for the homogeneous case -i.e., in the absence of a wall -is then given by: In classical heterogeneous nucleation, additional interfaces can lower the energetic cost of forming a new droplet interface, thereby reducing the work for nucleating the new phase at the boundary. In this case, a droplet in contact with the wall takes the shape of a spherical cap, for which the volume can be expressed in terms of the radius of curvature R Het and the contact angle q ( Figure 7F): Het ð2 + cos qÞð1 À cos qÞ 2 : The contact angle is modified by the additional interfacial tensions with the wall as given by the Young equation: In the following, we denote by g W = g W2 À g W1 , the difference between the surface tensions associated with the wall-tissue and wall-lumen interfaces. The heterogenous configuration is only favourable when the properties of the wall are such that À g< g W < g, i.e., when the system is in the partial wetting regime. The radius of curvature -which sets the surface term in Equation 3 -is then given by: s : Figure 7G shows how R Het varies as a function of the surface tensions. Note that R Het >R Hom . The regimes of growth and shrinkage for the homogeneous and heterogeneous cases are depicted in Figure 7H.
In conclusion, if the interfacial tensions favor the formation of a new interface between the lumen and the wall, lumen expansion is facilitated by the presence of the wall. Lumen formation in the mouse epiblast During embryonic development in mouse, a lumen called the pro-amniotic cavity forms within the EPI. The EPI at this stage is adjacent to the ExE ( Figure 1A). We hypothesize that the extra-embryonic interface may facilitate luminogenesis in analogy with the mechanism of heterogeneous nucleation. To enable heterogeneous nucleation, the interfacial tensions between ExE, EPI and the nascent lumen would need to fulfil the partial wetting condition À g<g W2 À g W1 <g.
Assuming that the interfacial tension between lumen and EPI is similar to that between lumen and ExE, i.e., that gz g W1 , we find that the condition for complete wetting is g W2 >2g. In this regime, lumen-tissue interfaces are strongly favoured over the tissue-tissue interface, and nucleating lumina would completely spread along the tissue boundary. Conversely, the condition for zero wetting is g W2 <0, i.e., where the presence of strong adhesion between the tissues renders the surface tension negative. A negative tension at the tissue-tissue interface however would be expected to lead to shape instabilities which are not observed.
If lumina at the interface between the EPI and the ExE reside within the partial wetting regime, their expansion should be facilitated at this boundary. Then, luminogenesis is predicted to occur predominantly adjacent to the extra-embryonic interface, and loss of this interface is expected to disrupt luminogenesis. Our experimental observations agree with these predictions (Figures 7I, 7J, S5F, and S5G).

Image analysis
Dimension measurements ( Figures 3B, 3D, 5E, S2F, and S2G), cell counts ( Figures 3C, 3E, 5F, 5G, 7B, 7I, S2C-S2E, and S2J-S2L), cell coordinates analysis ( Figures 4A-4C and S5A) and apical domain detection ( Figure 6L and 6M) were performed with Imaris v9.2.1 (Bitplane). Signal intensity measurements ( Figures 1D, 7C, 7D, S2H, S5C, S5D, and S5K) and cell shape analysis ( Figures 1B, 1G-1I, and S5J) were performed with Fiji (Schindelin et al., 2012). Cell tracking ( Figure S5A) was performed with Fiji and Imaris. Whole embryo images were used for E4.5-E5.25 embryos. To compensate for signal attenuation in thicker samples, the half of the egg cylinder closer to the objective were used for dimension measurements and cell counts. Evaluation of embryo morphology Dimension measurements of in utero and 3D-geec embryos were performed in 3D using Measurement Points. For blastocysts, the diameter is defined as the mean of the long and short transverse axes of the ICM, and the length is defined as the distance between the EPI-pTE boundary and the apical surface of the PrE. For egg cylinders, the diameter is defined as the mean of the long and short transverse axes of the egg cylinder, and the length is defined as the distance between the ExE-EPI boundary and the distal tip of the egg cylinder. Evaluation of embryo development based on cell numbers Cell counts of in utero and 3D-geec embryos were performed in 3D using automated Spots detection with manual correction. Initial cell number (Figures S2J and S2K) was based on all nuclei stained by Hoechst 33342. VE (Figures 3C and 5F; also Figure 4) is defined as the visceral endoderm overlying EPI; visceral endoderm overlying ExE is excluded from this analysis. Total cell number is defined as the sum of VE and EPI.
To calculate the corresponding ''in utero age'' of D1 and D2 embryos based on their total cell numbers, a linear regression line was generated from the total cell numbers of in utero embryos (y = 75.06e 0.0712x , R 2 = 0.933, where y is the total cell number ( Figure 3E) and x is the age of the embryo in hours from conception; Figure S3D). Similarly, a linear regression line was generated from the EPI cell numbers of in utero embryos (y = 36.77e 0.0818x , R 2 = 0.929, where y is the EPI cell number ( Figure 3C) and x is the age of the embryo in hours from conception; Figure S3E). Evaluation of cell differentiation and embryo patterning at D2 VE cells were annotated for AVE identity by co-immunostaining of Gata4 and AVE markers, Lefty1 or Cerberus1, and their positions marked using automated Spots detection with manual correction. The distal tip of the egg cylinder was marked manually as a Spots object and set as the origin for the polar and Cartesian plots. A Reference Frame (X, Y, Z) was created with the Z-axis aligned along the proximal-distal axis of the egg cylinder. The 3D coordinates of the Spots in the given Reference Frame were used to calculate linear distance from origin r and angle of rotation q about the Z-axis of each VE cell: where ðx; y; zÞ are the coordinates of the VE cell. E5.25 and E6.0 embryos were manually classified as Asymmetric, Symmetric or Borderline by qualitative AVE distribution. Polar plots of the spread of VE cells in each E5.25, E6.0 or D2 embryo were generated and converted to Cartesian coordinates, and the centroid of the AVE cells for each embryo was calculated using the Cartesian coordinates. The linear distance of the AVE centroid from the origin r cent , scaled to the largest VE linear distance of that embryo r max , was taken as the AVE Asymmetry Index of the embryo, with a value ranging from 0 to 1: As all Symmetric embryos have an AVE Asymmetry Index lower than 0.15, this value was taken as the threshold for evaluation of 3D-geec embryo development at D2 based on AVE asymmetry. The AVE Asymmetry Index for each D2 embryo was calculated as described, and the percentage of embryos evaluated as having successfully specified body axis was 67% (n = 18) (Figure 4). Dynamics of pro-amniotic cavity formation Apical domain detection was performed in 3D using manual Spots generation. Spots objects were generated based on Ezrin-mCherry reporter signal, and their 3D coordinates were used to calculate their distance from the embryo center, scaled by the average radius of the EPI tissue at the respective time points ( Figure 6M). Analysis of cell dynamics in the EPI Ten EPI cells in a cluster before ExE invagination in an H2B-GFP;mT embryo were tracked over 16 hours. The mean displacements of these cells in 3D from the centroid over time were calculated as an indicator of cell dispersion ( Figure S5A). Analysis of signaling activity in the EPI Immunostaining of Id1 was used as a readout for BMP signaling. The reporter lines Dusp4-T2A-mVenus and A 7 -Venus were used as readouts for FGF-Dusp4 and Nodal-Foxh1 signaling, respectively. As signaling activity is heterogeneous within the EPI tissue, we used a proportion of cells in a high expression state as a readout of local signaling activity in the tissue. Intensity measurements were performed on a Z-projection of 10 mm slices around the equatorial plane of the embryo, processed to subtract background using a rolling ball of radius 100 px (pixel size of 0.165 mm/px). Circular ROIs were drawn on EPI nuclei in the resultant image so that each ROI was of the largest diameter that fits in the nucleus, and care was taken to avoid including regions where two nuclei overlapped due to Z-projection. The mean signal intensity in the Id1 or Dusp4-T2A-mVenus and Hoechst channels of each ROI was measured, along with the coordinates of its center. ROIs were segregated into either the proximal half or the distal half of the EPI based on their position. Due to EPI being misshapen in the absence of ExE, the left and right 20% of cells were discarded from the analysis. A cell with a Hoechst-normalized Id1 or Dusp4-T2A-mVenus signal intensity higher than the median value of all EPI cells in the embryo was annotated as Id1 high or Dusp4 high . The percentage of Id1 high or Dusp4 high cells in the proximal and distal halves of each embryo was calculated and correlated with each other by a solid black line to represent the signaling landscape ( Figures 7C and 7D). Analysis of FGF-Dusp4 signalling landscapes in embryos after immunosurgery Image acquisition and pre-processing were performed as described above for Dusp4-T2A-mVenus embryos after immunosurgery. After cropping out the EPI area, a linear ROI was set, radiating from the centre of the EPI, and rotated clockwise around the image at steps of 1 . The mean signal intensity in the Dusp4-T2A-mVenus and Hoechst channels was measured and averaged for each ROI, so that 360 pairs of intensity measurements are generated for each embryo. The intensities were normalized to the mean intensity in each channel for each embryo, and the ratio of the intensity in the Dusp4-T2A-mVenus channel to the intensity in the Hoechst channel was calculated for each ROI. The deviation of the intensity ratio from the mean intensity ratio across the embryo is calculated for each ROI and plotted against the angle of that ROI to visualise the spatial pattern of Dusp4 signalling in the EPI tissue.

Machine-learning-based segmentation and analysis
The segmentation pipeline used to process the 3D images of the mTmG membrane signal consists of four steps. In the first step the 3D input images are pre-processed, where every Z-slice is down-sampled by a factor of 4 along each axis by locally averaging squares of 434 pixels. The resulting images display the same physical volume with a dimension of 51235123400 voxels and a physical voxel size of 0.83230.83231.000 mm 3 (X,Y,Z). In the second step a neural network implementation from PlantSeg is used to generate a probability map of the membrane locations. In the third step the probability maps are segmented using a set of algorithms provided by Plant-Seg (Wolny et al., 2020). The best segmentation algorithm and its corresponding hyper-parameters were found by a custom-made pipeline which explored thousands of different configuration parameters simultaneously using EMBL's computing cluster. In the fourth step the EPI cell segmentation output is manually selected through visual inspection, followed by manual correction as appropriate, and used for further analyses.
Since no ground truth segmentation was initially available, performance of the complete segmentation pipeline was improved by the following iterative procedure. In the first iteration a pre-trained neural network available in the PlantSeg package was used to generate the initial membrane probability maps. In particular, we used a CNN trained on the Arabidopsis ovules dataset (https:// osf.io/w38uf) named ''confocal_unet_bce_dice_ds2x''. Having the cell boundary prediction, the initial segmentation was produced with PlantSeg. The segmentation results were improved by choosing the most correctly segmented volumes (inspected visually) and using them as ground truth labels to train a dedicated neural network for the membrane prediction task. The process of choosing the best segmentation results and re-training the network was performed four times.
Analysis of cell parameters was performed using Python 3.8 based on the segmentation generated by the above process. From two representative H2B-GFP;mT embryos live-imaged ( Figure 5B), segmentations of EPI cells were picked up every 20 min until proamniotic cavity expansion and used for analysis with tracking lineages based on 3D coordinates of nuclear signal. Daughter cells that cannot be tracked with confidence through a mitotic event are excluded from analysis. Aspect ratio is calculated by fitting an ellipsoid to the cell and dividing the longest axis (LA) of the ellipsoid by the average of its two shorter axes (SA and MA, not depicted). Long-axis alignment is calculated as the angle between the LA of the cell and a line segment connecting the outermost voxel of the cell to the center of the cell. A low angle indicates an alignment of the long axis along the inside-outside axis of the egg cylinder.
For the analysis of neighbour effects, one lineage where the daughter cells (#1A, 1B, 1C, and 1D) remain in close proximity to each other through time and exhibit synchronous elongation and radial alignment was identified. A distinct lineage with one of daughter cells (#2C) coming to close proximity with cells #1A-1D, was picked up for analysis, and the shortest distance in 3D between each daughter cell (#2A-2F) and the centroid of the #1A-1D cell cluster was calculated using their 3D coordinates of nuclear signal. Derivation of optimal initial cell number threshold A confusion matrix for each threshold level from 0 to 230 cells (with intervals of 10 cells) was constructed with the following definitions: True positives (TP): D0 embryos above a threshold that yield egg cylinders False positives (FP): D0 embryos above a threshold that do not yield egg cylinders True negatives (TN): D0 embryos below a threshold that do not yield egg cylinders False negatives (FN): D0 embryos below a threshold that yield egg cylinders. The threshold level that yields the highest Accuracy (i.e., ðTP + TNÞ=ðTP + FP + TN + FNÞ) provides the best tradeoff between sample retention and egg cylinder formation efficiency. As such, a threshold of R110 cells provided the highest optimality, qualifying 66% of E4.5 embryos recovered from natural mating and resulting in 74% egg cylinder formation efficiency (n = 35) ( Figure S2K).

Statistical analysis and data reproducibility
Experiments in this study were performed at least at three independent times, except for the data shown in Figures S2L and S5B. N values represent the number of independent experiments, while n values represent the total number of embryos collected from independent experiments, unless specified otherwise. Performance of 3D-geec was independently replicated by two operators, T.I. and HT.Z. Data analysis and statistical tests were performed in Rstudio or OriginPro. Details of the statistical analysis are provided in the figure legends. Briefly, the normality of the distribution for each dataset was tested by the Shapiro-Wilk test. When the data followed a normal distribution, difference among groups in comparison was examined by either t-test (for comparison of two groups) or one-way ANOVA (for comparison of more than two groups) followed by Tukey's post hoc test. Otherwise, nonparametric Kruskal-Wallis ANOVA was used with Mann-Whitney U-test. No statistical method was used to predetermine the sample size. Experiments were not randomized, and the investigators were not blinded to allocation during the experiments and outcome assessment. Data visualization was also performed in Rstudio using the ggplot2 package or OriginPro. Box and whisker plots show the following: boxes represent the 25 th and 75 th percentile range, whiskers represent the 1.5x interquartile range. Comparison of trends in embryos developed in utero versus 3D-geec The statistical significance of the slopes between in utero and 3D-geec embryos was tested by two-way analysis of variance (ANOVA) in Rstudio. Data from E4.5 embryos was excluded as no corresponding data for 3D-geec embryos exists ( Figures S3B and S3C).    (A) Schematic of the experimental workflow. Embryos are recovered at E3.5 and cultured in medium for 24 hours, followed by microsurgery to remove mTE. Then embryos are embedded in Matrigel-collagen mix and submerged in IVC medium.
(I) Immunofluorescence of representative E4.5 blastocysts upon mechanical dissection of mTE (left) and after 30 minutes incubation in IVC1 medium (right) stained for Sox2 + EPI, Gata4 + VE and Cdx2 + TE. Note the tissue shape change, due possibly to pTE contraction.
(K) Histograms of the number of embryos recovered at E4.5 (blue) and those developed to egg cylinder by 3D-geec at D2 (green) for a given total number of ICM and pTE cells (bin size = 10), with a line chart of optimality (see STAR Methods). A threshold level of ³110 cells provides the best optimality of 0.74. n = 35 embryos; N = 4.
P values calculated using t-test (C-H) and Mann-Whitney U test (L).

Figure S3
(B, C) The trends of 3D-geec and in utero embryos shown in Figure 3B and 3C in terms of dimensions (B, P = 0.0076) and cell numbers (C, P = 0.2451). P values calculated using twoway ANOVA.   Figure S4. Quantitative analysis of cellular dynamics in peri-implantation development, Related to Figure 6 (A-F) Cell volume (A and D), aspect ratio (B and E) and long-axis radial alignment against the outer embryonic surface (C and F) of two additional representative lineages in the embryo shown in Figure 6B. n = 18 lineages. Black diamonds in a lineage tree and in plots represent mitoses.
(G-I) Cell volume (G), aspect ratio (H) and long-axis radial alignment against the outer embryonic surface (I) of EPI cells in another embryo. Cells are analyzed every 20 min for 20 hours of 3D-geec until pro-amniotic cavity formation.
(J-L) Cell volume (J), aspect ratio (K) and long-axis radial alignment against the outer embryonic surface (L) of a representative lineage of EPI cells in the embryo (G-I).
(M) Pair-wise distance of Ezrin spot signals scaled to the diameter of the embryo shown in Figure 6L. Note that the number of pair-wise distance measurements decreases over 24 hours as Ezrin spots fused.
See also Videos S5 and S6.