•Dorsal pre-somitic mesoderm of chicken embryos epithelializes before somite formation•Dorsal epithelium shows signs of apical constriction and early segmentation•A mechanical instability model can reproduce sequential segmentation•A single ratio describes spatial and temporal patterns of segmentation Somitogenesis is often described using the clock-and-wavefront (CW) model, which does not explain how molecular signaling rearranges the pre-somitic mesoderm (PSM) cells into somites. Our scanning electron microscopy analysis of chicken embryos reveals a caudally-progressing epithelialization front in the dorsal PSM that precedes somite formation. Signs of apical constriction and tissue segmentation appear in this layer 3-4 somite lengths caudal to the last-formed somite. We propose a mechanical instability model in which a steady increase of apical contractility leads to periodic failure of adhesion junctions within the dorsal PSM and positions the future inter-somite boundaries. This model produces spatially periodic segments whose size depends on the speed of the activation front of contraction (F), and the buildup rate of contractility (Λ). The Λ/F ratio determines whether this mechanism produces spatially and temporally regular or irregular segments, and whether segment size increases with the front speed. Somitogenesis is often described using the clock-and-wavefront (CW) model, which does not explain how molecular signaling rearranges the pre-somitic mesoderm (PSM) cells into somites. Our scanning electron microscopy analysis of chicken embryos reveals a caudally-progressing epithelialization front in the dorsal PSM that precedes somite formation. Signs of apical constriction and tissue segmentation appear in this layer 3-4 somite lengths caudal to the last-formed somite. We propose a mechanical instability model in which a steady increase of apical contractility leads to periodic failure of adhesion junctions within the dorsal PSM and positions the future inter-somite boundaries. This model produces spatially periodic segments whose size depends on the speed of the activation front of contraction (F), and the buildup rate of contractility (Λ). The Λ/F ratio determines whether this mechanism produces spatially and temporally regular or irregular segments, and whether segment size increases with the front speed. Somitogenesis in vertebrate development sequentially and periodically creates metameric epithelial balls (somites) along the elongating embryo body from bilateral rods of loosely connected mesenchymal cells called pre-somitic mesoderm (PSM). As cells leave the rostral/anterior (head) end of the PSM to form each somite, new cells continuously move from the tail bud to join the PSM at the caudal/posterior (tail) end of the embryo (Pourquié, 2001Pourquié O. Vertebrate somitogenesis.Annu. Rev. Cell Dev. Biol. 2001; 17: 311-350Crossref PubMed Scopus (193) Google Scholar). At any given rostral-caudal position, a pair of nearly equal-sized somites form simultaneously on both sides of the neural tube, between the ectoderm and the endoderm. These transient structures are the precursors of vertebrae, ribs, and many skeletal muscles; many birth defects arise from a failure in one or more steps of these developmental steps (Christ and Ordahl, 1995Christ B. Ordahl C.P. Early stages of chick somite development.Anat. Embryol. 1995; 191: 381-396Crossref PubMed Scopus (622) Google Scholar). Somitogenesis is strikingly robust to perturbations (both spatial and temporal). Changes in the total number of embryonic cells or in the rate of new cell addition at the caudal end of the PSM lead to compensating changes in the size and timing of somite formation so that the embryo eventually produces the same final number of somites as in normal development (Cooke, 1975Cooke J. Control of somite number during morphogenesis of a vertebrate, Xenopus laevis.Nature. 1975; 254: 196-199Crossref PubMed Scopus (86) Google Scholar; Snow and Tam, 1979Snow M.H.L. Tam P.P.L. Is compensatory growth a complicating factor in mouse teratology?.Nature. 1979; 279: 555-557Crossref PubMed Scopus (94) Google Scholar). A linear increase (scaling) of the somite size with the speed of the caudal-moving position of the determination front (Cooke and Zeeman, 1976Cooke J. Zeeman E.C. A clock and wavefront model for control of the number of repeated structures during animal morphogenesis.J. Theor. Biol. 1976; 58: 455-476Crossref PubMed Scopus (521) Google Scholar; Dubrulle et al., 2001Dubrulle J. McGrew M.J. Pourquié O. FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal hox gene activation.Cell. 2001; 106: 219-232Abstract Full Text Full Text PDF PubMed Scopus (506) Google Scholar) or with the rate at which cells join the caudal end of the PSM can result in this number conservation. Models seeking to explain somite formation include the “cell-cycle model”, which couples the timing of segmentation to the progression of cells through the cell-cycle and a cell-intrinsic gating mechanism (Stern et al., 1988Stern C.D. Fraser S.E. Keynes R.J. Primmett D.R.N. A cell lineage analysis of segmentation in the chick embryo.Development. 1988; 104: 231-244Crossref PubMed Google Scholar; Primmett et al., 1989Primmett D.R.N. Norris W.E. Carlson G.J. Keynes R.J. Stern C.D. Periodic segmental anomalies induced by heat shock in the chick embryo are associated with the cell cycle.Development. 1989; 105: 119-130Crossref PubMed Google Scholar; Collier et al., 2000Collier J.R. Mcinerney D. Schnell S. Maini P.K. Gavaghan D.J. Houston P. Stern C.D. A cell cycle model for somitogenesis: mathematical formulation and numerical simulation.J. Theor. Biol. 2000; 207: 305-316Crossref PubMed Scopus (49) Google Scholar) and reaction-diffusion models (Meinhardt, 1982Meinhardt H. Models of Biological Pattern Formation. Academic Press, 1982Google Scholar; Cotterell et al., 2015Cotterell J. Robert-Moreno A. Sharpe J. A local, self-organizing reaction-diffusion model can explain somite patterning in embryos.Cell Syst. 2015; 1: 257-269Abstract Full Text Full Text PDF PubMed Scopus (48) Google Scholar). Currently, the most widely accepted family of models employ a “clock-and-wavefront” (CW) mechanism, which combines caudally progressing fronts of determination and differentiation with an intracellular oscillator which determines cell fate based on its phase at the moment of determination (Cooke and Zeeman, 1976Cooke J. Zeeman E.C. A clock and wavefront model for control of the number of repeated structures during animal morphogenesis.J. Theor. Biol. 1976; 58: 455-476Crossref PubMed Scopus (521) Google Scholar). Following the identification of the first oscillating transcripts (hairy1 and hairy2) in the PSM (Palmeirim et al., 1997Palmeirim I. Henrique D. Ish-Horowicz D. Pourquié O. Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis.Cell. 1997; 91: 639-648Abstract Full Text Full Text PDF PubMed Scopus (702) Google Scholar), many computer simulations of varying complexity have implemented different CW models. Most CW models reproduce the experimentally-observed scaling of somite size with clock period, front speed and rate of elongation of the PSM (Hester et al., 2011Hester S.D. Belmonte J.M. Gens J.S. Clendenon S.G. Glazier J.A. A multi-cell, multi-scale model of vertebrate segmentation and somite formation.PLoS Comput. Biol. 2011; 7: e1002155Crossref PubMed Scopus (82) Google Scholar; Tiedemann et al., 2012Tiedemann H.B. Schneltzer E. Zeiser S. Hoesel B. Beckers J. Przemeck G.K.H. de Angelis M.H. From dynamic expression patterns to boundary formation in the presomitic mesoderm.PLoS Comput. Biol. 2012; 8: e1002586Crossref PubMed Scopus (17) Google Scholar; Baker et al., 2006Baker R.E. Schnell S. Maini P.K. A clock and wavefront mechanism for somite formation.Dev. Biol. 2006; 293: 116-126Crossref PubMed Scopus (84) Google Scholar). Recent experiments have shown that somite-like structures can form without either a clock or a progressing determination front (Cotterell et al., 2015Cotterell J. Robert-Moreno A. Sharpe J. A local, self-organizing reaction-diffusion model can explain somite patterning in embryos.Cell Syst. 2015; 1: 257-269Abstract Full Text Full Text PDF PubMed Scopus (48) Google Scholar; Dias et al., 2014Dias A.S. de Almeida I. Belmonte J.M. Glazier J.A. Stern C.D. Somites without a clock.Science. 2014; 343: 791-795Crossref PubMed Scopus (81) Google Scholar). The ability of somites to form without either a clock or a front suggests that we should consider other mechanisms that could lead to spatially and temporally periodic sequential division of the PSM into regular segments. Recent experiments by Nelemans et al. showed that applied tension along the rostral-caudal axis can induce the formation of intersomitic boundaries in locations not specified by CW signaling (Nelemans et al., 2020Nelemans B.K.A. Schmitz M. Tahir H. Merks R.M.H. Smit T.H. Somite division and new boundary formation by mechanical strain.iScience. 2020; 23: 100976Abstract Full Text Full Text PDF PubMed Scopus (3) Google Scholar), suggesting that mechanical mechanisms may be important in generating intersomitic boundaries. Truskinovsky et al. explored how mechanical instabilities could result in vertebrate segmentation (Truskinovsky et al., 2014Truskinovsky L. Vitale G. Smit T.H. A mechanical perspective on vertebral segmentation.Int. J. Eng. Sci. 2014; 83: 124-137Crossref Scopus (11) Google Scholar). Assuming relaxation of junctional adhesion sites as the PSM elongates, their pre-patterning mechanism generates a number of somites independent of the final segmentation mechanism. Their model, however, does not consider the sequential development of the boundaries nor any active processes within the tissue. In 2009, Martins et al. imaged the morphology of cells during chicken somitogenesis in vivo, showing that cells elongate, crawl, and align with each other as they form a somite (Martins et al., 2009Martins G.G. Rifes P. Amândio R. Rodrigues G. Palmeirim I. Thorsteinsdóttir S. Dynamic 3D cell rearrangements guided by a fibronectin matrix underlie somitogenesis.PLoS One. 2009; 4: e7429Crossref PubMed Scopus (50) Google Scholar). They found that cells epithelialize gradually during somite formation, with epithelialization beginning before segments separate from each other. Their finding is consistent with other reports showing that PSM cells gradually increase their density of cell-cell adhesion molecules (Duband et al., 1987Duband J.L. Dufour S. Hatta K. Takeichi M. Edelman G.M. Thiery J.P. Adhesion molecules during somitogenesis in the avian embryo.J. Cell Biol. 1987; 104: 1361-1374Crossref PubMed Scopus (229) Google Scholar) and decrease their motility (Bénazéraf et al., 2010Bénazéraf B. Francois P. Baker R.E. Denans N. Little C.D. Pourquié O. A random cell motility gradient downstream of FGF controls elongation of an amniote embryo.Nature. 2010; 466: 248-252Crossref PubMed Scopus (190) Google Scholar; Mongera et al., 2018Mongera A. Rowghanian P. Gustafson H.J. Shelton E. Kealhofer D.A. Carn E.K. Serwane F. Lucio A.A. Giammona J. Campàs O. A fluid-to-solid jamming transition underlies vertebrate body axis elongation.Nature. 2018; 561: 401-405Crossref PubMed Scopus (193) Google Scholar) as they approach the time of the physical reorganization associated with somite formation. Several decades ago, scanning electron microscopy (SEM) observations of the PSM in a variety of species led to the suggestion that “pre-somite”-like structures, named “somitomeres”, precede the condensation of cells into somites by at least 2-3 somite lengths (Meier, 1979Meier S. Development of the chick embryo mesoblast.Dev. Biol. 1979; 73: 25-45Crossref Scopus (145) Google Scholar; Tam et al., 1982Tam P.P.L. Meier S. Jacobson A.G. Differentiation of the metameric pattern in the embryonic Axis of the mouse.Differentiation. 1982; 21: 109-122Crossref PubMed Scopus (42) Google Scholar). However, these observations in randomly fractured fixed embryos could not reveal the detailed progression of somitogenesis. Here we investigated this early organization in more detail. Our observations showed that dorsal PSM cells undergo early maturation, forming an epithelial monolayer along the ectoderm boundary, beginning long before somite formation. This pre-somitic epithelium also shows signs of pre-segmentation, with clusters of cells forming arched tissue segments roughly the length of a somite diameter. These observations suggest that periodic tissue segmentation and somite boundary positioning could result from a mechanical instability, similar to periodic cracking of materials subjected to stress. We developed a model of the dorsal epithelial monolayer where the observed boundaries between dorsal segments arise from the loss of contact between neighboring cells due to increased apical tension between cells. We simulated this scenario with a 2D computational model of a cross-section of the epithelial monolayer and showed that a simple mechanical model without a clock can explain the spatial periodicity in segment sizes. We also showed that this model can produce either roughly constant-size segments or segments whose size increases (scales) with activation-front speed and inverse rate of increase of apical contractility. A critical threshold for the ratio of the buildup rate of apical contractility to the activation-front speed defines the boundary between these two domains. A second threshold for this ratio predicts whether this mechanism produces spatially and temporally regular segments or irregular segments. To investigate the beginning of epithelialization, we performed 3D SEM of chick embryos fixed at various Hamburger-Hamilton stages of somitogenesis, fractured as precisely as possible along parasagittal or transverse planes (Stern and Piatkowska, 2015Stern C.D. Piatkowska A.M. Multiple roles of timing in somite formation.Semin. Cell Dev. Biol. 2015; 42: 134-139Crossref PubMed Scopus (15) Google Scholar). We then manually defined the contour of each individual PSM cell and calculated its aspect ratios (Figures 1A and 1B ). Our observations show that a dorsal layer of PSM cells begins to epithelialize at least as early as 4-5 somite lengths caudal to the most recently formed somite (S1). Cells within this dorsal epithelium form a series of clusters, arched groups of cells, at least 3-4 somite lengths caudal to the forming somite (Figure 1A). Cells near the dorsal surface in these clusters are usually wedged shaped, with their apical (ventral-facing) sides more constricted than their basal (dorsal-facing) sides. Estimates of side-to-side cell distances along the dorsal surface (Figure 1E), beginning with the rostral-most pair of S1, show instances of increased apical-side separation (Figure 1C). These peaks (black arrows in Figure 1B) roughly correspond to the cluster boundaries. The number of adjacent cell pairs (Figures 1C and S1A–S1C) within each peak is 14.27 ± 2.72, excluding the already formed caudal boundary of S0/S1. This value is similar to the rostral-caudal length of the future somites, calculated from measurements of dorsal cell pairs within the already formed somite (S1) of 12.25 ± 2.22 (Figure 1D). Fewer peaks along the basal sides indicate that the cells start their separation from the apical side (Figures S1A–S1C). Our experimental results point to the formation of a continuous dorsal epithelium and the appearance of a series of clusters before the formation of intersomitic boundaries. Based on these observations, we hypothesize that these structures arise from a pre-patterning of the future boundaries and we propose a model for segmenting the dorsal epithelium. Here, we take the convergence of the cells' apical sides within the cluster as an indication that cells are apically constricting as the PSM matures. Apical constriction results from contractile forces generated by myosin activity at the cells' apical side, which often brings neighboring cells together and gives them a wedge shape (Baker and Schroeder, 1967Baker P.C. Schroeder T.E. Cytoplasmic filaments and in the amphibian.Dev. 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Excessive apical contractile forces on junctional adhesion sites can cause junctions to fail and the tissue to tear, as observed in Drosophila embryos (Martin et al., 2010Martin A.C. Gelbart M. Fernandez-Gonzalez R. Kaschube M. Wieschaus E.F. Integration of contractile forces during tissue invagination.J. Cell Biol. 2010; 188: 735-749Crossref PubMed Scopus (343) Google Scholar; Manning et al., 2019Manning L.A. Perez-Vale K.Z. Schaefer K.N. Sewell M.T. Peifer M. The Drosophila Afadin and ZO-1 homologues Canoe and Polychaetoid act in parallel to maintain epithelial integrity when challenged by adherens junction remodeling.Mol. Biol. Cell. 2019; 30: 1938-1960Crossref PubMed Scopus (15) Google Scholar). We postulate that such a mechanical instability may create the pre-segmentation pattern we observe: a caudally traveling activation-front induces apical constriction in the maturing PSM cells, leading to a buildup of cell-cell apical tension that eventually subdivides the monolayer into regularly-sized segments (Figure 2B). Figures 2C-D illustrate some other possible mechanistic models that could also lead to segment formation, including a cell-clustering model with a continuously caudally-progressing front (Figure 2C), and models where changes in cell behaviors do not progress caudally (Figure 2D). Our mechanical instability model has three main parameters (F, Λ and ΓBreak): the speed at which this caudally-traveling activation-front (which we will refer to simply as the front for compatness) passes through the tissue (F), the rate (Λ, which we will refer to as the buildup rate of contractility) at which each pair of activated cells increases its apical contractility (the variable λA), and the maximum tension the link between adjacent apical domains of neighboring cells can sustain before the cells lose their connection with each other (ΓBreak). We implemented a stochastic Cellular Potts/Glazier-Graner-Hogeweg (CP/GGH) model version of dorsal tissue segmentation (Graner and Glazier, 1992Graner F. Glazier J.A. Simulation of biological cell sorting using a two-dimensional extended Potts model.Phys. Rev. Lett. 1992; 69: 2013-2016Crossref PubMed Scopus (818) Google Scholar; Swat et al., 2012Swat M.H. Thomas G.L. Belmonte J.M. Shirinifard A. Hmeljak D. Glazier J.A. Multi-scale modeling of tissues using CompuCell3D.Methods Cell Biol. 2012; : 325-366Crossref PubMed Scopus (231) Google Scholar) (for more details see transparent methods). In this model, the cells are spatially extended objects similar to the schematic cells in Figures 2A–2D, with a width and height; apical, basal and core domains; and elastic connections between neighboring apical domains representing apical junctional adhesion domains (Dias et al., 2014Dias A.S. de Almeida I. Belmonte J.M. Glazier J.A. Stern C.D. Somites without a clock.Science. 2014; 343: 791-795Crossref PubMed Scopus (81) Google Scholar; Belmonte et al., 2016aBelmonte J.M. Swat M.H. Glazier J.A. Filopodial-tension model of convergent-extension of tissues.PLoS Comput. Biol. 2016; 12: e1004952Crossref PubMed Scopus (11) Google Scholar, Belmonte et al., 2016bBelmonte J.M. Clendenon S.G. Oliveira G.M. Swat M.H. Greene E.V. Jeyaraman S. Glazier J.A. Bacallao R.L. Virtual-tissue computer simulations define the roles of cell adhesion and proliferation in the onset of kidney cystic disease.Mol. Biol. Cell. 2016; 27: 3673-3685Crossref PubMed Scopus (17) Google Scholar) (Table S1). We first characterize the model behavior for different fixed values of λA and then for simultaneous increase of λA in all cells at a rate Λ, before exploring the effect of a gradual, caudally-progressing front (F) of apical constriction activation. We first tested our model by creating small epithelial monolayers of fixed aspect ratio AR = 2 (Figure 3A). We increased the strength of apical contractility of all cell pairs simultaneously at a fixed buildup rate Λ=0.05, from λA = 0 up to a maximum value of λA ranging from 20 to 600, without allowing apical links to break. We then observed the shape of the tissue and the average cell-pair tension (Equation 7) over 20,000 simulation time units (defined in terms of Monte Carlo Steps [MCSs]), after λA reached its maximum value (Videos S1-S4). As the number of cells in the monolayer increases, cell-pairs in the middle of the segment experience higher tension than cell-pairs near the periphery (Figures 3B and 3C). This dependence of tension on position within a segment forms the premise of our model—as the tissue becomes larger, tension between cell pairs increases. Since the junctional bonds between cells have a defined breaking tension, higher local tensions predispose the tissue to break into smaller segments. Next, we combine simultaneous activation of contraction with the breaking of the apical links between neighboring cells at breaking tension ΓBreak=−7500. In these simulations, the strength of apical contractility increases linearly from λA = 20 to a maximum of λA = 600 with different buildup rates of apical contractility (Λ=dλA/dt). Since all cell-cell links have the same breaking tension, and the link tension is initially uniform with small fluctuations, the position of the first break is random. This break relieves tension nearby, but the tension far from the break remains roughly uniform with small fluctuations, so the next breaks can occur in a wide variety of locations, provided they are distant from the first break. As this process of tension build-up and release of tension by breakage continues we obtain a broad distribution of segment sizes (Figures 3D–3F), with the average segment size increasing as the buildup rate decreases (Figure 3D). The shape of the distribution, however, is similar for all values of Λ below 10 (Figure 3E). For Λ>10, the apical links between most cell pairs break. The data in Figures 3D–3F are from simulations with periodic boundary conditions with the rostral- and caudal-most cells connected to each other through basal and apical links identical to the links between the other cells (Video S5), but the results are qualitatively the same for simulations with many cells (N > 400) and fixed boundaries (Figure S2, Video S6). We conclude that a simultaneous activation of constriction activity is insufficient to produce a regular pattern of pre-segments like those seen in our SEM observations of embryos (Figures 1A and 1B). Next, we investigated whether caudally-progressing activation of apical constriction can generate regularly-sized segments. From now on, all simulations include a large number of cells fixed between two immobile cells, and a caudally-moving front that sequentially initiates a gradual and linear increase in the strength of apical contractility of cell pairs. We vary the front speed F and buildup rate of apical contractility Λ systematically around their reference values (see Table S2 in transparent methods). In addition, apical links between neighboring cell pairs will have a breaking tension ΓBreak, allowing for tears between apical domains of neighboring cells. We quantify the positions of these tears. We do not impose additional tension loads between the basal domains. The basal domains only separate if these domains lose contact and separate by a distance more than three times the width of the cell. We selected the reference values so each segment's caudal boundary tear forms approximately three segment lengths rostral to the progressing front (Dubrulle et al., 2001Dubrulle J. McGrew M.J. Pourquié O. FGF signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal hox gene activation.Cell. 2001; 106: 219-232Abstract Full Text Full Text PDF PubMed Scopus (506) Google Scholar) and produces segments of size 11-13 cells, corresponsind to the size of formed somites in our experimnents (Figure 1D). Figure 4A shows a detail of a time series of a simulation with 115 cells in which 5 tissue segments form. Neglecting the outermost segments next to the immobile fixed cells, all segments are of similar size (⟨S⟩=11.36+/−1.45) and segmentation occurs at similar time intervals (⟨τ⟩=3442.37+/−587.87) for our reference parameter (see Table S2, Video S7). We also looked at the evolution of the tension profile in two sequential segments. After the activation front passes, the tension between cell pairs gradually increases, with the rostral-most pair having highest tension (Figure 4B and red lines in Figure 4C). After the formation of the rostral-most boundary/tear, the pattern inverts, with the rostral-most cell pairs now more relaxed and the caudal-most pairs now under highest tension (compare red and blue lines in Figure 4C). Formation of the caudal-most boundary relaxes the tension of these pairs and the segment tension profile is now symmetrically convex, with a lower average tension than in the intermediate steps (black lines in Figure 4C). Subsequent segments form similarly. The CW model can explain how somite size adjusts to variations of embryo size (Cooke and Zeeman, 1976Cooke J. Zeeman E.C. A clock and wavefront model for control of the number of repeated structures during animal morphogenesis.J. Theor. Biol. 1976; 58: 455-476Crossref PubMed Scopus (521) Google Scholar): all else being equal, a faster clock produces smaller somites, while a faster wavefront generates larger somites. We now investigate if our mechanical model of segmentation has the same scaling features: does a faster activation front (F) lead to larger segments? How does average segment size change with different buildup rates of apical contractility (Λ)? In the results that follow, we systematically varied both parameters, averaging all metrics over 5 simulation replicas. We first fixed the buildup rate of apical contractility Λ and varied the activation-front speed F. We observe two regimes for the average segment size ⟨S⟩ with respect to the front speed. For front speeds below a critical value (<F∗), average segment size ⟨S∗⟩ was nearly constant. For faster front speeds (>F∗) average segment size increased as a power law of F with exponents close to ¼ (Figure 5A). The critical value of the front speed F∗ and average segment size ⟨S∗⟩ for the change from nearly constant segment size to the scaling regime depends on the buildup rate Λ (Figure S3A). These results suggest that the spatial compartmentalization of the tissue into cells imposes a lower limit on segment size as a function of Λ (Figure S3A). Our simulations with simultaneous contraction indicated that the maximum tension between cell pairs increases with the number of cells within a forming segment (Figure 3B), so slow fronts should lead to tears at regular size intervals. The average time interval between the formation of successive tears/boundaries ⟨τ⟩ depends strongly on F, and very weakly on Λ, with faster activation-front speeds decreasing the segmentation time as a power law with exponent −0.80 ± 0.008 (Figure 5B). Next, we fixed the activation-front speed F and varied the buildup rate of apical contractility Λ. Average segment sizes ⟨S⟩ decrease logarithmically with higher buildup rates, but became roughly constant for Λ above Λ∗ (Figures S3B and S3C). As before, mean segment size outside the scaling regime (⟨S∗⟩) depends on the front speed F (Figure S3C). We can understand these results from the way cell-pair tension increases with segment size (Figure 3B). For slow buildup rates (<Λ∗), the sole factor determining segment size is the front speed, with faster speeds adding more cells to the forming segment before boundary formation (Figure 5A). For higher buildup rates (>Λ∗), however, segment size is nearly independent of F and primarily determined by the dependence of the shape of the tension profile as a function of number of cells (Figure 3B). The critical values for the activation-front speed F∗ and buildup rate of apical contractility Λ∗ for the transition between the nearly constant segment size and scaling regimes shown in Figures S3A and S3C are related. Rescaling the horizontal axis in Figures 5A and S3B for each curve by its corresponding value of Λ and F, respectively, shows that in both cases, the transition occurs near the same ratio of Λ/F = 22 MCS2/cell (Figures 6A and 6B ). This critical ratio allows us to define a boundary in parameter space that separates regions where segment sizes change with either Λ or F from regions where the segment sizes remain nearly constant with changes in one of these parameters (Figure 6C, blue and green regions, respectively). Note that we use the word constant in contrast to the size scaling of the segments with respect to either Λ or F; segment sizes change gradually within the green region in Figure 6C (see Figures S4A and S