XB-ART-58752Dev Cell 2022 Jan 10;571:95-111.e12. doi: 10.1016/j.devcel.2021.11.021.
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Targeted search for scaling genes reveals matrixmetalloproteinase 3 as a scaler of the dorsal-ventral pattern in Xenopus laevis embryos.
How embryos scale patterning according to size is still not fully understood. Through in silico screening and analysis of reaction-diffusion systems that could be responsible for scaling, we predicted the existence of genes whose expression is sensitive to embryo size and which regulate the scaling of embryonic patterning. To find these scalers, we identified genes with strongly altered expression in half-size Xenopus laevis embryos compared with full-size siblings at the gastrula stage. Among found genes, we investigated the role of matrix metalloproteinase-3 (mmp3), which was most strongly downregulated in half-size embryos. We show that Mmp3 scales dorsal-ventral patterning by degrading the slowly diffusing embryonic inducers Noggin1 and Noggin2 but preventing cleavage of the more rapidly diffusing inducer Chordin via degradation of a Tolloid-type proteinase. In addition to unraveling the mechanism underlying the scaling of dorsal-ventral patterning, this work provides proof of principal for scalers identification in embryos of other species.
PubMed ID: 34919801
Article link: Dev Cell
Species referenced: Xenopus laevis
Genes referenced: admp bmp1 bmp4 chrd.1 gtf2ird1 mcf2 mmp3 myc nog nog2 pam shh sst.1 szl tll1
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|Figure 1. Mathematical analysis of scaling in RE and IC models (A) BMP/Chordin gradients in the wild-size and half-size Xenopus embryos schematically shown at the early gastrula stage from the vegetal pole. Curved DV axis is shown by arrow. (B) The concentration profiles of a morphogen in the wild-type embryo and in a smaller one (for better distinguishing of gradients this diagram is built for an embryo smaller than half-size one). The defining scaling score and scaling ratio are shown below (see Equations 4 and 5 for details). (C) Sets of points corresponding to different parametric sets of RE and IC models in space of scaling score and scalability ratio. Moving from worse to better scaling quality, morphogen (yellow points) and expander/contractor (blue points) significantly diverges by scalability ratio (indicated by two-end arrows). See also Figure S1.|
|Figure 2. Obtaining the half-size Xenopus laevis embryos and finding potential scalers (A–F) Obtaining the half-size embryos by separating left and right blastomeres at two-cell stage (note that the development of the same pair of half-size embryos is shown on A–C) and testing in such embryos the expression of the axial tissues markers at the early middle neurula stage. Red bars indicate the theoretic value of the corresponding area in half-size embryo calculated in supposition of ideal scaling. (G) Wild-type tadpole and a pair of tadpoles developed from left and right blastomeres of the same two-cell embryo. (H) Testing by qRT-PCR (in five independent series of experiments) the expression of genes that demonstrated with high confidence a significant difference in expression between the half-size and wild-type embryos according to the results of RNA-seq. (I) Expression of mmp3 in the wild-type and half-size embryos at the early middle neurula stage. Dashed lines on (D) and (I) indicate level of sections. Scale bars: 600 μm. Experiments shown on (D), (G), and (I) were done in three independent replicates. For these and other experiments described below statistical analysis of results was done by Student’s t test, the total number of analyzed samples is indicated within the columns of the diagrams. See also Figure S2.|
|Figure 3. Expression pattern of mmp3 and effects of its downregulation (A and B) At the first half of gastrulation mmp3 is expressed as a smooth gradient along the blastopore MZ, with a maximum on the dorsal side. The expression is localized in the internal layer of the ectoderm and in the underlying mesoderm, i.e., on both sides of Brachet’s cleft (Bl). (C–D′) At the middle neurula, mmp3 is expressed in the internal layer of the non-neural ectoderm. (E–V) Mmp3 knockdown in the wild-size embryos affected sizes of the axial tissues similarly to the diminishing of the overall embryo size: it reduced the neural plate and somites, whereas caused non-proportional enlargement of the notochord. Experiments were done in three independent replicates. (W) The embryos with mmp3 knockdown diminished their overall sizes. The same triplets of control and experimental embryos are shown at the late tailbud and early tadpole stages. (X and Y) Similar small tadpoles developed from embryos with knocked down and knocked out mmp3. Abbreviations: Bc, Brachet’s cleft; dbl, dorsal blastopore lip; ep, epidermis; gc, gastrocele; iel, internal ectoderm layer; lm, lateral mesoderm; dm, dorsal mesoderm; np, neural plate; not, notochord; sel, superficial ectoderm layer; som, somite. Scale bars: (A–D) and (E–U), 300 μm; (D′), 150 μm; (W–Y), 1 mm. See also Figures S2–S4.|
|Figure 4. Effects of Mmp3 on morphogens secreted by Spemann’s organizer (A–F) Effects of Mmp3 on the indicated Bmp antagonists secreted by Spemann’s organizer. Note that catalytic point mutant of Mmp3 does not degrade Noggin2, taken as a tested target. (G and H) Effects of Mmp3 downregulation by MO on the endogenous Chordin and Noggin2. (I) In the half-size embryos, in which mmp3 expression is drastically decreased, the level of endogenous Chordin is also reduced. (J and K) Mmp3 (J), but not its catalytic point mutant (K), degrades mature Tll1. (L) Immature Tll1 is predominantly contained in the intracellular fraction of embryos, while the mature Tll1 in the extracellular ones, where it degrades by Mmp3. (M–O) Mmp3 cannot degrade three other key components of the BMP/Chordin patterning system: Admp, Bmp4, and Sizzled. For all experiments, excepting (G–I), embryos were injected with synthetic mRNA encoding indicated proteins labeled by Flag or Myc-epitopes. Lysates of embryos were analyzed by western blotting (STAR Methods for details). Coomassie-stained gels were used as loading controls in (G–I) and (L) since in those cases the proteins in the extracellular space were analyzed. For each experiment, from 3 to 5 independent replicates using different clutches of embryos were done. See also Figure S4.|
|Figure 5. Effects of mmp3 downregulation on the ventral marker sizzled expression (A–D′) Effects of downregulation of mmp3, tll1, and chordin on sizzled expression pattern are consistent with the role of Mmp3 in an increase of Chordin level due to degradation of the mature Tll1. (A–D) Embryos at the middle gastrula stage (stage 11) hybridized in whole mount with the probe to sizzled mRNA. (A′–D′) Schemes explaining the observed effects. Embryos are shown from vegetal pole, dorsal side up. Experiments were done in three independent replicates. (E) Statistical analysis by Student’s t test of the angular size of sizzled expression domains in the control and experimental embryos shown on (A–D). (F–H′) Despite mmp3 expression is reduced in the half-size embryos, sizzled expression is not expanded, like in the wild-size embryos with downregulated mmp3, because reduced Chordin's level appears to be sufficient to inhibit ventral Bmp due to shorter distance between dorsal and ventral sides (G–H′). (I and I′) By contrast, in embryoids developed from the ventral halves of embryos dissected at the blastula stage sizzled expression is strongly enhanced because of almost lack of Chordin. For (F–I), experiments were done in three independent replicates. (J) Statistical analysis by Student’s t test of the angular size of sizzled expression domains in the control and experimental embryos shown on (F–I). Scale bars: 250 μm.|
|Figure 6. Effects of chordin, noggin1/2 downregulation, and tll1 overexpression on sizes of somites and notochord (A–C) Downregulation of chordin elicited reduction of the neural plate (A) and somites (B) sizes similar to the effects observed in embryos with overexpressed tll1 (C). In the contrast, no such effect was seen in embryos with downregulated noggin1/2 (A and B). (D) Downregulation of chordin, noggin1, or noggin2 was unable to elicit reduction of the notochord size. (E) In the wild-size embryos, only downregulation of chordin with any of noggins or both elicits diminishing of the notochord. (F and G) Only downregulation of noggin2, but not of noggin1, reduced the notochord size in the wild-type embryos with downregulated mmp3 or in the half-size embryos (F). Scale bar of 300 μm, the same for all photos, is shown on (A). (H and I) Diagrams schematically summarizing experimental data and demonstrating Chordin and Noggn1/2 contribution to the lowering the starting level of BMP signaling (blue dotted line) in relation to the threshold of the notochord specification (red dotted line) in wild-size (H) and half-size (I) embryos. See also Figures S4M–S4Q. All experiments were done in two independent replicates. Scale bar of 200 μm valid for all photo is shown on (A). See also Figures S4 and S5.|
|Figure 7. The model of mesoderm patterning and scaling (A) The model’s geometry is the half of the mesoderm “belt” at the early gastrula stage (left; see Figure S6E for details). All interactions of agents included in the model and operating within this mesoderm “half-belt” are shown on the background of its flat sweep (right): Noggin1/2 and Chordin affect the notochord and somites borders, correspondingly; ENAF induces initial notochord-fate differentiation and, in turn, Noggin1/2 and Chordin expression; Mmp3 degrades Noggin1/2 and stabilize Chordin via Tll1 degradation. (B) The schema explaining modeling of the notochord differentiation with a state variable δ, which has two stationary points: negative (notochord) and positive (non-chordal mesoderm) (see STAR Methods; Figure S6A for details). (C) The model’s equation system implements interactions shown on (A) and (B) and includes competency timing in the last equation (see also Figure S6D). (D) The schema illustrating the general idea of the model. (E) Patterning of embryos simulated under the indicated experimental conditions. Lines of different thicknesses correspond to development progression from early (thin) to late (thick) gastrula stages (see Figures S7 and S8 for detailed simulation results). The INS forms the initial condition for the differentiation state variable δ. (F–K″) Analysis of the nuclear pSmad1/5/8 patterns in MZ of embryos at the early (stage 10) and late (stage 12) gastrula under three experimental conditions corresponding to those modeled on (E) comparing with their wild-type siblings: in embryos with downregulated mmp3 (F–G″); in half-size embryos (H–I″); in half-size embryos with downregulated noggin2 (J–K″). Dorsal side up, view from vegetal pole. Scale bar of 300 μm valid for all photos is shown on (F). Angles α demarcating dorsal sector of MZ free of visible nuclei labeled by pSmad1/5/8 are shown in black in the wild-type embryos and in red in the experimental ones. For ease of comparison, the red angle from each experimental embryo is superimposed to the black angle of its corresponding wild-type sibling. White dashed and black dotted circles indicate the animal (conditional) and vegetal borders of MZ, respectively. All experiments were done in two independent replicates. (L–O) Gradients of pSmad1/5/8 nuclei labeling along MZ for the indicated series of embryos built automatically via trainable neural network-based segmentation (see STAR Methods for details). As can be seen, at stage 10, the front of the intensity wave of pSmad1/5/8 Labeling (FIWSL) in embryos with downregulated mmp3 and half-size embryos is ahead of FIWSL in control embryos (L and M). At the same time, in half-size embryos with downregulated noggin2, FIWSL at stage 10 is less ahead of FIWSL in control embryos than in half-size embryos with not downregulated noggin2 (M and N). By contrast to the downregulation in the wild-size embryos of mmp3, downregulation of noggin2 does not change the rate of FIWSL comparing with the control (L and O). Each series of experiments was done in two independent replicates. See also Figures S5–S8.|
|Figure S1. Example simulation results of scaling models, and the parameteric space, where these models were analyzed, Related to Figure 1. a-c’. Concentration profiles of morphogen and regulator agents in scaling models after 105 time units of the simulation in volume 100 (left column) and 50 (right column) space units. Here we present separate results for ER model (equation 1), original CI model (equation 2) and improved CI model (equation 3). Dashed curves demonstrate the morphogen profile of the half-sized embryo in the coordinates of the normal-sized one. One variant among those with best scaling score were randomly selected for demonstration for each model. d-d’. Discrete parameter values used in parametric scan of phenomenological models: original CI and ER models (d) and for modified CI model (d’). Parameters for original models are reproduced from Ben-Zvi–Barkai paper (Ben-Zvi and Barkai 2010).|
|Figure S2. QRT-PCR analysis of mmp3 expression in embryos of different size, The analysis of the mmp3 expression by in situ hybridization in the wild-type embryos during gastrulation, pie diagrams of gene expression according to single-cell sequencing database, the effects of the mmp3 downregulation on the notochord tested by shh expression, as well as testing the mmp3 MO specificity and efficiency, Related to Figures 2 and 3. A. QRT-PCR analysis of mmp3, chordin, admp, bmp4, and sizzled expression in stage 12 half-size embryos developed from dorsal, sagittal and ventral halves of the dissected blastula. B. QRT-PCR analysis of mmp3 expression in stage 12 embryos of different size obtained by removing of 1 blastomere at 8-, 4- and 2-cells stages, as well as, 3 blastomeres at 4-cells stage. C and D. In situ hybridisation with anti-sense and sens probe to mmp3 on the right and left halves of the same embryo at stage 10 demonstrates specificity of the signal revealed with the anti-sense probe. E and F. Whole embryo at stage 10.5 hybridized with the probe to mmp3 mRNA and its left half after cutting the embryo in half. G and H. In situ hybridisation with anti-sense and sens probe to mmp3 on the right and left halves of the same embryo at stage 12 demonstrates specificity of the signal revealed with the anti-sense probe. I and I’. The transverse vibratome section at the equatorial level of the late gastrula embryo hybridized with the probe to mmp3 mRNA. J. Pie diagrams showing distribution of transcripts of mmp3, chordin, noggin1 and noggin2 the indicated genes in different embryonic tissues at three developmental stages according to the single-cell sequencing database (Briggs et al. 2018). See STAR Methods for details. K. Effects of mmp3 downregulation in the half-size and wild-size embryos on the notochord size tested by shh expression. L. Scheme of the morpholino target site localization on mmp3.L mRNA of the Xenopus laevis. There is no mmp3.S pseudo-allele in the Xenopus laevis genome. To test specificity of this MO, mRNA containing the MO site and encoding mmp3 tagged from C-terminus with Myc-epitop was injected into each blastomere of 2-cell X. laevis embryos (100 pg/blastomere) either alone or in mixture with indicated MOs (8 nl of 0.2 mM water solution). The injected embryos were collected at the middle gastrula stage and analyzed for presence of Myc-tagged proteins by Western blotting with anti-Myc antibody (see STAR Methods for details). M. The results of analysis of the mmp3 MO effects rescuing by co-injection of the mmp3 mRNA starting from AUG start codon and thus lacking most of the MO target site (see the MO site on E). The expression areas of the indicated markers of the neural plate, somitic mesoderm and notochord were measured as described in STAR Methods in three indicated samples of embryos. In experiments results of which are shown on A and B, from 15 to 30 embryos or their fragments were used for each type of samples, sually combined in 3-4 independent groups. In other cases the numbers of embryos analyzed are shown within chart bars. The statistical significance of the difference between samples here and below was estimated by Student’s t-test. Abbreviations: Bc – Brachet’s cleft; bl – blastocele; dbl – dorsal blastopore lip; en – endoderm; ep – epidermis; gc – gastrocele; iel – internal ectoderm layer; lm – lateral mesoderm; dm – mesoderm; ne – neuoectoderm; not – notochord; sel – superficial ectoderm layer; som – somite. 300 µm bar is shown for all photos of the same type.|
|Figure S3. The analysis of the effects of mmp3 and chordin downregulation on the notochord and somitic mesoderm by in situ hybridization on the histological sections, as well as, effects of mmp3 overexpression and downregulation on sizes of the neural plate, somitic mesoderm and notochord in the half-size and wild-size embryos, Related to STAR Methods, Figure 3 A-D. The notochord labeled by in situ hybridization with chordin probe on the middle transverse vibratome sections of the wild-type embryo (A), the half-size embryo developed from single blastomer separated at 2-cells stage (B) and the wild-size embryo with mmp3 mRNA translation inhibited by mmp3 MO. As one may see, the average depth of the notochord is similar in all these cases (D). By contrast, its width is significantly larger in the half-size embryos and in the wild-size ones with downregulated mmp3. However, as we established, the surface area of the notochord in the half-size embryos is similar to that in the wild-type embryos (Figure 2 and 3 in the main text). This means that the volume of the notochord in the half-size embryos is also approximately identical to that in the Wild-type onesl. By contrast, the notochord surface area in the wild-size embryos with downregulated mmp3 is larger than those in the wild-type embryos (Figure 3 in the main text), which means that the volume of the notochord in the wild-size embryos with downregulated mmp3 is also larger. E-H. The somitic mesoderm labeled by in situ hybridization with cardiac actin probe on the middle transverse vibratome sections of the wild-type embryo (E), the half-size embryo developed from single blastomer separated at 2-cells stage (F) and the wild-size embryo with mmp3 mRNA translation inhibited by mmp3 MO (G). As one may see, the average maximal depth of somitic mesoderm in the half-size embryos and the wild-size embryos with downregulated mmp3 is lower than that in the wild-type embryos (H). Obviously, these result strengthens our conclusion made on the base of measuring surface areas about diminishing of the somitic mesoderm in the first two types of embryos. I1-K3. While overexpresion of mmp3 in the half-size embryos reverts scaling (neurectoderm and somitic mesoderm) and anti-scaling(notochord) effects elicited by the embryo size diminishing, the downregulation of mmp3 in these embryos appeared to be unable to further enhance these effects. The latter is consistent with significant depletion of the mmp3 endogenous mRNA in half-size embryos. L1-N3. Overexpression of mmp3 in the wild-size embryos elicit enlargement of the neroectoderm and somitic mesoderm, but narrowing of the notochord. Abbreviations: gc – gastrocele; np – neural plate; not – notochord; som – somite. 300 µm bar is shown for all photos of the same type.|
|Figure S4. Results of the embryo genotyping after CRISPR mmp3 knockout, expression of noggin1, noggin2, chordin and tll1 in Spemann’s organizer at the early gastrula stage, labeling of the notochord in embryos with downregulated chordin by the probe to shh mRNA, as well as, effects of chordin and noggin2 downregulation on the notochord size in half-size embryos, Related to Figures 3, 4 and 6. A-D. The results of embryo genotyping after mmp3 CRISPR/Cas9 knockout. Diagrams showing percentage of mutations after CRISPR/Cas9 procedure in ten randomly picked embryos at late gastrula stage injected with the mixture of sgRNA for target site in 1st and 2nd mmp3 exons, respectively, and Cas9 protein (A and B). Target sites are in green and PAM sites are in red on sequences shown at the first lines on F and G. Examples of deletions (dashes) and insertions (in blue) in the 1st and 2nd mmp3 exons, respectively revealed by NGS sequencings of PCR amplicons overlapping target sites and obtained from DNA samples extracted from embryos subjected to CRISPR/Cas9 procedure (see STAR Methods for details) (C and D). E-H. Expression of chordin (E), tll1 (F), noggin1 (G) and noggin2 (H) in deep layers of the dorsal blastopore lip (Spemann’s organizer) at the early gastrula as revealed by the in situ hybridization on the vibratome sagittal sections of embryos at the early gastrula stage. Dorsal side to the right, animal pole to the top. Please note that if for noggin2 and tll1 the hybridization time was 48 and 30 hours, it was only 3 and 10 hours in case of chordin and noggin1, respectively. I and I’. In situ hybridisation with anti-sense and sens probe to noggin2 on the right and left halves of the same embryo demonstrates specificity of the signal revealed with the anti-sense probe. J-L. Like the in situ hybridization with the probe to chordin, the in situ hybridization with the probe to shh reveals changes of the notochord aspect ratio in embryos with downregulated chordin, in the absence of a change in the overall size of the notochord. This validates using of the probe to chordin as the notochord marker. M-Q. Downregulation of chordin in the half-size embryos does not change the size of the notochord (M, N and Q). By contrast, the notochord diminished if noggin1 or noggin2 is also downregulated (O, P and Q). For all photos bar is 300 µm.|
|Figure S5. Comparison of the notochord and somitic mesoderm depths in the late gastrula and middle neurula wildtype embryos and in the middle neurula embryos with retardation of the morphogenetic movements elicited by chordin downregulation, analysis of the angular size of the chordin expression sector of marginal zone in the wild- and half-size embryos at the late blastula and early gastrula stages, as well as revealing of pSmad1/5/8 on the vibratom sections of the gastrula marginal zone, Related to Figures 6, 7 and STAR Methods.A. Despite different aspect ratios, the surface areas of the notochord rudiment are not statistically distinguishable between the late gastrula and middle neural embryos. Dashed lines indicate approximate levels of the transverse sections shown below. Whole-mount in situ hybridization with the probe to chordin mRNA. B and C. Whereas the notochord depths do not distinguish on the transverse sections of the late gastrula and the middle neural embryos, the maximal depth of somitic mesoderm is lesser, although its width larger, in the late gastrula embryos. In situ hybridization with the probe to chordin mRNA was done on the vibratome sections of the embryos. D and E. Whereas the notochord depths do not distinguish on the transverse sections of the wild type embryos at the middle neural stage and their siblings with downregulated mmp3, the maximal depth of somitic mesoderm is lesser in embryos with downregulated mmp3. In situ hybridization with the probe to chordin mRNA was done on the vibratome sections of the embryos. F and G. While at the late blastula stage the angular size of the chordin expression sector (at this stage this area corresponds to the territory of Initial Notochord Seed, INS) is lesser in the half-size embryos than in the wild-size ones, at the early gastrula stage the angular size of this sector, on the contrary, becomes larger in the half-size embryos because of more fast propagation of the notochord specification wave in this embryos. This is due to higher level of Noggins in the notochord cells of the half-size embryos, in which the destructor of Noggins, Mmp3 is expressed at low level. H/H’ and I/I’. Revealing of pSmad1/5/8 in deep layers of marginal zone by the antybody staining on the vibratom sections in the gastrula embryos at stage 11 and 12. Red dashed line indicates the border between the dorsal sector of the marginal zone free of pSmad1/5/8 and the ventral sector with cell nuclei stained by pSmad1/5/8 antibody. For all photos, except H’ and I’, bar is 300 µm. For H’ and I’, bar is 100 µm.|
|Figure S6. Construction of mesoderm patterning model, Related to Figure 7. A. Phase-parametric plot of ODE (equation 7) using fixed h = 1, K = 2 and various Φ. Right and left biffurcation values are shown with vertical arrows. B. Simulation of the simple model (equation 8) with/without competency fading (upper: exp(−t/τ) = 1, lower: τ = 7200). Consequence snapshots are shown: the light gray for the beginning and the black for the end (10, 60, 110, 160, 260, 360 sec); red arrows: 10 → 360. βm = 4 · 10−4 , αm = 2 · 10−3 , D = 4, ν = 2 · 10−3 , K = 1, h = 1, k = 5. Initial conditions are δ(x,t = 0) = 0, m(x,t = 0) = for x ∈ [0;675]∪[825;1500], and m(x,t = 0) = 10 · for x ∈ [675;825]. is random value distributed uniformly at [0;1]. Boundary conditions are zero flux for m. C/C’. Phase-parametric diagram of δ equation of equation (13). Fitted parameters from Table S4 were used. Curve for ENAF was plotted considering pSmad1/3/5 is exactly at threshold value. Curve for pSmad1/3/5 was plotted considering ENAF is at threshold level as well. D. Competency curves of BMP-independent (blue line) and BMP-dependent (red line) notochord patterning over the modelling time using in equation (13). τc, τs , and µs was set for define competency timing in this equation. E. Different views to the Xenopus laevis germ layers at stage 9. Ectoderm, mesoderm, and endoderm are indicated with blue, red, and yellow colors, respectively. Chordamesoderm and other mesoderm are shown with brown red and light red, respectively. Black arrow at frontal section marks the 1D-reactor selected for modelling. F. Sensitivity analysis of model parameters (see “Sensitivity analysis” chapter of STAR Methods). Sobol first rank sensitivity indices measured for notochord area and somitic mesoderm area under different conditions corresponding to rows of Table S3. Parameters were sampled in the 5% neighborhood of the equilibrium point. Notations of model parameters are explained in Table S4. Abbreviations: “1/2” – half-sized; “WT” – wild-type; “-N2” – noggin2-MO; “-M3” – mmp3-MO; “-Ch” – chordin-MO.|
|Figure S7. Noggin2 and Chordin profiles simulated under different conditions indicated above each pair of plots, Related to Figure 7. ‘1a’–‘2c’ abbreviations corresponds those in Table S3. Profiles are plotted every 103 seconds. Curves with lighter colors correspond to the earlier time of the simulation.|
|Figure S8. Simulated profiles of differentiation variable δ and of free Bmp under different conditions indicated above each pair of plots, Related to Figure 7. ‘1a’–‘2c’ abbreviations corresponds those in Table S3. In left panes, horizontal dashed lines mean the threshold of notochord fate (negative values of δ). In right panes, horizontal solid lines indicate total concentration of BMP proteins (including binding substances). Vertical red dashed lines indicate somite mesoderm arbitrary border calculated as the point where free BMP level reaches the threshold value (horizontal dashed lines). Profiles are plotted every 103 seconds. Curves with lighter colors correspond to the earlier time of the simulation.|