Individuals can vary substantially in size, but the proportions of their body plans are often maintained. We generated smaller zebrafish by removing 30% of their cells at the blastula stages and found that these embryos developed into normally patterned individuals. Strikingly, the proportions of all germ layers adjusted to the new embryo size within 2 hours after cell removal. As Nodal–Lefty signalling controls germ-layer patterning, we performed a computational screen for scale-invariant models of this activator–inhibitor system. This analysis predicted that the concentration of the highly diffusive inhibitor Lefty increases in smaller embryos, leading to a decreased Nodal activity range and contracted germ-layer dimensions. In vivo studies confirmed that Lefty concentration increased in smaller embryos, and embryos with reduced Lefty levels or with diffusion-hindered Lefty failed to scale their tissue proportions. These results reveal that size-dependent inhibition of Nodal signalling allows scale-invariant patterning.

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  1. 1.

    Morgan, T. H. Half embryos and whole embryos from one of the first two blastomeres. Anat. Anz. 10, 623–685 (1895).

  2. 2.

    Cooke, J. Control of somite number during morphogenesis of a vertebrate, Xenopus laevis. Nature 254, 196–199 (1975).

  3. 3.

    Inomata, H. Scaling of pattern formations and morphogen gradients. Dev. Growth Differ. 59, 41–51 (2017).

  4. 4.

    Garcia, M., Nahmad, M., Reeves, G. T. & Stathopoulos, A. Size-dependent regulation of dorsal–ventral patterning in the early Drosophila embryo. Dev. Biol. 381, 286–299 (2013).

  5. 5.

    Lauschke, V. M., Tsiairis, C. D., Francois, P. & Aulehla, A. Scaling of embryonic patterning based on phase-gradient encoding. Nature 493, 101–105 (2013).

  6. 6.

    Kicheva, A. et al. Kinetics of morphogen gradient formation. Science 315, 521–525 (2007).

  7. 7.

    Wartlick, O., Kicheva, A. & González-Gaitán, M. Morphogen gradient formation. Cold Spring Harb. Perspect. Biol. 1, a001255 (2009).

  8. 8.

    Yu, S. R. et al. Fgf8 morphogen gradient forms by a source–sink mechanism with freely diffusing molecules. Nature 461, 533–536 (2009).

  9. 9.

    Rogers, K. W. & Schier, A. F. Morphogen gradients: from generation to interpretation. Annu. Rev. Cell Dev. Biol. 27, 377–407 (2011).

  10. 10.

    Rogers, K. W. & Müller, P. Nodal and BMP dispersal during early zebrafish development. Dev. Biol. https://doi.org/10.1016/j.ydbio.2018.04.002 (2018).

  11. 11.

    Umulis, D. M. & Othmer, H. G. Mechanisms of scaling in pattern formation. Development 140, 4830–4843 (2013).

  12. 12.

    Gregor, T., Bialek, W., de Ruyter van Steveninck, R. R., Tank, D. W. & Wieschaus, E. F. Diffusion and scaling during early embryonic pattern formation. Proc. Natl Acad. Sci. USA 102, 18403–18407 (2005).

  13. 13.

    Gregor, T., McGregor, A. P. & Wieschaus, E. F. Shape and function of the bicoid morphogen gradient in dipteran species with different sized embryos. Dev. Biol. 316, 350–358 (2008).

  14. 14.

    Ben-Zvi, D., Shilo, B.-Z., Fainsod, A. & Barkai, N. Scaling of the BMP activation gradient in Xenopus embryos. Nature 453, 1205–1211 (2008).

  15. 15.

    Ben-Zvi, D., Pyrowolakis, G., Barkai, N. & Shilo, B. Z. Expansion–repression mechanism for scaling the Dpp activation gradient in Drosophila wing imaginal discs. Curr. Biol. 21, 1391–1396 (2011).

  16. 16.

    Hamaratoglu, F., de Lachapelle, A. M., Pyrowolakis, G., Bergmann, S. & Affolter, M. Dpp signaling activity requires pentagone to scale with tissue size in the growing Drosophila wing imaginal disc. PLoS Biol. 9, e1001182 (2011).

  17. 17.

    Wartlick, O. et al. Dynamics of Dpp signaling and proliferation control. Science 331, 1154–1159 (2011).

  18. 18.

    Cheung, D., Miles, C., Kreitman, M. & Ma, J. Scaling of the bicoid morphogen gradient by a volume-dependent production rate. Development 138, 2741–2749 (2011).

  19. 19.

    Wartlick, O., Jülicher, F. & González-Gaitán, M. Growth control by a moving morphogen gradient during Drosophila eye development. Development 141, 1884–1893 (2014).

  20. 20.

    Kicheva, A. et al. Coordination of progenitor specification and growth in mouse and chick spinal cord. Science 345, 1254927 (2014).

  21. 21.

    Uygur, A. et al. Scaling pattern to variations in size during development of the vertebrate neural tube. Dev. Cell 37, 127–135 (2016).

  22. 22.

    Schulte-Merker, S. et al. Expression of zebrafish goosecoid and no tail gene products in wild-type and mutant no tail embryos. Development 120, 843–852 (1994).

  23. 23.

    Schier, A. F. Nodal morphogens. Cold Spring Harb. Perspect. Biol. 1, a003459 (2009).

  24. 24.

    Chen, C. & Shen, M. M. Two modes by which Lefty proteins inhibit Nodal signaling. Curr. Biol. 14, 618–624 (2004).

  25. 25.

    Feldman, B. et al. Zebrafish organizer development and germ-layer formation require Nodal-related signals. Nature 395, 181–185 (1998).

  26. 26.

    Rebagliati, M. R., Toyama, R., Fricke, C., Haffter, P. & Dawid, I. B. Zebrafish Nodal-related genes are implicated in axial patterning and establishing left–right asymmetry. Dev. Biol. 199, 261–272 (1998).

  27. 27.

    Sampath, K. et al. Induction of the zebrafish ventral brain and floorplate requires Cyclops/Nodal signalling. Nature 395, 185–189 (1998).

  28. 28.

    Meno, C. et al. Mouse Lefty2 and zebrafish antivin are feedback inhibitors of nodal signaling during vertebrate gastrulation. Mol. Cell 4, 287–298 (1999).

  29. 29.

    Feldman, B. et al. Lefty antagonism of Squint is essential for normal gastrulation. Curr. Biol. 12, 2129–2135 (2002).

  30. 30.

    Chen, Y. & Schier, A. F. Lefty proteins are long-range inhibitors of Squint-mediated Nodal signaling. Curr. Biol. 12, 2124–2128 (2002).

  31. 31.

    Cheng, S. K., Olale, F., Brivanlou, A. H. & Schier, A. F. Lefty blocks a subset of TGFβ signals by antagonizing EGF-CFC coreceptors. PLoS Biol. 2, e30 (2004).

  32. 32.

    Choi, W. Y., Giraldez, A. J. & Schier, A. F. Target protectors reveal dampening and balancing of Nodal agonist and antagonist by miR-430. Science 318, 271–274 (2007).

  33. 33.

    Müller, P. et al. Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system. Science 336, 721–724 (2012).

  34. 34.

    Wang, Y., Wang, X., Wohland, T. & Sampath, K. Extracellular interactions and ligand degradation shape the Nodal morphogen gradient. eLife 5, e13879 (2016).

  35. 35.

    van Boxtel, A. L. et al. A temporal window for signal activation dictates the dimensions of a Nodal signaling domain. Dev. Cell 35, 175–185 (2015).

  36. 36.

    Rogers, K. W. et al. Nodal patterning without Lefty inhibitory feedback is functional but fragile. eLife 6, e28785 (2017).

  37. 37.

    Xu, C. et al. Nanog-like regulates endoderm formation through the Mxtx2–Nodal pathway. Dev. Cell 22, 625–638 (2012).

  38. 38.

    Marcon, L., Diego, X., Sharpe, J. & Müller, P. High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals. eLife 5, e14022 (2016).

  39. 39.

    Müller, P., Rogers, K. W., Yu, S. R., Brand, M. & Schier, A. F. Morphogen transport. Development 140, 1621–1638 (2013).

  40. 40.

    Harmansa, S., Hamaratoglu, F., Affolter, M. & Caussinus, E. Dpp spreading is required for medial but not for lateral wing disc growth. Nature 527, 317–322 (2015).

  41. 41.

    Gritsman, K. et al. The EGF-CFC protein one-eyed pinhead is essential for Nodal signaling. Cell 97, 121–132 (1999).

  42. 42.

    Mathieu, J. et al. Nodal and Fgf pathways interact through a positive regulatory loop and synergize to maintain mesodermal cell populations. Development 131, 629–641 (2004).

  43. 43.

    Bennett, J. T. et al. Nodal signaling activates differentiation genes during zebrafish gastrulation. Dev. Biol. 304, 525–540 (2007).

  44. 44.

    Liu, Z. et al. Fscn1 is required for the trafficking of TGF-β family type I receptors during endoderm formation. Nat. Commun. 7, 12603 (2016).

  45. 45.

    van Boxtel, A. L., Economou, A. D., Heliot, C. & Hill, C. S. Long-range signaling activation and local inhibition separate the mesoderm and endoderm lineages. Dev. Cell 44, 179–191 (2018).

  46. 46.

    Dougan, S. T. The role of the zebrafish Nodal-related genes squint and cyclops in patterning of mesendoderm. Development 130, 1837–1851 (2003).

  47. 47.

    Pei, W., Williams, P. H., Clark, M. D., Stemple, D. L. & Feldman, B. Environmental and genetic modifiers of squint penetrance during zebrafish embryogenesis. Dev. Biol. 308, 368–378 (2007).

  48. 48.

    Gierer, A. & Meinhardt, H. A theory of biological pattern formation. Kybernetik 12, 30–39 (1972).

  49. 49.

    Othmer, H. G. & Pate, E. Scale-invariance in reaction-diffusion models of spatial pattern formation. Proc. Natl Acad. Sci. USA 77, 4180–4184 (1980).

  50. 50.

    Francois, P., Vonica, A., Brivanlou, A. H. & Siggia, E. D. Scaling of BMP gradients in Xenopus embryos. Nature 461, E1 (2009).

  51. 51.

    Ben-Zvi, D. & Barkai, N. Scaling of morphogen gradients by an expansion–repression integral feedback control. Proc. Natl Acad. Sci. USA 107, 6924–6929 (2010).

  52. 52.

    Umulis, D. M. Analysis of dynamic morphogen scale invariance. J. R. Soc. Interface 6, 1179–1191 (2009).

  53. 53.

    Inomata, H., Shibata, T., Haraguchi, T. & Sasai, Y. Scaling of dorsal–ventral patterning by embryo size-dependent degradation of Spemann’s organizer signals. Cell 153, 1296–1311 (2013).

  54. 54.

    Ben-Zvi, D., Fainsod, A., Shilo, B. Z. & Barkai, N. Scaling of dorsal–ventral patterning in the Xenopus laevis embryo. Bioessays 36, 151–156 (2014).

  55. 55.

    Werner, S. et al. Scaling and regeneration of self-organized patterns. Phys. Rev. Lett. 114, 138101 (2015).

  56. 56.

    Rasolonjanahary, M. & Vasiev, B. Scaling of morphogenetic patterns in reaction-diffusion systems. J. Theor. Biol. 404, 109–119 (2016).

  57. 57.

    Schmoller, K. M., Turner, J. J., Koivomagi, M. & Skotheim, J. M. Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size. Nature 526, 268–272 (2015).

  58. 58.

    Thisse, C. & Thisse, B. High-resolution in situ hybridization to whole-mount zebrafish embryos. Nat. Protoc. 3, 59–69 (2008).

  59. 59.

    Lauter, G., Soll, I. & Hauptmann, G. Two-color fluorescent in situ hybridization in the embryonic zebrafish brain using differential detection systems. BMC Dev. Biol. 11, 43 (2011).

  60. 60.

    Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).

  61. 61.

    Dee, C. T. et al. A change in response to BMP signalling precedes ectodermal fate choice. Int J. Dev. Biol. 51, 79–84 (2007).

  62. 62.

    Feng, X., Adiarte, E. G. & Devoto, S. H. Hedgehog acts directly on the zebrafish dermomyotome to promote myogenic differentiation. Dev. Biol. 300, 736–746 (2006).

  63. 63.

    Pauls, S., Geldmacher-Voss, B. & Campos-Ortega, J. A. A zebrafish histone variant H2A.F/Z and a transgenic H2A.F/Z:GFP fusion protein for in vivo studies of embryonic development. Dev. Genes Evol. 211, 603–610 (2001).

  64. 64.

    Schmid, B. et al. High-speed panoramic light-sheet microscopy reveals global endodermal cell dynamics. Nat. Commun. 4, 2207 (2013).

  65. 65.

    Link, V., Shevchenko, A. & Heisenberg, C. P. Proteomics of early zebrafish embryos. BMC Dev. Biol. 6, 1 (2006).

  66. 66.

    Saerens, D. et al. Identification of a universal VHH framework to graft non-canonical antigen-binding loops of camel single-domain antibodies. J. Mol. Biol. 352, 597–607 (2005).

  67. 67.

    Pomreinke, A. P. et al. Dynamics of BMP signaling and distribution during zebrafish dorsal–ventral patterning. eLife 6, e25861 (2017).

  68. 68.

    Blässle, A. et al. Quantitative diffusion measurements using the open-source software PyFRAP. Nat. Commun. 9, 1582 (2018).

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We thank C. Hill for providing the Lefty1 antibody, M. Affolter for providing the morphotrap construct and J. Raspopovic and N. Lord for helpful comments. This work was supported by EMBO (M.A.-C., L.M. and P.M.) and HFSP (P.M.) long-term fellowships, the NSF Graduate Research Fellowship Program (K.W.R.), NIH grant GM56211 (A.F.S.), and funding from the Max Planck Society, ERC Starting Grant 637840 and HFSP Career Development Award CDA00031/2013-C (P.M.).

Author information

Author notes

    • María Almuedo-Castillo
    •  & Luciano Marcon

    Present address: Centro Andaluz de Biología del Desarrollo, Universidad Pablo de Olavide, Sevilla, Spain


  1. Friedrich Miescher Laboratory of the Max Planck Society, Tübingen, Germany

    • María Almuedo-Castillo
    • , Alexander Bläßle
    • , David Mörsdorf
    • , Luciano Marcon
    • , Gary H. Soh
    • , Katherine W. Rogers
    •  & Patrick Müller
  2. Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA, USA

    • Katherine W. Rogers
    •  & Alexander F. Schier


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M.A.-C., A.F.S. and P.M. conceived the study. P.M. developed the extirpation assay and supervised the project. G.H.S. developed the extirpation device and the 2D map visualization workflow and optimized the pSmad2/3 immunostaining protocol. D.M. performed the experiments in Fig. 6i,j, Supplementary Figs. 4f,g, 5 and 8 and contributed to experiments in Fig. 6f,h. K.W.R. and A.F.S. contributed the data in Supplementary Fig. 3d,e and provided the lft mutants before publication. M.A.-C. performed all other experiments. M.A.-C., A.B., D.M. and P.M. analysed the data. A.F.S. and P.M. conceptualized the scaling model. A.B. performed the mathematical analysis and simulations with assistance from L.M. and P.M. M.A.-C. and P.M. wrote the manuscript with input from all authors.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Patrick Müller.

Integrated supplementary information

  1. Supplementary Figure 1 Similar developmental speed in untreated and extirpated embryos.

    Animal pole view images of goosecoid expression. Changes in the goosecoid expression domain during development proceed with a similar speed in untreated and extirpated embryos. Unt: Untreated; Ext: Extirpated. 0.75 hpe: n[untreated] = 9, n[extirpated] = 7; 1.25 hpe: n[untreated] = 12, n[extirpated] = 11; 2 hpe: n[untreated] = 9, n[extirpated] = 11; 2.75 hpe: n[untreated] = 7, n[extirpated] = 13; 3.5 hpe: n[untreated] = 10, n[extirpated] = 14. Scale bar: 200 μm.

  2. Supplementary Figure 2 Scaling of Nodal signaling after extirpation.

    (a) Maximum intensity projections of lateral confocal pSmad2/3 immunostaining stacks, and (b) quantification of relative and absolute pSmad2/3 domains in untreated and extirpated embryos at different times after extirpation. 0.75 h post extirpation (hpe): n[untreated] = 5, n[extirpated] = 7; 1.5 hpe: n[untreated] = 5, n[extirpated] = 9; 2 hpe: n[untreated] = 19, n[extirpated] = 21. *p < 0.05, ***p < 0.001. Two-sided Student’s t-tests were performed (α = 0.05). See Supplementary Table 1 for statistics source data. Box plots show median (blue line), mean (untreated: black; extirpated: grey lines), 25% quantiles (box), and all included data points (red markers). Whiskers extend to the smallest data point within the 1.5 interquartile range of the lower quartile, and to the largest data point within the 1.5 interquartile range of the upper quartile. Scale bar: 200 μm.

  3. Supplementary Figure 3 Lack of Lefty1 precludes germ layer scaling.

    (a) Lateral views of representative 24 hpf untreated and extirpated embryos with different numbers of functional lefty alleles. Numbers in the figure panel represent the fraction of these representative embryos. (b) Chart showing the fraction of phenotypes in different lefty mutants. “Mild lft1-/-;lft2-/- phenotype” refers to embryos that do not exhibit the severe lft1-/-;lft2-/- phenotype but show shorter or thicker tails or slightly reduced cephalic structures. (c) Fraction of lefty mutants with normal mesendoderm proportion (22-33%), high mesendoderm proportion (34-42%), and very high mesendoderm proportion ( > = 42%). (d) Schematic of experiments to assess the activity of Lefty1 and Lefty2. Embryos were injected at the one-cell stage with different amounts of lefty1- or lefty2-gfp mRNA as indicated in figure panel (e). Some embryos were also injected with 100 pg Alexa546-dextran for subsequent generation of intracellular masks for extracellular intensity measurements. Extracellular GFP intensity was quantified at 5 hpf, and sibling embryos were collected at 50% epiboly. qRT-PCR using primers for the Nodal target gene no tail (ntl) was used to assess inhibitory activity. (e) Average ntl expression is plotted against average extracellular intensity. At similar intensities, Lefty2-GFP consistently repressed ntl expression more effectively than Lefty1-GFP. For fluorescence measurements: n[5 pg Lefty2-GFP] = 5, n[10 pg Lefty2-GFP] = 4, n[20 pg Lefty2-GFP] = 3, n[22 pg Lefty1-GFP] = 4, n[43 pg Lefty1-GFP] = 5, n[86 pg Lefty1-GFP] = 4. For qRT-PCR measurements, 3 samples with 8 embryos each were analysed per condition. Error bars: SEM. See Supplementary Table 1 for statistics source data. Scale bars: 200 μm (a) and 100 μm (d).

  4. Supplementary Figure 4 Manipulation of Lefty1-GFP diffusion in zebrafish embryos.

    (a,c) Maximum intensity projections of lateral confocal stacks of fascin expression in lft1-/-;lft2-/- embryos subjected to different treatments. Representative embryos for each treatment are shown. Numbers in the figure panel represent the fraction of these representative embryos. (b,d) Mesendoderm proportions in differently sized embryos. Note that the fraction of embryos with normal mesendoderm extent is equivalent to the fraction of rescued lft1-/-;lft2-/- embryos shown in Fig. 6. (e) Maximum intensity projections of confocal stacks of 30-50% epiboly stage embryos. Animal pole views. The upper image shows an embryo injected with lefty1-GFP mRNA at the one-cell stage. The middle panel shows an embryo co-injected with morphotrap-encoding mRNA and lefty1-GFP mRNA at the one-cell stage. The lower panel shows an embryo injected with lefty1-GFP mRNA at the one-cell stage and transplanted with a morphotrap-expressing clone at sphere stage. The morphotrap changes the distribution of Lefty1-GFP from uniform extracellular to strongly membrane-associated. (f,g) Morphotrap binding affects Lefty activity. Lateral and ventral views of 24 hpf wild type embryos injected with morphotrap and different concentrations of lefty1-GFP mRNA. Representative embryos for each phenotypic category are shown (f). Distribution of phenotypes after different treatments (g). Three groups of Nodal loss-of-function phenotypes were defined according to their strength: mild (S1), intermediate (S2), and severe (S3). For 5 pg of lft1-GFP mRNA: n[uninjected] = 32, n[ +lft1-GFP] = 34, n[ + morphotrap + lft1-GFP] = 24. For 30 pg of lft1-GFP mRNA: n[uninjected] = 30, n[ + lft1-GFP] = 26, n[ + morphotrap + lft1-GFP] = 34. See Supplementary Table 1 for statistics source data. Scale bars: 200 μm.

  5. Supplementary Figure 5 Endogenous Lefty1 concentration increases in smaller embryos.

    (a,b) Immunoblot analysis indicates a more pronounced decrease of the cellular marker Histone H3 compared to Lefty1, suggesting an increase in Lefty concentration in extirpated embryos (b). The samples derive from the same experiment, but for technical reasons (see Methods) Lefty1 and H3 levels were determined from independent immunoblots (see Supplementary Fig. 8 for raw data). (c) Quantification of Lefty1 and Histone H3 levels in the blots shown in Supplementary Fig. 8. All Lefty1 levels were normalised to the Lefty1 levels in the “10 embryos” sample, and all H3 levels were normalised to the H3 levels in the “10 embryos”. The Lefty1 and H3 levels in the “10 embryos” sample were set to 10. Note the approximately linear increase in Lefty1 and H3 levels between samples with different embryo numbers. On average, the decrease in H3 levels in extirpated compared to untreated embryos is more pronounced than the decrease in Lefty1 levels, similar to the model prediction in Fig. 7b. Box plots shows median (blue line), mean (untreated: black; extirpated: grey lines), 25% quantiles (box) and all included data points (red markers). Whiskers extend to the smallest data point within the 1.5 interquartile range of the lower quartile, and to the largest data point within the 1.5 interquartile range of the upper quartile.

  6. Supplementary Figure 6 An increase in Lefty concentration is required for scale-invariant patterning.

    (a-d) Simplified qualitative models of Nodal (i.e. total Nodal, in contrast to the free Nodal shown in the simulations throughout the paper) and Lefty gradients in different scenarios to explain experimental observations. In contrast to our approach using ectopic Lefty gradients, most of the extirpated lft1-/-;lft2-/- mutants exposed to levels of the Nodal inhibitor SB-505124 that rescue normally sized embryos are unable to restore normal mesendoderm proportions. In contrast to ectopic Lefty proteins (c), the Nodal inhibitor is provided tonically, and its concentration does not increase after a reduction in embryo size (d). (e) Maximum intensity projections of confocal stacks of fascin expression in lft1-/-;lft2-/- embryos exposed to 4.8 μM of the Nodal inhibitor SB-505124. Lateral views. Representative embryos for each treatment are shown. Numbers in the figure panel represent the proportion of these representative embryos. (f) Mesendoderm proportions in embryos treated with 4.8 μM of the Nodal inhibitor SB-505124. (g) Lateral views of 26 hpf lft1-/-;lft2-/- embryos exposed to different concentrations of the Nodal inhibitor SB-505124. Embryos representing the majority of phenotypes are shown for each treatment. Numbers in the figure panel indicate the number of these representative phenotypes out of all analysed embryos. Scale bars: 200 μm.

  7. Supplementary Figure 7 Summary and extensions of the size-dependent inhibition model for scale-invariant patterning.

    (a-e) Normalised Nodal and Lefty protein profiles scaled to embryo size for simulations of the size-dependent inhibition model with normal Lefty production (a), no Lefty production (b), reduced Lefty production (c), and feedback-less Lefty inhibition in the absence (d) or presence of morphotrap (e). In contrast to the graphs shown in Figs. 4, 5 and 6, these graphs show normalised length for both untreated and extirpated embryos. Here, models scale when the dashed and solid lines overlap at the intercept with the signaling threshold. In (c), Lefty induction was reduced by 30%. Normal Lefty diffusivity was set to DL = 15 μm2/s, and Lefty diffusivity in the presence of morphotrap (e) was set to DL = 0.35 μm2/s. All simulation parameter values are listed in Supplementary Table 2 [Parameter Tables 3 and 4]. (f,g) Relationship between the maximum rate of Lefty induction and the strength of Lefty-mediated Nodal inhibition (f) or between the maximum rate of Lefty induction and Lefty induction steepness (g). The plots show maximum projections through the six-dimensional parameter space of the size-dependent inhibition model. (h) Simulation of the full model with different values for Lefty diffusivities. A minimal diffusion coefficient of approximately 7-10 μm2/s is required for scale-invariant patterning. (i,j) Implementation of the size-dependent inhibition model with linear Lefty inhibition. Scaling solutions are also found with a linear inhibition term, showing that the general mechanism of the size-dependent inhibition model is not dependent on the assumption of non-linear inhibition. (k-p) Extensions of the size-dependent inhibition model. (k,l) Simulations of the size-dependent inhibition system explicitly modelling total, free, and Lefty-bound (inhibited) Nodal protein, showing results for absolute (k) and normalised (l) embryo length. (m,n) Simulations with separate variables for signalling and protein levels showing results for absolute (m) and normalised (n) embryo length. (o,p) Simulations with separate variables for Nodal and FGF proteins and signalling.

  8. Supplementary Figure 8 Raw immunoblot data.

    (a) Marker lanes are shown as overlay of the white light image at the edge of the membranes. Experiments 1, 2, and 4 are biological replicates, whereas experiment 3 is a technical replicate of experiment 1. Turquoise boxes indicate the regions shown in Supplementary Fig. 5a, and red boxes outline the regions used for quantification in Supplementary Fig. 5b,c. Unt: Untreated, Ext: Extirpated.

Supplementary information

  1. Supplementary Information

    Supplementary Figures 1–8 and legends for Supplementary Note 1, Supplementary Tables 1 and 2, and Supplementary Movies 1–4

  2. Reporting Summary

  3. Supplementary Note 1

  4. Supplementary Table 1

  5. Supplementary Table 2

  6. Supplementary Movie 1

  7. Supplementary Movie 2

  8. Supplementary Movie 3

  9. Supplementary Movie 4

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