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The ability of amphibian embryos to scale pattern with size is evident from the large variability in egg size, and is a pre-assumption of our study. In his 1938 monograph, H. Spemann reports his manipulation of newt embryos: “...when the two halves are completely separated, the dorsal half develops into a small embryo of normal proportions”3 (Fig. 1a). This experiment is cited in standard textbooks4 and reproduced in laboratories5 and teaching courses. Clearly, not all half-embryos develop normally, but this is not surprising given the likelihood of secondary damage. The key point is that surviving embryos maintain mesodermal ventral tissues (for example, blood and heart), expected to be lost in the absence of scaling.

Figure 1: Scaling pattern with size.
figure 1

a, A newt dorsal half-embryo (a, left) develops into a small embryo of normal proportions, in contrast to the ventral half (b, right). (Panel a is from ref. 3.) b, The BMP activation profile predicted by our model for wild-type (black line) and half-sized (grey line) embryos. L is the length of the dorsal-ventral axis and T1, T2 and T3 are arbitrary thresholds differing by less than tenfold. c, Numerical simulation of profiles in a wild-type embryo (black line), embryo depleted of Admp by admp morpholino (MO) (blue line) or depleted of Bmp2/4/7 (green line). d, Numerical simulation of profiles in wild-type (black line) and half-sized (grey line) embryos, and of an embryo depleted of Chordin (dashed black line, chordin morpholino). The same parameters were used in all figures (contact the authors for further information on parameters).

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The possibility that scaling results from over-growth was ruled out by J. Cooke, who demonstrated that proportionate assignment of trunk mesodermal cells to tissues is maintained in embryos in which as much as ∼70% of the cells are removed6. The tissues examined depend on bone morphogenetic protein (BMP) and thus provide readout of the early gradient.

Scaling in our model2 is robust to the parameter choice, but the range of the gradient depends on parameters. We do not attempt to predict the in vivo parameters. The ∼100-fold concentration difference shown (Fig. 1b) is comparable with the estimated range of the Dpp gradient in the significantly smaller Drosophila wing imaginal disc7. Quantitative measures of the pSmad1 profile in the opaque Xenopus embryo are still limited (see ref. 8 for example).

Our model is consistent with existing experiments. The severe phenotype of Bmp2/4/7 depletion (Fig. 1c) reflects the positive feedback on bmp4 expression, which increases ventral Bmp4 levels. Similarly, the remaining polarity of Chordin-depleted embryos (Fig. 1d) is explained by the additional BMP inhibitors (for example, Noggin), which are structurally different from Chordin, and are not likely to be cleaved by Xlr or to mediate shuttling. Both properties were included in our original simulations and do not alter the robustness of the scaling mechanism.

Our model is robust to ligand production rate, but we do not expect this robustness to hold for arbitrarily high levels which can override available Chordin. Importantly, our conclusion that dorsally produced Admp accumulates ventrally was in fact tested: Bmp2/4/7-depleted embryos retain dorsal–ventral polarity9 and this polarity is abolished only when Admp is also depleted5.

Francois et al.1 are concerned that separation of Bmp4-Myc from its site of injection may be due to ligand secretion into the blastocoel, and non-uniform uptake by ventral cells. However, separation was abolished when Chordin was depleted, with no apparent reason to assume that such secretion and uptake requires Chordin.

The novel point of our secondary-axis experiment is the removal of Admp from the secondary organizer. This eliminates an auxiliary source of a BMP ligand, which could contribute to the increase of BMP in mid-embryo. Francois et al. imply that a BMP profile that peaks in the centre of the embryo to a level similar to the normal ‘lateral’ level is sufficient to obtain sizzled expression. Clearly, this is not the case, because sizzled expression requires high BMP levels normally found in ventral positions.

Our model refers to the gastrulation stage, when BMP functions in dorsal–ventral patterning, and not the pre-gastrula stage, when BMP represses the organizer10. Francois et al. suggest that patterning can be explained by a different reaction–diffusion model. Their underlying assumptions11, however, do not reflect the known network topology12, and the resulting profiles are inconsistent with the system properties. Hence, we do not find their model to be a valid alternative.