# Limitations of the study

Despite various evidences of the role of MMP3 and Noggin2 in volume-sensing and scaling effects in early *Xenopus* development, there could still exists another factors, which play similar role or interfere with ones described in this study. **Firstly**, the described effect of Mmp3 on the Tolloid activity against Chordin is obligatory supplemented with analogous effect of Sizzled protein, which was also shown to participate in volume-sensing. As a result, our mechanism of somite size determination cannot predict effects that works through Sizzled protein. **Secondly**, dependency between free BMP local concentration and the amount of phosphorilated SMAD was taken as arbitrary non-linear and does not reflect any real process. At the same time, lower pSMAD threshold determining notochord border is very low. Indeed, dorsal part of pSMAD gradient lays close to zero and, probably, cannot be properly visualized by antibody staining. Further quantitative studies on SMAD1 signalling can ensure or modify the proposed mechanism.

**Thirdly**, starting period of the studied process is under high influence of early inductors Fgf, Nodal et cetera. We took it into account only as an integral effect (and named it Early Notochord Activating Factors, ENAF), but its influence to scaling evidently requires further investigation. **Finally**, effects of different protein factors and developing cells on each other forms complicated and highly redundant regulatory network, which should be investigated at system level. The level of our study is lower and the observed mechanism could be a projection of more complicated process occuring in this network to few highlighted actors.

## v2

**Limitations of the study**

We may indicate the following main limitations of our study. **Firstly**, when modeling the role of Mmp3 as a scaler in the regulation of BMP gradient, we did not considered other scalers, like Sizzled, for example, which also adjust BMP gradient in a size-dependent manner. We also did not include in the model many other known factors regulating formation of BMP gradient. Therefore, one may consider our model only as a very simplified version of a highly complex real network of interactions responsible for the formation of BMP gradient and its scaling. **Secondly**, we considered the dependency between free BMP local concentration and the phosphorylated pSmad1 as arbitrary non-linear. This does not reflect the natural process properly. **Thirdly**, we revealed that the dorsal sector of MZ free of pSmad1 nuclear staining is progressively expanded ventrally during gastrulation. *Our mechanism suggest that low-level pSmad1 gradient in this sector affects notochord size, however we could not visualize this "hidden" gradient by the antibody staining method. While such an invisible part of pSmad1 gradient cannot compromise our conclusions on somitic mesoderm scaling, its detailed visualization by more sensitive methods should help in clarification of our proposed mechanism of notochord size determination.* **Finally**, many intracellular and extracellular factors, besides extracellular BMP inhibitors, operating before and just after the beginning of gastrulation regulate DV patterning. For simplicity, we considered their influence only as an integral effect, named Early Notochord Activating Factors, ENAF. Further investigation of the individual impact of each of these factors upon DV patterning is required.

## removed

> morphogenetic movements ignored in our considerations could strongly affect a delivery of proteins from one cells to another. It can be more pronounced for notochord formation process as it is subjected to huge convergent extension during the considered stages (10.5 -- 15).