Response to the reviewer.
We thank the reviewer for the constructive comments which have helped us to considerably improve
the quality of the manuscript.
We have largely rewritten the article, modified the plates, added numerous experimental data, in
response to many if not all reviewer’s criticism.

We have added several lines and references about existing work on visco-elastic flows in
embryos, including in the drosophila model, as suggested by the reviewer.

About the experiments consisting in relaxing the stretch in the vitelline membrane.
a-The reviewer criticized that we did not prove that there was tension in the vitelline membrane inovo, and also that we did not give the images of the embryos prior to relaxing the stretch. We have
therefore gathered new data, taking pictures before and after removing the stretch. This gives an
entirely new plate (Fig. 10(A)),much improved compared to its previous version.
b-The fact that the vitelline membrane is in a state of tension is actually known. We have quoted a
few references, and also have given an estimate of the tension, as deduced from analyzing the shape
of the yolk.

About the visco-elastic nature of the tissue.
The reviewer commented that we discuss at some points elastic issues, while at others we
mention viscous flows. We have clarified this point. The tissue is visco-elastic, and behaves
like a viscous fluid on time scales >10 minutes. The elastic experiments are performed at
short time scales, while the development is a long process on time scales of hours. We can
actually measure the viscous decay by recording the force in the stretch bench, after a
stepwise elongation. This shows that the embryo behaves like a classical visco-elastic
material. We present such data in the Supp. Material. We actually have many more now and
plan to publish another article in the future on this issue. However since the visco-elastic
behaviour of the tissue in embryos has already been discussed in the litterature (we give a
reference) we mention these issues in the text but shifted the data to Supp. Material. The
rationale of the morphogenetic process is that elastic deformations are converted to
irreversible deformations by viscous dissipation. Anecdotally, it is a well-known fact in
embryology that when embryos die during development, they tend to relax the forces, which
“looks like” a winding back of the developmental process (example : if the embryo dies while
the neural folds are closing, they will reopen).

About the coupling between cell size and differentiation.
Actually there exist entire databases in which it is easy to pick up genetic markers which
overlap the pattern of cell sizes (especially Cadherins) described in our manuscript. We have
submitted elsewhere an article on the molecular aspects. We give to the reviewer the
manuscript of this article. In the manuscript we quote the data base Geisha, and we give
examples in Supp. Material. Due to the collaborative aspect of this work with biologists, we
have to split the physics work and the molecular work.

About the boundaries between domains having different cell sizes and position of the folds
The reviewer was right in observing that we did not give clear examples of cell boundaries
during the experiments, showing that the embryo was folding exactly there. This is why we
have collected new data, where cells are as resolved as possible. We give cell-resolved
images of the spontaneously relaxed embryos, and of the compressed embryos, in which the
boundaries are resolved. The folds are seen to form exactly at the boundaries. We give also a
closer view of the boundary in the physiological case showing that the fold forms again
exactly at the boundary. We kindly inform the reviewer that it is very difficult to obtain such
images. Since the embryo is not strictly flat, high definition photos can hardly be in focus in
all the field of view, when observing embryos in a physiological position, especially at a
moment when they are folded (observing a sharp image, of a 3D fold is a contradictory
demand). We believe that such image as the following show very clearly the position of the
folds (here in the physiological case):

About the smoothness of the boundary.
This question is indeed an important one. We generated new pictures of the embryos, trying
to image exactly the boundary, at cell resolved resolution. Our best shot is given in the
paper. We were able to analyze the medium-sized cells/large-sized cells boundary, which
shows a smooth variation across a boundary about 10 cell diameter wide. However, while we
have clear evidence that the small cell/medium cells is very sharp, we do not give an actual
quantitative form of the variation, because we found the cells too small and the boundary
too narrow to extract a clear gradient of cell size across this boundary.
It is clear that this issue is important, esp. considering a possible feedback between folding
and sharpening of the boundary: a smooth boundary might be sufficient to localize the fold,
and in return, it is likely that the fold itself helps to sharpen the territories. We have
qualitative evidence that this is the case, but we shall investigate this question deeper in the
future.

About the physics of buckling and the locking of folds at boundaries of elastic constrasts.
We have modified the text in response to this comment. Especially, we have generated soft
elastic foils having a well-defined area of stiffer material. This is prepared in the following
way: silion elastomer is spread on a rubber foil by flattening (using a classical property of
stability of the interface of viscous flows in thin Hele-Shaw cells).
This simple experiment shows generically the phenomenon of locking of folds at the
boundary of elastic contrast. It even very distinctly evokes the shape of the neural folds
propagating in the posterior area of actual embryos.
In the rest of article, many small modifications have been brought here and there, both in
the text and in the figures. Scale bars have been added, figures have been cropped etc. There
was also a scale error in one figure due to an error on the size of the CCD captor in a camera
which has been corrected.
We downplayed several overstatements, especially the statements in the conclusion
regarding the mechanism of formation of the vertebrate body plan and the statement
regarding the analysis of the movement of the mesoderm (proportionality between the
observed pattern of movement and the traction force field).
Due to the deadline of two months (one being August), we acknowledge that some of the
new data may look crude. For example, It would be interesting to study in greater detail the
tension in the vitelline membrane by the sessile drop method, by fitting Worthington’s
formula over, say, a hundred embryos, instead of four, as done here. However, we believe
that the core of the article does not depend on such a precise determination, and that we
may leave such a precise measurement for future work. In the same spirit, the elastic foil+
silicon patterns, which we suggest as models of embryo buckling, may deserve a work of
their own, but the result is so demonstrative that we believe this can be left for an
independent study.
We insist that most movies and images in this article are HD (1600x1200) movies, which
actually often have cell resolution in full scale. We give in the Supp. Material part one image
of cell domains in full scale at magnification 10X.
We believe the article has much improved, especially on the most important points raised by
the reviewer, which, we believe, we have addressed by working harder on collecting new and
better data, rather than waving hands; this was done in a very short time.
We feel it worth insisting that the images presented here were done on a classical
microscope, with classical white light and optics, and the results can be reproduced by
anyone at moderate cost. Sample preparation in embryology is often an important and
tedious issue, and we managed to produce cell resolved time-lapse movies of many
important steps in the developmental process of amniotes by our method, which, we
believe, clarify the early steps of the development, and improves the understanding of the
relationship between cell differentiation and biomechanical morphogenesis.
The reviewer seemed convinced that this work is original and interesting; we feel that, by
seriously addressing the main points raised by the reviewer, the manuscript quality has
dramatically improved. We respectfully acknowledge the reviewer’s valuable and
constructive help.
With our best regards,
V. Fleury