An Elasto-Plastic Model of Avian Gastrulation #1

An Elasto-Plastic Model of Avian Gastrulation

Vincent Fleury

Organogenesis 2:1, 6-16, January/February/March 2005

The motions observed during avian gastrulation may be simply interpreted in terms of elasto-plastic flow of sheets. Such a model allows one to calculate the flow map inside the blastodisc, hence the evolution of its shape. In addition, the model predicts that there exists a region of high stress oriented radially from the caudal pole towards the center of the blastodisc, with a tensile component oriented orthoradially. If the stress generated by cellular motion is enough to provoke a crack in the extra cellular matrix, then mesoderm ingression proceeds through a “streak” (the primitive streak) oriented from the caudal pole inwards, which relieves the stress while it creates the three germ layers. The model predicts that crack opening is next followed by crack retreat (primitive streak retreat), as mesoderm ingression continues. As mesoderm ingression proceeds around the area pellucida, similar phenomena in the anterior pole may contribute to formation of the embryo. This gives a mechanical description of avian gastrulation which complements the biochemical approach. In addition, the model provides a simple explanation to the shape of the embryo at very early stages, and possibly an explanation of the entry point of the vitteline arteries into the mesoderm.

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As the paper is freely available from Organogenesis, I’ll assume that the pdf is on your desktop¹ and thus limit quotes at minima.

It’s time to have a closer look at this paper about which Fleury made such a fuzz and often cited as a peer-reviewed part of his theory. Peer-reviewed it is, certainly, and Jamie Davies assured me that it was reviewed properly. But I will focus on a first time to the fact that it presents a set of hypotheses that require experimental validation prior to any use as a support to any theory. Recently, Fleury asserted that there are only two hypotheses:

Especially the article which you discuss with Prof. Davies contains only two true hypothesis, namely

first : that the blastula is much wider than thick, a fact well established (the “sheets” of the blastula being about a hundred times wider than thick,).

The second hypothesis is that there exists a contraction area in the shape of a crescent or sickle. I, of course, did not invent out of nothing the existence of this. It is the well known Koller-Rauber sickle. These are the only hypothesis of the model, and they are based on wet biology, as you say.

The use of the word hypothesis to describe facts, the ratio of dimensions of the blastodisk and the Kohler’s sickle, a well distinguishable feature, is absolutely inappropriate. And it cast shadow to the set of assumptions that need to be supported by data before the proposed model could be considered as validated. Some of them it may be easy to prove correct, others certainly need sophisticated experimental settings to be tested and probably a few ones are in contradiction with already available data.

When I first read it (Jan 2007) I found it interesting as a description of cell movements during gastrulation and commented that with some more work to connect it to the cells’ properties it could evolve to something much more interesting. The reaction wasn’t what I would call friendly and the exchanges rapidly diverged toward general considerations on the role of genes and their products, chemical organizers and genetic determinism; the paper pes se was set aside and I didn’t gave it more attention, as Fleury had posted a lot of supplementary material in his website.

Following Davies e-mail contact, I read it again, this time more critically, with the main intend to evaluate not the mathematical part of the model but the premises upon which it is built. Mathematical models must be tightly connected to physical reality to present some interest.

The very first thing that came up is the description of gastrulation (p6, §2):

It requires a huge cellular motion which has the shape of two vortices converging towards the posterior pole an along the antero-posterior (AP) axis

So, the model is based on the presence of two vortices, schematically presented at fig 2. Later, Fleury presented us four vortices, each causing the budding necessary to form a limb. But this late hypothesis, implicating four vortices, isn’t presented in this paper. I haven’t see it in another of Fleury’s papers; so it goes as unpublished, not yet peer-reviewed, as well as unsupported by data.

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1 – The pdf is « copy/paste » and « print » protected. MacUsers may find convenient to display it using Skim, a handy freeware fro displaying and annotating pdf files, which bypass both limitations; Select and -N to transfert in a new annotation box, then -C. -P is direct.