geometry

I’m greek and during my young years I was feed a lot of geometry. You know how it is, national pride for the ancestors, especially under a military junta. So, I’m quite sensible when one presents geometrical problems incorrectly.

My very first objection concerning Fleury’s model1 was that he described the epiblast cells as contained between two extracellular membranes. When I pointed that his only response was that if there is a single basal membrane that doesn’t affect his model, the flow would be just faster. From that point on you can’t trust the guy with any description.

Assuming, once more for argument’s sake, that there would be four vortices on the center of which the limb fields develop, could that explain, as Fleury presents the flexion of the limbs ? I asked one question which is still unanswered by Fleury more than ten days later.

His description doesn’t fit with his description. We have here an inner contradiction of his model that gone under his radar. The limbs growth doesn’t follow the vortices flow. That’s sad, but it’s not the worse part of it. Let’s add an new-dimension.

Fleury so much like to consider embryos as rather flat entities that he forgotten the third dimension. Not completely. In Fig 37, panel a, he present us a stage 4 embryo of Eleutherodactylus coqui, with a personal annotation showing the vortices:

mfig1.jpg

On the left the original from Richardson MK et al.2 paper, on the right Fleury’s interpretation of the positioning of the vortices. As we have see, when it come to limbs flexion, this third dimension vanish and the schemas of fig. 38 are flat.

The growth of the limb bud is orthogonal to the plane of the vortex, let’s represent it as below:

1.jpg

the vortex in yellow, rotating clockwise and the bud growing upwards.

When it come to define the flexion at the junction between the stylo- and zeugo-pode what would be the mechanical mechanism that would instruct a particular direction for the bending ? I represented below the development of the limb with the stylopode in blue, the zeugopode in green and the articulation (elbow or knee) as a pale blue sphere. (four directions in color, plus four as gray ghosts, and infinity of case not represented)

noinstruction.jpg

None presented, despite the role Fleury attribute to limbs flexion.

Let’s see what that would give us if we try to map it to the four vortices model:

withorthogonal.jpg

(here the vortices are in red to improve visibility) The AnteroPosterior and DorsoVentral directions are annotated, along with the cartesian (orthogonal) coordinates system. The latter is just represented to show how much inappropriate it may be to confound the embryos axes to it.

There is no relation between the vortices and the limbs flexion, limbs proximodistal axes being parallel between them and to the Z axis.
The real stuff in almost the same orientation as the above schema:

RS.jpg

with the direction of growth of the limbs in white (insert, original).


Both papers freely available
1. An Elasto-Plastic Model of Avian Gastrulation, Vincent Fleury, Organogenesis 2:1, 6-16, 2005
2. Limb development and evolution: a frog embryo with no apical ectodermal ridge (AER), Richardson MK, Carl TF, Hanken J, Elinson RP, Cope C, Bagley P. J Anat. 1998 Apr;192 ( Pt 3):379-90, doi: 10.1046/j.1469-7580.1998.19230379.x.

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4 Responses

  1. [...] les plus consultés 4 The paleontological point of view geometrythe WTF factorQuestionOops 090617Quite [...]

  2. [...] Allons, allons, Fleury lui même soutient l’imagination des artistes, enfin, au moins quand ça l’arrange et ça ne l’arrange pas toujours. On constate ? Comme quand Rosetta-Man tire des conclusions à partir de données inexistantes ? Ou nous donne son interprétation fantaisiste de ses lectures ? Ca c’est de la Science-Fiction (et de la Géometrie-Fiction) [...]

  3. [...] know that Fleury have real difficulties dealing with more than two dimensions at a time and connecting dot. He also have tremendous difficulties when it comes to know where the lateral [...]

  4. [...] quelqu’un de si calé en embryologie/anatomie/développement ce n’est pas de chance ! Je sais qu’il a des problèmes avec la géométrie, mais il aurait dû se rendre compte qu’il parlait des nageoires dorsale et ventrales de la [...]

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