Sommaire:

Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level, physicists, following Turing and d'Arcy Thomson, have developed theories where patterns arise spontaneously. Here, we propose that volume constraints restrict the possible shapes of leaves. Focusing on palmate leaves (with lobes), the central observation is that developing leaves first grow folded inside a bud, limited by the previous and subsequent leaves. We show that the lobe perimeters end at the border of this small volume. This induces a direct relationship between the way it was folded and the final unfolded shape of the leaf. These dependencies can be approximated as simple geometrical relationships that we confirm on both folded embryonic and unfolded mature leaves. We find that independently of their position in the phylogenetic tree, these relationships work for folded species, but do not work for non-folded species. We also realized observations and experiments to understand how leaves folds appear during the development and to understand the role of mechanical constrain inside the bud on the development of leaf shape.

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