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Steric Constraints as a Global Regulation of Growing Leaf Shape

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 [1], physicists, following Turing [2] and d'Arcy Thomson [3], have developed theories where patterns arise spontaneously [4]. Here, we propose a volume constraint that restricts the possible shapes of leaves. Focusing on palmate leaves, the central observation is that developing leaves first grow folded inside a bud, limited by the previous and subsequent leaves. We show that growing folded in this small volume controls globally the leaf development. 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. This steric constraint is a simple way to impose a global regulation for the leaf growth. Such steric regulation should be more general and considered as a new simple means of global regulation.