title: A global regulation inducing the shape of growing folded leaves.
abstract: 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 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 independent of their position in the phylogenetic tree, these relationships work for folded species, but do not work for non-folded species. This global regulation for the leaf growth could come from a mechanical steric constraint. Such steric regulation should be more general and considered as a new simple means of global regulation.
authors: Laboratoire MSC, Matière et Systèmes Complexes, UMR 7057, CNRS & Université Paris-Diderot, Paris, France.
authors: Etienne
authors: E
authors: Couturier
authors: Sylvain
authors: S
authors: Courrech du Pont
authors: Stéphane
authors: S
authors: Douady
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D018506:Gene Expression Regulation, Plant; D017343:Genes, Plant; D008855:Microscopy, Electron, Scanning / Q000379:methods; D008954:Models, Biological; D008962:Models, Theoretical; D010802:Phylogeny; D018515:Plant Leaves / Q000502:physiology*; D018521:Plant Physiological Phenomena; D010944:Plants / Q000378:metabolism; D012984:Software