Laboratoire MSC, Matière et Systèmes Complexes, UMR 7057, CNRS & Université Paris-Diderot, Paris, France.
PLoS One. 2009 Nov 23;4(11):e7968. doi: 10.1371/journal.pone.0007968.
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.
形状是生物体内观察到的结构的重要特征之一。生物学家提出了形状在分子水平上受到控制的模型[1]，而物理学家则追随图灵[2]和达西·汤姆森[3]的脚步，提出了模式自发出现的理论[4]。在这里，我们提出体积限制限制了叶片可能的形状。以掌状叶（有裂片）为例，主要观察结果是，发育中的叶子首先在芽内折叠生长，受到前一片和后一片叶子的限制。我们表明，裂片的周长终止于这个小体积的边界。这就导致了叶子折叠的方式与其最终展开的形状之间存在直接关系。这些依赖性可以近似为简单的几何关系，我们在折叠的胚胎叶和展开的成熟叶上都进行了验证。我们发现，无论它们在系统发育树上的位置如何，这些关系都适用于折叠的物种，但不适用于不折叠的物种。这种对叶片生长的全局调控可能来自于机械空间限制。这种空间调节应该更普遍，并被视为一种新的简单的全局调节手段。
