Abstract
We explore the possible role of elastic mismatch between epidermis and mesophyll as a driving force for the development of leaf venation. The current prevalent ‘canalization’ hypothesis for the formation of veins claims that the transport of the hormone auxin out of the leaves triggers cell differentiation to form veins. Although there is evidence that auxin plays a fundamental role in vein formation, the simple canalization mechanism may not be enough to explain some features observed in the vascular system of leaves, in particular, the abundance of vein loops. We present a model based on the existence of mechanical instabilities that leads very naturally to hierarchical patterns with a large number of closed loops. When applied to the structure of high-order veins, the numerical results show the same qualitative features as actual venation patterns and, furthermore, have the same statistical properties. We argue that the agreement between actual and simulated patterns provides strong evidence for the role of mechanical effects on venation development.
Highlights
IntroductionVenation patterns are different from one leaf to another, even in the same plant, but share some common features that are preserved throughout all angiosperm leaves [1]
For many years leaf venation motifs have marveled people, whether scientists or not
A second, very robust, feature of the venation pattern is the abundance of closed loops: the leaf surface is divided into small polygonal sectors by the venation array; only the fine veins of the highest orders do not connect at both ends and are often open ended
Summary
Venation patterns are different from one leaf to another, even in the same plant, but share some common features that are preserved throughout all angiosperm leaves [1]. A second, very robust, feature of the venation pattern is the abundance of closed loops: the leaf surface is divided into small polygonal sectors by the venation array; only the fine veins of the highest orders do not connect at both ends and are often open ended (see Figure 1). The straightforward optimization of steady state irrigation within the leaf must lead to tree-like open topologies [4,5] with strictly no loops [6]. It has been suggested that venation may play a mechanical stabilization role for the leaf, but the optimization of the mechanical stabilization leads to very unnatural venation geometries [5]
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