Generating venation of plants is an intriguing pattern formation in biological systems. Three hypotheses have been proposed to explain the venation pattern formation: auxin canalization hypothesis, activator-inhibitor-type reaction-diffusion hypothesis, and substrate-depletion-type reaction-diffusion hypothesis which is recently proposed by S. Tohya and A.M. The first hypothesis is based on the assumption of the positive feedback regulation between auxin flux and localization of PIN1 auxin efflux carrier on plasma membrane. Auxin is a diffusible plant hormone of small molecule and is thought to be important for vascular development. Here we investigated a model based on the assumption of this feedback regulation.
First, this model can generate auxin flow pathways with high density, so-called “polar auxin transport”, from almost uniform field. Using this feature we tried to generate various leaf venation patterns. Venation patterns largely depend on the shape of leaf area. For example, dicot pattern and Ginkgo pattern are generated from different diamond-shaped leaves. Place and direction of cell division also affects venation pattern crucially. In the case of cell division at apical leaf part, secondary veins elongate preferably toward apical side. In contrast cell division at basal part generates secondary veins that elongate toward basal side like Arabidopsis. Under the condition of cell division at the base of a leaf like monocots, parallel vein pattern is generated. Moreover, anisotropy of auxin diffusion has also large effect on pattern formation; veins tend to elongate along more diffusible direction. These results indicate that the positive feedback dynamics between auxin flow and PIN1 localization generates diverse venation patterns of plants depending on various conditions such as leaf shape, cell division and anisotropy.