Canalization-based vein formation in a growing leaf

Vein formation is an important process in plant leaf development. The phytohormone auxin is known as the most important molecule for the control of venation patterning; and the canalization model, in which cells experiencing higher auxin flux differentiate into specific cells for auxin transportation, is widely accepted. To date, several mathematical models based on the canalization hypothesis have been proposed that have succeeded in reproducing vein patterns similar to those observed in actual leaves. However, most previous studies focused on patterning in fixed domains, and, in a few exceptional studies, limited tissue growth – such as cell proliferation at leaf margins and small deformations without large changes in cell number – were dealt with. Considering that, in actual leaf development, venation patterning occurs in an exponentially growing tissue, whether the canalization hypothesis still applies is an important issue to be addressed. In this study, I first show through a pilot simulation that the coupling of chemical dynamics for canalization and tissue growth as independent models cannot reproduce normal venation patterning. I then examine conditions sufficient for achieving normal patterning in a growing leaf by introducing various constraints on chemical dynamics, tissue growth, and cell mechanics; in doing so, I found that auxin flux- or differentiation-dependent modification of the cell cycle and elasticity of cell edges are essential. The predictions given by my simulation study will serve as guideposts in experiments aimed at finding the key factors for achieving normal venation patterning in developing plant leaves.