Modeling leaf venation morphogenesis

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Abstract
We explore the possibility that the formation of leaf venation patterns is driven by mechanical instabilities in the growing leaf. In contrast to the prevalent canalization hypothesis based on polar auxin transport, mechanical instabilities lead very naturally to hierarchical patterns with an abundant number of closed loops as they exists in almost every leaf venation. We propose a continuum model where the vein formation is driven by a mechanical collapse of the mesophyll layer in the growing leaf, and present a numerical study of this model using a phase field approach. The results show the same qualitative features as real venation patterns and, furthermore, have the same statistical properties.

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