Mathematical modeling for morphogenesis of leaf with employing cell automata and reaction-diffusion equation

The phenome analysis is used for an elucidation of the leaf morphogenesis. However, it is difficult to identify a complicated biochemical system which exists between genome and phenome. Designing a mathematical model for the morphogenesis has a possibility to infer the complicated system by using the observed data on phenome analysis. We attempted to design a novel mathematical model in order to analyze the effects of the interaction between the expansion of leaf blade and elongation of leaf venation in the development of leaf shape, and discussed an availability of the proposed model on the numerical analysis of development of leaf. The expansion of leaf blade and the elongation of leaf venation were designed by employing the reaction-diffusion equation and cellular automata (CA) theory, respectively. As for the numerical simulation for development of gingko's leaf primordium, the proposed model could realize several well-known biological findings such as a reconnection of leaf venation. Moreover, the numerical analysis demonstrated that the interaction between the elongation of leaf venation and the expansion of leaf blade was indispensable for the complicated pattern formation of leaf venation. These results agreed with biological findings, which implied that the proposed model was useful for elucidating a development of leaf.