Workshop on Pattern Formation and Functional Morphology, Wed, 09 Jan, 2008
Speaker: Nadya Mozorova
Abstract
To explain the diversity of plant forms, sizes, and lifetimes, we introduce a new model of plant growth based on simplified but realistic biological mechanisms. Growth of plants is described by means of a free boundary problem where the moving boundary corresponds to the apical meristem and depends upon the conducting of nutrients and metabolites from other plant tissues.
In the one-dimensional model the plant endogenous rhythms and the branching conditions are studied. The model includes four variables, corresponding to the main physiological factors of plant growth and development: concentrations of the plant hormones, regulation of cell cycle progression and the supplement of nutrients. Numerical simulations show a wide variety of plant forms for different values of parameters and allow us to study more specifically the involvement of the each variable in the branching process.
In the two-dimensional model, numerical simulations show the emergence of complex structures, reflecting the formation of plant tissue and organs. We discuss two types of growth in this model: the growth without differentiation (corresponding to
meristematic or tumor tissue) and the growth with differentiation (corresponding to tissue and organ formation). However, numerical realization of the 2D model encounters essential difficulties because the free boundary can have a complex form with singularities and points of self-intersection.
These models allow us to study a number of important biological questions such as appearance and formation of plant organs, apical domination and some others. On the other hand, there are many related mathematical and numerical questions including nonlinear dynamics, pattern formation and structural stability.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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