The tensor-based model of plant growth applied to leaves of Arabidopsis thaliana: a two-dimensional computer model

Abstract

Plant organs grow in coordinated and continuous way. Such growth is of a tensor nature, hence there is an infinite number of different directions of growth rate in each point of the growing organ. Three mutually orthogonal directions of growth can be recognized in which growth achieves extreme values (principal directions of growth [PDGs]). Models based on the growth tensor have already been successfully applied to the root and shoot apex. This paper presents the 2D model of growth applied to the arabidopsis leaf. The model employs the growth tensor method with a non-stationary velocity field. The postulated velocity functions are confirmed by growth measurements with the aid of the replica method.

Keywords: Displacement velocity; EDD; Extreme directions of deformation; GT; Growth rate; Growth tensor; I(a); L-NCS; PDG; Principal directions of growth; R(a); area increment; areal growth rate; extreme directions of deformation; growth rate; leaf natural coordinate system; principal directions of growth.