MODELING OF MERISTEMATIC GROWTH OF ROOT APICES IN A NATURAL COORDINATE SYSTEM

A curvilinear, orthogonal coordinate system, which resembles the pattern of periclines and anticlines in the cellular network of root apices, is presented. The system makes possible an analysis of the dynamics of apical growth: the relationship between growth rates and tensile stresses in cell walls. In this paper the coordinate system is used in modeling the growth and cell partitioning in the apical domes. The symplastic growth is described by means of the growth tensor which is assumed to have diagonal form in the system, so its coordinate lines represent the principal directions of growth rate. The coordinate system and the growth tensor in diagonal form assure temporal stability of form and cellular structure of the modeled apex including transition from the dome to the cylindrical part of the apex. The spatial and temporal aspects of the dome part of two types of root apices—one with maximum of volumetric relative growth rate at the center region of the apex, and another with minimum of the rate (quiescent center)—are described. The maximum of the rate at the center results in the cellular pattern with an apical cell and merophytes, the minimum results in ribs of cells (inside the root proper) converging toward the quiescent center.