Abstract
Growth and cellular organization of the Arabidopsis root apex are investigated in various aspects, but still little is known about spatial and directional variation of growth rates in very apical part of the apex, especially in 3D. The present paper aims to fill this gap with the aid of a computer modelling based on the growth tensor method. The root apex with a typical shape and cellular pattern is considered. Previously, on the basis of two types of empirical data: the published velocity profile along the root axis and dimensions of cell packets formed in the lateral part of the root cap, the displacement velocity field for the root apex was determined. Here this field is adopted to calculate the linear growth rate in different points and directions. The results are interpreted taking principal growth directions into account. The root apex manifests a significant anisotropy of the linear growth rate. The directional preferences depend on a position within the root apex. In the root proper the rate in the periclinal direction predominates everywhere, while in the root cap the predominating direction varies with distance from the quiescent centre. The rhizodermis is distinguished from the neighbouring tissues (cortex, root cap) by relatively high contribution of the growth rate in the anticlinal direction. The degree of growth anisotropy calculated for planes defined by principal growth directions and exemplary cell walls may be as high as 25. The changes in the growth rate variation are modelled.
Highlights
The symplastic growth, typical for plant tissue, means the coordinated growth of cells during which mutual contacts between neighbouring cells are preserved [1,2]
The map of linear growth rates for the Arabidopsis root apex is shown in Figure 4 and Movie S1
A significant anisotropy of growth rate occurs in the apical part of the root The variation of growth rates in the apical region of Arabidopsis root has been modelled assuming the displacement velocity field, determined previously [28]
Summary
The symplastic growth, typical for plant tissue, means the coordinated growth of cells during which mutual contacts between neighbouring cells are preserved [1,2]. A measure of growth at a point is the relative elemental rate of the linear growth, Rl [6,7], The Rl for the direction es is defined by the equation [5]: Rl(s) = (gradV⋅es)⋅es where es is the unit vector of the direction and each dot means a scalar product. As this quantity may change with a direction [5,8], values of Rl at a point obtained for many es are arranged into the 3D surface (Figure 1), called indicatrix [9,10]. They are plotted using the rule that positive Rl is for enlargement, whereas negative (green in Figure 1D) - for contraction [5,8]
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