Maps of R_l indicatrices obtained for V field with modified values of the parameters c (B, C) and d (D, E); the map (A) corresponding to Figure 4 is a reference.

<p>The change in c leads to decrease (B) and increase (C) of R_l in zones 2 and 4 whereas the rates in zone 3 remain unchanged. In turn, the change in d leads to decrease (D) and increase (E) of R_l in zones 3 and 4 whereas the rates in zone 2 remain unchanged. The indicatrices indicated by circles are considered in the text.</p

Spatial and Directional Variation of Growth Rates in <i>Arabidopsis</i> Root Apex: A Modelling Study

<div><p>Growth and cellular organization of the <i>Arabidopsis</i> 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. </p> </div

Anisotropy of growth rate in exemplary cell walls (red in the cell pattern), which are oblique with respect to PDGs.

<p>In every case, R_l indicatrices and their intersections by two planes: one representing the wall (red) and the other, defined by G_a and G_l (yellow), are shown. Both intersections are symmetrical with respect to these directions. The values of DGA calculated as the ratio of R_l in G_a to R_l in G_l (i.e. as in Fig. 5C) for yellow and red plots, respectively, are the following: (A) 0.92 and 2.06, (B) 1.56 and 1.62, (C) 0.44 and 0.52.</p

Anisotropy of growth rates in <i>Arabidopsis</i> root apex obtained for V field from Figure 3.

<p>The 3D plots show R_l indicatrices; those drawn in red are for initial cells (see Fig.2). In the indicatrix labelled by circle maximal R_l is about 8.2% h^-1. The green plots represent negative values of the rate.</p

Anisotropy of growth rates in the planes defined by pairs of PDGs, visualized by the degree of growth anisotropy (DGA); the inserts show orientation of the considered planes.

<p>(A) DGA given by the ratio of R_l in G_p to R_l in G_a; (B) DGA given by the ratio of R_l in G_p to R_l in G_l, (C) DGA given by the ratio of R_l in G_a to R_l in G_l. The DGA values are attributed to cells from Figure 2 using color-coding, the negative ones (dark green) result from compression in G_a. For the cells localized in QC (white), the DGA has not been computed.</p

The maps of Rl indicatrices as in Figure 7 but obtained assuming modification of the proximal border of the quiescent centre (zone 1) and the central part of the root cap (zone 3); the indicatrices drawn in red are for initials from Figure 2: (A) the reference map corresponding to Figure 4 where the border is represented by the line u0=0.35; (B, C) as in (A) but for u0=0.30 and u0=0.40, respectively; (D) the border drawn on the basis of cell pattern in Figure 2; (E) as in (D) but the velocity V=0.01 m min-1 at the whole QC border is assumed.

<p>The maps of Rl indicatrices as in Figure 7 but obtained assuming modification of the proximal border of the quiescent centre (zone 1) and the central part of the root cap (zone 3); the indicatrices drawn in red are for initials from Figure 2: (A) the reference map corresponding to Figure 4 where the border is represented by the line u0=0.35; (B, C) as in (A) but for u0=0.30 and u0=0.40, respectively; (D) the border drawn on the basis of cell pattern in Figure 2; (E) as in (D) but the velocity V=0.01 m min-1 at the whole QC border is assumed.</p

The R_l indicatrices representing various growth at a point: isotropic (A) and anisotropic (B-D): (B) symmetry with respect to <i>y</i>, i.e. the R_l along each direction in <i>xz</i> plane is the same, (C) pure elongation along <i>z</i>, i.e. there is no growth in <i>xy</i> plane, (D) elongation along <i>z</i> with contraction (green) along <i>x</i>.

<p>The scheme on the left shows deformation of the exemplary cell resulting from each growth. In every case R_l in a considered direction is proportional to the distance from the calculation point to the indicatrix surface along this direction; the growth rate along <i>z</i> axis is always the same.</p

The <i>Arabidopsis</i> root apex (longitudinal section adopted from Van der Berg et al. 1998) with the root-natural coordinate system, R-NC (<i>u</i>,<i>v</i>,φ) for φ <i>=const</i>., applied to it.

<p>The exemplary initial cells (red) and two of three principal growth directions (G_a, G_p) are indicated; the insert shows all three PDGs in 3D. The <i>u</i> and <i>v</i> lines (thin blue) represent PDG trajectories, two of them <i>u</i>₀ and <i>v</i>₀ turning into -v_<i>0</i> (thick blue), divide the apex into four zones corresponding to: 1, 2 -the root proper without epidermis, 3, 4- the root cap with epidermis, the zone 1 represents QC. Bar = 20 µm .</p

Echos transport / Air France, Direction du transport

19831983 (N24)