Fig 1.
Multiple evolutionary origins of supplemental vascular bundles in stems and roots.
(A) Turnip [Brassica rapa rapa (Brassicaceae)] tuberous root cross section. Small dots in the center of the section are vascular bundles in a zone where parenchyma cells are proliferating (PP). (B) Close-up of vascular bundle in turnip root tuber. A small zone of xylem (X) encircles crushed internal phloem (P) in the amphivasal bundle arrangement. (C) Older medullary SVB (i.e., SVB in pith) from stem of Pachypodium namaquanum (Apocynaceae) with two zones of xylem and a zone of phloem interior to the xylem. (D) Close-up of an old medullary SVB from the trunk of Trichocereus chilensis (Cactaceae) showing a long tail of xylem and phloem that is capped with crushed secondary phloem (dark band). (E) Cross section of young stem just below the shoot apical meristem of Subpilocereus ottoni (Cactaceae) showing the distribution of five medullary SVBs (arrows). (F) Old collateral vascular bundle from root tuber of Adenia inermis (Passifloraceae). (G) Large (note scale) collateral medullary SVBs from stem of Adenia metamorpha. (H) Old collateral medullary SVB from stem of Adenia keramanthus. (I) Cross section through tuberous root of Ipomoea batatas (Convolvulaceae). Dark spots in the center of the root are zones of proliferating parenchyma and vascular bundles. Taxonomic orders (numbered blocks) 1 –Brassicales; 2 –Caryophyllales; 3 –Gentianales; 4 –Malpighiales; 5 –Solanales. Scale: (A), (J)– 10mm; (B)-(H)– 250 μm. (C) adapted from [29] with permission; (D), (E) adapted from [32] with permission.
Fig 2.
Spatial context of the reaction-diffusion model in 2D with molecules H, B, and M.
(A) H (regulatory molecule responsible for vascular development initiation) and B (a substrate of H) are constitutively produced everywhere, whereas production of an inhibitory molecule, M, is restricted to the cortex in this model. M diffuses (arrows) from regions ‘A’ (cortex) into ‘B’ and suppresses SVB development by reducing the level of H. Upon release of suppression in region ‘C’ (medulla or pith), H, in concert with B, promotes differentiation of SVBs (black spots). (B) Cross section through a wide kohlrabi (Brassica oleracea gongylodes) stem provides an example that follows the ‘A’ ‘B’ ‘C’ zonation and SVB patterning of (A). Inset shows close-up of two SVBs. Stem diameter is ~6.5 cm. Stem regions ‘A’ = cortex, ‘B’ = stem region with no SVBs next to vascular cambium (inner black circle), ‘C’ = pith stem region with SVBs.
Table 1.
Chemical reactions.
Fig 3.
Model development and simulation results.
This figure illustrates results of simulations from the two-molecule HB model through to the four-molecule HBPM model. The text guides through the incremental addition of molecules to the model. S1 and S2 Tables and S1 through S19 Movies provide simulation parameters and visualizations, respectively. (A) The two-molecule (HB) model in 3D. Under appropriate parameterizations (S1 Model provides parameter values and simulates the HB model when run by the program Ready v. 0.8), the Gray-Scott-Schnakenberg model produces a network of vessels with high [H], but longitudinally-oriented vessels are largely absent. The color image represents a cross-section with color intensities scaled between least (0.000) and maximal (1.00) concentrations. (B)-(V) Black circles represent edges of the stems, and black lines across circular cross sections show where longitudinal sections were made in 3D models. Color bars show concentrations (in numbers of molecules per voxel) with the maximum concentration value shown ranging down to 0 at the bottom of the color bar. White color is background color, representing the absence of molecules. (B)-(D) The HBP model with a longitudinal flux transporter, P, results in spots of high [H] in cross section and longitudinally-oriented cylinders of high [H] in longitudinal section, akin to plant stem vessels. (E)-(L) HBPM model showing suppressive effects of M on the spatial distribution of supplemental vascular bundles. Production of M at the periphery of the stem restricts the SVBs to the central region of the stems. (E)-(F) High M production, high rate of M diffusion. (G)-(H) High M production, low rate of M diffusion. (I)-(J) Low M production, high rate of M diffusion. (K)-(L) Low M production, low rate of M diffusion. Panels (M)-(T) display [H]. (M)-(O) Gain and loss of SVBs with changes in stem size. (M) Large diameter stem. (N) Medium diameter stem is 75% of the diameter of the large diameter. (O) Small diameter stem is 37% of the diameter of the large stem. M suppresses vascular bundle formation in the narrowest stem. (P)-(V) Simulation results that resemble stelar patterning in plants. The HBPM model was used and simulated [H] is shown in the figures. (P) Eustele pattern. (Q) Eustele pattern with SVB patterns internally. (R)-(S) Siphonostele pattern with SVB patterns internally. (T) Haplostele pattern. (U)-(V) Monocot stem patterning. Atactostele vessel patterning similar to those of monocots, such as Zea mays, in (U), illustrating a uniform ring of bundles at the stem periphery and scattered bundles in the stem center. (W)-(X) Lycopod stem patterning. (W) Lycopodium scariosum stem in cross section illustrating a plectostele. (X) 2D deterministic simulation of the Gray-Scott model recreating the plectostele pattern. S2 Model file provides a plectostele model file which runs in the program Ready v. 0.5. Panel (W) adapted from [46].
Fig 4.
Parameter symbols are as in the Table 1. Dark lines with circle end points indicate suppression in the direction of the circle. Arrowed lines indicate activation in the direction of the arrow. Arrows with only one connected end represent constitutive or background production (arrow pointing to box) or degradation (arrow pointing away from box). Squiggly arrows represent diffusion. Some simulations also included mutual inhibition between M and B, but this was removed in later simulations.
Fig 5.
Density and size of supplemental vascular bundles varies with diffusion rates of H and B.
(A) [H] for various diffusion rates of H (y-axis) and ratio of diffusion rates of B and H (DB/DH) (x-axis). Legend shows mapping between [H] and color (Black represents no molecules). (B) Diameter of regions of high [H] (>400 molecules per voxel) as a function of DB/DH. (C) Number of regions of high [H] as a function of DB/DH. Legends for (B) and (C) show color coding for diffusion rates of H. Note that x-axes are not to scale in (B) and (C). Box plots are based on 3 simulation replicates of each parameter combination. S10 and S11 Movies provide example animations of H diffusion rate at 0.05 and ratios at 10 and 1000, respectively.
Fig 6.
Evolutionary-developmental model of stem vasculature.
When seen in the context of the entire plant stem, the HBPM model (Fig 4, Table 1) accounts for much variation in plant stem vascular structure. In each panel of the figure, the top represents the shoot apex, followed by a cross section with the primary state of growth (compare to Fig 3P), followed by a cross section of the mature stem. (A) Monocot stem vascular patterning as seen in corn or bamboo (compare to Fig 3V). (B) Woody plant with primary vascular bundles that merge and develop into the vascular cambium which produces lignified xylem (black sectors). Reduced axial parenchyma and pith may impose limits the production of SVBs although these are occasionally found in pith of woody plants [27]. (C) An herbaceous eudicot maintains the primary state of growth with limited cambial development and limited increase in stem girth. Narrow stems restrict the production of SVBs (compare to Fig 3O and 3P). (D) A stem-succulent plant with extensive parenchymatous wood. The primary vasculature transitions into a secondary vascular cambium that produces parenchyma primarily. H and B interact in wide zones of parenchyma to produce SVBs in the stem centers away from the suppressive effects of M (compare to Fig 2B and Fig 4Q–4S).