Orchestration of three transporters and distinct vascular structures in node for intervascular transfer of silicon in rice

Significance

Requirement of mineral elements differs with different organs and tissues; therefore, plants have developed systems for preferentially delivering mineral elements to tissues with high requirement. However, the molecular mechanisms for these systems are poorly understood. We took silicon (Si) as an example and revealed an efficient distribution system occurring in the node of rice, which is a hub for distribution. We found that hyperaccumulation of Si in the husk (more than 10%) is achieved by cooperation of three different Si transporters localized at the different cell layers in the node. Furthermore, mathematical modeling showed that an apoplastic barrier and development of enlarged vascular bundles are also required. Our work revealed a set of players for efficient distribution control in node.

Abstract

Requirement of mineral elements in different plant tissues is not often consistent with their transpiration rate; therefore, plants have developed systems for preferential distribution of mineral elements to the developing tissues with low transpiration. Here we took silicon (Si) as an example and revealed an efficient system for preferential distribution of Si in the node of rice (Oryza sativa). Rice is able to accumulate more than 10% Si of the dry weight in the husk, which is required for protecting the grains from water loss and pathogen infection. However, it has been unknown for a long time how this hyperaccumulation is achieved. We found that three transporters (Lsi2, Lsi3, and Lsi6) located at the node are involved in the intervascular transfer, which is required for the preferential distribution of Si. Lsi2 was polarly localized to the bundle sheath cell layer around the enlarged vascular bundles, which is next to the xylem transfer cell layer where Lsi6 is localized. Lsi3 was located in the parenchyma tissues between enlarged vascular bundles and diffuse vascular bundles. Similar to Lsi6, knockout of Lsi2 and Lsi3 also resulted in decreased distribution of Si to the panicles but increased Si to the flag leaf. Furthermore, we constructed a mathematical model for Si distribution and revealed that in addition to cooperation of three transporters, an apoplastic barrier localized at the bundle sheath cells and development of the enlarged vascular bundles in node are also required for the hyperaccumulation of Si in rice husk.

Plants have different requirement for mineral elements depending on organs and tissues. For examples, developing tissues such as new leaves and reproductive organs require more mineral elements for their active growth (1). However, these tissues usually have low transpiration; therefore, transpiration-dependent distribution of mineral elements is not sufficient to meet their high requirements. Plants must have developed systems for preferential distribution of mineral elements depending on the requirements. However, the molecular mechanisms for these systems are poorly understood. Recently, several studies have shown that nodes function as a hub for distribution of mineral elements in graminaceous plants (2).

Node is a key component of the phytomer in graminaceous plants, which is connected with a leaf, a tiller (or a tiller bud), and crown roots (or these primordia) to the culm or panicle (2, 3). Therefore, graminaceous plants are composed of repeated nodes. Nodes have apparently complicated but regularly organized vascular bundles (VBs). No VBs are continuously connected from the bottom to the top of the culm, but a unit of VB is repeated with a two-thirds overlapped rule; one axial VB is connected with three nodes and a leaf and specialized at different nodes as diffuse VB (DVB), transit VB (TVB), and enlarged VB (EVB) from basal to apical (2, 3). In a node, three different axial VBs with different phases coexist and connected transversely by nodal vascular anastomosis (NVA). TVB is a passage phase, but its appearance and function within the node are similar to one of the multiple DVBs. After EVB phase, the VB is continued to a VB of the leaf associating the node (2–4). As an exception, DVBs in the uppermost two nodes (nodes I and II), in which VBs have no corresponding leaves, become VBs in the panicle without EVB phase as detailed in ref. 2. Based on these repetitive vascular constructions, intervascular transfers between axial VBs are required for preferential delivery of nutrients to apical tissues such as developing leaf or panicle (2). Furthermore, the node also shows distinct structures at cellular and subcellular level, which are characterized by (i) expanded xylem area of EVBs; (ii) differentiation of xylem transfer cells (XTCs), which have expanded cell surface due to cell wall ingrowth facing to the xylem vessel; (iii) increased number of DVBs around the EVBs; and (iv) parenchyma cell bridge (PCB) with dense plasmodesmata between EVB and DVB (2, 4, 5). However, the role of these structures in intervascular transfer of nutrients has not been examined.

In the present study, we examined the preferential distribution system of silicon (Si) in rice. Silicon, the most abundant mineral element, shows beneficial effects for plant growth (6). The beneficial effects are characterized by protecting plants from abiotic and biotic stresses (6). Silicon is especially important for high and sustainable production of rice (Oryza sativa), a typical Si accumulating species. Rice is able to accumulate Si up to 10% of the shoot dry weight, which is severalfold more than macronutrients such as nitrogen, phosphorus, and potassium (7). Low accumulation of Si in rice results in significant reduction of the yield (8); therefore, Si fertilization has been considered as a practice of rice production in many countries, especially under heavy application of nitrogen fertilizers (7).

Silicon in soil solution is present in the form of silicic acid, an uncharged molecule (7). Silicic acid is taken by the roots through two different transporters: Lsi1 and Lsi2 in rice (9, 10). Lsi1 belongs to NIP subgroup of aquaporin and preamble to silicic acid, whereas Lsi2 is an efflux transporter of silicic acid (9, 10). Both Lsi1 and Lsi2 are localized at the exodermis and endodermis cells of rice roots, but in contrast to Lsi1, which is localized at the distal side, Lsi2 is localized at the proximal side (9, 10). Knockout of either Lsi1 or Lsi2 results in defect of Si uptake (9, 10). Recently, in silico mathematical modeling revealed that in addition to cooperation of Lsi1 and Lsi2, presence of the Casparian strips at the exodermis and endodermis is also required for efficient Si uptake and high accumulation (11).

After uptake, more than 95% of Si is rapidly translocated from the roots to the shoots (7). Silicon is also present in the form of silicic acid in the xylem sap (12), which is unloaded by Lsi6, a homolog of Lsi1 (13). Lsi6 is polarly localized in the adaxial side of the xylem parenchyma cells in the leaf sheaths and leaf blades (13). With water loss due to transpiration, silicic acid is gradually concentrated and polymerized to amorphous silica, which is deposited beneath the cuticle, forming cuticle–silica double layers, and inside of particular cells of leaf epidermis (motor cells and short silica cells) (7). Knockout of Lsi6 results in leakage of large amount of silicic acid into the leaf guttation and altered deposition of Si in the leaves (13).

At the reproductive stage, higher Si is finally deposited in the husk, which can reach more than 10% of the dry weight (7). Silicon in the husk is also deposited between the epidermal cell wall and the cuticle, forming a cuticle–silica double layer (7). This heavy deposition of Si in the husk is very important for rice grain fertility because it prevents water loss and pathogen (e.g., panicle blast) infection (6–8). However, the question arises on how Si is highly deposited in the husk. The rice husk does not have stoma at the outside. Furthermore, compared with the leaves, the surface area is much smaller. Therefore, transpiration-dependent distribution is unlikely responsible for the high Si accumulation in the husk.

Previously, Lsi6 highly expressed in the nodes was reported to be involved in the intervascular transfer for preferential distribution of Si. Lsi6 in nodes is polarly localized at the xylem parenchyma cells (mainly XTCs) of EVBs (14). Knockout of Lsi6 resulted in decreased Si accumulation in the husk but increased Si in the flag leaf (14). However, Lsi6 is a channel-type passive transporter, which transports silicic acid following concentration gradient (13, 15). Therefore, Lsi6 alone cannot explain hyperaccumulation of Si in the husk. In the present study, we found that the other two active efflux transporters are also involved in the intervascular transfer required for high accumulation of Si in the husk. Furthermore, our mathematical modeling revealed that the distinct nodal structures including EVBs, XTCs, and apoplastic barrier are also required for the efficient intervascular transfer of Si in rice.

Results

Expression Profiles of Si Transporters in Nodes.

To find out transporters involved in the intervascular transfer of Si in nodes, we investigated the expression profile of both passive Si channel (Lsi1-like) and active Si efflux transporter (SIET/Lsi2-like) homolog genes using node I RNA at heading stage. In rice genome, there is only one homolog of Lsi1 (Lsi6) (9) but four homologs of Lsi2/SIET1 (Lsi3/SIET2 and SIET3–5) (10). Among them, Lsi6, Lsi2, and Lsi3 showed high-level expression in the node I (Fig. 1A). By contrast, expression of Lsi1 and SIET3 was not detected, and only trace expression of SIET4 and SIET5 was found in node I (Fig. 1A).

Fig. 1.

Expression analysis. (A) Semiquantitative RT-PCR of Lsi1-like genes (Lsi1 and Lsi6) and Lsi2-like genes (Lsi2, Lsi3, SIET3, SIET4, and SIET5) in node I of rice sampled at the heading stage. PCR products (25 cycle) with ladder marker (m) were electrophoresed and stained by ethidium bromide. (B and C) Expression pattern of Lsi2 (B) and Lsi3 (C) determined by quantitative real-time RT-PCR in various organs at flowering stages. Expression level relative to node I was shown. Actin was used as an internal standard. Data are means ± SD of three biological replicates.

A detailed expression pattern was further investigated by quantitative RT-PCR using various organs of rice at the flowering stage. These samples were also used for analysis of Lsi6 previously (14). Similar to Lsi6, the highest expression of both Lsi2 and Lsi3 was found in the uppermost node I (Fig. 1 B and C). Expression of Lsi2 and Lsi3 was also detected in lower nodes including nodes II and III (Fig. 1 B and C). In contrast to Lsi3, which was also expressed in the peduncle (internode I) and rachis, there was no expression of Lsi2 in these organs (Fig. 1 B and C). Expressions of both Lsi2 and Lsi3 were also not detected in caryopsis (Fig. 1 B and C).

Functional Characterization of Lsi3.

Among Si transporter genes highly expressed in node I, Lsi6 and Lsi2 proteins have been functionally characterized, but Lsi3 is uncharacterized in terms of transport activity and subcellular localization. Lsi3 shares 80% identity with Lsi2 at amino acid sequence (Fig. S1). To examine whether Lsi3 also has efflux transport activity for silicic acid, we expressed Lsi3 in Xenopus laevis oocyte and determined its efflux transport activity. Similar to Lsi2, Lsi3 also showed efflux transport activity for Si (Fig. S2).

Fig. S1.

Gene structure and protein sequence of Lsi3. (A) Gene structure of Lsi3. Closed box, open box, and horizontal line indicate UTR region of the exon and ORF region of the exon and intron, respectively. Insertion position of T-DNA in lsi3 mutant and target region of RT-PCR are indicated. (B) Expression level of Lsi3 in lsi3 mutant and its wild-type rice (WT1) determined by quantitative real-time RT-PCR in root. (C) Alignment of amino acid sequences of Lsi2 and Lsi3. The alignment is generated by ClustalW using default settings (clustalw.ddbj.nig.ac.jp/). Green boxes indicate transmembrane domains predicted by SOSUI (bp.nuap.nagoya-u.ac.jp/sosui/).

Fig. S2.

Si efflux transport activity of Lsi3. (A) Si efflux transport assay in Xenopus oocyte. cRNA of Lsi2, Lsi3, or water was injected to the oocytes, which were exposed to Si (1 mM) labeled with ⁶⁸Ge. After 4 h of incubation, the amount of Si released to the solution and inside the oocytes was determined. Efflux transport activity was expressed as the amount of released Si of the total Si injected. Data are means ± SD of four to five biological replicates. (B) Complementation test of Si uptake in lsi2 mutant harboring Lsi3 gene under the control of Lsi2 promoter. For uptake test, two independent transgenic lines, lsi2 mutant and their corresponding wild-type rice (WT2), were exposed to a solution containing 1.0 mM Si for 12 h. Data are means ± SD of 3–10 biological replicates. Different letters indicate significant differences at P < 0.05 by Tukey’s test.

Furthermore, we expressed Lsi3 in the lsi2 rice mutant under the control of Lsi2 promoter. Analysis of two independent transgenic lines showed that introduction of Lsi3 significantly increased Si uptake (Fig. S2).

To investigate subcellular localization of Lsi3 protein, we prepared a fusion gene of GFP and Lsi3 (GFP-Lsi3) and transiently introduced it into onion epidermal cells together with DsRed as a marker for cytosol and nucleus by particle bombardment. Fluorescence signal from GFP-Lsi3 was observed mainly at outer region of the cell, which is located outside of fluorescence of DsRed (Fig. S3). In situ subcellular localization of Lsi3 protein was also investigated by immunohistochemical staining in rice node I. No signal in the lsi3 knockout mutant as described below was detected (Fig. S4), indicating high specificity of this antibody against Lsi3. Double staining with 4′,6-diamidino-2-phenylindole (DAPI) for nuclei showed that the fluorescence signal from Lsi3 antibody was localized mainly at the peripheral region of the cells, which was circumscribed but did not envelope the nuclei (Fig. S4). Taken together, these results show that Lsi3 is a plasma membrane-localized efflux transporter of silicic acid.

Fig. S3.

Subcellular localization of GFP-Lsi3. GFP-Lsi3 fusion gene and DsRed were transiently introduced into onion epidermal cells. GFP fluorescence (A); DsRed fluorescence (B); and merged image of GFP, DsRed, and transmitted light (C). (Scale bars, 100 μm.) (Right) Magnified images of yellow boxed areas.

Fig. S4.

Subcellular localization of Lsi3 in node I. Costaining with DAPI (blue) and Lsi3 antibody (red) was conducted in node I of the wild-type rice (A, C, and D) and lsi3 mutant (B). Blue color shows both DAPI and cell wall autofluorescence. C and D are magnified images of yellow boxed areas in A. (Scale bar, 100 µm.)

Tissue-Specific Localization of Si Transporters in Node.

Lsi6 is localized at the xylem parenchyma cells of EVBs of node I with polarity facing toward the xylem vessels (14), but the tissue localizations of Lsi2 and Lsi3 in nodes are unknown. To examine the tissue specificity of localization of Lsi2 and Lsi3, we performed coimmunostaining of Lsi2 or Lsi3 with Lsi6. Lsi2 protein (magenta) was localized at the bundle sheath (bs) cells around the EVBs (Fig. 2A), which is next to the cell layer where Lsi6 is localized (green). Furthermore, Lsi2 showed a polar localization at the distal side of the vasculature (Fig. 2B), which is the opposite side of Lsi6. On the other hand, Lsi3 protein (magenta) was detected in the parenchyma cells between the bundle sheath cell layer of EVBs and DVBs (Fig. 2 C and D). Unlike Lsi2 and Lsi6, Lsi3 did not show polarity (Fig. 2D).

Fig. 2.

Tissue specificity of localization of Lsi6, Lsi2, and Lsi3 in node I. Node I of the wild-type rice at heading stage was sampled for immunostaining. Coimmunostaining using Lsi6 antibody (green) and Lsi2 antibody (magenta in A and B) or Lsi3 antibody (magenta in C and D) was performed. Autofluorescence of the cell wall is shown in blue/cyan color. Nonspecific signals in nuclei by Lsi2 antibody was also observed in A and B. B and D are magnified image of yellow boxes area in A and C, respectively. DVB, xylem and phloem regions of EVBs (EVx and EVp), xylem and phloem regions of DVBs (DVx and DVp), and bundle sheath cell layer of EVBs (bs) are indicated. (Scale bar, 100 µm.)

Detection of Apoplastic Barrier in Node.

In rice roots, presence of Casparian strips at the exodermis and endodermis prevents apoplastic flow of water and solutes; therefore, cooperation of polarly localized Lsi1 and Lsi2 at these cell layers is required for efficient Si uptake (9–11). In node, Lsi2 and Lsi6 also showed back-to-back polar localization (Fig. 2 A and B), although at different cell layers next to each other. To understand the significance of this polar localization, we examined whether apoplastic barrier is also present in node. We fed periodic acid, a tracer of apoplastic flow (16), from cut end of the internode below node II, followed by Schiff’s staining. At the cross section of node I, the xylem regions of the EVBs were heavily stained, but the phloem regions of EVBs and DVBs were hardly stained (Fig. S5). No staining was observed at the bundle sheath cell layer of EVBs and outer parenchyma cells between EVBs and DVBs (Fig. S5). This result shows that the apoplastic tracer was blocked inside the bundle sheath cell layer, indicating the presence of an apoplastic barrier at the bundle sheath of EVBs.

Fig. S5.

Periodic acid staining of node I. (A–C) Wild-type rice at the flowering stage was cut at the internode III below the node II, and periodic acid was fed from the cut end, followed by feeding with reducing solution. Cross section of node I was then prepared and stained by Schiff’s reagent. (B and C) Magnified images of dotted areas in A and B, respectively. Width of bundle sheath (bs) and xylem region of EVBs (EVx) are indicated in C. (Scale bar, 100 µm.)

Stem-Fed Si Distribution to Different Organs.

To investigate the exact roles of three Si transporters highly expressed in node, we compared the distribution pattern of Si to different organs between knockout lines and their wild-type rice.

Knockout lines of Lsi2 and Lsi6 were used in previous studies (6, 9), whereas lsi3 mutant is a T-DNA insertion line (Fig. S1). The expression of Lsi3 at the 3′-untranslated region was hardly detected in the lsi3 mutant (Fig. S1). Because Lsi2 and Lsi6 are also expressed in the roots (10, 13), to rule out the effect from root Si uptake, we fed Si as well as Rb and Sr as tracer of symplastic and apoplastic transfer from the cut end of the internode II for 24 h. Sr is a phloem-immobile and xylem-mobile element, whereas Rb is transported through the phloem (17). Knockout of either Lsi6, Lsi2, or Lsi3 resulted in decreased distribution of Si to the panicle organs including spikelet, rachis, and peduncle but increased distribution to the flag leaf (Fig. 3A). Among Lsi6, Lsi2, and Lsi3, knockout of Lsi6 showed the largest effect in decreasing Si distribution to the panicles. By contrast, there was almost no difference in the distribution of Rb and Sr to different organs between mutants and their corresponding WTs (Fig. 3 B and C). Based on Sr distribution, it was estimated that 70–80% of transpiration occurred from the flag leaf in this experiment (Fig. 3B).

Fig. 3.

Distribution pattern of stem-fed Si, Rb, and Sr. Three mutants (lsi6, lsi3, and lsi2) and their corresponding wild types (WT1, cv. Dongjin for lsi6 and lsi3; WT2, cv. Taichung-65 for lsi2) were grown hydroponically until flowering in the absence of Si and cut at the internode II. Solution containing 2 mM Si and 50 µM of Rb and Sr was fed from the cut end. After 24 h, each organ was separately harvested and subjected to determination of Si, Rb, and Sr by ICP-MS. Distribution ratio of Si (A), Rb (B), and Sr (C) in different organs above node I was calculated. Data are means ± SD of three biological replicates. Asterisks indicate significant differences from corresponding WT at *P < 0.05 and **P < 0.01 by Tukey’s test.

Construction of Mathematical Model for Si Distribution in Node I.

To comprehensively understand the distribution system of Si in node, we constructed a mathematical model. We simulated the transfer of Si in the node I by using a diffusion equation on the 2D grids (11) and a 2D explicit finite difference method. The simulations represent a 2D longitudinal section of node I. For simplicity, the simulation region includes only one EVB and one DVB connected by NVA (Fig. S6). Areas of EVB and DVB (2), the location of the Si transporters (Fig. 2), apoplastic barrier (Fig. S5), and transpiration rate (i.e., distribution of Sr) from panicle and flag leaf (Fig. 3C) were estimated according to the experimental data. Then, we calibrated the model parameters, Si transport activity of three transporters, and background of Si permeability of cell membrane per unit simulation area based on the results of the stem-fed in vivo experiment shown in Fig. 3. Using these parameter sets, we established a model for Si distribution in node I. Using this model, we were able to reproduce the Si distribution pattern in lsi6, lsi2, and lsi3 mutants as observed in the feeding experiment (Fig. S7).

Fig. S6.

Diagram of the model of node I. The dynamics of Si in the node is simulated by using a diffusion equation on the 2D grids. A cell unit has 5 × 10 grids. The PCB is represented by three cell layers. The three cells of PCB are connected by symplast region (assuming plasmodesmata). At the symplast and apoplast regions (red and blue regions), Si diffuses freely at a rate determined by specific diffusion coefficients. Across the symplast and apoplast regions (plasma membrane), Si moves via transporters (but we assumed a low permeability of the cell membrane itself). At the xylem site (brown region), Si moves toward the panicle or the flag leaf (upper direction) according to an advection–diffusion equation.

Fig. S7.

Calibration of mathematical model for Si movement in node I. Based on the result of in vivo stem-feeding experiment (A), parameter set of the model, Si transport activity of three transporters, and background Si permeability of cell membrane per unit simulation area were calibrated. Using this parameter set, Si distribution in WT and mutant of each transporter gene was simulated by the model (B).

In Silico Simulation Experiments of Si Distribution.

Based on the model constructed, we conducted in silico modeling experiments to estimate the importance of the cooperative effect of three transporters and the contribution of nodal structural features to the distribution. In the normal setting of the model (corresponding to the wild-type rice), the Si concentration in the DVB was much higher than that in EVB, indicating a preferential transfer of Si to DVB in node I (Fig. 4A). However, if Lsi6 was absent, the difference in Si concentration between DVB and EVB disappeared, indicating the significant role of Lsi6 in the intervascular transfer of Si (Fig. 4A). If Lsi2 or Lsi3 was absent, the Si concentration in the DVB was higher than that in EVB due to presence of Lsi6 and another efflux transporter (Lsi3 or Lsi2), but compared with normal setting, the Si concentration in the DVB was much lower (Fig. 4A). Lack of both Lsi2 and Lsi3 resulted in no difference in the Si concentration between EVB and DVB (Fig. 4A). This simulation confirmed that Lsi2 and Lsi3 also play important roles in the intervascular transfer of Si.

Fig. 4.

In silico modeling experiments for Si distribution in node I. Diagram of the model is shown in Fig. S6. (A) Estimated Si concentration in each grid of the model at 10 min after 2 mM Si supply and (B) estimated Si distribution ratio to the panicle and flag leaf, under multiple experimental settings. Normal, normal setting as wild-type rice; lsi6, lack of Lsi6; lsi2, lack of Lsi2; lsi3, lack of Lsi3; lsi2lsi3, lack of both Lsi2 and Lsi3; no barrier, no apoplastic barrier at the bundle sheath of EVB; fast EVB, 10× faster velocity of the xylem in EVB; no XTC, permeability parameter of Lsi6 replaced by that of Lsi1 in root; no all, combined defect of all above factors. Results of the simulation with the parameter set that had the maximum likelihood among 3,000 simulations are shown for A. For B, the error bars indicate SDs estimated by 30 simulations that were sampled from 3,000 simulations according to the likelihoods.

Enlarged vascular bundle in node is structurally characterized by more than 10× enlargement of the xylem area, xylem transfer cells with folded plasma membrane, and apoplastic barrier at the bundle sheath (10–12) (Fig. S5). Simulation experiments showed that the apoplastic barrier is also essential for raising Si concentration in DVB (Fig. 4A). On the other hand, 10× faster velocity of the xylem in EVB (to mimic no enlargement of EVB) or lower permeability parameter of Lsi6 (to mimic no development of XTCs) only resulted in a slight effect on the Si concentration in the DVB (Fig. 4A). If all these transporters and structure features are defective, the Si enrichment in DVB completely disappeared (Fig. 4A).

We also simulated the Si distribution ratio to panicle and flag leaf using the model. Lack of Lsi6, Lsi2, Lsi3, and apoplastic barrier resulted in significant decrease of Si distribution to the panicle but increase to the flag leaf (Fig. 4B). In particular, lack of both Lsi2 and Lsi3 and absence of apoplastic barrier decreased Si distribution to the panicles from 51% to 18% (Fig. 4B), indicating their important role in preferential distribution of Si to the panicles. On the other hand, increase of xylem velocity and lower permeability parameter of Lsi6 did not have a significant effect on the Si distribution ratio (Fig. 4B). These trends in the distribution ratio did not change whether 2 mM or 20 mM Si was used for simulation input (Fig. S8). Another additional simulation was twofold axial extension of node. With this assumption, more Si was distributed to the panicle under normal condition, but defect of each transporter or nodal feature also resulted in decreased distribution of Si to the panicles (Fig. S8). Because enlargement of EVB also provides more space for expressing more transporters, we further simulated the distribution ratio of Si on the assumption that the transport activity in EVB was simply decreased by 1/3.16, which corresponded to the decrease of circumference of one-tens area circle, together with 10× faster velocity of the xylem flow. Under these settings, Si distribution to the panicle was decreased from 56–66% to 22–32%, regardless of Si concentration supplied and extension of node length (Fig. S9).

Fig. S8.

Additional simulation experiments of node model. Si distribution ratio to the panicle was simulated with different conditions: (A) higher-input Si concentration (20 mM) and (B) twofold axial extension of node.

Fig. S9.

Additional simulation experiments of node model. Estimated Si distribution ratio to the panicle and flag leaf, under different experimental settings. Normal, normal setting as wild-type rice; fast EVB, 10× faster velocity of the xylem in EVB; narrow EVB, 10× faster velocity of the xylem and 3.16× lower transport activity in EVB, with different conditions: 2 mM input Si concentration, 20 mM input Si concentration, and 2 mM input Si concentration with twofold axial extension of node.

Discussion

Essential mineral elements taken up by the roots are translocated to different organs and tissues in the aboveground part through the transpiration stream. However, it has been unknown for a long time how plants deliver these mineral elements to different tissues according to their different demands. There is an inconsistency between the transpiration rate and mineral element requirement. For example, developing tissues such as new leaves and reproductive organs have low or no transpiration but usually require more mineral elements for their active growth. Therefore, plants must have systems for preferentially delivering essential mineral elements to the developing tissues independent of transpiration rate.

Nodes of graminaceous plants are characterized by very complicated but well-organized vascular systems (2–4). Recently, identification of mineral nutrient transporters in node and physiological studies shed a new light on the importance of node for preferential distribution of mineral nutrients to developing and reproductive organs (2, 14, 18–23). The xylem flow in EVBs and DVBs, which are connected by nodal vascular anastomosis (NVA) at the base of the node, are simply divided following the transpiration rate of each upper organ. Therefore, for preferentially delivering mineral elements, an intervascular transfer from EVBs to DVBs in node is required (2). Based on the structure of the node, this intervascular transfer includes at least three steps: unloading of a mineral element from xylem flow in EVB, transfer through symplast or apoplast of PCB, and reloading to xylem or phloem of DVB (2) (Fig. 5). Although different transporters are supposed to be involved in these steps, only a few of them in some steps have been identified. For instance, Lsi6 is involved in Si unloading from EVB (14, 18); OsHMA5 and OsYSL16 are involved in Cu exclusion from xylem and loading to phloem of DVB, respectively (19, 20), whereas OsHMA2 is required for Zn/Cd reloading to phloem of DVB (21); and OsNramp3 has a dual role for both xylem unloading from EVB and phloem reloading to DVB of Mn (22). In the present study, by integrating in vivo experiments with mathematical modeling, we were able to identify all factors involved in the intervascular transfer for preferential distribution of Si in node (Fig. 5).

Fig. 5.

Schematic presentation of intervascular transfer pathway of Si in node I silicon in the xylem of EVB is unloaded by Lsi6 polarly localized at the XTCs, followed by symplastical transfer through plasmodesmata to the bs cells of EVB with an apoplastic barrier. Part of Si is then released by Lsi2 localized at the distal side of bs to the apoplast of PCB and transported to the xylem of DVB, whereas the remaining Si is simplistically transferred to the PCB and exported and reloaded to the xylem of DVB by Lsi3. The cooperation of these three transporters across the apoplastic barrier is required for the intervascular transfer of Si and subsequently for hyperaccumulation of Si in the rice husk. Modeling shows that a physical barrier on the bs and development of EVB are also required for efficient intervascular transfer of Si. For details, see text.

First, we identified two Si transporters (Lsi2 and Lsi3) highly expressed in the node in addition to Lsi6 reported previously (Fig. 1) (14). Both of them are efflux transporters of Si but localized at the different cell layers between EVB and DVB of node (Figs. 2 and 5). Lsi2 was localized at the distal side of bundle sheath cells of EVB having apoplastic barrier, which is the next cell layer where Lsi6 was localized (14) (Fig. 2), whereas Lsi3 was localized at the parenchyma cells without polarity between the bundle sheath and DVB (Fig. 2). The parenchyma cells between EVBs and DVBs are symplastically connected by dense plasmodesmata, so-called PCB (5) (Fig. 5). Therefore, Si in the xylem of EVB is taken up by Lsi6 and symplastically moved to the next cell layer, the bundle sheath through the plasmodesmata (Fig. 5). Part of Si is released to the apoplastic space of parenchyma cells by Lsi2, which is transferred to the xylem of DVB through apoplastic pathway, whereas remaining Si is moved to the parenchyma cells through the plasmodesmata, followed by releasing to the xylem of DVB by Lsi3 (Fig. 5). Knockout of either Lsi2 or Lsi3 resulted in decreased distribution of Si to the panicles but increased distribution to the flag leaf (Fig. 3), indicating that the cooperation of these three transporters is required for the preferential distribution of Si to the panicles and subsequently high accumulation of Si in the husk (Fig. 5).

Second, we constructed a mathematical model for distribution of Si in node I (Fig. S6), which is well fit to the experimental data (Fig. S7). We found that the apoplastic barrier identified at the bundle sheath of EVBs in this study is also required for efficient intervascular transfer of Si in node based on the mathematic modeling (Fig. 4 and Fig. S8). This barrier is essential for efficient cooperation of three transporters by generating a concentration gradient from xylem of EVB to XTC–PCB for promotion of Si transport via Lsi6 and further directional transport by Lsi2 and Lsi3 at the opposite side of the barrier (Figs. 4 and 5). This axisymmetric arrangement of passive channel (Lsi6) and active efflux transporters (Lsi2 and Lsi3) with an apoplastic barrier is very similar to the roots, where Lsi1 and Lsi2 for Si uptake are localized at the exodermis and endodermis with Casprian strips (9, 10). A previous modeling study also demonstrated that these apoplastic barriers in root are required for the efficient uptake and enrichment of Si to the stele (11). However, there are two differences in these cooperative systems between the root and node. One is that two efflux transporters (Lsi2 and Lsi3) are involved in node, but only one efflux transporter Lsi2 is involved in root. The second difference is that Lsi1 and Lsi2 are localized at the same cells with different polarity in root, but in node, Lsi6, Lsi2, and Lsi3 are localized at the different cell layers (Fig. 5). However, these two cooperative systems show similar function in root and node. This is because different from root, in node, cell layers expressing Lsi6, Lsi2, and Lsi3 are tightly connected to each other by plasmodesmata (5) (Fig. 5). These cell layers therefore behave like a single cell in the model. This connected multilayer structure by cells specialized for different functions is presumably more suitable for the more integrated multivascular structure of nodes compared with multifunctional single-cell layer(s) in the root. In fact, single knockout of Lsi2 or Lsi3 had smaller effect on the Si distribution to the panicle compared with that of Lsi6 (Fig. 3A), indicating that both Lsi2 and Lsi3 are involved in generation of the Si concentration gradient for motive force of Lsi6 channel (Figs. 4 and 5). This is supported by the fact that Si enrichment in the DVB was completely lost if both Lsi2 and Lsi3 were knocked out in the model (Fig. 4).

Xylem transfer cells where Lsi6 is located are characterized by folded plasma membrane due to cell wall ingrowth, resulting in increased uptake surface (2, 5). We simulated the importance of this distinct structure in Si distribution by using the model constructed. In our model, the estimated transport activity parameter of Lsi2 per unit modeling grid (7.05 ± 2.10 µm⋅s⁻¹) in node I was almost the same as that estimated in the root in a previous study (4.48 ± 0.26 µm⋅s⁻¹) (11). These are also comparable to the parameter of Lsi3 in node I (6.19 ± 2.17 µm⋅s⁻¹). By contrast, the estimated permeability of Lsi6 (136.25 ± 68.49 µm⋅s⁻¹) was much higher than that estimated for Lsi1 in the root (16.38 ± 3.40 µm⋅s⁻¹) (11). When the permeability parameter of Lsi6 was replaced by that of Lsi1 in the root to mimic no XTC development (no XTC), the estimated contribution of XTCs to Si distribution was relatively small (Fig. 4). Lsi6 is an aquaporin-like passive channel, which has much faster transport capacity compared with other types of active transporters (15). Therefore, transport capacity of Lsi6 for Si in the node is possibly high enough even if the XTC was not developed.

The xylem area of EVB is a mosaic of numerous vessels and parenchyma cells, which has more than 10× larger area compared with connecting VBs in both internode and leaf (2–4). This enlargement has two meanings: slowdown of the xylem mass flow and increase of space for expressing transporters. Both of them may contribute to efficient intervascular transfer. However, our simulation showed that if the velocity of xylem mass flow in EVB was increasing 10×, the distribution ratio of Si to the panicles was only slightly decreased, probably due to the invariable concentration of Si input in this model (Fig. 4 and Fig. S8). By contrast, when the transport capacity was simply decreased to 1/3 to mimic reduced space for transporters, the distribution of Si to the panicles was significantly decreased (Fig. S9). This simulation suggests that increased transport capacity due to enlargement of EVB is also important for the efficient intervascular transfer of Si.

In conclusion, we identified a complete set of players involved in the intervascular transfer of Si in the node, which is required for the preferential distribution of Si to the husk. Transporters localized at the different cell layers are responsible for movement of Si from EVB to DVB, and the distinct structure of the node helps to enhance this movement. Although we focused on Si distribution in uppermost node I in this study, distribution controls of all mineral nutrients at each node throughout the developing processes are required. Furthermore, graminaceous plants are composed of repeated nodes, and the structure of each node is basically similar. Therefore, results shown in this study provide a model for studying the systems of preferential distribution of all minerals in graminaceous plants in future.

Materials and Methods

Seeds of T-DNA insertion mutants of Lsi6 (PFG_4A-01373) (13) and Lsi3 (PFG_3C-00346; Fig. S1) [Rice T-DNA Insertion Sequence Database (RISD), cbi.khu.ac.kr/RISD_DB.html] and their wild type (WT1, cv. Dongjin) and lsi2 single-nucleotide substitution mutant (10) and its wild type (WT2, cv. Taichung-65) were grown hydroponically in a half-strength Kimura B nutrient solution (24). For expression analysis of Si transporter genes, different organs of WT1 including unelongated stem, node I to III, peduncle, rachis, and caryopsis were sampled at the flowering stage and subjected to semiquantitative and quantitative RT-PCR with gene-specific primers shown in Table S1. Efflux transport activity assay of Lsi3 for Si in Xenopus oocytes was performed as described previously (10, 25). Furthermore, the transport activity of Lsi3 was determined by transforming the promoter region of Lsi2 (2.0 kb) (25) and ORF of Lsi3 into lsi2 mutant using an Agrobacterium-mediated transformation system. The subcellular localization of Lsi3 was investigated by introducing plasmids carrying GFP-Lsi3 fusion gene and DsRed-monomer (Clontech) into onion epidermal cells using Helios Gene Gun system (Bio-Rad). Immunostaining was performed for observing localization of Lsi6, Lsi2, and Lsi3 in node I as described previously (22). Fluorescence signals were observed with a confocal laser-scanning microscopy (LSM700; Carl Zeiss). Apoplastic permeability test in node I was performed according to Shiono et al. (16). For stem feeding experiment, WT1, WT2, and three mutants (lsi6, lsi2, and lsi3) were grown hydroponically without Si until flowering and cut at the internode II below the node I. Nutrient solution containing 2 mM Si and 50 µM of Rb and Sr was fed from the cut end for 24 h. Concentrations of Si, Rb, and Sr in each part were determined by inductively coupled plasma mass spectrometry (7700X; Agilent Technologies).

Table S1.

Primers used for RT-PCR

Gene	Forward (5′ to 3′)	Reverse (5′ to 3′)
Lsi1	GCCAGCAACAACTCGAGAACAA	CATGGTAGGCATGGTGCCGT
Lsi6	CGTTGATTCGTTGTCCTAGATAG	GATATCACCTTCTTGAGGAGGTT
Lsi2	ATCTGGGACTTCATGGCCC	ACGTTTGATGCGAGGTTGG
Lsi3	CTGTATCCCTGTTGCCAGCTG	TAATCCGGCATGCGTACTTG
SIET3	ATTAAGCACGGATATCATGGTGC	GATTTTCTCTTCTCCTGCCTATAC
SIET4	AAGCAGACGGTGATTGAGAAGG	GCATGTGCAGTTGTACAAACACC
SIET5	GATGGATGCAGATGGGGACTG	CCAAGTTCCATCGACTGGGTC
Actin	GACTCTGGTGATGGTGTCAGC	GGCTGGAAGAGGACCTCAGG

For mathematical modeling of Si transport in node I, we divided the node I by 32 grid points in a transverse direction and 48 grid points in a longitudinal direction, with each grid point representing 4 × 40 µm (Fig. S6). We simulated the transfer of Si in the region by using a diffusion equation on the 2D grids (11, 26) and a 2D explicit finite difference method.

For more detail, see SI Materials and Methods.

SI Materials and Methods

Plant Materials and Growth Conditions.

Seeds of T-DNA insertion mutants of Lsi6 (PFG_4A-01373) (13) and Lsi3 (PFG_3C-00346; RISD, cbi.khu.ac.kr/RISD_DB.html) and their wild type (WT1, cv. Dongjin) and lsi2 single-nucleotide substitution mutant (10) and its wild type (WT2, cv. Taichung-65) were soaked in water overnight at 30 °C in dark and then transferred to nets floating on a 0.5 mM CaCl₂ solution. After 1-wk incubation, the seedlings were transferred to a half-strength Kimura B nutrient solution prepared by distilled water (24) in 3.5-L plastic pots. After 8 wk, nutrient solution was changed to one-strength Kimura B. The nutrient solution was renewed every 2 d. Plants were cultivated in a closed greenhouse under natural light at 25–30 °C until heading.

Expression Analysis of Si Transporter Genes.

At the flowering stage, different tissues of WT1, including unelongated stem, nodes I to III, peduncle, rachis, and caryopsis, were sampled. Total RNA was extracted using an RNeasy plant extraction mini kit (Qiagen), and first-strand cDNA was synthesized from 1 µg of total RNA using oligo dT₁₈ primer and SuperScript reverse transcriptase (Invitrogen) according to the manufacturer’s instructions. Actin was used as an internal standard. Semiquantitative RT-PCR was performed with gene-specific primers shown in Table S1 and ExTaq enzyme (Takara Bio) for 25 cycles. Quantitative real-time PCR was performed with gene-specific primers and SYBR Premix ExTaq (Takara Bio) using Mastercycler ep realplex (Eppendorf).

Transport Activity Assay by Xenopus Oocyte.

Efflux transport activity assay for Si was performed as described previously (9, 25). ORF of Lsi3 was amplified by RT-PCR with the following primers: 5′-TTGTACATGGCGCTGGCGTCGCTG-3′ and 5′-TGAATTCTGATCGTTGTAGA TAGTAGCT-3′. Τhe ORF was inserted into the BglII site of a Xenopus oocyte expression vector, pXβG-ev1. Capped RNA was then synthesized from linearized pXβG-ev1 plasmids by in vitro transcription with an mMASSAGE mMACHINE high-yield capped RNA transcription kit (Ambion), according to the manufacturer’s instructions. A volume of 50 nL (1 ng⋅nL⁻¹) cRNA was injected into the oocytes using a Nanoject II automatic injector (Drummond Scientific). As a negative control, 50 nL of RNase-free water was also injected. After incubation in MBS at 18 °C for 1 d, the oocytes were used for the transport activity assay. Silicic acid (1 mM) labeled with ⁶⁸Ge (Perkin-Elmer; 2 GBq⋅mmol⁻¹) was injected into oocytes. After 4 h of incubation, the external solutions were collected, and the remaining oocytes were homogenized with 0.1 N HNO₃. Radioactivity of the external solution and homogenized oocytes was determined by a liquid scintillation analyzer (Perkin–Elmer).

Complementation of lsi2 Mutant and Si Uptake Experiment.

The promoter region of Lsi2 (2.0 kb) (25) and ORF of Lsi3 described above were inserted into a binary vector (pPZP2H-nos) (25). The plasmid was transformed into Agrobacterium tumefaciens strain EHA101 and then transferred into calli derived from the rice mutant lsi2 using an Agrobacterium-mediated transformation system.

The Si uptake experiment was performed with two independent transgenic lines, lsi2 mutant and WT2. Seedlings (4 wk old) were placed in 50-mL black bottles containing half-strength Kimura B solution (pH 5.6) and 1.0 mM Si as silicic acid. After 12 h, a 0.3-mL aliquot of the solution was taken for determination of Si concentration by the colorimetric molybdenum blue method (27). Water loss was also recorded. At the end of the experiment, the roots were harvested, and their fresh weights were recorded.

Transient Expression of GFP-Lsi3 in Onion Epidermal Cells.

The Lsi3 ORF described above was inserted into CaMV 35S GFP vector (22). The resulting plasmid was designated GFP-Lsi3. Gold particles with a diameter of 1 µm coated with GFP-Lsi3 and DsRed-monomer (Clontech) were introduced into onion epidermal cells using Helios Gene Gun system (Bio-Rad). The GFP and DsRed signals were observed with a confocal laser-scanning microscopy (LSM700; Carl Zeiss).

Immunostaining of Lsi6, Lsi2, and Lsi3 in Node I.

Antibody against Lsi3 was prepared by immunizing rabbits with the synthetic peptide C-EDDDGGDAES (positions 251–260 of Lsi3). Antibodies against Lsi6 and Lsi2 have been described previously (10, 13). Node I at the flowering stage was sampled for immunostaining as described previously (22). Cross-sections of node I with 100-µm thickness were prepared by LinearSlicer PRO10 (Dosaka EM). For coimmunostaining of Lsi6-Lsi2 and Lsi6-Lsi3, we used a Zenon Rabbit IgG Labeling Kit (Molecular Probes) in accordance with the manufacturer’s instructions. Fluorescence signals were observed with a confocal laser-scanning microscopy (LSM700; Carl Zeiss).

Apoplastic Permeability Test in Node I.

Apoplastic permeability test in node I was performed according to Shiono et al. (16). WT rice at the flowering stage was cut at internode III below node II, and periodic acid solution containing 0.1% (wt/vol) H₅IO₆ was fed from the cut end for 30 min. After washing the cut ends with distilled water, the reducing solution (1 g of KI and 1 g of Na₂S₂O₃5H₂O dissolved in 50 mL of distilled water and acidified with 0.5 mL of 2 N HCl) was fed for 30 min. Then, cross-sections of node I with 100-µm thickness were prepared by LinearSlicer PRO10 (Dosaka EM) and were stained in Schiff’s reagent. The penetrated H₅IO₆ was visualized as purple staining in the cell walls under a light microscope (CKX41 with CCD camera FX630; Olympus).

Stem Feeding Experiment.

WT1, WT2, and three mutants (lsi6, lsi2, and lsi3) were grown hydroponically in Kimura B nutrient solution without Si until flowering and were cut at internode II below node I and recut in water by a sharp razor blade to avoid cavitation. Twofold Kimura B nutrient solution containing 2 mM Si and 50 µM of Rb and Sr was fed from the cut end in a growth chamber at 25 °C, 75% relative humidity, and continuous light. After incubation for 24 h, flag leaf blade, flag leaf sheath, node I, rachis–peduncle, and spikelets were harvested separately and dried at 70 °C in oven for 2 d and weighed. The samples were ground to a powder and then subjected to microwave digestion in a mixture of 3 mL of HNO₃ (62%; wt/wt), 3 mL of hydrogen peroxide (30%; wt/wt), and 2 mL of hydrofluoric acid (46%; wt/wt) (START D Microwave Digestion System; Milestone General). The digested samples were diluted to 50 mL with 4% (wt/vol) boric acid. Concentration of Si, Rb, and Sr were determined by inductively coupled plasma mass spectrometry (7700X; Agilent Technologies) after further dilution with H₂O by 20×.

Mathematical Modeling of Si Transport in Node I.

Node structure in the simulation.

The simulations represent a 2D longitudinal section through node I, which includes one DVB, one EVB, and PCB. The region is 128 µm in width and 1,920 µm in height (14). We divided the region by 32 grid points in a transverse direction and 48 grid points in a longitudinal direction, with each grid point representing 4 × 40 µm. We simulated the transfer of Si in the region by using a diffusion equation on the 2D grids (11, 26) and a 2D explicit finite difference method. In our model, we only considered three cell layers between DVB and EVB (Fig. S6). We assumed that each cell had 5 × 10 grids, in which the outermost grids were in the apoplast region. We also considered the presence of plasmodesmata between cell layers, through which the intracellular (symplast) regions are directly connected to each other. At the center of the three cell layers, we assumed an apoplastic barrier, where water and Si cannot diffuse through the apoplast region. Therefore, Si should move within the symplast regions to cross the central cell layer. Both ends of the simulation region are vascular bundles. We assumed that the radius of the DVB is 20 µm (5 grid widths) and that of EVB is 44 µm (11 grid widths), which is close to the average length measured from the images of the node cross-sections (2). We also assumed that Si cannot diffuse at the grid points not included in PCB, DVB, and EVB.

Model description.

At the symplast and apoplast, Si diffuses freely at a rate determined by specific diffusion coefficients as follows:

$$\frac{\mathrm{\partial }C}{\mathrm{\partial }t}=D\left(\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{y}^2}\right),$$ [S1]

where C is the Si concentration (mM), t is time (s), D is the diffusion coefficient (μm²⋅s⁻¹), x is the horizontal coordinate (µm), and y is the vertical coordinate (μm). We set the value of D to 1,000 μm²⋅s⁻¹ (11). At the xylem site, Si moves toward the panicle or the flag leaf according to an advection–diffusion equation:

$$\frac{\mathrm{\partial }C}{\mathrm{\partial }t}=D\left(\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{y}^2}\right)+\mathit{u}\frac{\mathrm{\partial }C}{\mathrm{\partial }y},$$ [S2]

where C is the Si concentration (mM⋅m⁻²), t is time (s), D is a diffusion coefficient (μm²⋅s⁻¹), x is the horizontal coordinate (μm), y is the vertical coordinate (μm), and u is the velocity of the xylem sap (μm⋅s⁻¹).

In the simulation, Si moves through the cell membrane following three pathways (11). First, Si can move between the symplast and apoplast through Lsi6, driven by a concentration difference between the two sites. Second, Si can be actively transported from the symplast to the apoplast through the active efflux transporters, Lsi2 and Lsi3, at a rate that depends on the Si concentration in the symplast (11, 26). Third, we assumed low permeability of the cell membrane itself (not via Lsi transporters: background leakage). In summary, the Si flux across the plasma membrane is described by the following equation:

$$J_{\text{mem}}=-\left({\rho }_{\text{Lsi}6}\mathbf{n}\right)\left(C_{\text{in}}-C_{\text{out}}\right)-\left({\rho }_{\text{Lsi}2}\mathbf{n}\right)C_{\text{in}}-\left({\rho }_{\text{Lsi}3}\mathbf{n}\right)C_{\text{in}}-\left({\rho }_m\mathbf{n}\right)\left(C_{\text{in}}-C_{\text{out}}\right),$$ [S3]

where J_mem is the Si flux across the plasma membrane (mM⋅μm⋅s⁻¹); C_in and C_out are the Si concentrations in the symplast and apoplast, respectively, at the grid points immediately adjacent to the plasma membrane; ρ_m is the permeability of the plasma membrane (μm⋅s⁻¹) (i.e., the background leaking); ρ_Lsi6 is the permeability of the Lsi6 transporter (μm⋅s⁻¹); ρ_Lsi2 and ρ_Lsi3 are the Lsi2 and Lsi3 transporter activities (μm⋅s⁻¹); and n is the inward (from apoplast to symplast) directed unit vector that is perpendicular to the plasma membrane (26). Therefore, the dynamics for Si in the grid points that are immediately adjacent to the plasma membrane become

$$\frac{\mathrm{\partial }C}{\mathrm{\partial }t}=D\left(\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^{2}C}{\mathrm{\partial }{y}^2}\right)+\frac{J_{\text{mem,x}}}{\mathrm{\partial }x}+\frac{J_{\text{mem,y}}}{\mathrm{\partial }y},$$ [S4]

where J_mem,x is the Si flux across the plasma membrane in the x direction and J_mem,y is the Si flux across the plasma membrane in the y direction (mM⋅µm⋅s⁻¹).

The boundary conditions at the upper limit and both ends of the vascular bundles were Neumann boundary conditions (with the fluxes across the boundary set to zero). The boundary conditions at the lower limit of the vascular bundles were Dirichlet boundary conditions (with the Si concentration set to 2.0 mM).

Velocity of the xylem in node I.

The water transpiration from the panicle and flag leaf in the stem feed experiment was calculated by using strontium (Sr) accumulated in each organ. Average transpirations from panicle and flag leaf were 16.1 ± 2.4 mL⋅d^–1 and 3.2 ± 0.7 mL⋅d^–1, respectively. We measured the area of each DVB and EVB on the cross-section image of the node I (2). The average area of each DVB and EVB were 0.0065 and 0.015 (cm²), respectively. Therefore, we estimated that the velocity of the xylem in the EVB and DVB were 124.2 and 42.74 (µm⋅s⁻¹), respectively.

Ratio of Si distribution in the panicle and flag leaf.

The distribution ratio of Si to the panicle was calculated as follows:

$$R_{\text{Si}}=\frac{M_{\text{Si},\text{panicle}}}{M_{\text{Si},\text{panicle}}+M_{\text{Si},\text{leaf}}}=\frac{r_{\text{Sr}}{C}_{\text{Si,panicule}}}{{\mathit{r}}_{\text{Sr}}{C}_{\text{Si,panicule}}+C_{\text{Si},\text{leaf}}},$$ [S5]

where R_Si is the distribution ratio of Si in the panicle to that in the flag leaf and the panicle, M_Si,panicle is the amount of Si accumulated in the panicle, M_Si,leaf is the amount of Si accumulated in the flag leaf, r_Sr is the distribution ratio of Sr used as the proxy of the water transpiration in the panicle to that in the flag leaf (=3.2/16.1 = 0.199), C_Si,panicle is the concentration of Si at upper boundary of the DVB, and C_Si,leaf is the concentration of Si at upper boundary of the EVB.

Model calibration.

To estimate the probability distributions of ρ_Lsi2, ρ_Lsi3, ρ_Lsi6, and ρ_m, we calculated 3,000 simulations with different parameter sets. First, we randomly generated the parameter values of ρ_Lsi2, ρ_Lsi3, ρ_Lsi6, and ρ_m from uniform distributions that ranged from 0.0 to 20.0 μm⋅s⁻¹ for ρ_Lsi2 and ρ_Lsi3, from 0.0 to 250.0 μm⋅s⁻¹ for ρ_Lsi6, and from 0.0 to 1.0 μm⋅s⁻¹ for ρ_m. Then, we simulated the model using each parameter set. We simulated the Si concentration in the upper boundaries of the DVB and EVB at 10 min after 2.0 mM Si supply from lower boundary of the node (start of the simulation). For each parameter set, we conducted four simulations: WT, each parameter value ≠ 0; lsi2, ρ_Lsi2 = 0; lsi3, ρ_Lsi3 = 0; and lsi6, ρ_Lsi6 = 0. Then, we calculated the likelihood for each simulation in accordance with the in vivo experimental data. We calculated the likelihood for each parameter set as follows:

$$L\left(\theta |\text{Data}\right)={\displaystyle \prod \frac{1}{\sqrt{2\mathrm{\pi }{\sigma }_i^2}}}\exp \left[-\frac{{\left(r_{\text{Si,est}\left(\mathit{i}\right)}\left(\theta \right)-r_{Si,\text{obs}\left(i\right)}\right)}^2}{2{\sigma }_i^2}\right],$$ [S6]

where L is the likelihood of parameter set θ under the observed dataset Data; σ_i is the SD of the error distribution; r_{Si, est(i)} (θ) is the simulated Si ratio with parameter set θ; r_{Si, obs(i)} (θ) is the observed Si ratio; and subscript i indicates WT, lsi2, lsi3, or lsi6. We used the SD of the experimental data for σ_i to calculate the likelihood for 3,000 parameter sets. Finally, we resampled the parameter sets based on their likelihood and estimated the means and SD of the parameters. The average of the estimated probability distribution for the transport activity of Lsi2 was 7.05 ± 2.10 µm⋅s⁻¹, the transport activity of Lsi3 was 6.19 ± 2.17 µm⋅s⁻¹, the permeability of Lsi6 was 136.25 ± 68.49 µm⋅s⁻¹, and the permeability of the cell membrane (i.e., the background leaking) was 0.30 ± 0.24 µm⋅s⁻².

Simulation experiments.

We conducted nine simulation experiments under the following settings: normal, normal setting as wild-type rice; lsi6, lack of Lsi6; lsi3, lack of Lsi3; lsi2, lack of Lsi2; lsi2lsi3, lack of both Lsi2 and Lsi3; no barrier, no apoplastic barrier at the bundle sheath of EVB; fast EVB, 10× faster velocity of the xylem in EVB as proxy for no enlargement of EVB; no XTC, the permeability parameter of Lsi6 replaced by that of Lsi1 in root (11) to mimic no xylem transfer cell development; and no all, the combined defect of all these factors. We conducted simulation experiments using 30 parameter sets that were randomly selected from the 3,000. These simulations were conducted with different input Si concentrations at 2.0 and 20.0 mM.

We further simulated with doubled resolution of y axis. In the default setting, each grid size was 4 × 40 µm because of the limitation of the computational resource. However, the resulting number of the cells vertically located in the default setting was only three, and this may affect the result of the simulation experiments. We confirmed the results of the default experiments by changing the y axis resolution (4 × 20 µm) and changing the number of cells located vertically (six).