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First published online December 29, 2005; 10.1104/pp.105.073130 Plant Physiology 140:603-612 (2006) © 2006 American Society of Plant Biologists
Progressive Inhibition by Water Deficit of Cell Wall Extensibility and Growth along the Elongation Zone of Maize Roots Is Related to Increased Lignin Metabolism and Progressive Stelar Accumulation of Wall Phenolics1Plant Physiology Laboratory, Department of Environmental, Water, and Agricultural Engineering, Faculty of Civil and Environmental Engineering (L.F., R.L., P.M.N.) and Faculty of Biology (S.G.), Technion-Israel Institute of Technology, Haifa 32000, Israel; Plant Physiology Laboratory, Department of Information and Biological Sciences, Graduate School of Natural Sciences, Nagoya City University, Nagoya 4678501, Japan (E.T.); and Biology and Chemistry Laboratory, Tezukayama University, Nara 6318585, Japan (R.Y.)
Water deficit caused by addition of polyethylene glycol 6000 at 0.5 MPa water potential to well-aerated nutrient solution for 48 h inhibited the elongation of maize (Zea mays) seedling primary roots. Segmental growth rates in the root elongation zone were maintained 0 to 3 mm behind the tip, but in comparison with well-watered control roots, progressive growth inhibition was initiated by water deficit as expanding cells crossed the region 3 to 9 mm behind the tip. The mechanical extensibility of the cell walls was also progressively inhibited. We investigated the possible involvement in root growth inhibition by water deficit of alterations in metabolism and accumulation of wall-linked phenolic substances. Water deficit increased expression in the root elongation zone of transcripts of two genes involved in lignin biosynthesis, cinnamoyl-CoA reductase 1 and 2, after only 1 h, i.e. before decreases in wall extensibility. Further increases in transcript expression and increased lignin staining were detected after 48 h. Progressive stress-induced increases in wall-linked phenolics at 3 to 6 and 6 to 9 mm behind the root tip were detected by comparing Fourier transform infrared spectra and UV-fluorescence images of isolated cell walls from water deficit and control roots. Increased UV fluorescence and lignin staining colocated to vascular tissues in the stele. Longitudinal bisection of the elongation zone resulted in inward curvature, suggesting that inner, stelar tissues were also rate limiting for root growth. We suggest that spatially localized changes in wall-phenolic metabolism are involved in the progressive inhibition of wall extensibility and root growth and may facilitate root acclimation to drying environments.
Water deficit occurs in drying environments when water uptake via the plant root system cannot meet water requirements for unrestricted growth, photosynthesis, and transpiration in the shoots. Water deficit can reduce root growth, shoot growth, and crop yields on a world wide scale (Boyer, 1982
In maize (Zea mays) primary roots, cell production, final cell length, the length of the root elongation zone, and overall root elongation rates are all reduced under water deficit (Fraser et al., 1990
Micropressure probe measurements indicated that turgor pressures remain fairly constant along and beyond the length of the elongation zone of maize roots under well-watered and water deficit conditions, despite the segmental variation in growth rates (Spollen and Sharp, 1991
The mechanisms involved in regulating cell wall extension capacity and hence growth in roots (and elsewhere in plants) remain the subject of intensive investigation and frequent review (e.g. Taiz, 1984
Maize has type 2 cell walls, which are composed of proteins, cellulose microfibrils, glucuronoarabinoxylans of varying degrees of side group substitution, and mixed-linkage We reasoned that maize root tissues grow at comparable rates from 0 to 3 mm behind the tip under control and water deficit conditions, while the growth-inhibitory developmental changes induced by water deficit begin to take effect in the region situated 3 to 9 mm behind the tip. We therefore investigated changes in metabolism and accumulation of cell wall-linked phenolic substances and the progressive inhibition by water deficit of wall extensibility and growth rates in this region.
Lignin is well known as a phenolic compound involved in reducing wall extensibility. Moreover, enzymes such as cinnamoyl-CoA reductase (CCR, EC 1.2.1.44) are active at the entry point to the monolignol-specific branch of the lignin biosynthetic pathway in maize and other species (Pichon et al., 1998
Effects of Polyethylene Glycol 6000-Induced Water Deficit on Root Growth Parameters
Water deficit is known to cause reductions in cell size and differential changes in segmental growth rates and wall extensibility along the approximately 10-mm long elongation zone at the apex of maize primary roots. We added a nonpenetrating osmoticum, polyethylene glycol (PEG) 6000 (at 0.5 MPa water potential) to the well-aerated nutrient medium to impose a 48-h water deficit on maize seedlings. After 48 h under these conditions, rates of root elongation were quasi-linear and approximately half that of well-watered control roots (Fan and Neumann, 2004
The mean lengths of fully elongated cortical cells were also reduced, from 0.238 ± 0.002 mm for unstressed controls to 0.157 ± 0.001 mm under water deficit (means ± SE, n = 210). The progressively increasing inhibition by water deficit of root segmental growth rates along the region 3 to 9 mm behind the tip was associated with significant (P = 0.05) reductions in comparative mechanical extensibility (assayed at pH 4.6 to maximize wall loosening) of cell walls in alcohol-extracted root tissue segments from the same region. Thus, wall extensibility in the 3-to-6-mm region, where growth inhibition was initiated, was reduced from 0.219 ± 0.003 mm mm1 in well-watered controls to 0.199 ± 0.005 mm mm1 under water deficit (means ± SE, n Having established that our water deficit regime resulted in spatially localized root growth responses similar to those previously reported by others, we proceeded to investigate the possible involvement of cell wall phenolics in these responses.
CCR1 and CCR2 are important genes in the biochemical pathways of lignin biosynthesis. Using a candidate gene approach, PCR amplification, and northern-blot assays (as described in "Materials and Methods") we detected basal levels of CCR transcript expression in the elongation zone of control roots. These were up-regulated after 1 and 48 h of water deficit treatment as shown by the CCR1 and CCR2 amplicons and the related bar graph, which shows the progressive increases in ratio-corrected (in comparison with 18S RNA) pixel densities for each PCR product after 1 or 48 h of water deficit (Fig. 1A). The CCR products of the PCR appeared in the expected positions on the gel, and when sequenced they showed 96% and 100% homology to equivalent sequences in the gene database for CCR1 and CCR2, respectively. Similar stress-induced increases in CCR transcript expression were revealed by the northern-blot analyses (Fig. 1B). Thus, transcripts of genes involved in biosynthesis of lignin from its phenolic precursors were expressed within the root elongation zones of well-watered roots and of roots under water deficit. Since transcript levels were up-regulated within 1 h of imposition of water deficit and before measurable changes in wall extensibility, they may be causally related to changes in wall lignin deposition, which could stiffen the wall and reduce its extensibility. We have not yet determined the spatial distribution of CCR gene transcripts. However, direct evidence for localized effects of water deficit on accumulation in the root elongation zone of cell wall phenolics and lignin was provided by IR, UV, and lignin staining.
Water Deficit Causes Spatial Changes in Cell Wall Composition
FTIR spectral analyses were performed on root cell walls that were repeatedly alcohol extracted to ensure relative freedom from interference by soluble contaminants. To establish the segmental distribution of stress-induced cell wall changes, FTIR spectra were collected in the mid-IR range for separate batches of cell wall material from 0 to 3, 3 to 6, 6 to 9, and 9 to 12 mm behind the root tip. The left-hand side of Figure 2 shows FTIR spectra at 2,000 to 800 cm1 for cell wall material from water deficit treated (upper spectrum) and control roots. The arrow (Fig. 2, a) marks a typical shoulder in the 1,720 to 1,740 cm1 region, which is indicative for alkyl and phenolic esters. The horizontal bar (Fig. 2, b) emphasizes major bands indicative of amide I and amide II. The arrow (Fig. 2, d) points to an absorbance band around 1,245 cm1, which also suggests phenolic and ester groupings. The bar (Fig. 2, e) indicates carbohydrate absorbance bands (Séné et al., 1994
The FTIR spectra were statistically analyzed for possible differences induced by water deficit using principal component analysis (PCA). Exploratory PCA was able to detect significant differences between cell wall spectra from water deficit and control treatments only in the 1,800 to 1,600 cm1 region surrounding the 1,720 to 1,740 cm1 shoulder and in the 1,260 to 1,220 cm1 region surrounding the 1,245 cm1 peak. These treatment-induced differences appeared in each of the root regions that were investigated and are indicated by the separation between white and black symbols in Figure 3, A and B, respectively. Thus, water deficit induced statistically significant differences in the phenolic absorbance of cell wall material along the entire root elongation zone, while carbohydrate and amide (protein) absorbance did not appear to change.
The progressive effects of water deficit on the absorbance of phenolics and esters in walls from different regions along the root elongation zone were clearly revealed by digital subtraction of appropriate spectral absorbance values for nonstressed roots from spectral absorbance values of equivalent regions in roots under water deficit. The difference spectra for 1,780 to 1,680 cm1 and for 1,300 to 1,200 cm1 are shown in separate plots on the right-hand side of Figure 2. The plots reveal the progressive increases in absorbance (points above the horizontal zero line) that were induced by the water deficit treatment at increasing distances from the tip (03, 36, and 69 cm) and at two independent sets of wave numbers associated with wall phenolic and ester linkages, i.e. 1,720 to 1,740 cm1 and 1,245 cm1. The mean absorbance difference at 1,720 cm1 progressively increased from 0.75 ± 0.60 cm1 at 0 to 3 cm from the tip to 2.34 ± 0.37 cm1 at 3 to 6 cm and 3.93 ± 1.16 cm1 at 6 to 9 cm. Similarly, absorbance difference at 1,245 cm1 progressively increased from 1.63 ± 0.32 cm1 at 0 to 3 cm from the tip to 2.19 ± 0.11 cm1 at 3 to 6 cm and 2.98 ± 0.26 cm1 at 6 to 9 cm (means ± SE, n = 6). The water deficit-induced increase in absorbance of phenolics at 6 to 9 cm from the tip was spatially associated with the region of greatest root growth inhibition by water deficit. The increases in this region might be caused by direct stress effects on development or as a developmental result of stress-induced and premature cessation of elongation. Water deficit also appeared to increase absorbance by phenolics in expanding cell walls from 3 to 6 mm behind the tip, where segmental elongation rates in water deficit-treated roots first began to decrease. The longitudinal and radial distribution of phenolic substances in cell walls of different tissues was investigated in more detail by microscopic assay of the UV-induced autofluorescence produced by phenolics in thin (50 µm) microtome cross sections from along the elongation zone of alcohol-extracted roots. The color images in horizontal column A of Figure 4 show that for well-watered control roots, the bright blue-green autofluorescence associated with wall phenolics was virtually absent from cortical and stelar tissues midway along the region 0 to 3 mm behind the tip and was relatively weak at 3 to 6 mm behind the tip. The autofluorescence became somewhat stronger in the inner stelar tissues of the 6-to-9-mm region while fluorescence in the outer epidermal and cortical tissues remained relatively weak.
Horizontal column B shows cross sections excised at equivalent distances from the tips of roots growing under water deficit and viewed at the same intensity of incident UV light. The diameters of these cross sections were relatively reduced, and this is consistent with the thinning of maize roots noted under water deficit regimes (Sharp et al., 1988
Weak autofluorescence also occurred along the epidermal regions of the elongation zones of roots under water deficit or control conditions, and treatment-related differences were occasionally observed. These and the treatment-related differences detected by FTIR in bulked cell wall preparations from 0 to 3 mm behind the tip might involve UV fluorescence of phenolic substances trapped in root mucilages secreted by the epidermis (Walker et al., 2003 Figure 4, C and D, show the inward curvature observed 2 h after bisecting the elongation zone of live roots under control or water deficit conditions (i.e. in PEG). The inward curvature suggests that growth-limiting tissues in the water deficit-treated roots, as in well-watered controls, were located in the inner (stelar) part of the root, rather than the outer cortical tissues and epidermis. Treatment of cell walls with Maule reagent should produce brown staining in the presence of lignins. Figure 4E shows a section 6 to 9 mm from the root tip of control roots, and Figure 4F shows the equivalently located section from roots under water deficit. Increases in lignin staining were detectable in vascular regions of the stele in water deficit-treated roots. Interestingly, this staining colocalized with stress-induced increases in UV fluorescence. Phloroglucinol-HCl treatment also revealed stress-enhanced lignin staining but only in the walls of a few stelar cells (data not shown).
The phenolic identity of the wall compounds producing UV fluorescence was confirmed by chemical treatments. Treatment of plant cell walls with hot acidic chlorite can oxidize wall-associated phenolics, including those in lignins. Figure 4G shows that most of the autofluorescence in a cell wall cross section taken 6 to 9 mm from the root tip had disappeared after a 1-h chlorite treatment. The same response was observed at other locations along the roots. In addition, the expected enhancement of fluorescence by wall phenolics was observed after exposure of root cell wall cross sections to 0.1 M ammonium hydroxide solution (data not shown; Harris and Hartley, 1976
Water deficit caused by addition of PEG 6000 to the root medium induced reductions in final cell length and progressive reductions in segmental growth rates in basal regions of the elongation zone. These were similar to the results reported by others (Sharp et al., 1988 It might be argued that the changes induced by water deficit in the region 6 to 9 mm behind the root tip simply reflected the shortening of the effective length of the elongation zone from approximately 9 mm to approximately 6 mm and developmental changes associated with (premature) cell maturation. However, the important question that remains is by what cellular mechanisms does water deficit act to shorten final cell lengths, progressively inhibit segmental growth rates, and decrease the effective length of the root elongation zone? Since segmental growth rates were not inhibited by water deficit in the region 0 to 3 mm behind the tip, we looked for possible stress-induced changes in wall composition along the region 3 to 9 mm behind the tip. In this region the reductions in segmental growth rates caused by water deficit are initiated (36 mm behind the tip) and increased (69 mm), as the traversing cells rapidly move toward maturity.
Our finding that transcripts of CCR genes are expressed in the elongation zone of control and water deficit-treated roots is consistent with the idea that water deficit affected lignin metabolism. CCR (EC 1.2.1.44) catalyzes the conversion of hydroxycinnamoyl-CoA thioesters to cinnamaldehydes at the entry point to the monolignol-specific branch of the lignin biosynthetic pathway. Genetic transformations in tobacco (Nicotiana tabacum), Arabidopsis, and poplar (Populus spp.) have directly confirmed that CCR can affect the amount and composition of lignin accumulated in plant cell walls (Boerjan et al., 2003
Water deficit for 1 or 48 h had distinct up-regulatory effects on levels of CCR transcripts, particularly CCR2, which was only weakly expressed in the well-watered roots (compare with Pichon et al., 1998
Increased deposition of lignin would be expected to stiffen the affected cell walls, thereby reducing their extensibility and decreasing rates of cell expansion. It is therefore noteworthy that up-regulated levels of both CCR1 and CCR2 were detectable as early as 1 h after imposing water deficit, i.e. before the onset of significant stress-induced reductions in wall mechanical extensibility. Since the increased expression of CCR transcripts preceded the onset of wall stiffening, a causal relationship between the two events is conceivable. The increased lignin deposition revealed by chemical staining of cell walls in the 6-to-9-mm region of 48-h water-stressed roots directly supports this conclusion. Increased wall deposition of lignin may also help explain limited in vitro response of cell wall extension to acid pH and limited in vivo growth response to acid pH in basal regions of the elongation zone of roots under water deficit, as compared with more apical regions (Wu et al., 1996
The altered deposition of lignin and wall-bound phenolics induced by water deficit was located primarily in the inner tissues of the root elongation zone. Several reports involving surgical treatments indicate that it is the slower expansion of the inner tissues, as compared with cortical and epidermal tissues, which limits overall rates of maize root elongation under well-watered conditions (compare with Björkman and Cleland, 1991
The digital subtraction of mid-IR spectra of cell walls from control and water-stressed roots provided additional evidence for local and progressive effects of water deficit on the phenolic composition of cell walls. Thus, water deficit caused progressive increases in phenolic-associated FTIR absorbance in expanding root cell walls from regions 3 to 6 and 6 to 9 mm behind the tip, i.e. the regions where growth inhibition was initiated and then progressively increased. The UV-fluorescence microscopy images of cross sections of root cell wall ghosts further confirmed the spatially progressive effects of water deficit. Thus, water deficit resulted in comparative increases in the accumulation in stelar cell walls of the blue-green autofluorescence indicative of phenolics and in chemical staining for lignin. The finding that wall fluorescence was removed by hot acid chlorite and enhanced by ammonium hydroxide further supported the conclusion that water deficit affected the deposition of phenolics (Harris and Hartley, 1976
A possible regulatory role of phenolic wall constituents in the progressive onset of wall hardening and growth inhibition is suggested by the progressive stress-induced increases in levels of wall-bound phenolics indicated by both the FTIR and UV analyses at 3 to 6 and 6 to 9 mm behind the root tip. These increases are consistent with increased ester binding of p-coumaric or ferulic acids. Other phenolic constituents such as Tyr, which is a constituent of wall structural proteins and can form dityrosine linkages between them, might also be involved in decreasing wall mechanical extensibility (Fry, 2004 Although beyond the scope of this report, chemical investigations of the specific types of phenolic molecules accumulated in the cell walls of the stelar tissues of the maize root elongation zone under water deficit are still needed. Selective inhibition of their synthesis by genetic or pharmacological means might then provide conclusive evidence for functional relationships between their accumulation and the local growth inhibition induced by water deficit. Nevertheless, our data provide support for the hypothesis that novel, spatially localized increases in the accumulation of wall-bound phenolics, including lignin, are linked to local root growth inhibition by water deficit and suggest future avenues of enquiry.
Could the local shifts in root cell wall composition induced by water deficit and the associated inhibition of wall extensibility and root growth contribute in any way to plant acclimation to drying environments? One possibility is that specific inhibition of growth in basal regions of the root elongation zone increases the relative availability of water, minerals, and sugars needed for maintaining minimal growth and survival of the younger cells in more apical regions. Keeping younger cells alive during episodes of intermittent water deficit could facilitate root growth recovery after rehydration.
Maize root growth under water deficit is well maintained in the region of the elongation zone situated 0 to 3 mm behind the tip and is progressively inhibited, along with progressive reductions in cell wall extensibility, from 3 to 9 mm behind the tip. This spatially localized growth inhibition may facilitate root acclimation to and survival of drying environments by diverting resources to essential meristemic tissues at the tip. Four lines of interrelated evidence support the hypothesis that alterations in patterns of wall-phenolic accumulation in the root elongation zone may be involved in regulating the inhibition by water deficit of wall extensibility and root growth: (1) Transcripts of two CCR genes involved in lignin biosynthesis were detected in the elongation zone of well-watered and stressed roots; (2) CCR transcript levels increased after only 1 h under water deficit and before reductions in cell wall extensibility, suggesting a possibly causal association; (3) progressive increases in IR absorbance and UV fluorescence, both indicative of wall-bound phenolics, were observed from 3 to 9 mm behind the tips of water deficit-treated roots and colocalized with the progressive inhibition of wall extensibility and growth; and (4) the increases in UV fluorescence and lignin staining induced by water deficit were located primarily to cell walls of inner tissues in the stele, and these tissues appeared to specifically limit root growth rates.
Plant Growth
Maize seeds (Zea mays cv 647) supplied by Galilee Seeds were germinated on moistened filter paper for 4 d and then transferred to hydroponic culture with roots in well-aerated 0.1-strength nutrient solutions under a controlled environment, as in Fan and Neumann (2004) Lengths of fully elongated cortical cells in hand-cut longitudinal strips from approximately 2 cm behind the growing zone of control or water deficit-treated roots were estimated using images of cell files a few layers outside the vascular cylinder. Images from 14 roots were analyzed. Images were captured using a digital microscope/camera (Olympus, MIC-D/DP01) and the lengths of around 15 clear-cut cells per root were measured by counting pixels at a resolution of 1,105 pixels/mm. Unless otherwise stated, seedlings were equilibrated under water deficit for 48 h so that all of the cells within and immediately beyond the root elongation zone were representative of cells that developed under water deficit.
Roots of maize seedlings were grown for 48 h in 0.1-strength Hoagland solution without PEG or with PEG at 0.5 MPa water potential. The apical 20 mm of the roots were then excised and extracted in boiling methanol for 5 min. The resultant cell wall ghosts were stored in methanol. Root samples were hydrated in 0.2 M sodium acetate buffer at pH 4.6 for 15 min. Diameters of the root samples were measured with a low-power microscope and used to determine cross-sectional areas. Individual root samples were secured between two clamps of a Rheoner creep meter (Yamaden RE-33005) so that the extension capacity of root sections at 3 to 6 or 6 to 9 mm from the tip could be assayed (Tanimoto et al., 2000
Approximately 3 g of root material was excised from the elongation zone starting 1 mm behind the tip of control seedlings and of seedlings exposed to 1 or 48 h of water deficit treatment. The root material was immediately ground in liquid nitrogen. Total cellular RNA was extracted from the ground tissue according to Puissant and Houdebine (1990) Semiquantitative RT-PCR was carried out using a QuantumRNA18S Internal Standard kit (Ambion) according to the manufacturer's recommendations. The linear range was determined by plotting cycles (1836) against pixel density of PCR product with equal loading volumes for each sample. Thirty cycles and a 2:8 ratio of 18S primer to competimer was found to be optimal for both genes. The PCR products were separated in a 2% agarose EtBr gel. The pixel density of gel images was read and calculated by MATLAB command. The relative quantity of each sample was obtained as the pixel densities for the gene-specific amplicon divided by the 18S amplicon. In addition, the CCR products of the PCR were cloned into pGEM-easy vector (Promega) and sequenced (Macrogene) to confirm the gene identities.
Samples of 20 µg (for CCR1) and 30 µg (for CCR2) of total RNA were separated in 1.2% agarose-formaldehyde gels, transferred to Amersham Hybond-N nylon membranes, and cross-linked by UV radiation. Hybridization probes were made by cloning the PCR fragments into pGEM-easy vector, and the gene identity was confirmed by its sequence. Specific primers were used to amplify the sequences. Labeling was generated by random priming in the presence of [a-32P] dCTP (Amersham). Prehybridization, hybridization, and washing were conducted according to Sambrook et al. (1989)
Maize roots were grown for 48 h in 0.1-strength Hoagland solution ± 0.5 MPa PEG 6000. Roots were excised at about 2 cm from the tip. The 2-cm sections were plunged into 50% ethanol at 85°C for 10 min. The roots were subsequently extracted in 80% ethanol at 85°C for 10 min and absolute ethanol at 85°C for 10 min. The resultant root cell wall ghosts were then cut into sections 0 to 3, 3 to 6, 6 to 9, and 9 to 12 mm from the tip and stored in absolute ethanol at 4°C.
Prior to use, root sections were removed from alcohol and dried at 45°C for 0.5 h. Aliquots of 2 mg were then ground in a mortar with 200 mg of pure desiccated KBr to produce a uniform powder. The mixture was transferred to a 13-mm die and pressure at approximately 9,000 kg was applied for 2 min under continuous evacuation. This produced a 13-mm diameter and 1-mm thick disc as described by Stuart (1997) A FTIR spectrometer (Vector 22, Bruker Optic) was used to obtain the IR spectra. The spectrometer was equipped with a mercury-cadmium-telluride detector. Each disc was scanned 32 times, and the average absorbance spectrum in the 4,000 to 400 cm1 range was recorded. The spectrum was baseline corrected and area normalized in the region 2,000 to 800 cm1 by using OPUS-NT spectroscopic software (version 3, Bruker Optic). Results of six replicate experiments were combined to produce average spectra for each section of the root.
Differences between spectra of walls of roots from control and water deficit treatments were investigated using PCA, a mathematical procedure commonly used for data reduction and/or data classification (e.g. Jackson, 1991
Root cell wall ghosts were prepared by hot alcohol extraction. Sections 1 mm long were then hand cut from the middle of regions 0 to 3, 3 to 6, 6 to 9, and 9 to 12 mm from the tip. For chlorite treatment, sections were transferred to 0.34 M NaClO2 in 65 mM acetic acid at 65°C for 1 h, rinsed in distilled water several times, and stored in ethanol (Carpita et al., 2001
For staining experiments, root cross sections were hand cut from the middle of the region 6 to 9 mm behind the tip of alcohol-extracted and rehydrated cell wall ghosts prepared from well-watered and water deficit-treated roots. These were stained using Maule reagent as described by Chapple et al. (1992) Received October 20, 2005; returned for revision October 20, 2005; accepted November 21, 2005.
1 This work was supported by FMW chair and Manlam (grant to P.M.N.) and a Zeff Fellowship (to R.L.). The author responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors (www.plantphysiol.org) is: Peter M. Neumann (agpetern{at}tx.technion.ac.il). Article, publication date, and citation information can be found at www.plantphysiol.org/cgi/doi/10.1104/pp.105.073130. * Corresponding author; e-mail agpetern{at}tx.technion.ac.il; fax 97248228898.
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