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First published online January 27, 2006; 10.1104/pp.105.071845 Plant Physiology 140:1070-1084 (2006) © 2006 American Society of Plant Biologists Function and Characterization of Starch Synthase I Using Mutants in RiceDepartment of Biological Production, Akita Prefectural University, Akita City, Akita 0100195, Japan (N.F., M.Y., N.A., T.O., Y.N.); Core Research for Evolutional Science and Technology, Japan Science and Technology, Kawaguchi, Saitama 3320012, Japan (N.F., M.Y., T.O., Y.N.); and National Institute of Agrobiological Sciences, Tsukuba, Ibaraki 3058602, Japan (A.M., H.H.)
Four starch synthase I (SSI)-deficient rice (Oryza sativa) mutant lines were generated using retrotransposon Tos17 insertion. The mutants exhibited different levels of SSI activities and produced significantly lower amounts of SSI protein ranging from 0% to 20% of the wild type. The mutant endosperm amylopectin showed a decrease in chains with degree of polymerization (DP) 8 to 12 and an increase in chains with DP 6 to 7 and DP 16 to 19. The degree of change in amylopectin chain-length distribution was positively correlated with the extent of decrease in SSI activity in the mutants. The structural changes in the amylopectin increased the gelatinization temperature of endosperm starch. Chain-length analysis of amylopectin in the SSI band excised from native-polyacrylamide gel electrophoresis/SS activity staining gel showed that SSI preferentially synthesized DP 7 to 11 chains by elongating DP 4 to 7 short chains of glycogen or amylopectin. These results show that SSI distinctly generates DP 8 to 12 chains from short DP 6 to 7 chains emerging from the branch point in the A or B1 chain of amylopectin. SSI seemingly functions from the very early through the late stage of endosperm development. Yet, the complete absence of SSI, despite being a major SS isozyme in the developing endosperm, had no effect on the size and shape of seeds and starch granules and the crystallinity of endosperm starch, suggesting that other SS enzymes are probably capable of partly compensating SSI function. In summary, this study strongly suggested that amylopectin chains are synthesized by the coordinated actions of SSI, SSIIa, and SSIIIa isoforms.
Starch biosynthesis in higher plants is catalyzed by four classes of enzymes; ADP-Glc pyrophosphorylase (AGPase), starch synthase (SS), starch branching enzyme (BE), and starch debranching enzyme (DBE; Smith et al., 1997
SS (EC 2.4.1.21) elongates glucans by adding Glc residues from ADP-Glc to the glucan nonreducing ends through
Various SS isoforms have been identified through gene sequences in several plant genomes. In rice, there are 10 SS isoforms separated into five types; two granule-bound starch synthase (GBSS) isoforms (GBSSI and GBSSII) in the GBSS type, one SSI isoform in the SSI type, three SSII isoforms (SSIIa [SSII-3], SSIIb [SSII-2], and SSIIc [SSII-1]) in the SSII type, two SSIII isoforms (SSIIIa [SSIII-2] and SSIIIb [SSIII-1]) in the SSIII type, and two SSIV isoforms (SSIVa [SSIV-1] and SSIVb [SSIV-2]) in the SSIV type (Hirose and Terao, 2004
SSI probably plays important role(s) in starch biosynthesis in plants since it has no multiple isoforms, unlike all other SS types having more than two isoforms in rice (SSII, SSIII, SSIV, and GBSS; Hirose and Terao, 2004
Although these reports suggest that monocot or dicot SSIs have a specific role in the elongation of short chains in vitro, there are very few reports regarding their function in vivo. Kossmann et al. (1999) In this study, four allelic mutant lines of rice generated by retrotransposon Tos17 insertion and carrying SSI mutations expressed in endosperm, one containing a null mutation and three exhibiting different levels of SSI activity, were biochemically characterized. Analysis of amylopectin chain-length distribution and starch physicochemical traits of these mutants clarified the in vivo function of rice SSI in amylopectin biosynthesis.
Characterization of SSI in Developing Rice Endosperm
In this study, soluble fraction from rice developing endosperm was separated by anion-exchange (HiTrapQ, Pharmacia) chromatography with a linear gradient of 0 to 0.5 M NaCl. One peak of SS activity that eluted at 0.2 to 0.25 M of NaCl was detected in the presence of 0.5 M citrate and the absence of exogenous primers, whereas two SS activity peaks were detected at about 0.2 to 0.25 M and 0.35 M, in the absence of citrate but in the presence of glycogen primer (Fig. 1A
). These results are similar to those obtained from maize fractionation by Q-sepharose (Cao et al., 2000
Mu-Forster et al. (1996) SSI and SSIIIa activities of the endosperm SP were detectable from DAF 9 to DAF 25 (dehydration stage of endosperm; Fig. 1C). To analyze the changes in the localization of rice SSI in starch granules during endosperm development, the three protein fractions extracted from developing endosperms at DAF 12 to 30 were subjected to immunoblotting using SSI antiserum, and the amounts of SSI protein were estimated from band densities (Fig. 1D). The amounts of SSI proteins in the endosperm SP per endosperm were high at early stages (DAF 1216) but gradually diminished at later stages during which LBP and TBP increased (Fig. 1D), while the total amount of SSI protein gradually increased (Fig. 1D). GBSSI was detected in TBP, but not in SP or LBP, and rapidly increased after DAF 16 (Fig. 1D).
Nine lines containing Tos17 insertion in the rice SSI gene (OsSSI) were isolated by PCR screening of approximately 40,000 Tos17 knockout rice population (see "Materials and Methods"). OsSSI is composed of 15 exons and 14 introns (Fig. 2A ). Four lines carrying Tos17 insertion in intron 2 (lines i2-1, i2-2), intron 4 (line i4), or exon 7 (line e7) were chosen for this study (Fig. 2A). The genotype of the lines were determined as either homozygous for Tos17 (/) or wild homozygous (+/+) using nested PCR (see "Materials and Methods"; Fig. 2B). For instance, in line i2-1+/+, the PCR reaction using the T1R, T2R/1F, 2F primer pairs had no product (Fig. 2B, left section, lane i2-1+/+), while 1F, 2F/4R, 5R primer pairs generated an approximately 2 kbp band (Fig. 2B, right section, lane i2-1+/+). In line i2-1/, the PCR product of the T1R, T2R/1F, 2F primer pairs was an approximately 0.35 kbp band (Fig. 2B, left section, lane i2-1/), while the 1F, 2F/4R, 5R primer pairs had no product (Fig. 2B, right section, lane i2-1/). The same PCR results were obtained in other lines (Fig. 2B). The / lines were used as the mutants and +/+ lines as the controls since the background of the +/+ lines was more similar to those of / lines than to the wild-type Nipponbare.
The expression of the OsSSI gene in mutant lines was confirmed by northern blotting. The 2.9 kb mRNA band previously reported to be the normal mRNA of the OsSSI gene (Tanaka et al., 2004
To evaluate the effect of the insertion of Tos17 into the OsSSI gene, SSI activity of the SP from DAF 16 developing endosperm was estimated by native-PAGE/SS activity staining using gels containing oyster glycogen (Fig. 3A ). The SSI bands in every mutant line (/) were significantly decreased or completely lacking compared to those of control lines (+/+). These bands were identical to the SSI band in Figure 1, B and C. To estimate the amount of remaining SSI activity in these mutant lines, varying amounts of SP from control lines were loaded adjacent to the mutant SP on the gel (Fig. 3A). The SSI activities were calculated to be 0 in e7/, roughly 17% in i2-2/, 20% in i2-1/, and 25% in i4/, respectively, of the control lines. In contrast, SSIIIa activity bands in i2-1/, i2-2/, and i4/ were comparable to those of their control lines and appeared to be enhanced 2 to 3 times in e7/ SSI null mutant compared with its e7+/+ control line. The amount of SSI protein in the three fractions (SP, LBP, and TBP) of DAF 12 developing endosperm detected by immunoblotting using antiserum raised against rice SSI was also significantly decreased in SSI mutant lines and was not detected in any fractions from e7/ (Fig. 3B). The total amount of the remaining SSI protein in every fraction in lines e7/, i2-1/, i2-2/, and i4/ was 0%, 3%, 9%, and 20%, respectively, of their control lines, this order being correlated with remaining SSI activity in the respective mutant lines as determined by native-PAGE/SS activity staining (Fig. 3A). To test whether the reduction in SSI protein has pleiotropic effects, activities of other enzymes involved in starch biosynthesis were measured. The activities of BEI, BEIIa, BEIIb, phosphorylase, isoamylase1, and pullulanase detected by native-PAGE/activity staining and the amount of GBSSI protein detected by SDS-PAGE of TBP showed no obvious differences (data not shown). In contrast, AGPase activity in e7/ was approximately 1.6 times (10.58 ± 0.20 mmol min1 endosperm1) of that of its control (6.59 ± 0.36) and the wild type (6.03 ± 0.37), while AGPase activities in nonnull SSI mutants (i2-1/, i2-2/, and i4/) were not significantly different from their respective control lines (data not shown).
The seed morphology of the SSI null mutant line e7/ (Fig. 4A ) and other lines (data not shown) was similar to that of their respective control lines and the wild type. The seed weights of lines i2-1/ and e7/ were not significantly different from those of their control lines and the wild type, while lines i2-2/ and i4/ and their control lines had lighter seeds than the wild type (Table I ), indicating that these decreases in seed weight could not be caused by SSI deficiency but by the insertion of Tos17 in other genes. The amounts of endosperm starch were similar in SSI mutant and control lines (data not shown). This is one of the reasons for the difficulty in the isolation of SSI-deficient mutants by the screening for seed morphology.
X-ray diffraction pattern of the starch granules of Nipponbare, e7+/+, and e7/ was similar, all exhibiting a typical A type (Fig. 4B), indicating that their starches share similar crystalline properties. Examination of the morphology of the starch granules using scanning electron micrograph (SEM) yielded no significant differences among e7/, e7+/+, and the wild-type Nipponbare (Fig. 4C) as well as among i2-1, its control line, and wild type (data not shown).
To examine the effects of SSI deficiency on the amylose content of endosperm starch, the
To evaluate the effects of the SSI activity level on the fine structure of the endosperm amylopectin, the chain-length distribution of isoamylolysate of endosperm amylopectin in the four SSI mutant lines was determined by capillary electrophoresis (Fig. 5, A and B
). In all mutant lines, chains with DP 6 to 7 and DP 16 to 19 were increased and DP 8 to 12 chains were decreased, while DP 20 to 40 chains were slightly increased, although the change was gradually reduced from DP 20 to DP 40 (Fig. 5B). These chain-length distribution patterns of SSI mutant amylopectin are specific as compared with those of other mutant amylopectin analyzed so far (Nakamura, 2002
Starch accumulation in rice endosperm becomes evident after DAF 5 (Sato, 1984 17 chains and less DP 18 chains as compared with those at the early (DAF 7) stage (Fig. 5C, inset). The fact that the alteration of the chain-length pattern in e7/ was already apparent at DAF 7 (Fig. 5C) indicates that SSI is functional from the very early stage of rice endosperm development. In contrast, the patterns from DAF 16 through seed maturity were the same (Fig. 5, B and C), indicating that the function of SSI does not vary during these periods. The DP 20 to 33 chains decreased (0.13 molar %; Fig. 5C) at DAF 7, although the slight increase in DP 20 chains (less than 0.1 molar %; Fig. 5, B and C) was evident from DAF 16 through endosperm maturity, suggesting a different physiological role of SSI in the synthesis of amylopectin structure at the very early stage of endosperm development when starch synthesis is being initiated.
To evaluate the physicochemical properties of endosperm starch in SSI mutant lines, the thermal-gelatinization temperature of endosperm starch was analyzed by differential scanning calorimetry (DSC). The temperatures for the onset (To), peak (Tp), and conclusion (Tc) of gelatinization of endosperm starch in SSI mutant lines were 1°C to approximately 3°C higher than those of control lines (data not shown). The magnitude of Tp change (
The pasting property of the endosperm starch was analyzed by rapid visco analyzer (Fig. 6B). The rate of the rise in the viscosity of e7/ starch as temperature increased was slower than that of e7+/+, and the peak viscosity of e7/ starch was 77% of that of e7+/+. The final viscosity of starch in both lines was similar.
To evaluate the in vitro functions of rice SS isozymes in the wild-type Nipponbare, the changes in chain-length distribution of amylopectin or glycogen in the SS activity band after SS enzymatic reactions in native-PAGE gel were examined. The band corresponding to the SS activity in the gel containing 0.1% of rice amylopectin or 0.8% of oyster glycogen after SS enzymatic reactions for 20 h was excised, and a portion of gel without any activity band at all was also taken as a control. The SS activity band gel segment contained substrate modified by SS isozymes whereas the control gel fragment was assumed to contain unmodified substrate only. The polyglucans in both gel fragments were extracted, processed, and their chain-length distribution patterns were examined and compared.
When oyster glycogen was used as the substrate, the polyglucans produced by the SSI activity band on native-PAGE gel had less DP 6 chains and more DP 8 chains compared to the unmodified glycogen (Fig. 7A
). In contrast, the chain-length pattern of polyglucans produced by the SSIIIa band showed that shorter glycogen chains with DP
The polyglucans produced by the partially purified SSI activity band (Fig. 1B, SSI band in lane 4) on native-PAGE/SS activity staining rice amylopectin gel had less chains with DP 4 to 6 and DP 12 to 18 but more chains with DP 7 to 11 and DP 19 as compared to the unmodified substrate (Fig. 7B). It is likely that SSI elongates the very short DP 6 chains into DP 7 to 11, and converts the intermediate DP 15 to 17 chains to DP 19 by adding 1 to 5 Glc units. This pattern of changes in the range of DP 18 chains was almost a mirror image of the differences between the SSI mutants and their respective control lines (for example, [e7/] [e7+/+]; Fig. 7B), indicating that the results of the in vitro analysis of chain preference of SSI on native gel are consistent with those obtained in vivo in SSI mutant lines. Therefore, chain analysis of the SS activity bands excised from native-PAGE/SS activity staining gels is a powerful, yet simple method for dissecting the functions of SS isozymes because it does not require the complete purification of the isozymes to be examined.
Isolation and Characterization of Rice SSI Mutant Lines
To date, no mutants deficient in SSI have been characterized in any plant species that accumulate starch in storage tissues, while a lot of mutants defective in GBSSI, SSIIa, and SSIII in a variety of plant species have been examined. The SS isozymes in higher plants such as rice are divided into five isozyme types: SSI, SSII, SSIII, SSIV, and GBSS (Hirose and Terao, 2004
On the other hand, the fine structure of endosperm amylopectin was distinctly affected by SSI mutation. Chains with DP 6 to 7 and DP 16 to 19 increased while DP 8 to 12 chains decreased in all SSI mutant lines. These results sharply contrast with the findings in a SSIIa mutant (japonica rice) that DP
On the other hand, the maximum change in amylopectin chain length in SSIIa mutant was 2.3% (
The SS activity of the SP in rice developing endosperm obtained by anion-exchange chromatography in this study exhibited two peaks, designated as SSI and SSIIIa (Fig. 1A), consistent with the results obtained in maize endosperm (Ozbun et al., 1971
Based on the measurement of dissociation constants, Commuri and Keeling (2001) The decrease in DP > 20 chains was not evident in SSI mutant lines compared to their control lines after DAF 16 (Fig. 5C) and in the mature endosperm (Fig. 5B) in vivo. Probably, SSI is not able to elongate DP > 20 chains due to its entrapment by DP > 20 chains after starch concentration becomes high in vivo. In contrast, DP > 20 chains on native-PAGE/SS activity gels increased (Fig. 7B), indicating that SSI has an inherent ability to elongate DP > 20 chains provided it is free from binding by long polyglucans when starch concentration is low as in gels containing rice amylopectin. Increasing the in vitro reaction time for the SSI activity magnified the rate of increase in longer chains produced by the SSI activity band on native-PAGE gel (data not shown).
The activities (or Vmax) of maize SSI in developing endosperm (Ozbun et al., 1971
This study is the in vivo attempt to analyze SSI function in storage tissues. The schematic representation of a partial structure of amylopectin is shown in Figure 8A
. More than 90% of the chains in rice or maize amylopectin are composed of A chains (that carry no other chains and are linked to the other chains at their reducing ends) and B1 chains (that carry one or more chains belonging to only one cluster; Hizukuri, 1986
The crystalline domains of starch granules appear to be composed of A chains and the exterior parts of B chains of amylopectin, their average length being seemingly in the range of DP 12 to 16 (Hizukuri, 1986 12 to 16 exterior chains (long chains) result in increase and decrease of the starch gelatinization temperature, respectively, while the abundance and shortage of DP < 12 to 16 exterior chains (short chains) result in decrease and increase of the starch gelatinization temperature, respectively. According to our hypothesis described above, the increases in short A chains with DP 6 to 7 (Fig. 8C, inset a) and B1 chains with DP 16 to 19 (Fig. 8C, inset c-2) lower the gelatinization temperature while the decrease in short A chains with DP 8 to 12 (Fig. 8C, inset b) elevates it. The fact that the total increase in the molar percent of DP 6 to 7 plus DP 16 to 19 chains was almost the same as that of the decrease in DP 8 to 12 chains (Fig. 8B, b), tempts us to predict that the gelatinization temperature of the starch in rice SSI mutant and its control line would be the same. However, the Tp of the starch in the rice SSI mutant (e7/) was about 3°C higher than that of its control line (Fig. 6A). This inconsistency could be explained by assuming that the increased DP 16 to 19 chains must contain long A chain with DP 16 to 19 elongated by the other SS isozymes (Fig. 8C, inset c-1) as well as nonelongated B1 chains (Fig. 8C, inset c-2) due to SSI deficiency.
The broad increase of about 5% to 12% in chains around DP 27 to 40 might have resulted from the elongation of the exterior portions of B1 and B2 chains by other SS isozyme(s) (Fig. 8C, inset e). The elongation of the exterior parts of B chains or A chains with DP
Results of the analysis of polyglucans produced in vitro by the SSI activity band on native-PAGE/SS activity staining lend additional support for the current hypothesis. The changes in distribution patterns of amylopectin chains with DP
Results of the comparison of the chain-length distribution of amylopectin between SSIIa mutants and their respective parents in rice (japonica rice; Nakamura et al., 2002
SSIIIa activity bands in e7/ SSI null mutant appeared to be enhanced compared with its e7+/+ control line (Fig. 3A). In view of the report that SSI activity in maize SSIII mutant (dull-1) was higher than that of the wild type (Cao et al., 1999 In summary, in wild-type rice, the short DP 6 to 7 chains of A or B1 chain produced by BE are initially elongated by SSI to DP 8 to 12 chains. Further elongation to form DP > 20 chains should be performed by other SS isozymes including SSIIa and SSIIIa. SSI specifically elongates the narrow range of short chains with DP 6 to 7 and adds a limited number of Glc residues (DP 26) as compared with SSIIa and SSIIIa (Fig. 8D).
In vivo analysis of amylopectin chain-length distribution pattern was first attempted on leaves of Arabidopsis SSI mutant (Delvalle et al., 2005 More detailed analysis of amylopectin structure in rice SSI mutants, including a more precise estimation of the lengths of A and B chains is required to substantiate the current hypothesis.
Plant Materials The wild-type parental rice (Oryza sativa) cultivar Nipponbare, its four mutant lines (/) containing Tos17 insertion at the OsSSI gene, and their control plants (+/+; Tos17 not inserted on the SSI gene but have a genetic background common to all mutant lines) were used in the study. Rice plants were grown during the summer months in an experimental paddy field under natural environmental conditions.
Mutagenesis with Tos17 and pool sampling were performed as described previously (Hirochika, 2001
Developing rice grains at the midmilky stage (12 g fresh weight) were hand homogenized using a prechilled mortar and pestle on ice in 30 mL of grinding solution (GS) containing 50 mM imidazole-HCl (pH 7.4), 8 mM MgCl2, 500 mM 2-mercaptoethanol, and 12.5% (v/v) glycerol. The homogenate was squeezed through two layers of gauze and the filtrate was centrifuged at 10,000g at 4°C for 20 min. The supernatant was once more centrifuged at the same conditions and the supernatant was used as the crude enzyme extract. The crude enzyme preparation (about 30 mL) was applied to a HiTrapQ HP column (5 mL, Amersham Bioscience) equilibrated with Solution A (50 mM imidazole-HCl [pH 7.4], 8 mM MgCl2, 50 mM 2-mercaptoethanol). The column was washed with Solution A, followed by a linear gradient of 0 to 0.5 M NaCl in Solution A for 30 min at a flow rate of 1.0 mL min1.
The assay of SS for each fraction from the HiTrapQ column was conducted in a reaction mixture containing citrate and glycogen following the method of Nishi et al. (2001)
Native-PAGE/activity staining of DBE and BE was performed using the methods of Fujita et al. (1999)
One developing endosperm each from DAF 9 to 25 of Nipponbare, DAF 12 of SSI-deficient mutant lines, and their controls were individually homogenized using a plastic pestle in 3 volumes of cold GS. The homogenate was centrifuged at 20,000g at 4°C for 10 min and supernatant was set aside. The pellet was washed twice with 2 volumes of cold GS and the pooled supernatants (about 80 µL) were used as the SP fraction. The residual pellet was homogenized in 3 volumes of cold SDS solution containing 55 mM Tris-HCl (pH 6.8), 2.3% SDS, 5% 2-mercaptoethanol, and 10% glycerol. The homogenate was centrifuged at 20,000g at 4°C for 10 min and the supernatant was set aside. The pellet was washed twice with 2 volumes of cold SDS solution and the pooled supernatants (about 80 µL) were used as the LBP fraction. The residual pellet (starch granules) was washed with 1 mL of distilled water and twice with 1 mL of acetone and dried under pressure. The starch granules (about 4 mg) were suspended with 10 volumes of SDS solution and boiled for 7 min. After cooling, 10 volumes of SDS solution were added while stirring. The slurry was centrifuged at 20,000g for 10 min at 4°C. The supernatant was set aside and the pellet was resuspended in 10 volumes of SDS solution and recentrifuged. The pooled supernatants (about 80 µL) were used as the TBP fraction.
Polyclonal antibodies for rice SSI and GBSSI were prepared from SDS-PAGE purified granule-bound proteins. The SP and LBP were sequentially removed from 10 g of starch granules isolated from developing rice seeds. The remaining TBP was suspended in 24 volumes of SDS solution and boiled for 10 min. After cooling, the slurry was homogenized and centrifuged at 10,000g for 30 min at 4°C. The supernatant was set aside and the pellet was resuspended in 40 volumes of SDS solution and recentrifuged. An equal volume of 30% tricholoroacetic acid was added to the pooled supernatants (about 640 mL) and mixed. The solution was cooled on ice for 1 h and centrifuged at 40,000g for 15 min at 4°C. The pellet was washed with 50 mL of acetone and dried under pressure. The dried pellet was solubilized with 8 mL of SDS solution and analyzed on a 7.5% acrylamide SDS-PAGE gel (145 mm x 100 mm, 1 mm thick). The SSI (71 kD) and GBSSI (60 kD) proteins were excised and the gel slices containing 30 mg SSI and 200 mg GBSSI protein were homogenized with Freund's incomplete adjuvant and injected into rabbits. Four injections were administered at 2-week intervals until the titer of polyclonal antibodies against the rice SSI and GBSSI were fully elevated. The serum was pooled and used as a source of polyclonal antibodies. Immunoblotting was performed according to the methods of Fujita et al. (1999)
Extraction of starch from mature and developing rice endosperm for chain-length distribution was performed according to the methods of Fujita et al. (2001)
Native-PAGE/SS activity staining for analysis of modified
The chain-length distributions of
Northern blotting and RT-PCR of SSI gene using the primer pair 5'-gggccttcatggatcaacc-3' and 5'-ccgcttcaagcatcctcatc-3' were performed according to the methods of Tanaka et al. (2004)
Pasting properties of endosperm starch measured by rapid visco analyzer, x-ray diffraction measurement of endosperm starch, and observation of endosperm starch granules by SEM were performed as described previously (Fujita et al., 2003 Sequence data from this article can be found in the GenBank/EMBL data libraries under accession number D38221.
The authors are grateful to Professor Hikaru Satoh (Kyushu University) for kindly providing us the waxy mutant line EM-21, to Dr. Perigio B. Francisco Jr. (Japan Science and Technology-Core Research for Evolutional Science and Technology, Akita) for reading the manuscript, and to Professor Jay-Lin Jane (Iowa State University) for helpful discussions. Received September 26, 2005; returned for revision January 23, 2006; accepted January 24, 2006.
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: Naoko Fujita (naokof{at}akita-pu.ac.jp). Article, publication date, and citation information can be found at www.plantphysiol.org/cgi/doi/10.1104/pp.105.071845. * Corresponding author; e-mail naokof{at}akita-pu.ac.jp; fax 81188721681.
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