Molecular Plant Advance Access originally published online on August 1, 2008
Molecular Plant 2008 1(5):760-769; doi:10.1093/mp/ssn038
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Diverged Copies of the Seed Regulatory Opaque-2 Gene by a Segmental Duplication in the Progenitor Genome of Rice, Sorghum, and Maize
Waksman Institute of Microbiology, Rutgers University, 190 Frelinghuysen Road, Piscataway, NJ 08854, USA
1 To whom correspondence should be addressed. E-mail: messing{at}waksman.rutgers.edu, fax 732-445-0072, tel. 732-445-4257.
| Abstract |
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Comparative analyses of the sequence of entire genomes have shown that gene duplications, chromosomal segmental duplications, or even whole genome duplications (WGD) have played prominent roles in the evolution of many eukaryotic species. Here, we used the ancient duplication of a well known transcription factor in maize, encoded by the Opaque-2 (O2) locus, to examine the general features of divergences of chromosomal segmental duplications in a lineage-specific manner. We took advantage of contiguous chromosomal sequence information in rice (Oryza sativa, Nipponbare), sorghum (Sorghum bicolor, Btx623), and maize (Zea mays, B73) that were aligned by conserved gene order (synteny). This analysis showed that the maize O2 locus is contained within a 1.25 million base-pair (Mb) segment on chromosome 7, which was duplicated
56 million years ago (mya) before the split of rice and maize 50 mya. The duplicated region on chromosome 1 is only half the size and contains the maize OHP gene, which does not restore the o2 mutation although it encodes a protein with the same DNA and protein binding properties in endosperm. The segmental duplication is not only found in rice, but also in sorghum, which split from maize 11.9 mya. A detailed analysis of the duplicated regions provided examples for complex rearrangements including deletions, duplications, conversions, inversions, and translocations. Furthermore, the rice and sorghum genomes appeared to be more stable than the maize genome, probably because maize underwent allotetraploidization and then diploidization. Received for publication April 28, 2008. Accepted for publication June 12, 2008.
| INTRODUCTION |
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The grass family comprises the most important cereal crops, such as rice (Oryza sativa), sorghum (sorghum bicolor), maize (Zea mays), and wheat (Triticum ssp.). Although these species differ in chromosome numbers, genome sizes, and divergence of about 50 mya (Kellogg, 2001), comparative studies of orthologous regions have shown that gene content and gene order are conserved to a level that one can reconstruct ancestral chromosomal segments (Gale and Devos, 1998). Moreover, sequencing entire genomes of species like rice has shown that segmental duplications within a genome led frequently to the co-amplification and subfunctionalization or neofunctionalization of genes (International Rice Genome Sequencing Project, 2005; Yu et al., 2005). If these segmental duplications occur in the progenitor of related species, they should persist independently in each lineage.
So far, it has been unclear whether these segmental duplications in the rice genome are the result of a whole genome duplication (WGD) event because we do not have a genome sequence of a species that matches the rice duplications in a ratio of 2:1, as in the case of yeast (Kellis et al., 2004). Because these segmental duplications occurred before the origin of the grass family, it would require the identification of a species with greater evolutionary distance than other species of the grass family. On the other hand, recent polyploidy of plant species is easily recognized as a common phenomenon in the evolution of plants (Wendel, 2000). Moreover, using collinear genetic markers a 2:1 ratio can easily be demonstrated for those species that underwent WGD. In those cases, ancient segmental duplications are doubled again. Common to all chromosomal duplications, however, is divergence over time. The older the duplication event, the more time is available for sequence changes to occur, which includes gene loss and chromosomal rearrangement (Lynch and Force, 2000; Wolfe, 2001; Kashkush et al., 2002; Messing et al., 2004). After 50 million years of grass evolution, segmental duplications are rather small in size and are mostly detected by comparative analysis of specific gene families (Wu et al., 2008), duplicated genes in EST collections (Gaut and Doebley, 1997; Paterson et al., 2004; Salse et al., 2008), or a complete genome sequence to itself (Yu et al., 2005). Alignment of the rice genome sequence with mapped wheat ESTs yielded 13 synteny blocks representing 83.1 and 90.4% of the rice and wheat genomes, confirming that segmental duplications arose before the progenitor of rice and wheat split (Salse et al., 2008). Yu et al. (2005) identified 18 pairs of duplicated segments, which together cover an estimated 65.7% of the rice genome. Although they proposed a WGD event that occurred between 53 and 94 mya, the spread indicates that several rounds of individual duplications might have occurred. Furthermore, one segmental duplication between chromosomes 11 and 12, the largest of all, occurred only 5–7.7 mya, long after the divergence of the grass family, confirming that individual segmental duplications can occur (Rice Chromosomes 11 and 12 sequencing Consortia, 2005; Wang et al., 2005; Wei et al., 2007). On the other hand, it is clear that WGD occurred in maize versus rice and ancient duplications appear in 4:2 ratios. Although allotetraploidization produced temporarily 20 chromosomes, WGD shed 10 centromeres and reassembled larger chromosomes with 52 major maize–rice collinear blocks (Wei et al., 2007). Therefore, it appears that polyploidization can result in major reshuffling of duplicated regions in the genome.
While previous genomic analyses of segmental duplications are mostly based on gene models, we decided to approach an analysis of an ancient duplication through a known locus in maize that underwent subfunctionalization upon duplication. A mutation in the opaque-2 (o2) locus in maize has a well known kernel phenotype and practical importance as high-lysine corn. Through additional improvements, high-lysine corn is today a critical staple as Quality Protein Maize or QPM (Holding et al., 2008). The high-lysine content of the kernel is based on the reduced synthesis of certain storage proteins in the endosperm tissue of the seed, called zeins in maize, because O2 is a bZIP transcriptional regulatory factor of this multigene family (for review, see Schmidt, 1993). The lack of O2 leads to a decrease in the synthesis of zein proteins and increase in other lysine-rich proteins, thereby providing enhanced nutritional value for human food and animal feed. Based on sequence conservation, an endosperm-specific cDNA encoding another bZIP protein was isolated. It was named Opaque-2 heterodimerizing protein 1 (OHP1) because it can bind the O2 target site both as a homodimer and in a heterodimeric complex with O2 (Pysh et al., 1993). However, genetic data clearly indicate that OHP1 does not complement O2 in vivo. More recently, tandemly amplified target gene copies of one maize haplotype function normally in an o2 null-mutant, indicating that other genes can substitute for O2 (Song et al., 2001). Furthermore, the o2-676 allele has a single amino acid change that reduces DNA binding to the target promoter, indicating that O2 interacts directly with the promoter rather than through another protein (Aukerman et al., 1991). Therefore, it appears that after gene duplication, the O2 and OHP genes underwent subfunctionalization. Interestingly, a rice cDNA encoding a similar bZIP transcriptional activator, RISBZ1, was isolated from seed tissue (Onodera et al., 2001), indicating that the O2 gene arose before the progenitor of maize and rice split. Moreover, we could identify two duplicated regions in rice containing both O2 and OHP-related genes. Aligning these duplicated regions of rice with orthologous genomic regions of sorghum and maize allowed us to determine not only what happened to the O2 gene during the evolution of the grass family, but also the larger chromosomal sequence context around this locus.
| RESULTS |
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Ancestry of the Maize O2 and OHP Regions in Rice
To identify orthologous regions between rice and maize, we selected a 460-Kb chromosomal region in rice that contained the gene for the transcriptional activator RISBZ1 in the middle of this region (Onodera et al., 2001). This region is located on rice chromosome 7 (Rice 7, see Methods for BACs accessions). The sequence was manually annotated and found to contain 43 genes based on extrinsic evidence (Figure 1A and 1B). When this region was aligned with the chromosomal region containing the O2 gene on maize chromosome 7S, we concluded that RISBZ1 and O2 are orthologs.
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When the RISBZ1 sequence was compared to the rice genome itself, we discovered that a copy of RISBZ1 was contained in a duplication located on rice 3. This segment was about 220 Kb in size and contained 28 annotated genes (Figure 1A and 1C). When this region was compared to the maize genome, it was orthologous to a large expanded region on maize chromosome 1. This region contained the previously described OHP1 gene in maize (Pysh et al., 1993). It now becomes clear that O2 and OHP1 arose by a chromosomal duplication predating the split of the rice and maize lineages 50 mya. When genes in these two regions were compared to maize genomic sequences, two additional regions with collinear genes were found on chromosomes 2 and 5, respectively (Figure 1B and 1C). Therefore, we can demonstrate a 4:2 ratio of maize versus rice, illustrating that the ancient duplication in rice was duplicated during allotetraploidization, resulting in four chromosomal regions in maize that are collinear. In the two duplicated regions in rice, there are a total of 14 collinear gene pairs (Figure 1A). We refer to these two regions as the O2 region (on rice 7) and the OHP region (on rice 3) based on their homology to the O2 and OHP genes in maize, respectively.
Three-Way Comparison of the O2 and OHP Regions with Sorghum as a Reference
The O2 and OHP regions of rice were also aligned with orthologous regions of sorghum (Figure 1B and 1C). Indeed, we can find extensive collinearity between rice and sorghum as a 2:2 match on sorghum chromosomes 2 and 1. The three-way comparison illustrates that the duplication occurred before the origin of the grass family and that only maize underwent another WGD event, specifically allotetraploidization. In such a case, two species with divergent genomes hybridized as opposed to autotetraploidization of a single species (Gaut and Doebley, 1997). A summary of sequence length, location, and gene content of each chromosomal segment is shown in Table 1. One distinctive feature is the differential expansion of each region. Based on collinearity, the O2 regions have expanded to a greater degree than the OHP regions in all three species, perhaps suggesting that there is a bias to the susceptibility of sequence insertions manifested early in evolution as suggested previously (Song et al., 2002). Interestingly, in rice and sorghum, there are 18 (41.9%) and 11 (25.6%) noncollinear genes in the O2 regions (Table 1), indicating that such susceptibility might be critical for the formation of paralogous gene copies. It also shows that chromosome expansion not only occurs by LTR retrotransposition, but also through the addition of gene copies. The uneven expansion of the ancient duplication is even further enhanced after allotetraploidization in maize. The region containing O2 on maize chromosome 7S is twice the size of the region containing OHP on maize chromosome 1. On the other hand, the regions on maize 2 and 5 resulting from the second round of duplications by WGD are almost 5.5 times smaller than those of the other chromosome, indicating drastic changes over a relatively short time period (Table 1). The size variation is mostly made by LTR retrotransposon insertions and deletions of genomic region after maize allotetraploidization.
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The segmental duplication in rice has 10 additional genes in the O2 region and eight in the OHP region, which are also conserved in sorghum and maize. Therefore, the duplication in the ancestral species of the grasses underwent either gene loss on one segment or gained additional genes on the other. In any case, it indicates that a selection against duplicated gene copies occurred soon after duplication, as we have observed for the allotetraploidization of maize on a genome-wide level as well (Lai et al., 2004). Furthermore, selection continues because there are five genes in the O2 region and one in the OHP region that are only conserved between sorghum and maize. These also could be genes that were inserted into a common ancestor of these two species or were deleted from the rice region. Clearly, on a genome-wide level, there are many noncollinear genes in rice, sorghum, and maize, which could have steadily arisen by co-movement with transposable elements, translocation of sequence segments, or other mechanisms of gene movement (Messing and Bennetzen, 2008).
Gene Rearrangement in O2 and OHP Regions
As already described above, allotetraploidization resulted in drastic changes in homoeologous regions of maize. Because one region is even smaller than the orthologous regions in rice and sorghum and therefore smaller than the average genome expansion of maize versus rice and sorghum, these maize regions must have contracted in size (Table 1). In 14 ancient duplicated gene pairs, sorghum has only one gene deleted. However, maize 2 has 10 genes deleted, and maize 5 has three deleted; maizes 7 and 1 have two and three deleted, respectively (Figure 1). Indeed, losses of genes duplicated by allotetraploidization are quite common in the maize genome (Messing et al., 2004). However, here, we can show that such deletions preferentially occur in one homoeologous region rather than randomly in both.
Duplications of short sequences including genes within the segmental duplications occurred as well. The z1 and z2 genes (not related to zeins; see Methods) represent such a short duplication that occurred even before the segmental duplication. Then, each lineage has its own other short sequence duplications. In sorghum, the O2 gene is tandemly duplicated. The Indole-3-glycerol phosphate lyase (IGL) gene has three tandem copies in rice, one in sorghum, and one in maize. On maize chromosome 1, five genes including OHP1 are tandemly duplicated (Figure 1). These paralogous gene copies indicate a continuous dynamic process of chromosomal changes in gene content in a lineage-specific manner.
There is also indication that there was post-duplication interaction between the segmental duplications. Out of the 14 duplicated genes, two genes (Os07RISBZ1 and Sb01IGL2), shown in boxes in Figure 2, had distinct lower nucleotide substitutions than the other linked genes. Because they are next to each other, reduced divergence could be the result of gene conversion or concerted evolution. Although pairing of non-homologous chromosomes is very rare (McClintock, 1930), one could envision concerted evolution of genes in segmental duplicated regions. The structures of the two genes are further aligned with their orthologs and paralogs (Figure 2); for gene description, see Methods. Although exon/intron junctions and the number of exons and introns are mostly conserved, Os07RISBZ1 and Sb01IGL2 are more similar to their paralogs (Os03bZIP and Sb01IGL1) based on gene size, exon and intron size, exon or intron numbers than the other 12 orthologous pairs, consistent with an exchange in this position of the duplication. The two orthologous pairs are marked by red and green colors in Figure 2, respectively.
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More drastic changes required chromosome breakage and fusion in a lineage-specific manner. Six genes including the two duplicated O2 genes are inverted on sorghum 2; three genes including the O2 gene are also inverted on maize 7, but they are translocated 100 kb away from the original location (Figure 3). Interestingly, we found that almost all gene rearrangements including duplications, inversions, conversions, and translocations occurred at the O2 and OHP genes or nearby. Given the central role of the transcription factor in seed development, change of sequence context through chromosome breakage and fusion could have shaped seed morphology during the speciation of the grass family.
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Phylogenetic Analysis of Duplicated Gene Pairs
To narrow the time frame by which the duplication occurred in the progenitor of the grasses, a phylogenetic analysis was performed for each duplicated gene pair based on coding region sequences and using the best-matching sequence from Arabidopsis as an outgroup (Supplemental Figure). Furthermore, we can compute the nucleotide synonymous substitutions or Ks values (Messing and Bennetzen, 2008). The mean Ks values between duplicated gene pairs were calculated for the four possible comparisons: Rice 3–Rice 7 (Os03– Os07), Sb01–Sb02, Zm05–Zm02, and Zm01–Zm07. The Ks values of all gene pairs differ largely between 0.106 and 1.089 (Table 2), which means that each gene pair has very different synonymous substitution rates. Interestingly, the Ks value of Os03–Os07 falls into two groups; each has seven gene pairs, with average values of 0.30 and 0.60, respectively. Because of the hypothesized gene conversion at Sb01IGL2, the Ks value of the IGL–TSA gene pair in Sb01–Sb02 was excluded in the analysis. The average Ks values of rice, sorghum, and maize are 0.448, 0.479, 0.487, 0.548, respectively, and the average synonymous substitution rate is 3.99 x 10–9. Here, Ks values can be ranked in the order of Ks(Rice) > Ks(Sorghum) > Ks(Maize 1–7) > Ks(Maize 2–5). It is possible that with the genome size expansion, sorghum and maize experienced accelerated substitution rates compared with rice, especially maize, after allotetraploidization. Therefore, we estimated the timing of the ancient duplication event of the O2 and OHP regions based on rice Ks values, placing it about 56 mya, which is about the rate for the entire grass family, but slightly more than the divergence of the rice and sorghum/maize lineages of 50 mya (Kellogg, 2001). Therefore, phylogenetic analysis is consistent with genome alignment data of orthologous sequences, which shows that the duplication occurred in a common progenitor. That O2 is such an old gene and has been maintained in its chromosomal position throughout the evolution of the grass family probably reflects its pleiotropic role during seed development.
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| DISCUSSION |
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Ancient Duplications in the Grass Family
We have shown here that the gene encoding a transcription factor central to seed development in maize underwent differentiation at the time the grass family arose. Differentiation occurred via the duplication of an entire chromosomal segment rather than a single gene, resulting into two gene loci, which are called O2 and OHP in maize and behave as individual Mendelian factors. Our findings are based on alignment of collinear regions of three species of the grasses, rice, sorghum, and maize. Because the progenitor of these species split soon after the formation of this family, retention of collinear regions in all three species place the timing of the duplication in a common progenitor. A more precise estimate of the timing of the duplication, however, was based on nucleotide substitution rates. Almost all comparative studies used the same synonymous substitution rate (6.5 x 10–9) for dating duplication events (Vandepoele et al., 2003; Paterson et al., 2004; Yu et al., 2005). However, rates were always based on different gene pairs, which differ greatly in their divergence rates (Gaut et al., 1996; Lai et al., 2004; Swigonova et al., 2004). Here, we calculated average synonymous substitution rates to be 3.99 x 10–9, which is lower than a previous calculation by Yu et al. (2005). The 14 duplicated gene pairs in the O2 (0.46 Mb) and OHP (0.22 Mb) regions averaged a Ks value of 0.448. The duplication analyzed here appears to be part of a larger segmental duplication of 8.8 Mb on rice 7 and 4.0 Mb on rice 3. However, in a previous analysis, only a subset of gene pairs have been selected for the divergence analysis, resulting in an average Ks value of 0.706. Apparently, the omission of gene pairs in global genome-wide studies cannot replace the more detailed phylogenetic analysis of individual regions.
The O2 and OHP regions are diverse gene-rich loci and represent an interesting model for studying complex gene rearrangements during the evolution of grass genomes. Gene rearrangements, including insertions, deletions, inversions, conversions, translocations, and tandem duplications, occurred in O2 and OHP regions. A cladistic analysis of the origin and evolution of the ancient duplication regions in rice, sorghum, and maize is summarized in Figure 4.
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Neo- and Sub-Functionalization
Gene duplication and subsequent functional divergence of the descendant genes is likely a pivotal mechanism for generating new protein functions or proteins synthesized in different cell types at different levels. Based on these different end products, three alternative terms have been used in the evolution of duplicated genes: (1) nonfunctionalization, in which one copy might simply become silenced by trunctations, deletions, insertions, or epimutations; (2) neofunctionalization, in which one copy might encode an altered protein with a novel function whereas the function of the alternative copy remains unchanged; (3) subfunctionalization, in which each descendant copy might encode a protein with additional functions or produce the same protein under different conditions than the ancestral gene. Because the vast majority of mutations reducing optimal function are unfavorable, and because gene duplicates are generally assumed to be functionally redundant at the time of origin, frequently the donor copy undergoes nonfunctionalization. Interestingly, allotetraploidization of maize has resulted in a genome-wide loss of one of the duplicated copies (Messing et al., 2004), consistent with this assumption. Therefore, one would expect that neofunctionalization is probably the least likely outcome, specifically when subfunctionalizing mutations greatly outnumber neofunctionalizing mutations and the selective advantage of the neofunctional alleles is rather small (Lynch et al., 2001).
Interestingly, in the O2 and OHP regions, we found for all genes full-length cDNA except for Os03r60S. This suggests that only Os03r60S is not expressed in rice among all 14 duplicated genes. Os07RISBZ1 is expressed in pistal, and Os03bZIP in shoot and leaf. Three are not represented in the full-length cDNA library, but in others such as those from tissues inoculated with rice blast, of panicle mixture, or of mixed callus. Based on these alignments, duplicated genes appeared to be expressed in different tissues. While other genes are also expressed in the same tissue, many of them differ by frame shifts (data not shown). Taken together, these results suggest that functional diversification of the duplicated genes is a major feature of the long-term evolution of polyploids as shown for other datasets (Blanc and Wolfe, 2004; Byrne and Wolfe, 2007). This also indicates that ancient duplications are a major way for sub- and neofunctionalization.
Acceleration of Sequence Changes by Diploidization
Clearly, the ancient segmental duplication was followed by gene losses and chromosomal rearrangements. However, the two regions compared here are more stable in rice and sorghum than in maize (Figure 1 and Table 1). Almost all genes, which arose from a common ancestor of rice, sorghum, and maize, are present in rice and sorghum and differ by a few tandem duplications in each species. Because maize underwent allotetraploidization about 4.8 mya (Swigonova et al., 2004), it has two homoeologous regions, totalling four orthologous regions instead of two in rice and sorghum. Gene deletions are more frequent, especially on one of the maize homoeologous regions. This suggests the preferential elimination of genes from one maize chromosome (Bruggmann et al., 2006; Xu and Messing, unpublished). Furthermore, LTR retrotranspositions in one region and possibly elimination of LTR retrotransposons via unequal crossing over in the other can greatly affect uneven size of homoeologous regions in maize.
Unlike other recent polyploid plants (e.g. cotton (Gossypium hirsutum), wheat, sugarcane (Saccharum officinale)) increasing their chromosome numbers (Wendel, 2000; Osborn et al., 2003), the maize genome, like sorghum, retained only 10 chromosomes, although maize originated from two progenitors by allotetraploidization. This suggests that the maize genome underwent a diploidization process and a reorganization of its chromosomes. It appears that this diploidization pathway invoked major acceleration of sequence changes in the maize genome, and makes the maize genome more divergent from other grass species than expected from nucleotide substitution rates of orthologous gene pairs.
| METHODS |
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DNA Sequences
Sequences of maize and rice BAC clones were downloaded from GenBank; the accessions are as follows—O2 region: rice 7 (AP004307 [GenBank] , AP003826 [GenBank] , AP003800 [GenBank] , AP003835 [GenBank] , and AP003861 [GenBank] ), maize 2 (AC209768 [GenBank] , AC211997 [GenBank] , and AC197086 [GenBank] ), maize 7 (AC214119 [GenBank] , AC212126 [GenBank] , AC210164 [GenBank] , AC204935 [GenBank] , AC200329 [GenBank] , AC191027 [GenBank] , AC208337 [GenBank] , AC204533 [GenBank] , AC204826 [GenBank] , AC211651 [GenBank] , and AC208639 [GenBank] ); OHP region: rice 3 (AC092076 [GenBank] and AC093713 [GenBank] ), maize 5 (AC182413 [GenBank] and AC191048 [GenBank] ), maize 1 (AC215272 [GenBank] , AC185496 [GenBank] , AC191108 [GenBank] , AC177847 [GenBank] , AC190783 [GenBank] , AC195205 [GenBank] , AC196793 [GenBank] , and AC186656 [GenBank] ); the sorghum sequences were obtained from the Joint Genome Institute (JGI) website (www.phytozome.net/cgi-bin/gbrowse/sorghum/).
Sequence Annotation
Rice BAC clones annotated data were obtained from the RAP-DB (Tanaka et al., 2008). Repetitive DNA was masked with RepeatMasker before using gene prediction methods as described previously (Bruggmann et al., 2006). Predicted genes were manually annotated using EST and protein sequence resources. Standard features of transposable elements were used to determine their position and end points. Collinear regions were aligned in a pair-wise fashion using dot plot graphics of Lasergene (Madison, WI).
Phylogenetic Analysis
Phylogenetic analyses were performed by multiple alignments of nucleotide or amino acid sequences using the Clustal_W program (Thompson et al., 1994). The phylograms were drawn with the MEGA4 program using either NJ (Neighbor Joining) or UPGMA (Unweighted Pair-Group Method with Arithmetic Mean) methods (Tamura et al., 2007).
Rate of Synonymous Substitutions and Ancient Duplication Time
We used all 14 duplicated genes exon sequences to estimate synonymous substitutions (Ks) using the MEGA4 program (Tamura et al., 2007). Gene names are taken from rice annotated BACs of O2 (AP004307
[GenBank]
, AP003826
[GenBank]
, AP003800
[GenBank]
, AP003835
[GenBank]
, and AP003861
[GenBank]
) and OHP (AC092076
[GenBank]
and AC093713
[GenBank]
) regions: (1) leucine-rice receptor-like protein (LRR) and Extensin; (2) z-protein 1 (z1); (3) z-protein 2 (z2); (4) heat shock factor type DNA binding protein (HSF) and heat shock transcription factor (HSTF); (5) unknown protein 1 (UN1); (6) 60S ribosomal protein (r60S); (7) unknown protein 2 (UN2); (8) guanylate binding protein (GBP); (9) O2 and OHP; (10) indole-3-glycerol phosphate lyase (IGL) and Tryptophan synthase alpha (TSA); (11) basic helix-loop-helix transcription factor (bHLH); (12) auxin-induced protein (Auxin); (13) DNA methyltransferase (DNA met); and (14) 40S ribosomal protein (r40S). The divergence time T between maize, sorghum, and rice was set at 50 million years (Kellogg, 2001). The synonymous substitution rates (r) for all 14 duplicated genes copy 1 and copy 2 were calculated with the same methods as described previously (Xu and Messing, 2006). For estimation of the ancient duplication time t, we used t = Ks(rice 3-rice7)/2r.
| SUPPLEMENTARY DATA |
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Supplementary Data are available at Molecular Plant Online.
| FUNDING |
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The research described in this manuscript was supported by a grant from the DOE (#DE-FG05-95ER20194) to J.M. No conflict of interest declared.
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