RESUMO
BACKGROUND: Mimosa bimucronata originates from tropical America and exhibits distinctive leaf movement characterized by a relative slow speed. Additionally, this species possesses the ability to fix nitrogen. Despite these intriguing traits, comprehensive studies have been hindered by the lack of genomic resources for M. bimucronata. RESULTS: To unravel the intricacies of leaf movement and nitrogen fixation, we successfully assembled a high-quality, haplotype-resolved, reference genome at the chromosome level, spanning 648 Mb and anchored in 13 pseudochromosomes. A total of 32,146 protein-coding genes were annotated. In particular, haplotype A was annotated with 31,035 protein-coding genes, and haplotype B with 31,440 protein-coding genes. Structural variations (SVs) and allele specific expression (ASE) analyses uncovered the potential role of structural variants in leaf movement and nitrogen fixation in M. bimucronata. Two whole-genome duplication (WGD) events were detected, that occurred ~ 2.9 and ~ 73.5 million years ago. Transcriptome and co-expression network analyses revealed the involvement of aquaporins (AQPs) and Ca2+-related ion channel genes in leaf movement. Moreover, we also identified nodulation-related genes and analyzed the structure and evolution of the key gene NIN in the process of symbiotic nitrogen fixation (SNF). CONCLUSION: The detailed comparative genomic and transcriptomic analyses provided insights into the mechanisms governing leaf movement and nitrogen fixation in M. bimucronata. This research yielded genomic resources and provided an important reference for functional genomic studies of M. bimucronata and other legume species.
Assuntos
Fabaceae , Mimosa , Fixação de Nitrogênio/genética , Haplótipos , Folhas de Planta/genéticaRESUMO
Height is a critical component of plant architecture, significantly affecting crop yield. The genetic basis of this trait in soybean remains unclear. In this study, we report the characterization of the Compact mutant of soybean, which has short internodes. The candidate gene was mapped to chromosome 17, and the interval containing the causative mutation was further delineated using biparental mapping. Whole-genome sequencing of the mutant revealed an 8.7 kb deletion in the promoter of the Glyma.17g145200 gene, which encodes a member of the class III gibberellin (GA) 2-oxidases. The mutation has a dominant effect, likely via increased expression of the GA 2-oxidase transcript observed in green tissue, as a result of the deletion in the promoter of Glyma.17g145200. We further demonstrate that levels of GA precursors are altered in the Compact mutant, supporting a role in GA metabolism, and that the mutant phenotype can be rescued with exogenous GA3. We also determined that overexpression of Glyma.17g145200 in Arabidopsis results in dwarfed plants. Thus, gain of promoter activity in the Compact mutant leads to a short internode phenotype in soybean through altered metabolism of gibberellin precursors. These results provide an example of how structural variation can control an important crop trait and a role for Glyma.17g145200 in soybean architecture, with potential implications for increasing crop yield.
Assuntos
Giberelinas , Glycine max , Glycine max/genética , Glycine max/metabolismo , Giberelinas/metabolismo , Mutação , FenótipoRESUMO
WUSCHEL-related homeobox (WOX) is a plant-specific transcription factor (TF), which plays an essential role in the regulation of plant growth, development, and abiotic stress responses. However, little information is available on the specific roles of WOX TFs in sacred lotus (Nelumbo nucifera), which is a perennial aquatic plant with important edible, ornamental, and medicinal values. We identified 15 WOX TFs distributing on six chromosomes in the genome of N. nucifera. A total of 72 WOX genes from five species were divided into three clades and nine subclades based on the phylogenetic tree. NnWOXs in the same subclades had similar gene structures and conserved motifs. Cis-acting element analysis of the promoter regions of NnWOXs found many elements enriched in hormone induction, stress responses, and light responses, indicating their roles in growth and development. The Ka/Ks analysis showed that the WOX gene family had been intensely purified and selected in N. nucifera. The expression pattern analysis suggested that NnWOXs were involved in organ development and differentiation of N. nucifera. Furthermore, the protein-protein interaction analysis showed that NnWOXs might participate in the growth, development, and metabolic regulation of N. nucifera. Taken together, these findings laid a foundation for further analysis of NnWOX functions.
Assuntos
Genes Homeobox , Nelumbo , Nelumbo/genética , Filogenia , Fatores de Transcrição/genética , Desenvolvimento VegetalRESUMO
Rambutan is a popular tropical fruit known for its exotic appearance, has long flexible spines on shells, extraordinary aril growth, desirable nutrition, and a favorable taste. The genome of an elite rambutan cultivar Baoyan 7 was assembled into 328 Mb in 16 pseudo-chromosomes. Comparative genomics analysis between rambutan and lychee revealed that rambutan chromosomes 8 and 12 are collinear with lychee chromosome 1, which resulted in a chromosome fission event in rambutan (n = 16) or a fusion event in lychee (n = 15) after their divergence from a common ancestor 15.7 million years ago. Root development genes played a crucial role in spine development, such as endoplasmic reticulum pathway genes, jasmonic acid response genes, vascular bundle development genes, and K+ transport genes. Aril development was regulated by D-class genes (STK and SHP1), plant hormone and phenylpropanoid biosynthesis genes, and sugar metabolism genes. The lower rate of male sterility of hermaphroditic flowers appears to be regulated by MYB24. Population genomic analyses revealed genes in selective sweeps during domestication that are related to fruit morphology and environment stress response. These findings enhance our understanding of spine and aril development and provide genomic resources for rambutan improvement.
Assuntos
Frutas/genética , Redes Reguladoras de Genes/genética , Genoma de Planta/genética , Sapindaceae/genética , Transcriptoma , Adaptação Fisiológica , Domesticação , Flores/genética , Flores/crescimento & desenvolvimento , Frutas/crescimento & desenvolvimento , Perfilação da Expressão Gênica , Genômica , Glucosídeos/biossíntese , Taninos Hidrolisáveis , Anotação de Sequência Molecular , Fotossíntese , Sapindaceae/crescimento & desenvolvimento , Especificidade da Espécie , PaladarRESUMO
BACKGROUND: Structural variations (SVs) are a type of mutations that have not been widely detected in plant genomes and studies in animals have shown their role in the process of domestication. An in-depth study of SVs will help us to further understand the impact of SVs on the phenotype and environmental adaptability during papaya domestication and provide genomic resources for the development of molecular markers. RESULTS: We detected a total of 8083 SVs, including 5260 deletions, 552 tandem duplications and 2271 insertions with deletion being the predominant, indicating the universality of deletion in the evolution of papaya genome. The distribution of these SVs is non-random in each chromosome. A total of 1794 genes overlaps with SV, of which 1350 genes are expressed in at least one tissue. The weighted correlation network analysis (WGCNA) of these expressed genes reveals co-expression relationship between SVs-genes and different tissues, and functional enrichment analysis shows their role in biological growth and environmental responses. We also identified some domesticated SVs genes related to environmental adaptability, sexual reproduction, and important agronomic traits during the domestication of papaya. Analysis of artificially selected copy number variant genes (CNV-genes) also revealed genes associated with plant growth and environmental stress. CONCLUSIONS: SVs played an indispensable role in the process of papaya domestication, especially in the reproduction traits of hermaphrodite plants. The detection of genome-wide SVs and CNV-genes between cultivated gynodioecious populations and wild dioecious populations provides a reference for further understanding of the evolution process from male to hermaphrodite in papaya.
Assuntos
Carica , Animais , Carica/genética , Genoma de Planta , Variação Estrutural do Genoma , Genômica , Masculino , FenótipoRESUMO
A novel and practical palladium-catalyzed aerobic oxyarylthiolation of alkynone O-methyloximes for the assembly of 4-sulfenylisoxazole derivatives using S8 and arylhydrazines as the S-aryl sources is accomplished. In the presence of 0.1 mol% of IPr-Pd-allyl-Cl as the catalyst and O2 (1 atm) as the sole oxidant, both alkynone O-methyloximes and arylhydrazines are suitable substrates, delivering diverse 4-sulfenyl isoxazoles in moderate to good yields with good functional group tolerance. Notably, the phenyl diazonium salt and sodium phenyl sulfinate are also suitable arylation reagents, providing an alternative synthetic strategy to access structurally diverse 4-sulfenyl isoxazoles.
RESUMO
Photoredox catalytic radical acylation reactions, utilizing [Ir(dFCF3ppy)2(dtbbpy)]+ (IrIII) as the photocatalyst and α-keto acids as the starting substrates, have recently emerged as an attractive strategy for preparing ketone derivatives. While there is consensus on the importance of detailed mechanistic insights to maximize the formation of desired products, efforts focused on uncovering the underlying elementary mechanisms of IrIII photocatalytic radical acylation reactions are still lacking. Herein, using time-resolved spectroscopy, we observed the efficient quenching of the triplet state, 3IrIII*, via electron transfer from α-keto acids, resulting in the generatation of the reduced IrII. Subsequently, IrII rapidly transforms into a stable IrH+ species through protonation, with α-keto acid acting as a proton donor. Upon absorbing additional photon(s), IrH+ is expected to transform into IrH3, involving further hydrogenation/protonation. Emission and Fourier transform infrared (FTIR) spectroscopy, together with global analysis, identify the character of IrH3/3IrH3* and corroborate its contribution to representative radical acylation reactions (decarboxylative 1,4-addition of α-keto acids with Michael acceptors, decarboxylative coupling of α-keto acids with aryl halides, and decarboxylative cyclization of 2-alkenylarylisocyanides with α-keto acids), where IrH3/3IrH3* serves as the key species to trigger the second photoredox cycle. These results elucidate the existence and generality of the tandem photoredox catalysis mechanism for IrIII photocatalytic radical acylation reactions, providing advanced insights into the mechanism of IrIII-based photoredox processes and potentially expanding their application in the design and development of new synthetic methodologies.
RESUMO
The chloroplast genomes of wild loquat can help to determine their place in the history of evolution. Here, we sequenced and assembled two novel wild loquat's chloroplast genomes, one is Eriobotrya elliptica, and the other is an unidentified wild loquat, which we named "YN-1". Their sizes are 159,471 bp and 159,399 bp, respectively. We also assembled a cultivated loquat named 'JFZ', its chloroplast genome size is 159,156 bp. A comparative study was conducted with six distinct species of loquats, including five wild loquats and one cultivated loquat. The results showed that both E. elliptica and "YN-1" have 127 genes, one gene more than E. fragrans, which is psbK. Regions trnF-GAA-ndhJ, petG-trnP-UGG, and rpl32-trnL-UAG were found to exhibit high variability. It was discovered that there was a positive selection on rpl22 and rps12. RNA editing analysis found several chilling stress-specific RNA editing sites, especially in rpl2 gene. Phylogenetic analysis results showed that "YN-1" is closely related to E. elliptica, E. obovata and E. henryi.
Assuntos
Eriobotrya , Genoma de Cloroplastos , Filogenia , Eriobotrya/genética , Edição de RNA/genéticaRESUMO
Vinyl-substituted alcohols represent a highly useful class of molecular skeletons. The current method typically requires either stoichiometric metallic reagents or preformed precursors. Herein, we report a nickel catalysis-enabled synthesis of vinyl-substituted alcohols via a 5-membered oxa-metallacycle. In this protocol, acetylene, the simplest alkyne and abundant feedstock, is employed as an ideal C2 synthon. The reaction features mild conditions, good functional group tolerance and broad substrate scope. Mechanistic exploration implies that the oxa-metallacycle originated from the cyclometallation of aldehyde and acetylene is the key intermediate for this transformation, which is then terminated by a silane-mediated σ-bond metathesis and subsequent reductive elimination.
RESUMO
[This corrects the article DOI: 10.1039/D2SC06400F.].
RESUMO
The stereoselective synthesis of dienyl esters with high atom- and step-economy has been largely unexplored. Herein, we report an efficient approach for the synthesis of E-dienyl esters via rhodium catalysis using carboxylic acid and acetylene as C2 synthon through the cascade of cyclometalation and C-O coupling. This protocol features mild conditions, excellent functional group tolerance, and exclusive E-stereoselectivity and utility in the late-stage modification of pharmaceuticals and natural products.
RESUMO
Diabetic mellitus is one of the leading causes of chronic wounds and remains a challenging issue to be resolved. Herein, a hydrogel with conformal tissue adhesivity, skin-like conductivity, robust mechanical characteristics, as well as active antibacterial function is developed. In this hydrogel, silver nanoparticles decorated polypyrrole nanotubes (AgPPy) and cobalt ions (Co2+ ) are introduced into an in situ polymerized poly(acrylic acid) (PAA) and branched poly(ethylenimine) (PEI) network (PPCA hydrogel). The PPCA hydrogel provides active antibacterial function through synergic effects from protonated PEI and AgPPy nanotubes, with a tissue-like mechanical property (≈16.8 ± 4.5 kPa) and skin-like electrical conductivity (≈0.048 S m-1 ). The tensile and shear adhesive strength (≈15.88 and ≈12.76 kPa, respectively) of the PPCA hydrogel is about two- to threefold better than that of fibrin glue. In vitro studies show the PPCA hydrogel is highly effective against both gram-positive and gram-negative bacteria. In vivo results demonstrate that the PPCA hydrogel promotes diabetic wounds with accelerated healing, with notable inflammatory reduction and prominent angiogenesis regeneration. These results suggest the PPCA hydrogel provide a promising approach to promote diabetic wound healing.
Assuntos
Diabetes Mellitus , Nanopartículas Metálicas , Adesivos , Hidrogéis/farmacologia , Polímeros/farmacologia , Antibacterianos/farmacologia , Bactérias Gram-Negativas , Bactérias Gram-Positivas , Pirróis , Prata/farmacologia , Cicatrização , Condutividade ElétricaRESUMO
Delivering therapeutic agents efficiently to inflamed joints remains an intractable problem in rheumatoid arthritis (RA) treatment due to the complicated physiological barriers. Circulating monocytes could selectively migrate to inflamed sites and differentiate into resident macrophages to aggravate RA. Therefore, a drug carrier that can be specifically internalized by circulating monocytes and switch monocytes into anti-inflammatory phenotype when reaching inflamed sites, might bypass the in vivo physiological barriers and achieve efficient RA therapy. Herein, we design a dextran sulfate (DS) functionalized nanoparticle (ZDNP) to selectively deliver anti-inflammatory agent dexamethasone (Dex) to circulating monocytes via the scavenger receptors on monocytes. Monocytes engulfing drug-loaded ZDNP could subsequently home to arthritic joints and act as a "living drug depot" to combat RA. Results revealed that ZDNP could be preferentially internalized by circulating monocytes when intravenously administrated in vivo. In a rat arthritic model, we found that circulating monocytes remarkably facilitated drug distribution and retention in inflamed joints. Moreover, monocytes engulfing drug-loaded nanoparticles exhibited favorable anti-inflammatory ability and M2-biased differentiation. Our work offers a facile approach to achieve site-directed anti-inflammatory therapy by taking advantage of the inflammation-homing ability of circulating monocytes. STATEMENT OF SIGNIFICANCE: Circulating monocytes can migrate to inflamed sites and then differentiate into macrophages to aggravate arthritis. Therefore, a drug carrier that can be specifically internalized by circulating monocytes and switch monocytes into anti-inflammatory phenotype when reaching inflamed sites may achieve efficient arthritis therapy. Here, we designed a monocyte-targeting nanoparticle (ZDNP) to selectively deliver anti-inflammatory Dex to circulating monocytes. When injected intravenously, ZDNP was effectively internalized by circulating monocytes via a scavenger receptor and subsequently was transported to arthritic joints, where monocytes engulfing the drug-loaded nanoparticles could switch to an anti-inflammatory phenotype to inhibit arthritis progress. We provide detailed evidence about the in vivo fate of ZDNP and unravel how monocytes act as a "living drug depot" to achieve site-directed arthritis therapy.
Assuntos
Artrite Reumatoide , Animais , Artrite Reumatoide/tratamento farmacológico , Portadores de Fármacos/uso terapêutico , Inflamação/tratamento farmacológico , Macrófagos , Monócitos , RatosRESUMO
Transgenic papaya is widely publicized for controlling papaya ringspot virus. However, the impact of particle bombardment on the genome remains unknown. The transgenic SunUp and its progenitor Sunset genomes were assembled into 351.5 and 350.3 Mb in nine chromosomes, respectively. We identified a 1.64 Mb insertion containing three transgenic insertions in SunUp chromosome 5, consisting of 52 nuclear-plastid, 21 nuclear-mitochondrial and 1 nuclear genomic fragments. A 591.9 kb fragment in chromosome 5 was translocated into the 1.64 Mb insertion. We assembled a gapless 9.8 Mb hermaphrodite-specific region of the Yh chromosome and its 6.0 Mb X counterpart. Resequencing 86 genomes revealed three distinct groups, validating their geographic origin and breeding history. We identified 147 selective sweeps and defined the essential role of zeta-carotene desaturase in carotenoid accumulation during domestication. Our findings elucidated the impact of particle bombardment and improved our understanding of sex chromosomes and domestication to expedite papaya improvement.
Assuntos
Carica , Carica/genética , Cromossomos de Plantas/genética , Domesticação , Melhoramento Vegetal , Cromossomos SexuaisRESUMO
Rambutan (Nephelium lappaceum L.) is an important fruit tree that belongs to the family Sapindaceae and is widely cultivated in Southeast Asia. We sequenced its chloroplast genome for the first time and assembled 161,321 bp circular DNA. It is characterized by a typical quadripartite structure composed of a large (86,068 bp) and small (18,153 bp) single-copy region interspersed by two identical inverted repeats (IRs) (28,550 bp). We identified 132 genes including 78 protein-coding genes, 29 tRNA and 4 rRNA genes, with 21 genes duplicated in the IRs. Sixty-three simple sequence repeats (SSRs) and 98 repetitive sequences were detected. Twenty-nine codons showed biased usage and 49 potential RNA editing sites were predicted across 18 protein-coding genes in the rambutan chloroplast genome. In addition, coding gene sequence divergence analysis suggested that ccsA, clpP, rpoA, rps12, psbJ and rps19 were under positive selection, which might reflect specific adaptations of N. lappaceum to its particular living environment. Comparative chloroplast genome analyses from nine species in Sapindaceae revealed that a higher similarity was conserved in the IR regions than in the large single-copy (LSC) and small single-copy (SSC) regions. The phylogenetic analysis showed that N. lappaceum chloroplast genome has the closest relationship with that of Pometia tomentosa. The understanding of the chloroplast genomics of rambutan and comparative analysis of Sapindaceae species would provide insight into future research on the breeding of rambutan and Sapindaceae evolutionary studies.
RESUMO
The chloroplast genome is an integral part of plant genomes in a species along with nuclear and mitochondrial genomes, contributing to adaptation, diversification, and evolution of plant lineages. In the family Caricaceae, only the Carica papaya chloroplast genome and its nuclear and mitochondrial genomes were sequenced, and no chloroplast genome-wide comparison across genera was conducted. Here, we sequenced and assembled the chloroplast genome of Vasconcellea pubescens A.DC. using Oxford Nanopore Technology. The size of the genome is 158,712 bp, smaller than 160,100 bp of the C. papaya chloroplast genome. And two structural haplotypes, LSC_IRa_SSCrc_IRb and LSC_IRa_SSC_IRb, were identified in both V. pubescens and C. papaya chloroplast genomes. The insertion-deletion mutations may play an important role in Ycf1 gene evolution in family Caricaceae. Ycf2 is the only one gene positively selected in the V. pubescens chloroplast genome. In the C. papaya chloroplast genome, there are 46 RNA editing loci with an average RNA editing efficiency of 63%. These findings will improve our understanding of the genomes of these two crops in the family Caricaceae and will contribute to crop improvement.
Assuntos
Caricaceae/classificação , Caricaceae/genética , DNA de Cloroplastos/análise , Evolução Molecular , Genes de Plantas/genética , Genoma de Cloroplastos , Filogenia , DNA de Cloroplastos/genética , Genoma de PlantaRESUMO
Dof transcription factors plant-specific and associates with growth and development in plants. We conducted comprehensive and systematic analyses of Dof transcription factors in sugarcane, and identified 29 SsDof transcription factors in sugarcane genome. Those SsDof genes were divided into five groups, with similar gene structures and conserved motifs within the same groups. Segmental duplications are predominant in the evolution of Dof in sugarcane. Cis-element analysis suggested that the functions of SsDofs were involved in growth and development, hormones and abiotic stresses responses in sugarcane. Expression patterns indicated that SsDof7, SsDof23 and SsDof24 had a comparatively high expression in all detected tissues, indicating these genes are crucial in sugarcane growth and development. Moreover, we examined the transcription levels of SsDofs under four plant hormone treatments, SsDof7-3 and SsDof7-4 were down-regulated after ABA treatment, while SsDof7-1 and SsDof7-2 were induced after the same treatment, indicating different alleles may play different roles in response to plant hormones. We also analyzed SsDofs' expression profiling under four abiotic stresses, SsDof5 and SsDof28 significantly responded to these four stresses, indicating they are associate with abiotic stresses responses. Collectively, our results yielded allele specific expression of Dof genes responding to hormones and abiotic stresses in sugarcane, and their cis-elements could be crucial for sugarcane improvement.
Assuntos
Regulação da Expressão Gênica de Plantas/fisiologia , Proteínas de Plantas/metabolismo , Saccharum/fisiologia , Estresse Fisiológico/genética , Fatores de Transcrição/metabolismo , Alelos , Duplicação Gênica/fisiologia , Perfilação da Expressão Gênica , Regulação da Expressão Gênica de Plantas/efeitos dos fármacos , Genoma de Planta/genética , Filogenia , Reguladores de Crescimento de Plantas/farmacologia , Proteínas de Plantas/genética , Fatores de Transcrição/genéticaRESUMO
Domestication of clonally propagated crops such as pineapple from South America was hypothesized to be a 'one-step operation'. We sequenced the genome of Ananas comosus var. bracteatus CB5 and assembled 513 Mb into 25 chromosomes with 29,412 genes. Comparison of the genomes of CB5, F153 and MD2 elucidated the genomic basis of fiber production, color formation, sugar accumulation and fruit maturation. We also resequenced 89 Ananas genomes. Cultivars 'Smooth Cayenne' and 'Queen' exhibited ancient and recent admixture, while 'Singapore Spanish' supported a one-step operation of domestication. We identified 25 selective sweeps, including a strong sweep containing a pair of tandemly duplicated bromelain inhibitors. Four candidate genes for self-incompatibility were linked in F153, but were not functional in self-compatible CB5. Our findings support the coexistence of sexual recombination and a one-step operation in the domestication of clonally propagated crops. This work guides the exploration of sexual and asexual domestication trajectories in other clonally propagated crops.
Assuntos
Ananas/genética , Produtos Agrícolas/genética , Domesticação , Genoma de Planta , Proteínas de Plantas/genética , Plantas Geneticamente Modificadas/genética , Característica Quantitativa Herdável , Ananas/crescimento & desenvolvimento , Bromelaínas/metabolismo , Produtos Agrícolas/crescimento & desenvolvimento , Regulação da Expressão Gênica de Plantas , Fenótipo , Plantas Geneticamente Modificadas/crescimento & desenvolvimento , Dinâmica Populacional , Açúcares/metabolismoRESUMO
Modern sugarcanes are polyploid interspecific hybrids, combining high sugar content from Saccharum officinarum with hardiness, disease resistance and ratooning of Saccharum spontaneum. Sequencing of a haploid S. spontaneum, AP85-441, facilitated the assembly of 32 pseudo-chromosomes comprising 8 homologous groups of 4 members each, bearing 35,525 genes with alleles defined. The reduction of basic chromosome number from 10 to 8 in S. spontaneum was caused by fissions of 2 ancestral chromosomes followed by translocations to 4 chromosomes. Surprisingly, 80% of nucleotide binding site-encoding genes associated with disease resistance are located in 4 rearranged chromosomes and 51% of those in rearranged regions. Resequencing of 64 S. spontaneum genomes identified balancing selection in rearranged regions, maintaining their diversity. Introgressed S. spontaneum chromosomes in modern sugarcanes are randomly distributed in AP85-441 genome, indicating random recombination among homologs in different S. spontaneum accessions. The allele-defined Saccharum genome offers new knowledge and resources to accelerate sugarcane improvement.
Assuntos
Genoma de Planta/genética , Poliploidia , Saccharum/genética , Alelos , Quimera/genética , Duplicação Cromossômica , Cromossomos de Plantas , Sequenciamento de Nucleotídeos em Larga Escala , Filogenia , Seleção Genética , Sorghum/genética , Translocação GenéticaRESUMO
In the version of this article originally published, the accession codes listed in the data availability section were incorrect and the section was incomplete. The text for this section should have read "The genome assembly and gene annotation have been deposited in the NCBI database under accession number QVOL00000000, BioProject number PRJNA483885 and BioSample number SAMN09753102. The data can also be downloaded from the following link: http://www.life.illinois.edu/ming/downloads/Spontaneum_genome/ ." The errors have been corrected in the HTML and PDF versions of the article.