Proteomic Changes in Newly Synthesized <Emphasis Type="Italic">Brassica napus</Emphasis> Allotetraploids and Their Early Generations

Polyploidy is a prominent process in higher plants and is often described as a genomic shock that may induce stress and defense responses. The Brassica napus allotetraploid model was chosen to investigate the proteomic modifications that occur during allopolyploid formation. Large-scale analysis of the proteome from the leaves of B. napus was performed and compared with the homozygous diploid progenitors, Brassica rapa and Brassica oleracea, and among the proteomic changes in B. napus in the early generations (F₁–F₄). The abundance of all these differentially expressed proteins in the F₁ generation differed from that of the corresponding proteins expressed in its progenitors, some of which relatively deviated from mid-parent predictions, exhibiting somewhat non-additive expression repatterning. Proteomic changes in the resynthesized B. napus from the first to the fourth generations were detected, which indicated that gene silencing was a permanent phenomenon and it could be reactivated at any moment. Although leaf proteins were extensively modified in synthetic B. napus, the distribution of the “housekeeping” proteins was not disturbed. Moreover, no evidence of chaos or large disorder was observed after the merging of the two genomes. Instead, a novel order quickly developed, which might evolve in further generations of synthetic B. napus.     

Detection,introgression and localization of genes conferring specific resistance to <Emphasis Type="Italic">Leptosphaeria maculans</Emphasis> from <Emphasis Type="Italic">Brassica rapa</Emphasis> into <Emphasis Type="Italic">B. napus</Emphasis>

Blackleg (stem canker) caused by the fungus Leptosphaeria maculans is one of the most damaging diseases of oilseed rape (Brassica napus). Crop relatives represent a valuable source of “new” resistance genes that could be used to diversify cultivar resistance. B. rapa, one of the progenitors of B. napus, is a potential source of new resistance genes. However, most of the accessions are heterozygous so it is impossible to directly detect the plant genes conferring specific resistance due to the complex patterns of avirulence genes in L. maculans isolates. We developed a strategy to simultaneously characterize and introgress resistance genes from B. rapa, by homologous recombination, into B. napus. One B. rapa plant resistant to one L. maculans isolate was used to produce B. rapa backcross progeny and a resynthesized B. napus plant from which a population of doubled haploid lines was derived after crossing with natural B. napus. We then used molecular analyses and resistance tests on these populations to identify and map the resistance genes and to characterize their introgression from B. rapa into B. napus. Three specific genes conferring resistance to L. maculans (Rlm1, Rlm2 and Rlm7) were identified in B. rapa. Comparisons of genetic maps showed that two of these genes were located on the R7 linkage group, in a region homologous to the region on linkage group N7 in B. napus, where these genes have been reported previously. The results of our study offer new perspectives for gene introgression and cloning in Brassicas.     

Two seed coat-specific promoters are functionally conserved between <Emphasis Type="Italic">Arabidopsis thaliana</Emphasis> and <Emphasis Type="Italic">Brassica napus</Emphasis>

Canola is one of the most important cash crops in Canada, and a national project named “Designing Oilseeds for Tomorrow’s Market” was undertaken to improve seed meal quality of this strategically important crop. As a part of this project, our group is focusing on identifying seed coat-specific promoters for canola (Brassica napus). These promoters will be used to genetically modify canola seed coat to reduce or eliminate anti-nutritional components from the meal. The Arabidopsis thaliana BAN promoter (AtBANpro) and δVPE promoter (AtδVPEpro) were isolated and fused to GUS reporter gene to generate transgenic canola plants. These plants were analyzed by GUS staining and microtome sectioning which showed that both promoters are seed coat-specific in canola: AtBANpro in inner seed coat layer and AtδVPEpro in outer seed coat layer. Therefore, the two Arabidopsis promoters can be used to modify genes in seed coat of canola for further improving its seed qualities.     

<Emphasis Type="Italic">dw2</Emphasis>, a New Mutation of Beet <Emphasis Type="Italic">Beta vulgaris</Emphasis> L.

Twelve dwarf plants were found in the second hybrid generation of beet. The average height of mutant plants was 21.8 cm, their leaf blades and flowers were significantly smaller than normal, and the plants exhibited male and female sterility. This dwarfism was shown to be caused by a mutation differing from that previously described in beet, which is named dwarf2 (dw2). The experimental evidence suggests that this mutation appeared in one of the first-generation plants. Based on plant phenotype in the first hybrid generation and the number of mutant plants in the second one, this mutation is suggested to be under recessive monogenic control of the dw2 gene. The genotypic class segregation in the second hybrid generation indicates that the dw2 gene is inherited independently of genes m, a1, and ap that control choricarpousness, gene male sterility, and pollen grain aggregation into tetrads.__________Translated from Genetika, Vol. 41, No. 5, 2005, pp. 657–660.Original Russian Text Copyright © 2005 by Mglinets, Osipova.     

<Emphasis Type="Italic">Agrobacterium</Emphasis>-mediated transformation of the dwarf pomegranate (<Emphasis Type="Italic">Punica granatum</Emphasis> L. var. <Emphasis Type="Italic">nana</Emphasis>)

The dwarf pomegranate (Punica granatum L. var. nana) is a dwarf ornamental plant that has the potential to be the model plant of perennial fruit trees because it bears fruits within 1 year of seedling. We established an Agrobacterium-mediated transformation system for the dwarf pomegranate. Adventitious shoots regenerated from leaf segments were inoculated with A. tumefaciens strain EHA105 harboring the binary vector pBin19-sgfp, which contains neomycin phosphotransferase (npt II) and green fluorescent protein (gfp) gene as a selectable and visual marker, respectively. After co-cultivation, the inoculated adventitious shoots were cut into small pieces to induce regeneration, and then selected on MS medium supplemented with 0.5 μM α-naphthaleneacetic acid (NAA), 5 μM N⁶-benzyladenine (BA), 0.3% gellan gum, 50 mg/l kanamycin, and 10 mg/l meropenem. Putative transformed shoots were regenerated after 6–8 months of selection. PCR and PCR-Southern blot analysis revealed the integration of the transgene into the plant genome. Transformants bloomed and bore fruits within 3 months of being potted, and the inheritance of the transgene was confirmed in T₁ generations. The advantage of the transformation of dwarf pomegranate was shown to be the high transformation rate. The establishment of this transformation system is invaluable for investigating fruit-tree-specific phenomena.     

The self-compatibility mechanism in <Emphasis Type="Italic">Brassica napus</Emphasis> L. is applicable to F<Subscript>1</Subscript> hybrid breeding

Brassica napus, an allopolyploid species having the A genome of B. rapa and the C genome of B. oleracea, is self-compatible, although both B. rapa and B. oleracea are self-incompatible. We have previously reported that SP11/SCR alleles are not expressed in anthers, while SRK alleles are functional in the stigma in B. napus cv. ‘Westar’, which has BnS-1 similar to B. rapa S-47 and BnS-6 similar to B. oleracea S-15. This genotype is the most frequent S genotype in B. napus, and we hypothesized that the loss of the function of SP11 is the primary cause of the self-compatibility of ‘Westar’. To verify this hypothesis, we transformed ‘Westar’ plants with the SP11 allele of B. rapa S-47. All the transgenic plants and their progeny were completely self-incompatible, demonstrating self-compatibility to be due to the S haplotype having the non-functional SP11 allele in the A genome, which suppresses a functional recessive SP11 allele in the C genome. An artificially synthesized B. napus line having two recessive SP11 alleles was developed by interspecific hybridization between B. rapa and B. oleracea. This line was self-incompatible, but F₁ hybrids between this line and ‘Westar’ were self-compatible. These results suggest that the self-compatibility mechanism of ‘Westar’ is applicable to F₁ seed production in B. napus.     

Isolation and characterization of dominant dwarf mutants, <Emphasis Type="Italic">Slr1-d</Emphasis>, in rice

sd1 is known as the ‘green revolution’ gene in rice because its application in rice breeding has dramatically increased rice yield. Since the ‘green revolution,’ sd1 has been extensively used to produce modern semi-dwarf varieties. The extensive use of limited dwarfing sources may, however, cause a bottleneck effect in the genetic background of rice varieties. To circumvent this problem, novel and useful sources of dwarf genes must be identified. In this study, we identified three semi-dominant dwarf mutants. These mutants were categorized as dn-type dwarf mutants according to the elongation pattern of internodes. Gibberellin (GA) response tests showed that the mutants were still responsive to GA, although at a reduced rate. Map-based cloning revealed that the dwarf phenotype in these mutants was caused by gain-of-function mutations in the N-terminal region of SLR1. Degradation of the SLR1 protein in these mutants occurred later than in the wild type. Reduced interaction abilities of the SLR1 protein in these mutants with GID1 were also observed using the yeast two-hybrid system. Crossing experiments indicated that with the use of an appropriate genetic background, the semi-dominant dwarf alleles identified in this study could be used to alleviate the deficiency of dwarfing genes for breeding applications.     

Antisense suppression of thioredoxin<Emphasis Type="Italic">h</Emphasis>mRNA in <Emphasis Type="Italic">Brassica napus cv.</Emphasis>

In Brassica, the thioredoxinhproteins, THL1 and THL2, were previously found to be potential inhibitors of the S receptor kinase (SRK) in the Brassica self-incompatibilty response. To investigate the biological roles of THL1 and THL2 in pollen–pistil interactions, the stigma-specific SLR1 promoter was used to drive antisense THL1/2 expression in Brassica napus cv. Westar. This cultivar is normally compatible, but antisense suppression of THL1/2 led to a low level constitutive rejection of all Brassica napus pollen tested. Fluorescence microscopy revealed that the pollen rejection was a typical Brassica self-incompatibility rejection response with reduced pollen adhesion, germination and pollen tube growth. In addition, Westar was found to express the SLG₁₅ and SRK₁₅ proteins which may be the target of regulation by THL1 and THL2. Thus, these results indicate that the THL1 and THL2 are required for full pollen acceptance in B. napus cv. Westar.     

Molecular mapping of leaf rust resistance gene <Emphasis Type="Italic">Rph14</Emphasis> in <Emphasis Type="Italic">Hordeum vulgare</Emphasis>

An incompletely dominant gene conferring resistance to Puccinia hordei, Rph14, identified previously in an accession of Hordeum vulgare, confers resistance to all known pathotypes of P. hordei in Australia. Knowledge of the chromosomal location of Rph14 and the identification of DNA markers closely linked to it will facilitate combining it with other important leaf rust resistance genes to achieve long lasting resistance. The inheritance of Rph14 was confirmed using 146 and 106 F₃ lines derived from the crosses ‘Baudin’/‘PI 584760’ (Rph14) and ‘Ricardo’/‘PI 584760’ (Rph14), respectively. Bulk segregant analysis on DNA from the parental genotypes and resistant and susceptible DNA bulks using DArT markers located Rph14 to the short arm of chromosome 2H. DArT marker bPb-1664 was identified as having the closest genetic association with Rph14. PCR based marker analysis identified a single SSR marker, Bmag692, linked closely to Rph14 at a map distance of 2.1 and 3.8 cm in the ‘Baudin’/‘PI 584760’and ‘Ricardo’/‘PI 584760’ populations, respectively.     

Antioxidant defense system in leaves of Indian mustard (<Emphasis Type="Italic">Brassica juncea</Emphasis>) and rape (<Emphasis Type="Italic">Brassica napus</Emphasis>) under cadmium stress

Plant species capable of hyper-accumulating heavy metals are of considerable interest for phytoremediation, and differ in their ability to accumulate metals from environment. Using two brassica species (Brassica juncea and Brassica napus), nutrient solution experiments were conducted to study variation in tolerance to cadmium (Cd) toxicity based on (1) lipid peroxidation and (2) changes in antioxidative defense system in leaves of both plants (i.e., superoxide dismutase (SOD EC 1.15.1.1), catalase (CAT EC 1.11.1.6), ascorbate peroxidase (APX EC 1.11.1.11), guaiacol peroxidase (GPX EC 1.11.1.7), glutathione reductase (GR EC 1.6.4.2), levels of phytochelatins (PCs), non-protein thiols (NP-SH), and glutathione. Plants were grown in nutrient solution under controlled environmental conditions, and subjected to increasing concentrations of Cd (0, 10, 25 and 50 μM) for 15 days. Results showed marked differences between both species. Brassica napus under Cd stress exhibited increased level of lipid peroxidation, as was evidenced by the increased malondialdehyde (MDA) content in leaves. However, in Brassica juncea treated plants, MDA content remained unchanged. In Brassica napus, with the exception of GPX, activity levels of some antioxidant enzymes involved in detoxification of reactive oxygen species (ROS), including SOD, CAT, GR, and APX, decreased drastically at high Cd concentrations. By contrast, in leaves of Brassica juncea treated plants, there was either only slight or no change in the activities of the antioxidative enzymes. Analysis of the profile of anionic isoenzymes of GPX revealed qualitative changes occurring during Cd exposure for both species. Moreover, levels of NP-SH and PCs, monitored as metal detoxifying responses, were much increased in leaves of Brassica juncea by increasing Cd supply, but did not change in Brassica napus. These results indicate that Brassica juncea plants possess the greater potential for Cd accumulation and tolerance than Brassica napus.     

High-density <Emphasis Type="Italic">Brassica oleracea</Emphasis> linkage map: identification of useful new linkages

We constructed a 1,257-marker, high-density genetic map of Brassica oleracea spanning 703 cM in nine linkage groups, designated LG1–LG9. It was developed in an F2 segregating population of 143 individuals obtained by crossing double haploid plants of broccoli “Early-Big” and cauliflower “An-Nan Early”. These markers are randomly distributed throughout the map, which includes a total of 1,062 genomic SRAP markers, 155 cDNA SRAP markers, 26 SSR markers, 3 broccoli BAC end sequences and 11 known Brassica genes: BoGSL-ALK, BoGSL-ELONG, BoGSL-PROa, BoGSL-PROb, BoCS-lyase, BoGS-OH, BoCYP79F1, BoS-GT (glucosinolate pathway), BoDM1 (resistance to downy mildew), BoCALa, BoAP1a (inflorescence architecture). BoDM1 and BoGSL-ELONG are linked on LG 2 at 0.8 cM, making it possible to use the glucosinolate gene as a marker for the disease resistance gene. By QTL analysis, we found three segments involved in curd formation in cauliflower. The map was aligned to the C genome linkage groups and chromosomes of B. oleracea and B. napus, and anchored to the physical map of A. thaliana. This map adds over 1,000 new markers to Brassica molecular tools. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Characterization of Defense Signaling Pathways of <Emphasis Type="Italic">Brassica napus</Emphasis> and <Emphasis Type="Italic">Brassica carinata</Emphasis> in Response to <Emphasis Type="Italic">Sclerotinia sclerotiorum</Emphasis> Challenge

Canola (Brassica napus L.) is an agriculturally and economically important crop in Canada, and its growth and yield are frequently influenced by fungal pathogens. Sclerotinia sclerotiorum is among those fungal pathogens and causes stem rot disease in B. napus whereas it has been reported that Brassica carinata is moderately tolerant to S. sclerotiorum. Jasmonic acid/ethylene (JA/ET) and salicylic acid (SA) are phytohormones that are known to be involved in plant disease responses. To investigate the defense signaling cascades involved in the interaction of B. napus and B. carinata with S. sclerotiorum, we examined the expression of five orthologs of B. napus genes involved in JA/ET or SA signaling pathways using quantitative RT-PCR. Our results indicated that there are differences in the timing of JA/ET and SA signaling pathways between B. napus and B. carinata. Our results in these two Brassica species also support previous observations that necrotrophic pathogens trigger JA/ET signaling in response to infection. Finally, we observed that transgenic canola expressing 1-aminocyclopropane-1-carboxylate-deaminase producing low levels of ET was relatively more susceptible to S. sclerotiorum than its wild-type counterpart, suggesting that ET inhibits S. sclerotiorum-induced symptom development.     

Characterization and genetic analysis of a low-temperature-sensitive mutant, <Emphasis Type="Italic">sy</Emphasis>-<Emphasis Type="Italic">2</Emphasis>, in <Emphasis Type="Italic">Capsicum chinense</Emphasis>

A temperature-sensitive mutant of Capsicum chinense, sy-2, shows a normal developmental phenotype when grown above 24°C. However, when grown at 20°C, sy-2 exhibits developmental defects, such as chlorophyll deficiency and shrunken leaves. To understand the underlying mechanism of this temperature-dependent response, phenotypic characterization and genetic analysis were performed. The results revealed abnormal chloroplast structures and cell collapse in leaves of the sy-2 plants grown at 20°C. Moreover, an excessive accumulation of reactive oxygen species (ROS) resulting in cell death was detected in the chlorophyll-deficient sectors of the leaves. However, the expression profile of the ROS scavenging genes did not alter in sy-2 plants grown at 20°C. A further analysis of fatty acid content in the leaves showed the impaired pathway of linoleic acid (18:2) to linolenic acid (18:3). Additionally, the Cafad7 gene was downregulated in sy-2 plants. This change may lead to dramatic physiological disorder and alteration of leaf morphology in sy-2 plants by losing low-temperature tolerance. Genetic analysis of an F₂ population from a cross between C. chinense ‘sy-2’ and wild-type C. chinense ‘No. 3341’ showed that the sy-2 phenotype is controlled by a single recessive gene. Molecular mapping revealed that the sy-2 gene is located at a genomic region of the pepper linkage group 1, corresponding to the 300 kb region of the Ch1_scaffold 00106 in tomato chromosome 1. Candidate genes in this region will reveal the identity of sy-2 and the underlying mechanism of the temperature-dependent plant response.     

An <Emphasis Type="Italic">in vitro</Emphasis> method to evaluate grapevine cultivars for <Emphasis Type="Italic">Erysiphe necator</Emphasis> susceptibility

Powdery mildew, caused by the obligate biotrophic ascomycete Erysiphe necator, is one of the most destructive grapevine diseases worldwide. Cultivars of Vitis vinifera L, for wine and table grape production, are all susceptible to E. necator, whose attacks result in severe epidemics under the warm and dry conditions of the Mediterranean basin. The aim of the present study was to compare the susceptibility of different grapevine cultivars to E. necator by an in vitro assay for assessing the potentiality of this method in breeding programs for resistance to the pathogen. Leaves of 12 grapevine cultivars were spot-inoculated in vitro with about 10 conidia from five different isolates of E. necator, using colony growth and conidiation 3 wk post-inoculation as indicators of susceptibility to the disease. A remarkable difference was observed between highly susceptible cultivars like ‘Baresana’, ‘Malvasia’, ‘Bianca’, and ‘Italia’, and the less susceptible ‘Alphonse Lavallée’ and ‘Ohanez’, in accordance with their behavior in the field. No statistically significant differences were found in the virulence of E. necator isolates.     

Heterologous Expression of a Gibberellin 2-Oxidase Gene from <Emphasis Type="BoldItalic">Arabidopsis thaliana</Emphasis> Enhanced the Photosynthesis Capacity in <Emphasis Type="BoldItalic">Brassica napus</Emphasis> L.

Gibberellins (GAs) are endogenous hormones that play an important role in regulating plant stature by increasing cell division and promoting seed germination. The GA2-oxidase gene from Arabidopsis thaliana (AtGA2ox8) was introduced into Brassica napus L. by Agrobacterium-mediated floral-dip transformation with the aim of decreasing the amount of bioactive GA and hence reduced the plant height. As anticipated, the transgenic plant exhibited dwarf phenotype. Importantly, compared with the wild type, the transgenic plants had delayed the seed germination, increased the chlorophyll content (28.7–36.3%) and photosynthesis capacity (14.3–18.7%) in a single leaf. At the same time, the photosynthesis capacity of the whole plants was significantly enhanced (35.7–48.6%) due to the extra leaves and branches.     

Genetic characterization of a new cytoplasmic male sterility system (<Emphasis Type="Italic">hau</Emphasis>) in <Emphasis Type="Italic">Brassica </Emphasis><Emphasis Type="Italic">juncea</Emphasis> and its transfer to <Emphasis Type="Italic">B. napus</Emphasis>

A novel cytoplasmic male sterility (CMS) was identified in Brassica juncea, named as hau CMS (00-6-102A). Subsequently, the male sterility was transferred to B. napus by interspecific hybridization. The hau CMS has stable male sterility. Flowers on the A line are absolutely male sterile, and seeds harvested from the line following pollinations with the maintainer gave rise to 100% sterile progeny. The anthers in CMS plants are replaced by thickened petal-like structures and pollen grains were not detected. In contrast, in other CMS systems viz. pol, nap, tour, and ogu, anthers are formed but do not produce viable pollen. The sterility of hau CMS initiates at the stage of stamen primordium polarization, which is much earlier compared with the other four CMS systems. We have successfully transferred hau CMS from B. juncea to B. napus. Restorer lines for pol, ogu, nap, and tour CMS systems were found to be ineffective to restore fertility in hau CMS. Sixteen out of 40 combinations of mitochondrial probe/enzyme used for RFLP analysis distinguished the hau CMS system from the other four systems. Among these sixteen combinations, five ones alone could distinguish the five CMS systems from each other. The evidence from genetic, morphological, cytological and molecular studies confirmed that the hau CMS system is a novel CMS system. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Zero erucic acid trait of rapeseed (<Emphasis Type="Italic">Brassica napus</Emphasis> L.) results from a deletion of four base pairs in the <Emphasis Type="Italic">fatty acid elongase 1</Emphasis> gene

The fatty acid elongase 1 (FAE1) gene is a key gene in the erucic acid biosynthesis in rapeseed. The complete coding sequences of the FAE1 gene were isolated separately from eight high and zero erucic acid rapeseed cultivars (Brassica napus L.). A four base pair deletion between T1366 and G1369 in the FAE1 gene was found in a number of the cultivars, which leads to a frameshift mutation and a premature stop of the translation after the 466th amino acid residue. This deletion was predominantly found in the C-genome and rarely in the A-genome of B. napus. Expression of the gene isoforms with the four base pair deletion in a yeast system generated truncated proteins with no enzymatic activity and could not produce very long chain fatty acids as the control with an intact FAE1 gene did in yeast cells. In the developing rape seeds the FAE1 gene isoforms with the four base pair deletion were transcribed normally but failed to translate proteins to form a functional complex. The four base pair deletion proved to be a mutation responsible for the low erucic acid trait in rapeseed and independent from the point mutation reported by Han et al. (Plant Mol Biol 46:229–239, 2001). Gang Wu, Yuhua Wu contribute equally to this article.     

Mutations in the <Emphasis Type="Italic">S</Emphasis> gene region of hepatitis B virus genotype <Emphasis Type="Italic">D</Emphasis> in Turkish patients

The S gene region of the hepatitis B virus (HBV) is responsible for the expression of surface antigens and includes the ‘a’-determinant region. Thus, mutation(s) in this region would afford HBV variants a distinct survival advantage, permitting the mutant virus to escape from the immune system. The aim of this study was to search for mutations of the S gene region in different patient groups infected with genotype D variants of HBV, and to analyse the biological significance of these mutations. Moreover, we investigated S gene mutation inductance among family members. Forty HBV-DNA-positive patients were determined among 132 hepatitis B surface antigen (HbsAg) carriers by the first stage of seminested PCR. Genotypes and subtypes were established by sequencing of the amplified S gene regions. Variants were compared with original sequences of these serotypes, and mutations were identified. All variants were designated as genotype D and subtype ayw3. Ten kinds of point mutations were identified within the S region. The highest rates of mutation were found in chronic hepatitis patients and their family members. The amino acid mutations 125 (M → T) and 127 (T → P) were found on the first loop of ‘a’-determinant. The other consequence was mutation inductance in a family member. We found some mutations in the S gene region known to be stable and observed that some of these mutations affected S gene expression.     

Sequence,expression divergence,and complementation of homologous <Emphasis Type="Italic">ALCATRAZ</Emphasis> loci in <Emphasis Type="Italic">Brassica napus</Emphasis>

The genomic era provides new perspectives in understanding polyploidy evolution, mostly on the genome-wide scale. In this paper, we show the sequence and expression divergence between the homologous ALCATRAZ (ALC) loci in Brassica napus, responsible for silique dehiscence. We cloned two homologous ALC loci, namely BnaC.ALC.a and BnaA.ALC.a in B. napus. Driven by the 35S promoter, both the loci complemented to the alc mutation of Arabidopsis thaliana, yet only the expression of BnaC.ALC.a was detectable in the siliques of B. napus. Sequence alignment indicated that BnaC.ALC.a and BolC.ALC.a, or BnaA.ALC.a and BraA.ALC.a, possess a high level of similarity. The understanding of the sequence and expression divergence among homologous loci of a gene is of due importance for an effective gene manipulation and TILLING (or ECOTILLING) analysis for the allelic DNA variation at a given locus. S. Hua and I. H. Shamsi contributed equally to this work.