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PubMed2004

Pleiotropic effects of the 8.1 HLA haplotype in patients with autoimmune myasthenia gravis and thymus hyperplasia.

The 8.1 haplotype of the HLA complex has been reproducibly associated with several autoimmune diseases and traits, notably with thymus hyperplasia in patients with acquired generalized myasthenia gravis, an autoantibody-mediated disease directed at the muscle acetylcholine receptor. However, the strong linkage disequilibrium across this haplotype has prevented the identification of the causative locus, termed MYAS1. Here, we localized MYAS1 to a 1.2-Mb genome segment by reconstructing haplotypes and assessing their transmission in 73 simplex families. This segment encompasses the class III and proximal class I regions, between the BAT3 and C3-2-11 markers, therefore unambiguously excluding the class II loci. In addition, a case-control study revealed a very strong association with a core haplotype in this same region following an additive model (P=7 x 10(-11), odds ratio 6.5 for one copy and 42 for two copies of the core haplotype). Finally, we showed that this region is associated with a marked increase in serum titers of anti-acetylcholine receptor autoantibodies (P=8 x 10(-6)). Remarkably, this effect was suppressed by a second locus in cis on the 8.1 haplotype and located toward the class II region. Altogether, these data demonstrate the highly significant but complex effects of the 8.1 haplotype on the phenotype of myasthenia gravis patients and might shed light on its role in other autoimmune diseases.

Autoantibodies↗

PubMed2006

Complex haplotypes derived from noncoding polymorphisms of the intronless alpha2A-adrenergic gene diversify receptor expression.

Alpha(2A)-adrenergic receptors (alpha(2A)AR) regulate multiple central nervous system, cardiovascular, and metabolic processes including neurotransmitter release, platelet aggregation, blood pressure, insulin secretion, and lipolysis. Complex diseases associated with alpha(2A)AR dysfunction display familial clustering, phenotypic heterogeneity, and interindividual variability in response to therapy targeted to alpha(2A)ARs, suggesting common, functional polymorphisms. In a multiethnic discovery cohort we identified 16 single-nucleotide polymorphisms (SNPs) in the alpha(2A)AR gene organized into 17 haplotypes of two major phylogenetic clades. In contrast to other adrenergic genes, variability of the alpha(2A)AR was primarily due to SNPs in the promoter, 5' UTR and 3' UTR, as opposed to the coding block. Marked ethnic variability in the frequency of SNPs and haplotypes was observed: one haplotype represented 70% of Caucasians, whereas Africans and Asians had a wide distribution of less common haplotypes, with the highest haplotype frequencies being 16% and 35%, respectively. Despite the compact nature of this intronless gene, local linkage disequilibrium between a number of SNPs was low and ethnic-dependent. Whole-gene transfections into BE(2)-C human neuronal cells using vectors containing the entire approximately 5.3-kb gene without exogenous promoters were used to ascertain the effects of haplotypes on alpha(2A)AR expression. Substantial differences (P < 0.001) in transcript and cell-surface protein expression, by as much as approximately 5-fold, was observed between haplotypes, including those with common frequencies. Thus, signaling by this virtually ubiquitous receptor is under major genetic influence, which may be the basis for highly divergent phenotypes in complex diseases such as systemic and pulmonary hypertension, heart failure, diabetes, and obesity.

Cell Line↗

PubMed2002

A dynamic programming algorithm for haplotype block partitioning.

We develop a dynamic programming algorithm for haplotype block partitioning to minimize the number of representative single nucleotide polymorphisms (SNPs) required to account for most of the common haplotypes in each block. Any measure of haplotype quality can be used in the algorithm and of course the measure should depend on the specific application. The dynamic programming algorithm is applied to analyze the chromosome 21 haplotype data of Patil et al. [Patil, N., Berno, A. J., Hinds, D. A., Barrett, W. A., Doshi, J. M., Hacker, C. R., Kautzer, C. R., Lee, D. H., Marjoribanks, C., McDonough, D. P., et al. (2001) Science 294, 1719-1723], who searched for blocks of limited haplotype diversity. Using the same criteria as in Patil et al., we identify a total of 3,582 representative SNPs and 2,575 blocks that are 21.5% and 37.7% smaller, respectively, than those identified using a greedy algorithm of Patil et al. We also apply the dynamic programming algorithm to the same data set based on haplotype diversity. A total of 3,982 representative SNPs and 1,884 blocks are identified to account for 95% of the haplotype diversity in each block.

Algorithms↗

PubMed2003

Minimal haplotype tagging.

The high frequency of single-nucleotide polymorphisms (SNPs) in the human genome presents an unparalleled opportunity to track down the genetic basis of common diseases. At the same time, the sheer number of SNPs also makes unfeasible genome-wide disease association studies. The haplotypic nature of the human genome, however, lends itself to the selection of a parsimonious set of SNPs, called haplotype tagging SNPs (htSNPs), able to distinguish the haplotypic variations in a population. Current approaches rely on statistical analysis of transmission rates to identify htSNPs. In contrast to these approximate methods, this contribution describes an exact, analytical, and lossless method, called BEST (Best Enumeration of SNP Tags), able to identify the minimum set of SNPs tagging an arbitrary set of haplotypes from either pedigree or independent samples. Our results confirm that a small proportion of SNPs is sufficient to capture the haplotypic variations in a population and that this proportion decreases exponentially as the haplotype length increases. We used BEST to tag the haplotypes of 105 genes in an African-American and a European-American sample. An interesting finding of this analysis is that the vast majority (95%) of the htSNPs in the European-American sample is a subset of the htSNPs of the African-American sample. This result seems to provide further evidence that a severe bottleneck occurred during the founding of Europe and the conjectured "Out of Africa" event.

Algorithms↗

PubMed2002

Ancient mitochondrial haplotypes and evidence for intragenic recombination in a gynodioecious plant.

Because of their extremely low nucleotide mutation rates, plant mitochondrial genes are generally not expected to show variation within species. Remarkably, we found nine distinct cytochrome b sequence haplotypes in the gynodioecious alpine plant Silene acaulis, with two or more haplotypes coexisting locally in each of three sampled regions. Moreover, there is evidence for intragenic recombination in the history of the haplotype sample, implying at least transient heteroplasmy of mitochondrial DNA (mtDNA). Heteroplasmy might be achieved by one of two potential mechanisms, either continuous coexistence of subgenomic fragments in low stoichiometry, or occasional paternal leakage of mtDNA. On the basis of levels of synonymous nucleotide substitutions, the average divergence time between haplotypes is estimated to be at least 15 million years. Ancient coalescence of extant haplotypes is further indicated by the paucity of fixed differences in haplotypes obtained from related species, a pattern expected under trans-specific evolution. Our data are consistent with models of frequency-dependent selection on linked cytoplasmic male-sterility factors, the putative molecular basis of females in gynodioecious populations. However, associations between marker loci and the inferred male-sterility genes can be maintained only with very low rates of recombination. Heteroplasmy and recombination between divergent haplotypes imply unexplored consequences for the evolutionary dynamics of gynodioecy, a widespread plant breeding system.

Base Sequence↗

PubMed1990

Major histocompatibility complex haplotype studies in Ashkenazi Jewish patients with pemphigus vulgaris.

Of 26 Ashkenazi Jewish patients with pemphigus vulgaris, 24 (92.3%) carried the major histocompatibility complex (MHC) class II alleles HLA-DR4, DQw3, of which all were of the subtype DR4, DQw8. From studies of the patients and their families, haplotypes were defined. It was found that, of the patients who carried HLA-DR4, DQw8, 75% carried one or the other (and in one case, both) of two haplotypes [HLA-B38, SC21, DR4] or HLA-B35, SC31, DR4. The former is a known extended haplotype among normal Jews, with a frequency of 0.102, and the latter may also be an extended haplotype in this ethnic group, with a frequency of 0.017 among normal haplotypes from Jews. Of the remaining DR4-positive patients, all but one had a presumed D-region segment (defined as SC21, DR4, DQw8 or SC31, DR4, DQw8 with variable HLA-B) of these haplotypes. Only one patient had DR4, DQw8 without any other markers of the extended haplotypes. The number of homozygotes and heterozygotes for DR4, DQw8 was consistent with dominant but not recessive (P less than 0.01) inheritance of a class II or a class II-linked susceptibility gene for the disease. Since the disease is entirely attributable to the presence of an antibody to an intraepidermal intercellular cement substance, it is likely that the class II susceptibility gene (on [HLA-B38, SC21, DR4, DQw8], HLA-B35, SC31, DR4, DQw8, or their segments, in Jewish patients) controls the production of the antibody as a dominantly expressed immune response gene.

Alleles↗

PubMed1991

Major histocompatibility complex haplotypes and class II genes in non-Jewish patients with pemphigus vulgaris.

Previous studies demonstrated that HLA-DR4 was markedly increased among Ashkenazi Jewish patients with pemphigus vulgaris (PV), almost entirely as the common Jewish extended haplotype [HLA-B38, SC21, DR4, DQw8] or as the haplotype HLA-B35, SC31, DR4, DQw8, and that HLA-DR4, DQw8 was distributed among patients in a manner consistent with dominant expression of a class II (D-region or D-region-linked) susceptibility gene. In the present study of major histocompatibility complex (MHC) haplotypes in 25 non-Jewish PV patients, DR4, DQw8 was found in 12 of the patients and DRw6, DQw5 was found in 15. Only 3 patients had neither. Only 1 of the DR4, DQw8 haplotypes was [HLA-B38, SC21, DR4, DQw8] and 2 were HLA-B35, SC31, DR4, DQw8; most were the presumed fragments (SC31, DR4, DQw8) or (SC21, DR4, DQw8) or DR4, DQw8 with some other complotype. Of the patients with DRw6, DQw5, all were DRw14, DQw5, and 6 had a rare Caucasian haplotype, HLA-Bw55, SB45, DRw14, DQw5. Four of 6 of these were found in patients of Italian extraction, as was the 1 normal example. The non-Jewish patients were of more Southern European extraction than our controls. This suggests that there are two major MHC susceptibility alleles in American patients with PV. The more ancient apparently arose on a haplotype in the Jews, HLA-B38(35), SC21(SC31), DR4, DQw8, and spread to other populations largely as D-region segments. The other arose in or near Italy on the haplotype HLA-Bw55, SB45, DRw14, DQw5 and has also partially fragmented so that many patients carry only DRw14, DQw5. The available data do not permit the specific localization of either the DR4, DQw8- or the DRw14, DQw5-linked susceptibility genes.

Alleles↗

PubMed2006

Direct haplotype-specific DNA sequencing.

Determining haplotype-specific DNA sequence information is very important in a wide range of research fields. However, no simple and robust approaches are currently available for determining haplotype-specific sequence information. We have addressed this problem by developing a very simple and robust haplotype-specific sequencing approach. We utilise the fact that DNA sequencing polymerases are sensitive to 3'end mismatches in the sequencing primer. By using two sequencing primers with 3'end corresponding to the two alleles in a given SNP locus, we are able to obtain allele-specific DNA sequences from both alleles. We evaluated this direct haplotype-specific approach by determining haplotypes within the intron 2 sequence of the fructan-6-fructosyltransferase (6-ft) gene in Lolium perenne L. We obtained reliable haplotype-specific sequences for all primers and genotypes evaluated. We conclude that the haplotype-specific sequencing is robust, and that the approach has a potentially very wide application range for any diploid organism.

Base Sequence↗

PubMed1999

Assessment of linkage disequilibrium by the decay of haplotype sharing, with application to fine-scale genetic mapping.

Linkage disequilibrium (LD) is of great interest for gene mapping and the study of population history. We propose a multilocus model for LD, based on the decay of haplotype sharing (DHS). The DHS model is most appropriate when the LD in which one is interested is due to the introduction of a variant on an ancestral haplotype, with recombinations in succeeding generations resulting in preservation of only a small region of the ancestral haplotype around the variant. This is generally the scenario of interest for gene mapping by LD. The DHS parameter is a measure of LD that can be interpreted as the expected genetic distance to which the ancestral haplotype is preserved, or, equivalently, 1/(time in generations to the ancestral haplotype). The method allows for multiple origins of alleles and for mutations, and it takes into account missing observations and ambiguities in haplotype determination, via a hidden Markov model. Whereas most commonly used measures of LD apply to pairs of loci, the DHS measure is designed for application to the densely mapped haplotype data that are increasingly available. The DHS method explicitly models the dependence among multiple tightly linked loci on a chromosome. When the assumptions about population structure are sufficiently tractable, the estimate of LD is obtained by maximum likelihood. For more-complicated models of population history, we find means and covariances based on the model and solve a quasi-score estimating equation. Simulations show that this approach works extremely well both for estimation of LD and for fine mapping. We apply the DHS method to published data sets for cystic fibrosis and progressive myoclonus epilepsy.

Algorithms↗

PubMed2000

Apolipoprotein E variation at the sequence haplotype level: implications for the origin and maintenance of a major human polymorphism.

Three common protein isoforms of apolipoprotein E (apoE), encoded by the epsilon2, epsilon3, and epsilon4 alleles of the APOE gene, differ in their association with cardiovascular and Alzheimer's disease risk. To gain a better understanding of the genetic variation underlying this important polymorphism, we identified sequence haplotype variation in 5.5 kb of genomic DNA encompassing the whole of the APOE locus and adjoining flanking regions in 96 individuals from four populations: blacks from Jackson, MS (n=48 chromosomes), Mayans from Campeche, Mexico (n=48), Finns from North Karelia, Finland (n=48), and non-Hispanic whites from Rochester, MN (n=48). In the region sequenced, 23 sites varied (21 single nucleotide polymorphisms, or SNPs, 1 diallelic indel, and 1 multiallelic indel). The 22 diallelic sites defined 31 distinct haplotypes in the sample. The estimate of nucleotide diversity (site-specific heterozygosity) for the locus was 0.0005+/-0.0003. Sequence analysis of the chimpanzee APOE gene showed that it was most closely related to human epsilon4-type haplotypes, differing from the human consensus sequence at 67 synonymous (54 substitutions and 13 indels) and 9 nonsynonymous fixed positions. The evolutionary history of allelic divergence within humans was inferred from the pattern of haplotype relationships. This analysis suggests that haplotypes defining the epsilon3 and epsilon2 alleles are derived from the ancestral epsilon4s and that the epsilon3 group of haplotypes have increased in frequency, relative to epsilon4s, in the past 200,000 years. Substantial heterogeneity exists within all three classes of sequence haplotypes, and there are important interpopulation differences in the sequence variation underlying the protein isoforms that may be relevant to interpreting conflicting reports of phenotypic associations with variation in the common protein isoforms.

Alleles↗

PubMed2000

Haplotypes at ATM identify coding-sequence variation and indicate a region of extensive linkage disequilibrium.

Genetic variation in the human population may lead to functional variants of genes that contribute to risk for common chronic diseases such as cancer. In an effort to detect such possible predisposing variants, we constructed haplotypes for a candidate gene and tested their efficacy in association studies. We developed haplotypes consisting of 14 biallelic neutral-sequence variants that span 142 kb of the ATM locus. ATM is the gene responsible for the autosomal recessive disease ataxia-telangiectasia (AT). These ATM noncoding single-nucleotide polymorphisms (SNPs) were genotyped in nine CEPH families (89 individuals) and in 260 DNA samples from four different ethnic origins. Analysis of these data with an expectation-maximization algorithm revealed 22 haplotypes at this locus, with three major haplotypes having frequencies > or = .10. Tests for recombination and linkage disequilibrium (LD) show reduced recombination and extensive LD at the ATM locus, in all four ethnic groups studied. The most striking example was found in the study population of European ancestry, in which no evidence for recombination could be discerned. The potential of ATM haplotypes for detection of genetic variants through association studies was tested by analysis of 84 individuals carrying one of three ATM coding SNPs. Each coding SNP was detected by association with an ATM haplotype. We demonstrate that association studies with haplotypes for candidate genes have significant potential for the detection of genetic backgrounds that contribute to disease.

Algorithms↗

PubMed2001

An extensive analysis of Y-chromosomal microsatellite haplotypes in globally dispersed human populations.

The genetic variance at seven Y-chromosomal microsatellite loci (or short tandem repeats [STRs]) was studied among 986 male individuals from 20 globally dispersed human populations. A total of 598 different haplotypes were observed, of which 437 (73.1%) were each found in a single male only. Population-specific haplotype-diversity values were.86-.99. Analyses of haplotype diversity and population-specific haplotypes revealed marked population-structure differences between more-isolated indigenous populations (e.g., Central African Pygmies or Greenland Inuit) and more-admixed populations (e.g., Europeans or Surinamese). Furthermore, male individuals from isolated indigenous populations shared haplotypes mainly with male individuals from their own population. By analysis of molecular variance, we found that 76.8% of the total genetic variance present among these male individuals could be attributed to genetic differences between male individuals who were members of the same population. Haplotype sharing between populations, phi(ST) statistics, and phylogenetic analysis identified close genetic affinities among European populations and among New Guinean populations. Our data illustrate that Y-chromosomal STR haplotypes are an ideal tool for the study of the genetic affinities between groups of male subjects and for detection of population structure.

Africa↗

PubMed2002

Genetic dissection of the human leukocyte antigen region by use of haplotypes of Tasmanians with multiple sclerosis.

Association of multiple sclerosis (MS) with the human leukocyte antigen (HLA) class II haplotype DRB1*1501-DQB1*0602 is the most consistently replicated finding of genetic studies of the disease. However, the high level of linkage disequilibrium (LD) in the HLA region has hindered the identification of other loci that single-marker tests for association are unlikely to resolve. In order to address this issue, we generated haplotypes spanning 14.754 Mb (5 cM) across the entire HLA region. The haplotypes, which were inferred by genotyping relatives of 152 patients with MS and 105 unaffected control subjects of Tasmanian ancestry, define a genomic segment from D6S276 to D6S291, including 13 microsatellite markers integrated with allele-typing data for DRB1 and DQB1. Association to the DRB1*1501-DQB1*0602 haplotype was replicated. In addition, we found that the class I/extended class I region, defined by a genomic segment of approximately 400 kb between MOGCA and D6S265, harbors genes that independently increase risk of, or provide protection from, MS. Log-linear modeling analysis of constituent haplotypes that represent genomic regions containing class I (MOGCA-D6S265), class III (TNFa-TNFd-D6S273), and class II (DRB1-DQB1) genes indicated that having class I and class II susceptibility variants on the same haplotype provides an additive effect on risk. Moreover, we found no evidence for a disease locus in the class III region defined by a 150-kb genomic segment containing the TNF locus and 14 other genes. A global overview of LD performed using GOLD identified two discrete blocks of LD in the HLA region that correspond well with previous findings. We propose that the analysis of haplotypes, by use of the types of approaches outlined in the present article, should make it possible to more accurately define the contribution of the HLA to MS.

Alleles↗

PubMed2002

Distribution of recombination crossovers and the origin of haplotype blocks: the interplay of population history, recombination, and mutation.

Recent studies suggest that haplotypes are arranged into discrete blocklike structures throughout the human genome. Here, we present an alternative haplotype block definition that assumes no recombination within each block but allows for recombination between blocks, and we use it to study the combined effects of demographic history and various population genetic parameters on haplotype block characteristics. Through extensive coalescent simulations and analysis of published haplotype data on chromosome 21, we find that (1) the combined effects of population demographic history, recombination, and mutation dictate haplotype block characteristics and (2) haplotype blocks can arise in the absence of recombination hot spots. Finally, we provide practical guidelines for designing and interpreting studies investigating haplotype block structure.

Algorithms↗

PubMed2005

Promoter and 3'-untranslated-region haplotypes in the vitamin d receptor gene predispose to osteoporotic fracture: the rotterdam study.

Polymorphisms of the vitamin D receptor gene (VDR) have been shown to be associated with several complex diseases, including osteoporosis, but the mechanisms are unknown and study results have been inconsistent. We therefore determined sequence variation across the major relevant parts of VDR, including construction of linkage disequilibrium blocks and identification of haplotype alleles. We analyzed 15 haplotype-tagging SNPs in relation to 937 clinical fractures recorded in 6,148 elderly whites over a follow-up period of 7.4 years. Haplotype alleles of the 5' 1a/1e, 1b promoter region and of the 3' untranslated region (UTR) were strongly associated with increased fracture risk. For the 16% of subjects who had risk genotypes at both regions, their risk increased 48% for clinical fractures (P = .0002), independent of age, sex, height, weight, and bone mineral density. The population-attributable risk varied between 1% and 12% for each block and was 4% for the combined VDR risk genotypes. Functional analysis of the variants demonstrated 53% lower expression of a reporter construct with the 1e/1a promoter risk haplotype (P = 5 x 10(-7)) in two cell lines and 15% lower mRNA level of VDR expression constructs carrying 3'-UTR risk haplotype 1 in five cell lines (P = 2 x 10(-6)). In a further analysis, we showed 30% increased mRNA decay in an osteoblast cell line for the construct carrying the 3'-UTR risk haplotype (P = .02). This comprehensive candidate-gene analysis demonstrates that the risk allele of multiple VDR polymorphisms results in lower VDR mRNA levels. This could impact the vitamin D signaling efficiency and might contribute to the increased fracture risk we observed for these risk haplotype alleles.

3' Untranslated Regions↗

PubMed2006

Sequence and haplotype analysis supports HLA-C as the psoriasis susceptibility 1 gene.

Previous studies have narrowed the interval containing PSORS1, the psoriasis-susceptibility locus in the major histocompatibility complex (MHC), to an approximately 300-kb region containing HLA-C and at least 10 other genes. In an effort to identify the PSORS1 gene, we cloned and completely sequenced this region from both chromosomes of five individuals. Two of the sequenced haplotypes were associated with psoriasis (risk), and the other eight were clearly unassociated (nonrisk). Comparison of sequence of the two risk haplotypes identified a 298-kb region of homology, extending from just telomeric of HLA-B to the HCG22 gene, which was flanked by clearly nonhomologous regions. Similar haplotypes cloned from unrelated individuals had nearly identical sequence. Combinatorial analysis of exonic variations in the known genes of the candidate interval revealed that HCG27, PSORS1C3, OTF3, TCF19, HCR, STG, and HCG22 bore no alleles unique to risk haplotypes among the 10 sequenced haplotypes. SPR1 and SEEK1 both had messenger RNA alleles specific to risk haplotypes, but only HLA-C and CDSN yielded protein alleles unique to risk. The risk alleles of HLA-C and CDSN (HLA-Cw6 and CDSN*TTC) were genotyped in 678 families with early-onset psoriasis; 620 of these families were also typed for 34 microsatellite markers spanning the PSORS1 interval. Recombinant haplotypes retaining HLA-Cw6 but lacking CDSN*TTC were significantly associated with psoriasis, whereas recombinants retaining CDSN*TTC but lacking HLA-Cw6 were not associated, despite good statistical power. By grouping recombinants with similar breakpoints, the most telomeric quarter of the 298-kb candidate interval could be excluded with high confidence. These results strongly suggest that HLA-Cw6 is the PSORS1 risk allele that confers susceptibility to early-onset psoriasis.

Adult↗

PubMed2006

Mutation-positive and mutation-negative patients with Cowden and Bannayan-Riley-Ruvalcaba syndromes associated with distinct 10q haplotypes.

Phosphatase and tensin homolog deleted on chromosome 10 (PTEN) encodes a tumor-suppressor phosphatase frequently mutated in both sporadic and heritable forms of human cancer. Germline mutations are associated with a number of heritable cancer syndromes that are jointly referred to as the "PTEN hamartoma tumor syndrome" (PHTS) and include Cowden syndrome, Bannayan-Riley-Ruvalcaba syndrome, Proteus syndrome, and Proteus-like syndrome. Germline PTEN mutations have been identified in a significant proportion of patients with PHTS; however, there are still many individuals with classic diagnostic features for whom mutations have yet to be identified. To address this, we took a haplotype-based approach and investigated the association of specific genomic regions of the PTEN locus with PHTS. We found this locus to be characterized by three distinct haplotype blocks 33 kb, 65 kb, and 43 kb in length. Comparisons of the haplotype distributions for all three blocks differed significantly among patients with PHTS and controls (P=.0098, P<.0001, and P<.0001 for blocks 1, 2, and 3, respectively). "Rare" haplotype blocks and extended haplotypes account for two-to-threefold more PHTS chromosomes than control chromosomes. PTEN mutation-negative patients are strongly associated with a haplotype block spanning a region upstream of PTEN and the gene's first intron (P=.0027). Furthermore, allelic combinations contribute to the phenotypic complexity of this syndrome. Taken together, these data suggest that specific haplotypes and rare alleles underlie the disease etiology in these sample populations; constitute low-penetrance, modifying loci; and, specifically in the case of patients with PHTS for whom traditional mutations have yet to be identified, may harbor pathogenic variant(s) that have escaped detection by standard PTEN mutation-scanning methodologies.

Alleles↗

PubMed2005

An approximation algorithm for haplotype inference by maximum parsimony.

This paper studies haplotype inference by maximum parsimony using population data. We define the optimal haplotype inference (OHI) problem as given a set of genotypes and a set of related haplotypes, find a minimum subset of haplotypes that can resolve all the genotypes. We prove that OHI is NP-hard and can be formulated as an integer quadratic programming (IQP) problem. To solve the IQP problem, we propose an iterative semidefinite programming-based approximation algorithm, (called SDPHapInfer). We show that this algorithm finds a solution within a factor of O(log n) of the optimal solution, where n is the number of genotypes. This algorithm has been implemented and tested on a variety of simulated and biological data. In comparison with three other methods, (1) HAPAR, which was implemented based on the branching and bound algorithm, (2) HAPLOTYPER, which was implemented based on the expectation-maximization algorithm, and (3) PHASE, which combined the Gibbs sampling algorithm with an approximate coalescent prior, the experimental results indicate that SDPHapInfer and HAPLOTYPER have similar error rates. In addition, the results generated by PHASE have lower error rates on some data but higher error rates on others. The error rates of HAPAR are higher than the others on biological data. In terms of efficiency, SDPHapInfer, HAPLOTYPER, and PHASE output a solution in a stable and consistent way, and they run much faster than HAPAR when the number of genotypes becomes large.

Algorithms↗