Patterns of linkage disequilibrium and haplotype distribution in disease candidate genes

Background

The adequacy of association studies for complex diseases depends critically on the existence of linkage disequilibrium (LD) between functional alleles and surrounding SNP markers.

Results

We examined the patterns of LD and haplotype distribution in eight candidate genes for osteoporosis and/or obesity using 31 SNPs in 1,873 subjects. These eight genes are apolipoprotein E (APOE), type I collagen α1 (COL1A1), estrogen receptor-α (ER-α), leptin receptor (LEPR), parathyroid hormone (PTH)/PTH-related peptide receptor type 1 (PTHR1), transforming growth factor-β1 (TGF-β1), uncoupling protein 3 (UCP3), and vitamin D (1,25-dihydroxyvitamin D₃) receptor (VDR). Yin yang haplotypes, two high-frequency haplotypes composed of completely mismatching SNP alleles, were examined. To quantify LD patterns, two common measures of LD, D' and r², were calculated for the SNPs within the genes. The haplotype distribution varied in the different genes. Yin yang haplotypes were observed only in PTHR1 and UCP3. D' ranged from 0.020 to 1.000 with the average of 0.475, whereas the average r² was 0.158 (ranging from 0.000 to 0.883). A decay of LD was observed as the intermarker distance increased, however, there was a great difference in LD characteristics of different genes or even in different regions within gene.

Conclusion

The differences in haplotype distributions and LD patterns among the genes underscore the importance of characterizing genomic regions of interest prior to association studies.     

HLA class II linkage disequilibrium and haplotype evolution in the Cayapa Indians of Ecuador.

DNA-based typing of the HLA class II loci in a sample of the Cayapa Indians of Ecuador reveals several lines of evidence that selection has operated to maintain and to diversify the existing level of polymorphism in the class II region. As has been noticed for other Native American groups, the overall level of polymorphism at the DRB1, DQA1, DQB1, and DPB1 loci is reduced relative to that found in other human populations. Nonetheless, the relative evenness in the distribution of allele frequencies at each of the four loci points to the role of balancing selection in the maintenance of the polymorphism. The DQA1 and DQB1 loci, in particular, have near-maximum departures from the neutrality model, which suggests that balancing selection has been especially strong in these cases. Several novel DQA1-DQB1 haplotypes and the discovery of a new DRB1 allele demonstrate an evolutionary tendency favoring the diversification of class II alleles and haplotypes. The recombination interval between the centromeric DPB1 locus and the other class II loci will, in the absence of other forces such as selection, reduce disequilibrium across this region. However, nearly all common alleles were found to be part of DR-DP haplotypes in strong disequilibrium, consistent with the recent action of selection acting on these haplotypes in the Cayapa.     

Effect of two- and three-locus linkage disequilibrium on the power to detect marker/phenotype associations

There has been much recent interest in describing the patterns of linkage disequilibrium (LD) along a chromosome. Most empirical studies that have examined this issue have concentrated on LD between collections of pairs of markers and have not considered the joint effect of a group of markers beyond these pairwise connections. Here, we examine many different patterns of LD defined by both pairwise and joint multilocus LD terms. The LD patterns we considered were chosen in part by examining those seen in real data. We examine how changes in these patterns affect the power to detect association when performing single-marker and haplotype-based case-control tests, including a novel haplotype test based on contrasting LD between affected and unaffected individuals. Through our studies we find that differences in power between single-marker tests and haplotype-based tests in general do not appear to be large. Where moderate to high levels of multilocus LD exist, haplotype tests tend to be more powerful. Single-marker tests tend to prevail when pairwise LD is high. For moderate pairwise values and weak multilocus LD, either testing strategy may come out ahead, although it is also quite likely that neither has much power.     

Detecting population structure using STRUCTURE software: effect of background linkage disequilibrium

STRUCTURE is the most widely used clustering software to detect population genetic structure. The last version of this software (STRUCTURE 2.1) has been enhanced recently to take into account the occurrence of linkage disequilibrium (LD) caused by admixture between populations. This last version, however, still does not consider the effects of strong background LD caused by genetic drift, and which may cause spurious results. STRUCTURE authors have, therefore, suggested a rough threshold value of the distance (1.0 cM) between two loci below which the pair of loci should not be used. Because of the sensitiveness of LD to demographic events, the distance between loci is not always a good indicator of the strength of LD. In this study, we examine the link between genomic distance and the strength of the correlation between loci (r(LD)) in a free-ranging population of mouflon (Ovis aries), and we present an empirical test of effect of r(LD) on the clustering results provided by the linkage model in STRUCTURE. We showed that a high r(LD) value increases the probability of detecting spurious clustering. We propose to use r(LD) as an index to base a decision on whether or not to use a pair of loci in a clustering analysis.     

The extent of linkage disequilibrium and haplotype sharing around a polymorphic site

Various expressions related to the length of a conserved haplotype around a polymorphism of known frequency are derived. We obtain exact expressions for the probability that no recombination has occurred in a sample or subsample. We obtain an approximation for the probability that no recombination that could give rise to a detectable recombination event (through the four-gamete test) has occurred. The probabilities can be used to obtain approximate distributions for the length of variously defined haplotypes around a polymorphic site. The implications of our results for data analysis, and in particular for detecting selection, are discussed.     

Genome screens using linkage disequilibrium tests: optimal marker characteristics and feasibility.

Linkage disequilibrium (LD) testing has become a popular and effective method of fine-scale disease-gene localization. It has been proposed that LD testing could also be used for genome screening, particularly as dense maps of diallelic markers become available and automation allows inexpensive genotyping of diallelic markers. We compare diallelic markers and multiallelic markers in terms of sample sizes required for detection of LD, by use of a single marker locus in a case-control study, for rare monophyletic diseases with Mendelian inheritance. We extrapolate from our results to discuss the feasibility of single-marker LD screening in more-complex situations. We have used a deterministic population genetic model to calculate the expected power to detect LD as a function of marker density, age of mutation, number of marker alleles, mode of inheritance of a rare disease, and sample size. Our calculations show that multiallelic markers always have more power to detect LD than do diallelic markers (under otherwise equivalent conditions) and that the ratio of the number of diallelic to the number of multiallelic markers needed for equivalent power increases with mutation age and complexity of mode of inheritance. Power equivalent to that achieved by a multiallelic screen can theoretically be achieved by use of a more dense diallelic screen, but mapping panels of the necessary resolution are not currently available and may be difficult to achieve. Genome screening that uses single-marker LD testing may therefore be feasible only for young (<20 generations), rare, monophyletic Mendelian diseases, such as may be found in rapidly growing genetic isolates.     

A haplotype and linkage disequilibrium analysis of the hereditary hemochromatosis gene region

Hereditary hemochromatosis is a recessive disease of iron metabolism widely distributed among people of European descent. Most patients have inherited the causative mutation from a single ancestor. In the course of cloning the hemochromatosis gene, genotypes were generated for these samples at 43 microsatellite repeat markers that span the 6.5-Mb hemochromatosis gene region. The data used to reconstruct the ancestral haplotype across the hemochromatosis gene region are presented in this paper. Portions of the ancestral haplotype were present on 85% of patient chromosomes in this sample and ranged in size from approximately 500 kb to greater than 6.5 Mb. Only one marker, D6S2239, was identical by descent on all of the patient chromosomes containing the ancestral mutation. In contrast, only 3 of the 128 control chromosomes, or 2.3%, carried the ancestral mutation and the surrounding ancestral haplotype. To test new methods for gene finding using linkage disequilibrium we analyzed the genotypic data with a multilocus maximum likelihood method (DISMULT) and a single point method (DISLAMB), both written to analyze data generated from multi-allelic markers. The maximum value from DISLAMB analysis occurred at marker D6S2239, which is less than 20 kb from the hemochromatosis gene HFE, consistent with the haplotype analysis. The peak of the multi-point analysis was 700 kb from HFE, possibly due to the nonuniform recombination rates within this large region. The recombination rate appears to be lower than expected centromeric of the HFE gene. Received: 10 June 1997 / Accepted: 4 December 1997     

Implications of inter-population linkage disequilibrium patterns on the approach to a disease association study in the human MHC class III

There is presently much interest in utilizing patterns of linkage disequilibrium (LD) to further genetic association studies. This is particularly pertinent in the class III region of the human major histocompatibility complex (MHC), which has been extensively studied as a disease susceptibility locus in a number of ethnic groups. To date, however, few studies of LD in the MHC have considered non-Caucasian populations. With the advent of large-scale haplotyping of the human genome, the question of utilizing LD patterns across populations has come to the fore. We have previously used LD mapping to direct an MHC class III association study in a UK Caucasian population. As an extension of this, we sought to determine to what extent the pattern of LD observed in that study could be used to conduct a similar study in a West African Gambian population. We found that broad patterns of LD were similar in the two populations, resulting in similar candidate region delineations, but at a higher resolution, marker-specific patterns of LD and population-dependent allele frequencies confounded the choice of regional tagging SNPs. Our results have implications for the applicability of large-scale haplotype maps such as the HapMap to complex regions like the MHC.Electronic Supplementary Material Supplementary material is available for this article at .     

Accounting for linkage disequilibrium among markers in linkage analysis: impact of haplotype frequency estimation and molecular haplotypes for a gene in a candidate region for Alzheimer's disease

OBJECTIVES: Linkage disequilibrium (LD) between closely spaced SNPs can be accommodated in linkage analysis by specifying the multi-SNP haplotype frequencies, if known. Phased haplotypes in candidate regions can provide gold standard haplotype frequency estimates, and may be of inherent interest as markers. We evaluated the effects of different methods of haplotype frequency estimation, and the use of marker phase information, on linkage analysis of a multi-SNP cluster in a candidate region for Alzheimer's disease (AD). METHODS: We performed parametric linkage analysis of a five-SNP cluster in extended pedigrees to compare the use of: (1) haplotype frequencies estimated by molecular phase determination, maximum likelihood estimation, or by assuming linkage equilibrium (LE); (2) AD families or controls as the frequency source; and (3) unphased or molecularly phased SNP data. RESULTS: There was moderate to strong pairwise LD among the five SNPs. Falsely assuming LE substantially inflated the LOD score, but the method of haplotype frequency estimation and particular sample used made little difference provided that LD was accommodated. Use of phased haplotypes produced a modest increase in the LOD score over unphased SNPs. CONCLUSIONS: Ignoring LD between markers can lead to substantially inflated evidence for linkage in LOD score analysis of extended pedigrees with missing data. Use of marker phase information in linkage analysis may be important in disease studies where the costs of family recruitment and phenotyping greatly exceed the costs of phase determination.     

A global survey of haplotype frequencies and linkage disequilibrium at the DRD2 locus

A four-site haplotype system at the dopamine D2 receptor locus (DRD2) has been studied in a global sample of 28 distinct populations. The haplotype system spans about 25 kb, encompassing the coding region of the gene. The four individual markers include three TaqI restriction site polymorphisms (RSPs) – TaqI “A”, “B”, and “D” sites – and one dinucleotide short tandem repeat polymorphism (STRP). All four of the marker systems are polymorphic in all regions of the world and in most individual populations. The haplotype system shows the highest average heterozygosity in Africa, a slightly lower average heterozygosity in Europe, and the lowest average heterozygosities in East Asia and the Americas. Across all populations, 20 of the 48 possible haplotypes reached a frequency of at least 5% in at least one population sample. However, no single population had more than six haplotypes reaching that frequency. In general, African populations had more haplotypes present in each population and more haplotypes occurring at a frequency of at least 5% in that population. Permutation tests for significance of overall disequilibrium (all sites considered simultaneously) were highly significant (P<0.001) in all 28 populations. Except for three African samples, the pairwise disequilibrium between the outermost RSP markers, TaqI “B” and “A”, was highly significant with D’ values greater than 0.8; in two of those exceptions the RSP marker was not polymorphic. Except for those same two African populations, the 16-repeat allele at the STRP also showed highly significant disequilibrium with the TaqI “B” site in all populations, with D’ values usually greater than 0.7. Only four haplotypes account for more than 70% of all chromosomes in virtually all non-African populations, and two of those haplotypes account for more than 70% of all chromosomes in most East Asian and Amerindian populations. A new measure of the amount of overall disequilibrium shows least disequilibrium in African populations, somewhat more in European populations, and the greatest amount in East Asian and Amerindian populations. This pattern seems best explained by random genetic drift with low levels of recombination, a low mutation rate at the STRP, and essentially no recurrent mutation at the RSP sites, all in conjunction with an “Out of Africa” model for recent human evolution. Received: 14 January 1998 / Accepted 19 March 1998     

Expectation maximization algorithm based haplotype relative risk (EM-HRR): test of linkage disequilibrium using incomplete case-parents trios

The Haplotype Relative Risk (HRR) was first proposed [Falk et al., Ann Hum Genet 1987] to test for Linkage Disequilibrium (LD) between a marker and a putative disease locus using case-parent trios. Spurious association does not appear in such family-based studies under population admixture. In this paper, we extend the HRR to accommodate incomplete trios via the Expectation-Maximization (EM) algorithm [Dempster et al., J R Stat Soc Ser B, 1977]. In addition to triads and dyads (parent-offspring pair), the EM-HRR easily incorporates individuals with no parental genotype information available, which is excluded from the one parent Transmission/Disequilibrium Test (1-TDT) [Sun et al., Am J Epidemiol 1999]. Due to the data structure of EM-HRR, transmitted alleles are always available regardless of the number of missing parental genotypes. As a result of having a larger sample size, computer simulations reveal that the EM-HRR is more powerful in detecting LD than the 1-TDT in a population under Hardy-Weinberg Equilibirum (HWE). If admixture is not extreme, the EM-HRR remains more powerful. When a large degree of admixture exists, the EM-HRR performs better the 1-TDT when the association is strong, though not as well when the association is weak. We illustrate the proposed method with an application to the Framingham Heart Study.     

Novel measures of linkage disequilibrium that correct the bias due to population structure and relatedness

Among the several linkage disequilibrium measures known to capture different features of the non-independence between alleles at different loci, the most commonly used for diallelic loci is the r(2) measure. In the present study, we tackled the problem of the bias of r(2) estimate, which results from the sample structure and/or the relatedness between genotyped individuals. We derived two novel linkage disequilibrium measures for diallelic loci that are both extensions of the usual r(2) measure. The first one, r(S)(2), uses the population structure matrix, which consists of information about the origins of each individual and the admixture proportions of each individual genome. The second one, r(V)(2), includes the kinship matrix into the calculation. These two corrections can be applied together in order to correct for both biases and are defined either on phased or unphased genotypes.We proved that these novel measures are linked to the power of association tests under the mixed linear model including structure and kinship corrections. We validated them on simulated data and applied them to real data sets collected on Vitis vinifera plants. Our results clearly showed the usefulness of the two corrected r(2) measures, which actually captured 'true' linkage disequilibrium unlike the usual r(2) measure.     

Exome-based linkage disequilibrium maps of individual genes: functional clustering and relationship to disease

Exome sequencing identifies thousands of DNA variants and a proportion of these are involved in disease. Genotypes derived from exome sequences provide particularly high-resolution coverage enabling study of the linkage disequilibrium structure of individual genes. The extent and strength of linkage disequilibrium reflects the combined influences of mutation, recombination, selection and population history. By constructing linkage disequilibrium maps of individual genes, we show that genes containing OMIM-listed disease variants are significantly under-represented amongst genes with complete or very strong linkage disequilibrium (P = 0.0004). In contrast, genes with disease variants are significantly over-represented amongst genes with levels of linkage disequilibrium close to the average for genes not known to contain disease variants (P = 0.0038). Functional clustering reveals, amongst genes with particularly strong linkage disequilibrium, significant enrichment of essential biological functions (e.g. phosphorylation, cell division, cellular transport and metabolic processes). Strong linkage disequilibrium, corresponding to reduced haplotype diversity, may reflect selection in utero against deleterious mutations which have profound impact on the function of essential genes. Genes with very weak linkage disequilibrium show enrichment of functions requiring greater allelic diversity (e.g. sensory perception and immune response). This category is not enriched for genes containing disease variation. In contrast, there is significant enrichment of genes containing disease variants amongst genes with more average levels of linkage disequilibrium. Mutations in these genes may less likely lead to in utero lethality and be subject to less intense selection.     

A theoretical treatment of interval mapping of a disease gene using transmission disequilibrium tests

The genetic basis of the transmission disequilibrium test (TDT) for two-marker loci is explored from first principles. In this case, parents doubly heterozygous for a given haplotype at the pair of marker loci that are each in linkage disequilibrium with the disease gene with the further possibility of a second-order linkage disequilibrium are considered. The number of times such parents transmit the given haplotype to their affected offspring is counted and compared with the frequencies of haplotypes that are not transmitted. This is done separately for the coupling and repulsion phases of doubly heterozygous genotypes. Expectations of the counts for each of the sixteen cells possible with four-marker gametic types (transmitted vs not transmitted) are derived. Based on a test of symmetry in a square 4 x 4 contingency table, chi-square tests are proposed for the null hypothesis of no linkage between the markers and the disease gene. The power of the tests is discussed in terms of the corresponding non-centrality parameters for the alternative hypothesis that both the markers are linked with the disease locus. The results indicate that the power increases with the decrease in recombination probability and that it is higher for a lower frequency of the disease gene. Taking a pair of markers in an interval for exploring the linkage with the disease gene seems to be more informative than the single-marker case since the values of the non-centrality parameters tend to be consistently higher than their counterparts in the single-marker case. Limitations of the proposed test are also discussed.     

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.     

Cubic exact solutions for the estimation of pairwise haplotype frequencies: implications for linkage disequilibrium analyses and a web tool 'CubeX'

Background  

The frequency of a haplotype comprising one allele at each of two loci can be expressed as a cubic equation (the 'Hill equation'), the solution of which gives that frequency. Most haplotype and linkage disequilibrium analysis programs use iteration-based algorithms which substitute an estimate of haplotype frequency into the equation, producing a new estimate which is repeatedly fed back into the equation until the values converge to a maximum likelihood estimate (expectation-maximisation).     

A theoretical treatment of interval mapping of a disease gene using transmission disequilibrium tests

The genetic basis of the transmission disequilibrium test (TDT) for two-marker loci is explored from first principles. In this case, parents doubly heterozygous for a given haplotype at the pair of marker loci that are each in linkage disequilibrium with the disease gene with the further possibility of a second-order linkage disequilibrium are considered. The number of times such parents transmit the given haplotype to their affected offspring is counted and compared with the frequencies of haplotypes that are not transmitted. This is done separately for the coupling and repulsion phases of doubly heterozygous genotypes. Expectations of the counts for each of the sixteen cells possible with four-marker gametic types (transmitted vs not transmitted) are derived. Based on a test of symmetry in a square 4 × 4 contingency table, chi-square tests are proposed for the null hypothesis of no linkage between the markers and the disease gene. The power of the tests is discussed in terms of the corresponding non-centrality parameters for the alternative hypothesis that both the markers are linked with the disease locus. The results indicate that the power increases with the decrease in recombination probability and that it is higher for a lower frequency of the disease gene. Taking a pair of markers in an interval for exploring the linkage with the disease gene seems to be more informative than the single-marker case since the values of the non-centrality parameters tend to be consistently higher than their counterparts in the single-marker case. Limitations of the proposed test are also discussed.     

EpiSIM: simulation of multiple epistasis, linkage disequilibrium patterns and haplotype blocks for genome-wide interaction analysis

Epistasis is a ubiquitous phenomenon in genetics, and is considered to be one of the main factors in current efforts to detect missing heritability for complex diseases. Simulation is a critical tool in developing methodologies that can more effectively detect and study epistasis. Here we present a simulator, epiSIM (epistasis SIMulator), that can simulate some of the statistical properties of genetic data. EpiSIM is capable of expanding the range of the epistasis models that current simulators offer, including epistasis models that display marginal effects and those that display no marginal effects. One or more of these epistasis models can be embedded simultaneously into a single simulation data set, jointly determining the phenotype. In addition, epiSIM is independent of any outside data source in generating linkage disequilibrium patterns and haplotype blocks. We demonstrate the wide applicability of epiSIM by performing several data simulations, and examine its properties by comparing it with current representative simulators and by comparing the data that it generates with real data. Our experiments demonstrate that epiSIM is a valuable addition and a nice complement to the existing epistasis simulators. The software package is available online at https://sourceforge.net/projects/episimsimulator/files/.