Examining the effect of linkage disequilibrium on multipoint linkage analysis

Most linkage programs assume linkage equilibrium among multiple linked markers. This assumption may lead to bias for tightly linked markers where strong linkage disequilibrium (LD) exists. We used simulated data from Genetic Analysis Workshop 14 to examine the possible effect of LD on multipoint linkage analysis. Single-nucleotide polymorphism packets from a non-disease-related region that was generated with LD were used for both model-free and parametric linkage analyses. Results showed that high LD among markers can induce false-positive evidence of linkage for affected sib-pair analysis when parental data are missing. Bias can be eliminated with parental data and can be reduced when additional markers not in LD are included in the analyses.     

Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

Five new linkage groups in the canine linkage map

Nineteen further polymorphic loci were typed on the DogMap reference panel. Five new linkage groups were identified. Additionally, five markers were added to earlier defined linkage groups. Three of the new linkage groups contain markers mapped earlier to specific dog chromosomes by physical mapping. These results make a further contribution to the canine genome map and provides more linkage groups physically assigned to known chromosomes.     

The effect of linkage disequilibrium on linkage analysis of incomplete pedigrees

Dense SNP maps can be highly informative for linkage studies. But when parental genotypes are missing, multipoint linkage scores can be inflated in regions with substantial marker-marker linkage disequilibrium (LD). Such regions were observed in the Affymetrix SNP genotypes for the Genetic Analysis Workshop 14 (GAW14) Collaborative Study on the Genetics of Alcoholism (COGA) dataset, providing an opportunity to test a novel simulation strategy for studying this problem. First, an inheritance vector (with or without linkage present) is simulated for each replicate, i.e., locations of recombinations and transmission of parental chromosomes are determined for each meiosis. Then, two sets of founder haplotypes are superimposed onto the inheritance vector: one set that is inferred from the actual data and which contains the pattern of LD; and one set created by randomly selecting parental alleles based on the known allele frequencies, with no correlation (LD) between markers. Applying this strategy to a map of 176 SNPs (66 Mb of chromosome 7) for 100 replicates of 116 sibling pairs, significant inflation of multipoint linkage scores was observed in regions of high LD when parental genotypes were set to missing, with no linkage present. Similar inflation was observed in analyses of the COGA data for these affected sib pairs with parental genotypes set to missing, but not after reducing the marker map until r2 between any pair of markers was 相似文献   

Multilocus linkage analysis in humans: detection of linkage and estimation of recombination.

Multilocus linkage analysis is investigated from the viewpoint of the efficiency of recombination estimates under different strategies for detecting linkage and determining gene order within a linkage group. We consider the appropriateness of assuming no interference with data available in human genetic studies. Examples are given to show the significance of multilocus analysis in humans. A computer program package, LINKAGE, for multilocus linkage analysis is described.     

Decomposing multilocus linkage disequilibrium

We present a mathematically precise formulation of total linkage disequilibrium between multiple loci as the deviation from probabilistic independence and provide explicit formulas for all higher-order terms of linkage disequilibrium, thereby combining J. Dausset et al.'s 1978 definition of linkage disequilibrium with H. Geiringer's 1944 approach. We recursively decompose higher-order linkage disequilibrium terms into lower-order ones. Our greatest simplification comes from defining linkage disequilibrium at a single locus as allele frequency at that locus. At each level, decomposition of linkage disequilibrium is mathematically equivalent to number theoretic compositions of positive integers; i.e., we have converted a genetic decomposition into a mathematical decomposition.     

Detection of linkage for heterogeneous disorders by using multipoint linkage analysis.

We have compared the efficiency of the lod score test which assumes heterogeneity (lod2) to the standard lod score test which assumes homogeneity (lod1) when three-point linkage analysis is used in successive map intervals. If it is assumed that a gene located midway between two linked marker loci is responsible for a proportion of disease cases, then the lod1 test loses power relative to the lod2 test, as the proportion of linked families decreases, as the flanking markers are more closely linked, and as more map intervals are tested. Moreover, when multipoint analysis is used, linkage for a disease gene is more likely to be incorrectly excluded from a complete and dense linkage map if true genetic heterogeneity is ignored. We thus conclude that, in general, the lod2 linkage test is more efficient for detecting a true linkage when a complete genetic marker map is screened for a heterogeneous disorder.     

Human QTL linkage mapping

Human quantitative trait locus (QTL) linkage mapping, although based on classical statistical genetic methods that have been around for many years, has been employed for genome-wide screening for only the last 10–15 years. In this time, there have been many success stories, ranging from QTLs that have been replicated in independent studies to those for which one or more genes underlying the linkage peak have been identified to a few with specific functional variants that have been confirmed in in vitro laboratory assays. Despite these successes, there is a general perception that linkage approaches do not work for complex traits, possibly because many human QTL linkage studies have been limited in sample size and have not employed the family configurations that maximize the power to detect linkage. We predict that human QTL linkage studies will continue to be productive for the next several years, particularly in combination with RNA expression level traits that are showing evidence of regulatory QTLs of large effect sizes and in combination with high-density genome-wide SNP panels. These SNP panels are being used to identify QTLs previously localized by linkage and linkage results are being used to place informative priors on genome-wide association studies.     

Joint modeling of linkage and association: identifying SNPs responsible for a linkage signal

Once genetic linkage has been identified for a complex disease, the next step is often association analysis, in which single-nucleotide polymorphisms (SNPs) within the linkage region are genotyped and tested for association with the disease. If a SNP shows evidence of association, it is useful to know whether the linkage result can be explained, in part or in full, by the candidate SNP. We propose a novel approach that quantifies the degree of linkage disequilibrium (LD) between the candidate SNP and the putative disease locus through joint modeling of linkage and association. We describe a simple likelihood of the marker data conditional on the trait data for a sample of affected sib pairs, with disease penetrances and disease-SNP haplotype frequencies as parameters. We estimate model parameters by maximum likelihood and propose two likelihood-ratio tests to characterize the relationship of the candidate SNP and the disease locus. The first test assesses whether the candidate SNP and the disease locus are in linkage equilibrium so that the SNP plays no causal role in the linkage signal. The second test assesses whether the candidate SNP and the disease locus are in complete LD so that the SNP or a marker in complete LD with it may account fully for the linkage signal. Our method also yields a genetic model that includes parameter estimates for disease-SNP haplotype frequencies and the degree of disease-SNP LD. Our method provides a new tool for detecting linkage and association and can be extended to study designs that include unaffected family members.     

Hammerhead cleavage of the phosphorodithioate linkage

Under standard reaction conditions, a hammerhead ribozyme with a phosphorodithioate linkage at the cleavage site cleaved to the expected products with a rate about 500-fold slower than the corresponding phosphodiester linkage. When the greater stability of the dithioate linkage to nonenzymatic nucleophilic attack is taken into account, the hammerhead is remarkably effective at cleaving the dithioate linkage considering that the R(P)-phosphoromonothioate linkage is virtually inactive. On the basis of experiments determining the Mg(2+) concentration dependence of the cleavage rate and the stimulation of cleavage by thiophilic Cd(2+) ion, the lesser catalytic rate enhancement of the dithioate linkage is primarily due to the loss of a single Mg(2+) ion bound near the cleavage site. These results are qualitatively similar to, but quantitatively different from, similar experiments examining the hammerhead cleavage properties of the R(P)-phosphoromonothioate linkage. The dithioate linkage thus promises to be a valuable alternative phosphate analogue to the monothioate linkage in studying the mechanisms of RNA catalysis.     

Joint linkage and linkage disequilibrium mapping of quantitative trait loci in natural populations

Linkage analysis and allelic association (also referred to as linkage disequilibrium) studies are two major approaches for mapping genes that control simple or complex traits in plants, animals, and humans. But these two approaches have limited utility when used alone, because they use only part of the information that is available for a mapping population. More recently, a new mapping strategy has been designed to integrate the advantages of linkage analysis and linkage disequilibrium analysis for genome mapping in outcrossing populations. The new strategy makes use of a random sample from a panmictic population and the open-pollinated progeny of the sample. In this article, we extend the new strategy to map quantitative trait loci (QTL), using molecular markers within the EM-implemented maximum-likelihood framework. The most significant advantage of this extension is that both linkage and linkage disequilibrium between a marker and QTL can be estimated simultaneously, thus increasing the efficiency and effectiveness of genome mapping for recalcitrant outcrossing species. Simulation studies are performed to test the statistical properties of the MLEs of genetic and genomic parameters including QTL allele frequency, QTL effects, QTL position, and the linkage disequilibrium of the QTL and a marker. The potential utility of our mapping strategy is discussed.     

High-resolution joint linkage disequilibrium and linkage mapping of quantitative trait loci based on sibship data

This paper proposes variance component models for high resolution joint linkage disequilibrium (LD) and linkage mapping of quantitative trait loci (QTL) based on sibship data; this can include population data if independent individuals are treated as single sibships. One application of these models is late onset complex disease gene mapping, when parental data are not available. The models simultaneously incorporate both LD and linkage information. The LD information is contained in mean coefficients of sibship data. The linkage information is contained in the variance-covariance matrices of trait values for sibships with at least two siblings. We derive formulas for calculating the probability of sharing two trait alleles identical by descent (IBD) for sibpairs in interval mapping of QTL; this is the coefficient of dominant variance of the trait covariance of sibpairs on major QTL. To investigate the performance of the formulas, we calculate the numerical values via the formulas and get satisfactory approximations. We compare the power and sample sizes for both LD and linkage mapping. By simulation and theoretical analysis, we compare the results with those of Fulker and Abecasis "AbAw" approach. It is well known that the resolution of linkage analysis can be low for complex disease gene mapping. LD mapping, on the other hand, can increase mapping precision and is useful in high resolution mapping. Linkage analysis is less sensitive to population subdivisions and admixtures. The level of LD is sensitive to population stratification which may easily lead to spurious association. Performing a joint analysis of LD and linkage mapping can help to overcome the limits of both approaches. Moreover, the advantages of the two complementary strategies can be utilized maximally. In practice, linkage analysis may be performed using pedigree data to identify suggestive linkage between markers and trait loci based on a sparse marker map. In the presence of linkage, joint LD and linkage mapping can be carried out to do fine gene mapping based on a dense genetic map using both pedigree and population data. Population and pedigree data of any type can be combined to perform a joint analysis of high resolution LD and linkage mapping of QTL by generalizing the method.     

Ignoring linkage disequilibrium among tightly linked markers induces false-positive evidence of linkage for affected sib pair analysis

Most multipoint linkage programs assume linkage equilibrium among the markers being studied. The assumption is appropriate for the study of sparsely spaced markers with intermarker distances exceeding a few centimorgans, because linkage equilibrium is expected over these intervals for almost all populations. However, with recent advancements in high-throughput genotyping technology, much denser markers are available, and linkage disequilibrium (LD) may exist among the markers. Applying linkage analyses that assume linkage equilibrium to dense markers may lead to bias. Here, we demonstrated that, when some or all of the parental genotypes are missing, assuming linkage equilibrium among tightly linked markers where strong LD exists can cause apparent oversharing of multipoint identity by descent (IBD) between sib pairs and false-positive evidence for multipoint model-free linkage analysis of affected sib pair data. LD can also mimic linkage between a disease locus and multiple tightly linked markers, thus causing false-positive evidence of linkage using parametric models, particularly when heterogeneity LOD score approaches are applied. Bias can be eliminated by inclusion of parental genotype data and can be reduced when additional unaffected siblings are included in the analysis.     

Simultaneous maximum likelihood estimation of linkage and linkage phases in outcrossing species

With the advent of new molecular marker technologies, it is now feasible to initiate genome projects for outcrossing plant species, which have not received much attention in genetic research, despite their great agricultural and environmental value. Because outcrossing species typically have heterogeneous genomes, data structure for molecular markers representing an entire genome is complex: some markers may have more alleles than others, some markers are codominant whereas others are dominant, and some markers are heterozygous in one parent but fixed in the other parent whereas the opposite can be true for other markers. A major difficulty in analyzing these different types of marker at the same time arises from uncertainty about parental linkage phases over markers. In this paper, we present a general maximum-likelihood-based algorithm for simultaneously estimating linkage and linkage phases for a mixed set of different marker types containing fully informative markers (segregating 1:1:1:1) and partially informative markers (or missing markers, segregating 1:2:1, 3:1, and 1:1) in a full-sib family derived from two outbred parent plants. The characterization of linkage phases is based on the posterior probability distribution of the assignment of alternative alleles at given markers to two homologous chromosomes of each parent, conditional on the observed phenotypes of the markers. Two- and multi-point analyses are performed to estimate the recombination fraction and determine the most likely linkage phase between different types of markers. A numerical example is presented to demonstrate the statistical properties of the model for characterizing the linkage phase between markers.     

Sequence-based linkage analysis

The rapid decrease in the cost of DNA sequencing will enable its use for novel applications. Here, we investigate the use of DNA sequencing for simultaneous discovery and genotyping of polymorphisms in family linkage studies. In the proposed approach, short contiguous segments of genomic DNA, regularly spaced across the genome, are resequenced in each pedigree member, and all sequence polymorphisms discovered within a pedigree are used as genetic markers. We use computer simulations consistent with observed human sequence diversity to show that segments of 500-1,000 base pairs, spaced at intervals of 1-2 Mb across the genome, provide linkage information that equals or exceeds that of traditional marker-based approaches. We validate these results experimentally by implementing the sequence-based linkage approach for chromosome 19 in CEPH pedigrees.     

A genetic linkage map of rat Chromosome 5 reveals extensive linkage conservation with mouse Chromosome 4

Linkages among three biochemical loci (Acol, Ahd2, and Mup1) and four microsatellite loci (A8, Glut1, Jun, and Pnd) were determined to construct a linkage map of rat Chromosome (Chr) 5. Consequently, an extensive linkage map on rat Chr 5 was constructed with the following gene order: A8-Aco1-Mup1-Jun-Glut1-Ahd2-Pnd. In this linkage map, the Jun and A8 loci are newly placed, and two previously reported linkage groups on rat Chr 5 are connected by the Jun locus. The linkage map indicates an extensive linkage conservation between the loci on rat Chr 5 and those on mouse Chr 4.     

Towards linkage analysis with markers in linkage disequilibrium by graphical modelling

We review recent developments of MCMC integration methods for computations on graphical models for two applications in statistical genetics: modelling allelic association and pedigree based linkage analysis. We discuss and illustrate estimation of graphical models from haploid and diploid genotypes, and the importance of MCMC updating schemes beyond what is strictly necessary for irreducibility. We then outline an approach combining these methods to compute linkage statistics when alleles at the marker loci are in linkage disequilibrium. Other extensions suitable for analysis of SNP genotype data in pedigrees are also discussed and programs that implement these methods, and which are available from the author's web site, are described. We conclude with a discussion of how this still experimental approach might be further developed.     

Model-free linkage analysis with covariates confirms linkage of prostate cancer to chromosomes 1 and 4

As with many complex genetic diseases, genome scans for prostate cancer have given conflicting results, often failing to provide replication of previous findings. One factor contributing to the lack of consistency across studies is locus heterogeneity, which can weaken or even eliminate evidence for linkage that is present only in a subset of families. Currently, most analyses either fail to account for locus heterogeneity or attempt to account for it only by partitioning data sets into smaller and smaller portions. In the present study, we model locus heterogeneity among affected sib pairs with prostate cancer by including covariates in the linkage analysis that serve as surrogate measures of between-family linkage differences. The model is a modification of the Olson conditional logistic model for affected relative pairs. By including Gleason score, age at onset, male-to-male transmission, and/or number of affected first-degree family members as covariates, we detected linkage near three locations that were previously identified by linkage (1q24-25 [HPC1; LOD score 3.25, P=.00012], 1q42.2-43 [PCAP; LOD score 2.84, P=.0030], and 4q [LOD score 2.80, P=.00038]), near the androgen-receptor locus on Xq12-13 (AR; LOD score 3.06, P=.00053), and at five new locations (LOD score > 2.5). Without covariates, only a few weak-to-moderate linkage signals were found, none of which replicate findings of previous genome scans. We conclude that covariate-based linkage analysis greatly improves the likelihood that linked regions will be found by incorporation of information about heterogeneity within the sample.     

Disulphide linkage in mouse ST6Gal-I: determination of linkage positions and mutant analysis

All cloned sialyltransferases from vertebrates are classified into four subfamilies and are characterized as having type II transmembrane topology. The catalytic domain has highly conserved motifs known as sialylmotifs. Besides sialylmotifs, each family has several unique conserved cysteine (Cys) residues mainly in the catalytic domain. The number and loci of conserved amino acids, however, differ with each subfamily, suggesting that the conserved Cys-residues and/or disulphide linkages they make may contribute to linkage specificity. Using Matrix Assisted Laser Desorption/Ionization-Time of Flight Mass Spectrometry (MALDI-TOF)-mass spectrometry, the present study performed disulphide linkage analysis on soluble mouse ST6Gal-I, which has six Cys-residues. Results confirmed that there were no free Cys-residues, and all six residues contributed to disulphide linkage formation, C(139)-C(403), C(181)-C(332) and C(350)-C(361). Study of single amino acid-substituted mutants revealed that the disulphide linkage C(181)-C(332) was necessary for molecular expression of the enzyme, and that the disulphide linkage C(350)-C(361) was necessary for enzyme activity. The remaining disulphide linkage C(139)-C(403) was not necessary for enzyme expression or for activity, including substrate specificity. Crystallographic study of pig ST3Gal I has recently been reported. Interestingly, the loci of disulphide linkages in ST6Gal-I differ from those in ST3Gal I, suggesting that the linkage specificity of sialyltransferase may results from significant structural differences, including the loci of disulphide linkages.