Sequential imputation for multilocus linkage analysis

Multiple subsampling of dense SNP data localizes disease genes with increased precision

BACKGROUND/AIMS

Current linkage studies detect and localize trait loci using genotypes sampled at hundreds of thousands of single nucleotide polymorphisms (SNPs). Such data should provide precise estimates of trait location once linkage has been established. However, correlations between nearby SNPs can distort the information about trait location. Traditionally, when faced with this dilemma, three approaches have been used: (1) ignore the correlation; (2) approximate the correlation; or, (3) analyze a single, approximately uncorrelated subset of the original dense data.

METHODS

Here, we examine and test a simple and efficient estimator of trait location that averages location estimates across random subsamples of the original dense data. Based on pairwise estimates of correlation, we ensure that the SNPs within each subsample are approximately uncorrelated. In addition, we use the nonparametric bootstrap procedure to compute narrow, high-resolution candidate gene regions (i.e. confidence intervals for the true trait location).

RESULTS

Using simulated data, we show that the three existing approaches to dense SNP linkage analysis (described above) can yield biased and/or inefficient estimation depending on the underlying correlation structure. With respect to mean squared error, our estimator outperforms the third approach, and is as good as, but usually better than the first and second approaches. Relative to the third approach, our estimator led to a 47.5% reduction in the candidate gene region length based on the analysis of 15 hypertension families genotyped at approximately 500,000 SNPs.

CONCLUSION

The method we developed will be an important tool for constructing high-resolution candidate gene regions that could ultimately aid in targeting regions for sequencing projects.

Haplotyping methods for pedigrees

Haplotypes provide valuable information in the study of diseases, complex traits, population histories, and evolutionary genetics. With the dramatic increase in the number of available single nucleotide polymorphism (SNP) markers, haplotype inference (haplotyping) using observed genotype data has become an important component of genetic studies in general and of statistical gene mapping in particular. Existing haplotyping methods include (1) population-based methods, (2) methods for pooled DNA samples, and (3) methods for family and pedigree data. The methods and computer programs for population data and pooled DNA samples were reviewed recently in the literature. As several authors noted, family and pedigree datasets are abundant and have unique advantages. In the past twenty years, many haplotyping methods for family and pedigree data have been developed. Therefore, in this contribution we review haplotyping methods and the corresponding computer programs suitable for family and pedigree data and discuss their applications and limitations. We explore the connections among these methods, and describe the challenges that remain to be addressed.

Phylogenetic tree construction using sequential stochastic approximation Monte Carlo

Monte Carlo methods have received much attention recently in the literature of phylogenetic tree construction. However, they often suffer from two difficulties, the curse of dimensionality and the local-trap problem. The former one is due to that the number of possible phylogenetic trees increases at a super-exponential rate as the number of taxa increases. The latter one is due to that the phylogenetic tree has often a rugged energy landscape. In this paper, we propose a new phylogenetic tree construction method, which attempts to alleviate these two difficulties simultaneously by making use of the sequential structure of phylogenetic trees in conjunction with stochastic approximation Monte Carlo (SAMC) simulations. The use of the sequential structure of the problem provides substantial help to reduce the curse of dimensionality in simulations, and SAMC effectively prevents the system from getting trapped in local energy minima. The new method is compared with a variety of existing Bayesian and non-Bayesian methods on simulated and real datasets. Numerical results are in favor of the new method in terms of quality of the resulting phylogenetic trees.

Heme, heme oxygenase, and ferritin: how the vascular endothelium survives (and dies) in an iron-rich environment

Iron-derived reactive oxygen species are involved in the pathogenesis of numerous vascular disorders. One abundant source of redox active iron is heme, which is inherently dangerous when it escapes from its physiologic sites. Here, we present a review of the nature of heme-mediated cytotoxicity and of the strategies by which endothelium manages to protect itself from this clear and present danger. Of all sites in the body, the endothelium may be at greatest risk of exposure to heme. Heme greatly potentiates endothelial cell killing mediated by leukocytes and other sources of reactive oxygen. Heme also promotes the conversion of low-density lipoprotein to cytotoxic oxidized products. Hemoglobin in plasma, when oxidized, transfers heme to endothelium and lipoprotein, thereby enhancing susceptibility to oxidant-mediated injury. As a defense against such stress, endothelial cells upregulate heme oxygenase-1 and ferritin. Heme oxygenase opens the porphyrin ring, producing biliverdin, carbon monoxide, and a most dangerous product-redox active iron. The latter can be effectively controlled by ferritin via sequestration and ferroxidase activity. These homeostatic adjustments have been shown to be effective in the protection of endothelium against the damaging effects of heme and oxidants; lack of adaptation in an iron-rich environment led to extensive endothelial damage in humans.

Heme, heme oxygenase and ferritin in vascular endothelial cell injury

Iron-derived reactive oxygen species are implicated in the pathogenesis of numerous vascular disorders including atherosclerosis, microangiopathic hemolytic anemia, vasculitis, and reperfusion injury. One abundant source of redox active iron is heme, which is inherently dangerous when released from intracellular heme proteins. The present review concerns the involvement of heme in vascular endothelial cell damage and the strategies used by endothelium to minimize such damage. Exposure of endothelium to heme greatly potentiates cell killing mediated by polymorphonuclear leukocytes and other sources of reactive oxygen. Free heme also promotes the conversion of low-density lipoprotein (LDL) into cytotoxic oxidized products. Only because of its abundance, hemoglobin probably represents the most important potential source of heme within the vascular endothelium; hemoglobin in plasma, when oxidized, transfers heme to endothelium and LDL, thereby enhancing cellular susceptibility to oxidant-mediated injury. As a defense against such toxicity, upon exposure to heme or hemoglobin, endothelial cells up-regulate heme oxygenase-1 and ferritin. Heme oxygenase-1 is a heme-degrading enzyme that opens the porphyrin ring, producing biliverdin, carbon monoxide, and the most dangerous product - free redox active iron. The latter can be effectively controlled by ferritin via sequestration and ferroxidase activity. Ferritin serves as a protective gene by virtue of antioxidant, antiapoptotic, and antiproliferative actions. These homeostatic adjustments have been shown effective in the protection of endothelium against the damaging effects of exogenous heme and oxidants. The central importance of this protective system was recently highlighted by a child diagnosed with heme oxygenase-1 deficiency, who exhibited extensive endothelial damage.

Genetic Mapping of a Third Li-Fraumeni Syndrome Predisposition Locus to Human Chromosome 1q23

Li-Fraumeni syndrome (LFS) is a clinically and genetically heterogeneous inherited cancer syndrome. Most cases (∼70%) identified and characterized to date are associated with dominantly inherited germ line mutations in the tumor suppressor gene TP53 (p53) in chromosome 17p13.1. In a subset of non-p53 patients with LFS, CHEK2 in chromosome 22q11 has been identified as another predisposing locus. Studying a series of non-p53 LFS kindred, we have shown that there is additional genetic heterogeneity in LFS kindred with inherited predisposition at loci other than p53 or CHEK2. Using a genome-wide scan for linkage with complementing parametric and nonparametric analysis methods, we identified linkage to a region of approximately 4 cM in chromosome 1q23, a genomic region not previously implicated in this disease. Identification ofa third predisposing gene and its underlying mutation(s) should provide insight into other genetic events that predispose to the genesis of the diverse tumor types associated with LFS and its variants.

Recombination rate and reproductive success in humans

Intergenerational mixing of DNA through meiotic recombinations of homologous chromosomes during gametogenesis is a major event that generates diversity in the eukaryotic genome. We examined genome-wide microsatellite data for 23,066 individuals, providing information on recombination events of 14,140 maternal and paternal meioses each, and found a positive correlation between maternal recombination counts of an offspring and maternal age. We postulated that the recombination rate of eggs does not increase with maternal age, but that the apparent increase is the consequence of selection. Specifically, a high recombination count increased the chance of a gamete becoming a live birth, and this effect became more pronounced with advancing maternal age. Further support for this hypothesis came from our observation that mothers with high oocyte recombination rate tend to have more children. Hence, not only do recombinations have a role in evolution by yielding diverse combinations of gene variants for natural selection, but they are also under selection themselves.

Confirmation of the type 2 myotonic dystrophy (CCTG)n expansion mutation in patients with proximal myotonic myopathy/proximal myotonic dystrophy of different European origins: a single shared haplotype indicates an ancestral founder effect

Myotonic dystrophy (DM), the most common form of muscular dystrophy in adults, is a clinically and genetically heterogeneous neuromuscular disorder. DM is characterized by autosomal dominant inheritance, muscular dystrophy, myotonia, and multisystem involvement. Type 1 DM (DM1) is caused by a (CTG)(n) expansion in the 3' untranslated region of DMPK in 19q13.3. Multiple families, predominantly of German descent and with clinically variable presentation that included proximal myotonic myopathy (PROMM) and type 2 DM (DM2) but without the DM1 mutation, showed linkage to the 3q21 region and were recently shown to segregate a (CCTG)(n) expansion mutation in intron 1 of ZNF9. Here, we present linkage to 3q21 and mutational confirmation in 17 kindreds of European origin with PROMM and proximal myotonic dystrophy, from geographically distinct populations. All patients have the DM2 (CCTG)(n) expansion. To study the evolution of this mutation, we constructed a comprehensive physical map of the DM2 region around ZNF9. High-resolution haplotype analysis of disease chromosomes with five microsatellite and 22 single-nucleotide polymorphism markers around the DM2 mutation identified extensive linkage disequilibrium and a single shared haplotype of at least 132 kb among patients from the different populations. With the exception of the (CCTG)(n) expansion, the available markers indicate that the DM2 haplotype is identical to the most common haplotype in normal individuals. This situation is reminiscent of that seen in DM1. Taken together, these data suggest a single founding mutation in DM2 patients of European origin. We estimate the age of the founding haplotype and of the DM2 (CCTG) expansion mutation to be approximately 200-540 generations.

Linkage analysis with sequential imputation

Multilocus calculations, using all available information on all pedigree members, are important for linkage analysis. Exact calculation methods in linkage analysis are limited in either the number of loci or the number of pedigree members they can handle. In this article, we propose a Monte Carlo method for linkage analysis based on sequential imputation. Unlike exact methods, sequential imputation can handle large pedigrees with a moderate number of loci in its current implementation. This Monte Carlo method is an application of importance sampling, in which we sequentially impute ordered genotypes locus by locus, and then impute inheritance vectors conditioned on these genotypes. The resulting inheritance vectors, together with the importance sampling weights, are used to derive a consistent estimator of any linkage statistic of interest. The linkage statistic can be parametric or nonparametric; we focus on nonparametric linkage statistics. We demonstrate that accurate estimates can be achieved within a reasonable computing time. A simulation study illustrates the potential gain in power using our method for multilocus linkage analysis with large pedigrees. We simulated data at six markers under three models. We analyzed them using both sequential imputation and GENEHUNTER. GENEHUNTER had to drop between 38-54% of pedigree members, whereas our method was able to use all pedigree members. The power gains of using all pedigree members were substantial under 2 of the 3 models. We implemented sequential imputation for multilocus linkage analysis in a user-friendly software package called SIMPLE.

Finding starting points for Markov chain Monte Carlo analysis of genetic data from large and complex pedigrees

Genetic data from founder populations are advantageous for studies of complex traits that are often plagued by the problem of genetic heterogeneity. However, the desire to analyze large and complex pedigrees that often arise from such populations, coupled with the need to handle many linked and highly polymorphic loci simultaneously, poses challenges to current standard approaches. A viable alternative to solving such problems is via Markov chain Monte Carlo (MCMC) procedures, where a Markov chain, defined on the state space of a latent variable (e.g., genotypic configuration or inheritance vector), is constructed. However, finding starting points for the Markov chains is a difficult problem when the pedigree is not single-locus peelable; methods proposed in the literature have not yielded completely satisfactory solutions. We propose a generalization of the heated Gibbs sampler with relaxed penetrances (HGRP) of Lin et al., ([1993] IMA J. Math. Appl. Med. Biol. 10:1-17) to search for starting points. HGRP guarantees that a starting point will be found if there is no error in the data, but the chain usually needs to be run for a long time if the pedigree is extremely large and complex. By introducing a forcing step, the current algorithm substantially reduces the state space, and hence effectively speeds up the process of finding a starting point. Our algorithm also has a built-in preprocessing procedure for Mendelian error detection. The algorithm has been applied to both simulated and real data on two large and complex Hutterite pedigrees under many settings, and good results are obtained. The algorithm has been implemented in a user-friendly package called START.

A century of biometrical genetics

We briefly review the major contribution of biometrics to genetics over the last century (population genetic models, familial correlations, segregation analysis, and gene mapping) and current areas of active research and then speculate about what problems will be tackled in the next century.

Identification of a locus on chromosome 1q44 for familial cold urticaria

Familial cold urticaria (FCU) is a rare autosomal dominant inflammatory disorder characterized by intermittent episodes of rash with fever, arthralgias, conjunctivitis, and leukocytosis. These symptoms develop after generalized exposure to cold. Some individuals with FCU also develop late-onset reactive renal amyloidosis, which is consistent with Muckle-Wells syndrome. By analyzing individuals with FCU from five families, we identified linkage to chromosome 1q44. Two-point linkage analysis revealed a maximum LOD score (Zmax) of 8.13 (recombination fraction 0) for marker D1S2836; multipoint linkage analysis identified a Zmax of 10. 92 in the same region; and haplotype analysis defined a 10.5-cM region between markers D1S423 and D1S2682. Muckle-Wells syndrome was recently linked to chromosome 1q44, which suggests that the two disorders may be linked to the same locus.

Blocking Gibbs sampling for linkage analysis in large pedigrees with many loops

We apply the method of "blocking Gibbs" sampling to a problem of great importance and complexity-linkage analysis. Blocking Gibbs sampling combines exact local computations with Gibbs sampling, in a way that complements the strengths of both. The method is able to handle problems with very high complexity, such as linkage analysis in large pedigrees with many loops, a task that no other known method is able to handle. New developments of the method are outlined, and it is applied to a highly complex linkage problem in a human pedigree.

Mutations in the hepatocyte nuclear factor-4alpha gene in maturity-onset diabetes of the young (MODY1)

The disease maturity-onset diabetes of the young (MODY) is a genetically heterogeneous monogenic form of non-insulin-dependent (type 2) diabetes mellitus (NIDDM), characterized by early onset, usually before 25 years of age and often in adolescence or childhood, and by autosomal dominant inheritance. It has been estimated that 2-5% of patients with NIDDM may have this form of diabetes mellitus. Clinical studies have shown that prediabetic MODY subjects have normal insulin sensitivity but suffer from a defect in glucose-stimulated insulin secretion, suggesting that pancreatic beta-cell dysfunction rather than insulin resistance is the primary defect in this disorder. Linkage studies have localized the genes that are mutated in MODY on human chromosomes 20 (MODY1), 7 (MODY2) and 12 (MODY3), with MODY2 and MODY3 being allelic with the genes encoding glucokinase, a key regulator of insulin secretion, and hepatocyte nuclear factor-1alpha (HNF-1alpha), a transcription factor involved in tissue-specific regulation of liver genes but also expressed in pancreatic islets, insulinoma cells and other tissues. Here we show that MODY1 is the gene encoding HNF-4alpha (gene symbol, TCF14), a member of the steroid/thyroid hormone receptor superfamily and an upstream regulator of HNF-1alpha expression.

The VITESSE algorithm for rapid exact multilocus linkage analysis via genotype set-recoding and fuzzy inheritance

As genetic marker maps have improved, multipoint linkage analysis has become a crucial part of all disease mapping studies. Paradoxically, multipoint lod scores become increasingly difficult to compute, particularly as the numbers of markers, marker alleles and untyped people increase. We have solved this problem by using a novel set-recording scheme to recode each person's genotype and 'fuzzy inheritance' to infer transmission probabilities. Our approach is implemented in a memory-efficient computer program, VITESSE, for extremely rapid computation of exact multipoint likelihoods. VITESSE enables fast and precise multipoint mapping of disease loci with highly polymorphic markers.