Theoretical framework of population genetics with somatic mutations taken into account: application to copy number variations in humans

Traditionally, population genetics focuses on the dynamics of frequencies of alleles acquired by mutations on germ-lines, because only such mutations are heritable. Typical genotyping experiments, however, use DNA from some somatic tissues such as blood, which harbors somatic mutations at the current generation in addition to germ-line mutations accumulated since the most recent common ancestor of the sample. This common practice may sometimes cause erroneous interpretations of polymorphism data, unless we properly understand the role of somatic mutations in population genetics. We here introduce a very basic theoretical framework of population genetics with somatic mutations taken into account. It is easy to imagine that somatic mutations at the current generation simply add individual-specific variations, as errors in mutation detection do. Our theory quantifies this increment under various conditions. We find that the major contribution of somatic mutations plus errors is to very rare variants, particularly to singletons. The relative contribution is markedly large when mutations are deleterious. Because negative selection also increases rare variants, it is important to distinguish the roles of these mutually confounding factors when we interpret the data, even after correcting for demography. We apply this theory to human copy number variations (CNVs), for which the composite effect of somatic mutations and errors may not be negligible. Using genome-wide CNV data, we demonstrate how the joint action of the two factors, selection and somatic mutations plus errors, shapes the observed pattern of polymorphism.     

Rare and Low Frequency Variant Stratification in the UK Population: Description and Impact on Association Tests

Although variations in allele frequencies at common SNPs have been extensively studied in different populations, little is known about the stratification of rare variants and its impact on association tests. In this paper, we used Affymetrix 500K genotype data from the WTCCC to investigate if variants in three different frequency categories (below 1%, between 1 and 5%, above 5%) show different stratification patterns in the UK population. We found that these patterns are indeed different. The top principal component extracted from the rare variant category shows poor correlations with any principal component or combination of principal components from the low frequency or common variant categories. These results could suggest that a suitable solution to avoid false positive association due to population stratification would involve adjusting for the respective PCs when testing for variants in different allele frequency categories. However, we found this was not the case both on type 2 diabetes data and on simulated data. Indeed, adjusting rare variant association tests on PCs derived from rare variants does no better to correct for population stratification than adjusting on PCs derived from more common variants. Mixed models perform slightly better for low frequency variants than PC based adjustments but less well for the rarest variants. These results call for the need of new methodological developments specifically devoted to address rare variant stratification issues in association tests.     

Characterisation and Validation of Insertions and Deletions in 173 Patient Exomes

Recent advances in genomics technologies have spurred unprecedented efforts in genome and exome re-sequencing aiming to unravel the genetic component of rare and complex disorders. While in rare disorders this allowed the identification of novel causal genes, the missing heritability paradox in complex diseases remains so far elusive. Despite rapid advances of next-generation sequencing, both the technology and the analysis of the data it produces are in its infancy. At present there is abundant knowledge pertaining to the role of rare single nucleotide variants (SNVs) in rare disorders and of common SNVs in common disorders. Although the 1,000 genome project has clearly highlighted the prevalence of rare variants and more complex variants (e.g. insertions, deletions), their role in disease is as yet far from elucidated.We set out to analyse the properties of sequence variants identified in a comprehensive collection of exome re-sequencing studies performed on samples from patients affected by a broad range of complex and rare diseases (N = 173). Given the known potential for Loss of Function (LoF) variants to be false positive, we performed an extensive validation of the common, rare and private LoF variants identified, which indicated that most of the private and rare variants identified were indeed true, while common novel variants had a significantly higher false positive rate. Our results indicated a strong enrichment of very low-frequency insertion/deletion variants, so far under-investigated, which might be difficult to capture with low coverage and imputation approaches and for which most of study designs would be under-powered. These insertions and deletions might play a significant role in disease genetics, contributing specifically to the underlining rare and private variation predicted to be discovered through next generation sequencing.     

Testing for an unusual distribution of rare variants

Technological advances make it possible to use high-throughput sequencing as a primary discovery tool of medical genetics, specifically for assaying rare variation. Still this approach faces the analytic challenge that the influence of very rare variants can only be evaluated effectively as a group. A further complication is that any given rare variant could have no effect, could increase risk, or could be protective. We propose here the C-alpha test statistic as a novel approach for testing for the presence of this mixture of effects across a set of rare variants. Unlike existing burden tests, C-alpha, by testing the variance rather than the mean, maintains consistent power when the target set contains both risk and protective variants. Through simulations and analysis of case/control data, we demonstrate good power relative to existing methods that assess the burden of rare variants in individuals.     

Effect of Genome-Wide Genotyping and Reference Panels on Rare Variants Imputation

Common variants explain little of the variance of most common disease,prompting large-scale sequencing studies to understand the contribution of rare variants to these diseases.Imputation of rare variants from genome-wide genotypic arrays offers a cost-efficient strategy to achieve necessary sample sizes required for adequate statistical power.To estimate the performance of imputation of rare variants,we imputed 153 individuals,each of whom was genotyped on 3 different genotype arrays including 317k,610k and 1 million single nucleotide polymorphisms(SNPs),to two different reference panels:HapMap2 and 1000 Genomes pilot March 2010 release (lKGpilot) by using IMPUTE version 2.We found that more than 94%and 84%of all SNPs yield acceptable accuracy(info > 0.4) in HapMap2 and lKGpilot-based imputation,respectively.For rare variants(minor allele frequency(MAF) <5%),the proportion of wellimputed SNPs increased as the MAF increased from 0.3%to 5%across all 3 genome-wide association study(GWAS) datasets.The proportion of well-imputed SNPs was 69%,60%and 49%for SNPs with a MAF from 0.3%to 5%for 1M,610k and 317k,respectively. None of the very rare variants(MAF < 0.3%) were well imputed.We conclude that the imputation accuracy of rare variants increases with higher density of genome-wide genotyping arrays when the size of the reference panel is small.Variants with lower MAF are more difficult to impute.These findings have important implications in the design and replication of large-scale sequencing studies.     

U-statistics in genetic association studies

Many common human diseases are complex and are expected to be highly heterogeneous, with multiple causative loci and multiple rare and common variants at some of the causative loci contributing to the risk of these diseases. Data from the genome-wide association studies (GWAS) and metadata such as known gene functions and pathways provide the possibility of identifying genetic variants, genes and pathways that are associated with complex phenotypes. Single-marker-based tests have been very successful in identifying thousands of genetic variants for hundreds of complex phenotypes. However, these variants only explain very small percentages of the heritabilities. To account for the locus- and allelic-heterogeneity, gene-based and pathway-based tests can be very useful in the next stage of the analysis of GWAS data. U-statistics, which summarize the genomic similarity between pair of individuals and link the genomic similarity to phenotype similarity, have proved to be very useful for testing the associations between a set of single nucleotide polymorphisms and the phenotypes. Compared to single marker analysis, the advantages afforded by the U-statistics-based methods is large when the number of markers involved is large. We review several formulations of U-statistics in genetic association studies and point out the links of these statistics with other similarity-based tests of genetic association. Finally, potential application of U-statistics in analysis of the next-generation sequencing data and rare variants association studies are discussed.     

Networks of neuronal genes affected by common and rare variants in autism spectrum disorders

Autism spectrum disorders (ASD) are neurodevelopmental disorders with phenotypic and genetic heterogeneity. Recent studies have reported rare and de novo mutations in ASD, but the allelic architecture of ASD remains unclear. To assess the role of common and rare variations in ASD, we constructed a gene co-expression network based on a widespread survey of gene expression in the human brain. We identified modules associated with specific cell types and processes. By integrating known rare mutations and the results of an ASD genome-wide association study (GWAS), we identified two neuronal modules that are perturbed by both rare and common variations. These modules contain highly connected genes that are involved in synaptic and neuronal plasticity and that are expressed in areas associated with learning and memory and sensory perception. The enrichment of common risk variants was replicated in two additional samples which include both simplex and multiplex families. An analysis of the combined contribution of common variants in the neuronal modules revealed a polygenic component to the risk of ASD. The results of this study point toward contribution of minor and major perturbations in the two sub-networks of neuronal genes to ASD risk.     

Leveraging Identity-by-Descent for Accurate Genotype Inference in Family Sequencing Data

Sequencing family DNA samples provides an attractive alternative to population based designs to identify rare variants associated with human disease due to the enrichment of causal variants in pedigrees. Previous studies showed that genotype calling accuracy can be improved by modeling family relatedness compared to standard calling algorithms. Current family-based variant calling methods use sequencing data on single variants and ignore the identity-by-descent (IBD) sharing along the genome. In this study we describe a new computational framework to accurately estimate the IBD sharing from the sequencing data, and to utilize the inferred IBD among family members to jointly call genotypes in pedigrees. Through simulations and application to real data, we showed that IBD can be reliably estimated across the genome, even at very low coverage (e.g. 2X), and genotype accuracy can be dramatically improved. Moreover, the improvement is more pronounced for variants with low frequencies, especially at low to intermediate coverage (e.g. 10X to 20X), making our approach effective in studying rare variants in cost-effective whole genome sequencing in pedigrees. We hope that our tool is useful to the research community for identifying rare variants for human disease through family-based sequencing.     

Rare Variants Association Analysis in Large-Scale Sequencing Studies at the Single Locus Level

Genetic association analyses of rare variants in next-generation sequencing (NGS) studies are fundamentally challenging due to the presence of a very large number of candidate variants at extremely low minor allele frequencies. Recent developments often focus on pooling multiple variants to provide association analysis at the gene instead of the locus level. Nonetheless, pinpointing individual variants is a critical goal for genomic researches as such information can facilitate the precise delineation of molecular mechanisms and functions of genetic factors on diseases. Due to the extreme rarity of mutations and high-dimensionality, significances of causal variants cannot easily stand out from those of noncausal ones. Consequently, standard false-positive control procedures, such as the Bonferroni and false discovery rate (FDR), are often impractical to apply, as a majority of the causal variants can only be identified along with a few but unknown number of noncausal variants. To provide informative analysis of individual variants in large-scale sequencing studies, we propose the Adaptive False-Negative Control (AFNC) procedure that can include a large proportion of causal variants with high confidence by introducing a novel statistical inquiry to determine those variants that can be confidently dispatched as noncausal. The AFNC provides a general framework that can accommodate for a variety of models and significance tests. The procedure is computationally efficient and can adapt to the underlying proportion of causal variants and quality of significance rankings. Extensive simulation studies across a plethora of scenarios demonstrate that the AFNC is advantageous for identifying individual rare variants, whereas the Bonferroni and FDR are exceedingly over-conservative for rare variants association studies. In the analyses of the CoLaus dataset, AFNC has identified individual variants most responsible for gene-level significances. Moreover, single-variant results using the AFNC have been successfully applied to infer related genes with annotation information.     

HapFABIA: Identification of very short segments of identity by descent characterized by rare variants in large sequencing data

Identity by descent (IBD) can be reliably detected for long shared DNA segments, which are found in related individuals. However, many studies contain cohorts of unrelated individuals that share only short IBD segments. New sequencing technologies facilitate identification of short IBD segments through rare variants, which convey more information on IBD than common variants. Current IBD detection methods, however, are not designed to use rare variants for the detection of short IBD segments. Short IBD segments reveal genetic structures at high resolution. Therefore, they can help to improve imputation and phasing, to increase genotyping accuracy for low-coverage sequencing and to increase the power of association studies. Since short IBD segments are further assumed to be old, they can shed light on the evolutionary history of humans. We propose HapFABIA, a computational method that applies biclustering to identify very short IBD segments characterized by rare variants. HapFABIA is designed to detect short IBD segments in genotype data that were obtained from next-generation sequencing, but can also be applied to DNA microarray data. Especially in next-generation sequencing data, HapFABIA exploits rare variants for IBD detection. HapFABIA significantly outperformed competing algorithms at detecting short IBD segments on artificial and simulated data with rare variants. HapFABIA identified 160 588 different short IBD segments characterized by rare variants with a median length of 23 kb (mean 24 kb) in data for chromosome 1 of the 1000 Genomes Project. These short IBD segments contain 752 000 single nucleotide variants (SNVs), which account for 39% of the rare variants and 23.5% of all variants. The vast majority—152 000 IBD segments—are shared by Africans, while only 19 000 and 11 000 are shared by Europeans and Asians, respectively. IBD segments that match the Denisova or the Neandertal genome are found significantly more often in Asians and Europeans but also, in some cases exclusively, in Africans. The lengths of IBD segments and their sharing between continental populations indicate that many short IBD segments from chromosome 1 existed before humans migrated out of Africa. Thus, rare variants that tag these short IBD segments predate human migration from Africa. The software package HapFABIA is available from Bioconductor. All data sets, result files and programs for data simulation, preprocessing and evaluation are supplied at http://www.bioinf.jku.at/research/short-IBD.     

Rare variants regulate expression of nearby individual genes in multiple tissues

The rapid decrease in sequencing cost has enabled genetic studies to discover rare variants associated with complex diseases and traits. Once this association is identified, the next step is to understand the genetic mechanism of rare variants on how the variants influence diseases. Similar to the hypothesis of common variants, rare variants may affect diseases by regulating gene expression, and recently, several studies have identified the effects of rare variants on gene expression using heritability and expression outlier analyses. However, identifying individual genes whose expression is regulated by rare variants has been challenging due to the relatively small sample size of expression quantitative trait loci studies and statistical approaches not optimized to detect the effects of rare variants. In this study, we analyze whole-genome sequencing and RNA-seq data of 681 European individuals collected for the Genotype-Tissue Expression (GTEx) project (v8) to identify individual genes in 49 human tissues whose expression is regulated by rare variants. To improve statistical power, we develop an approach based on a likelihood ratio test that combines effects of multiple rare variants in a nonlinear manner and has higher power than previous approaches. Using GTEx data, we identify many genes regulated by rare variants, and some of them are only regulated by rare variants and not by common variants. We also find that genes regulated by rare variants are enriched for expression outliers and disease-causing genes. These results suggest the regulatory effects of rare variants, which would be important in interpreting associations of rare variants with complex traits.     

Performance of Genotype Imputation for Low Frequency and Rare Variants from the 1000 Genomes

Genotype imputation is now routinely applied in genome-wide association studies (GWAS) and meta-analyses. However, most of the imputations have been run using HapMap samples as reference, imputation of low frequency and rare variants (minor allele frequency (MAF) < 5%) are not systemically assessed. With the emergence of next-generation sequencing, large reference panels (such as the 1000 Genomes panel) are available to facilitate imputation of these variants. Therefore, in order to estimate the performance of low frequency and rare variants imputation, we imputed 153 individuals, each of whom had 3 different genotype array data including 317k, 610k and 1 million SNPs, to three different reference panels: the 1000 Genomes pilot March 2010 release (1KGpilot), the 1000 Genomes interim August 2010 release (1KGinterim), and the 1000 Genomes phase1 November 2010 and May 2011 release (1KGphase1) by using IMPUTE version 2. The differences between these three releases of the 1000 Genomes data are the sample size, ancestry diversity, number of variants and their frequency spectrum. We found that both reference panel and GWAS chip density affect the imputation of low frequency and rare variants. 1KGphase1 outperformed the other 2 panels, at higher concordance rate, higher proportion of well-imputed variants (info>0.4) and higher mean info score in each MAF bin. Similarly, 1M chip array outperformed 610K and 317K. However for very rare variants (MAF≤0.3%), only 0–1% of the variants were well imputed. We conclude that the imputation of low frequency and rare variants improves with larger reference panels and higher density of genome-wide genotyping arrays. Yet, despite a large reference panel size and dense genotyping density, very rare variants remain difficult to impute.     

Evidence for random distribution of sequence variants in Tenebrio molitor satellite DNA.

Tenebrio molitor satellite DNA has been analysed in order to study sequential organization of tandemly repeated monomers, i.e. to see whether different monomer variants are distributed randomly over the whole satellite, or clustered locally. Analysed sequence variants are products of single base substitutions in a consensus satellite sequence, producing additional restriction sites. The ladder of satellite multimers obtained after digestion with restriction enzymes was compared with theoretical calculations and revealed the distribution pattern of particular monomer variants within the satellite. A defined higher order repeating structure, indicating the existence of satellite subfamilies, could not be observed. Our results show that some sequence variants are very abundant, being present in nearly 50% of the monomers, while others are very rare (0-1% of monomers). However, the distribution of either very frequent, or very rare sequence variants in T. molitor satellite DNA is always random. Monomer variants are randomly distributed in the total satellite DNA and thus spread across all chromosomes, indicating a relatively high rate of sequence homogenization among different chromosomes. Such a distribution of monomer variants represents a transient stage in the process of sequence homogenization, indicating the high rate of spreading in comparison with the rate of sequence variant amplification.     

A Linkage Disequilibrium–Based Approach to Selecting Disease-Associated Rare Variants

Rare variants have increasingly been cited as major contributors in the disease etiology of several complex disorders. Recently, several approaches have been proposed for analyzing the association of rare variants with disease. These approaches include collapsing rare variants, summing rare variant test statistics within a particular locus to improve power, and selecting a subset of rare variants for association testing, e.g., the step-up approach. We found that (a) if the variants being pooled are in linkage disequilibrium, the standard step-up method of selecting the best subset of variants results in loss of power compared to a model that pools all rare variants and (b) if the variants are in linkage equilibrium, performing a subset selection using step-based selection methods results in a gain of power of association compared to a model that pools all rare variants. Therefore, we propose an approach to selecting the best subset of variants to include in the model that is based on the linkage disequilibrium pattern among the rare variants. The proposed linkage disequilibrium–based variant selection model is flexible and borrows strength from the model that pools all rare variants when the rare variants are in linkage disequilibrium and from step-based selection methods when the variants are in linkage equilibrium. We performed simulations under three different realistic scenarios based on: (1) the HapMap3 dataset of the DRD2 gene, and CHRNA3/A5/B4 gene cluster (2) the block structure of linkage disequilibrium, and (3) linkage equilibrium. We proposed a permutation-based approach to control the type 1 error rate. The power comparisons after controlling the type 1 error show that the proposed linkage disequilibrium–based subset selection approach is an attractive alternative method for subset selection of rare variants.     

A new expectation-maximization statistical test for case-control association studies considering rare variants obtained by high-throughput sequencing

Genome-wide association studies (GWAS) have been successful in identifying common genetic variation reproducibly associated with disease. However, most associated variants confer very small risk and after meta-analysis of large cohorts a large fraction of expected heritability still remains unexplained. A possible explanation is that rare variants currently undetected by GWAS with SNP arrays could contribute a large fraction of risk when present in cases. This concept has spurred great interest in exploring the role of rare variants in disease. As the cost of sequencing continue to plummet, it is becoming feasible to directly sequence case-control samples for testing disease association including rare variants. We have developed a test statistic that allows for association testing among cases and controls using data directly from sequencing reads. In addition, our method allows for random errors in reads. We determine the probability of a true genotype call based on the observed base pair reads using the expectation-maximization algorithm. We apply the SumStat procedure to obtain a single statistic for a group of multiple rare variant loci. We document the validity of our method through simulations. Our results suggest that our statistic maintains the correct type I error rate, even in the presence of differential misclassification for sequence reads, and that it has good power under a number of scenarios. Finally, our SumStat results show power at least as good as the maximum single locus results.     

A novel adaptive method for the analysis of next-generation sequencing data to detect complex trait associations with rare variants due to gene main effects and interactions

There is solid evidence that rare variants contribute to complex disease etiology. Next-generation sequencing technologies make it possible to uncover rare variants within candidate genes, exomes, and genomes. Working in a novel framework, the kernel-based adaptive cluster (KBAC) was developed to perform powerful gene/locus based rare variant association testing. The KBAC combines variant classification and association testing in a coherent framework. Covariates can also be incorporated in the analysis to control for potential confounders including age, sex, and population substructure. To evaluate the power of KBAC: 1) variant data was simulated using rigorous population genetic models for both Europeans and Africans, with parameters estimated from sequence data, and 2) phenotypes were generated using models motivated by complex diseases including breast cancer and Hirschsprung's disease. It is demonstrated that the KBAC has superior power compared to other rare variant analysis methods, such as the combined multivariate and collapsing and weight sum statistic. In the presence of variant misclassification and gene interaction, association testing using KBAC is particularly advantageous. The KBAC method was also applied to test for associations, using sequence data from the Dallas Heart Study, between energy metabolism traits and rare variants in ANGPTL 3,4,5 and 6 genes. A number of novel associations were identified, including the associations of high density lipoprotein and very low density lipoprotein with ANGPTL4. The KBAC method is implemented in a user-friendly R package.