A General Model for Multilocus Epistatic Interactions in Case-Control Studies

Background

Epistasis, i.e., the interaction of alleles at different loci, is thought to play a central role in the formation and progression of complex diseases. The complexity of disease expression should arise from a complex network of epistatic interactions involving multiple genes.

Methodology

We develop a general model for testing high-order epistatic interactions for a complex disease in a case-control study. We incorporate the quantitative genetic theory of high-order epistasis into the setting of cases and controls sampled from a natural population. The new model allows the identification and testing of epistasis and its various genetic components.

Conclusions

Simulation studies were used to examine the power and false positive rates of the model under different sampling strategies. The model was used to detect epistasis in a case-control study of inflammatory bowel disease, in which five SNPs at a candidate gene were typed, leading to the identification of a significant three-locus epistasis.     

Epistatic Interaction between BANK1 and BLK in Rheumatoid Arthritis: Results from a Large Trans-Ethnic Meta-Analysis

Background

BANK1 and BLK belong to the pleiotropic autoimmune genes; recently, epistasis between BANK1 and BLK was detected in systemic lupus erythematosus. Although BLK has been reproducibly identified as a risk factor in rheumatoid arthritis (RA), reports are conflicting about the contribution of BANK1 to RA susceptibility. To ascertain the real impact of BANK1 on RA genetic susceptibility, we performed a large meta-analysis including our original data and tested for an epistatic interaction between BANK1 and BLK in RA susceptibility.

Patients and Methods

We investigated data for 1,915 RA patients and 1,915 ethnically matched healthy controls genotyped for BANK1 rs10516487 and rs3733197 and BLK rs13277113. The association of each SNP and RA was tested by logistic regression. Multivariate analysis was then used with an interaction term to test for an epistatic interaction between the SNPs in the 2 genes.

Results

None of the SNPs tested individually was significantly associated with RA in the genotyped samples. However, we detected an epistatic interaction between BANK1 rs3733197 and BLK rs13277113 (P_interaction = 0.037). In individuals carrying the BLK rs13277113 GG genotype, presence of the BANK1 rs3733197 G allele increased the risk of RA (odds ratio 1.21 [95% confidence interval 1.04–1.41], P = 0.015. Combining our results with those of all other studies in a large trans-ethnic meta-analysis revealed an association of the BANK1 rs3733197 G allele and RA (1.11 [1.02–1.21], P = 0.012).

Conclusion

This study confirms BANK1 as an RA susceptibility gene and for the first time provides evidence for epistasis between BANK1 and BLK in RA. Our results illustrate the concept of pleiotropic epistatic interaction, suggesting that BANK1 and BLK might play a role in RA pathogenesis.     

Epistatic QTL pairs associated with meat quality and carcass composition traits in a porcine Duroc × Pietrain population

Background

Quantitative trait loci (QTL) analyses in pig have revealed numerous individual QTL affecting growth, carcass composition, reproduction and meat quality, indicating a complex genetic architecture. In general, statistical QTL models consider only additive and dominance effects and identification of epistatic effects in livestock is not yet widespread. The aim of this study was to identify and characterize epistatic effects between common and novel QTL regions for carcass composition and meat quality traits in pig.

Methods

Five hundred and eighty five F₂ pigs from a Duroc × Pietrain resource population were genotyped using 131 genetic markers (microsatellites and SNP) spread over the 18 pig autosomes. Phenotypic information for 26 carcass composition and meat quality traits was available for all F₂ animals. Linkage analysis was performed in a two-step procedure using a maximum likelihood approach implemented in the QxPak program.

Results

A number of interacting QTL was observed for different traits, leading to the identification of a variety of networks among chromosomal regions throughout the porcine genome. We distinguished 17 epistatic QTL pairs for carcass composition and 39 for meat quality traits. These interacting QTL pairs explained up to 8% of the phenotypic variance.

Conclusions

Our findings demonstrate the significance of epistasis in pigs. We have revealed evidence for epistatic relationships between different chromosomal regions, confirmed known QTL loci and connected regions reported in other studies. Considering interactions between loci allowed us to identify several novel QTL and trait-specific relationships of loci within and across chromosomes.     

Learning Predictive Interactions Using Information Gain and Bayesian Network Scoring

Background

The problems of correlation and classification are long-standing in the fields of statistics and machine learning, and techniques have been developed to address these problems. We are now in the era of high-dimensional data, which is data that can concern billions of variables. These data present new challenges. In particular, it is difficult to discover predictive variables, when each variable has little marginal effect. An example concerns Genome-wide Association Studies (GWAS) datasets, which involve millions of single nucleotide polymorphism (SNPs), where some of the SNPs interact epistatically to affect disease status. Towards determining these interacting SNPs, researchers developed techniques that addressed this specific problem. However, the problem is more general, and so these techniques are applicable to other problems concerning interactions. A difficulty with many of these techniques is that they do not distinguish whether a learned interaction is actually an interaction or whether it involves several variables with strong marginal effects.

Methodology/Findings

We address this problem using information gain and Bayesian network scoring. First, we identify candidate interactions by determining whether together variables provide more information than they do separately. Then we use Bayesian network scoring to see if a candidate interaction really is a likely model. Our strategy is called MBS-IGain. Using 100 simulated datasets and a real GWAS Alzheimer’s dataset, we investigated the performance of MBS-IGain.

Conclusions/Significance

When analyzing the simulated datasets, MBS-IGain substantially out-performed nine previous methods at locating interacting predictors, and at identifying interactions exactly. When analyzing the real Alzheimer’s dataset, we obtained new results and results that substantiated previous findings. We conclude that MBS-IGain is highly effective at finding interactions in high-dimensional datasets. This result is significant because we have increasingly abundant high-dimensional data in many domains, and to learn causes and perform prediction/classification using these data, we often must first identify interactions.     

Genome-wide eQTLs and heritability for gene expression traits in unrelated individuals

Background

While the possible sources underlying the so-called ‘missing heritability’ evident in current genome-wide association studies (GWAS) of complex traits have been actively pursued in recent years, resolving this mystery remains a challenging task. Studying heritability of genome-wide gene expression traits can shed light on the goal of understanding the relationship between phenotype and genotype. Here we used microarray gene expression measurements of lymphoblastoid cell lines and genome-wide SNP genotype data from 210 HapMap individuals to examine the heritability of gene expression traits.

Results

Heritability levels for expression of 10,720 genes were estimated by applying variance component model analyses and 1,043 expression quantitative loci (eQTLs) were detected. Our results indicate that gene expression traits display a bimodal distribution of heritability, one peak close to 0% and the other summit approaching 100%. Such a pattern of the within-population variability of gene expression heritability is common among different HapMap populations of unrelated individuals but different from that obtained in the CEU and YRI trio samples. Higher heritability levels are shown by housekeeping genes and genes associated with cis eQTLs. Both cis and trans eQTLs make comparable cumulative contributions to the heritability. Finally, we modelled gene-gene interactions (epistasis) for genes with multiple eQTLs and revealed that epistasis was not prevailing in all genes but made a substantial contribution in explaining total heritability for some genes analysed.

Conclusions

We utilised a mixed effect model analysis for estimating genetic components from population based samples. On basis of analyses of genome-wide gene expression from four HapMap populations, we demonstrated detailed exploitation of the distribution of genetic heritabilities for expression traits from different populations, and highlighted the importance of studying interaction at the gene expression level as an important source of variation underlying missing heritability.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-13) contains supplementary material, which is available to authorized users.     

Parallel and serial computing tools for testing single-locus and epistatic SNP effects of quantitative traits in genome-wide association studies

Background  

Genome-wide association studies (GWAS) using single nucleotide polymorphism (SNP) markers provide opportunities to detect epistatic SNPs associated with quantitative traits and to detect the exact mode of an epistasis effect. Computational difficulty is the main bottleneck for epistasis testing in large scale GWAS.     

A novel evolution-based method for detecting gene-gene interactions

Background

The rapid advance in large-scale SNP-chip technologies offers us great opportunities in elucidating the genetic basis of complex diseases. Methods for large-scale interactions analysis have been under development from several sources. Due to several difficult issues (e.g., sparseness of data in high dimensions and low replication or validation rate), development of fast, powerful and robust methods for detecting various forms of gene-gene interactions continues to be a challenging task.

Methodology/Principal Findings

In this article, we have developed an evolution-based method to search for genome-wide epistasis in a case-control design. From an evolutionary perspective, we view that human diseases originate from ancient mutations and consider that the underlying genetic variants play a role in differentiating human population into the healthy and the diseased. Based on this concept, traditional evolutionary measure, fixation index (Fst) for two unlinked loci, which measures the genetic distance between populations, should be able to reveal the responsible genetic interplays for disease traits. To validate our proposal, we first investigated the theoretical distribution of Fst by using extensive simulations. Then, we explored its power for detecting gene-gene interactions via SNP markers, and compared it with the conventional Pearson Chi-square test, mutual information based test and linkage disequilibrium based test under several disease models. The proposed evolution-based method outperformed these compared methods in dominant and additive models, no matter what the disease allele frequencies were. However, its performance was relatively poor in a recessive model. Finally, we applied the proposed evolution-based method to analysis of a published dataset. Our results showed that the P value of the Fst -based statistic is smaller than those obtained by the LD-based statistic or Poisson regression models.

Conclusions/Significance

With rapidly growing large-scale genetic association studies, the proposed evolution-based method can be a promising tool in the identification of epistatic effects.     

A Bayesian Outlier Criterion to Detect SNPs under Selection in Large Data Sets

Background

The recent advent of high-throughput SNP genotyping technologies has opened new avenues of research for population genetics. In particular, a growing interest in the identification of footprints of selection, based on genome scans for adaptive differentiation, has emerged.

Methodology/Principal Findings

The purpose of this study is to develop an efficient model-based approach to perform Bayesian exploratory analyses for adaptive differentiation in very large SNP data sets. The basic idea is to start with a very simple model for neutral loci that is easy to implement under a Bayesian framework and to identify selected loci as outliers via Posterior Predictive P-values (PPP-values). Applications of this strategy are considered using two different statistical models. The first one was initially interpreted in the context of populations evolving respectively under pure genetic drift from a common ancestral population while the second one relies on populations under migration-drift equilibrium. Robustness and power of the two resulting Bayesian model-based approaches to detect SNP under selection are further evaluated through extensive simulations. An application to a cattle data set is also provided.

Conclusions/Significance

The procedure described turns out to be much faster than former Bayesian approaches and also reasonably efficient especially to detect loci under positive selection.     

A phylogenetic study of Laeliinae (Orchidaceae) based on combined nuclear and plastid DNA sequences

Background and Aims

Laeliinae are a neotropical orchid subtribe with approx. 1500 species in 50 genera. In this study, an attempt is made to assess generic alliances based on molecular phylogenetic analysis of DNA sequence data.

Methods

Six DNA datasets were gathered: plastid trnL intron, trnL-F spacer, matK gene and trnK introns upstream and dowstream from matK and nuclear ITS rDNA. Data were analysed with maximum parsimony (MP) and Bayesian analysis with mixed models (BA).

Key Results

Although relationships between Laeliinae and outgroups are well supported, within the subtribe sequence variation is low considering the broad taxonomic range covered. Localized incongruence between the ITS and plastid trees was found. A combined tree followed the ITS trees more closely, but the levels of support obtained with MP were low. The Bayesian analysis recovered more well-supported nodes. The trees from combined MP and BA allowed eight generic alliances to be recognized within Laeliinae, all of which show trends in morphological characters but lack unambiguous synapomorphies.

Conclusions

By using combined plastid and nuclear DNA data in conjunction with mixed-models Bayesian inference, it is possible to delimit smaller groups within Laeliinae and discuss general patterns of pollination and hybridization compatibility. Furthermore, these small groups can now be used for further detailed studies to explain morphological evolution and diversification patterns within the subtribe.Key words: Laeliinae, Orchidaceae, ITS, trnL intron, trnL-F spacer, matK     

Inferring Multiple Refugia and Phylogeographical Patterns in Pinus massoniana Based on Nucleotide Sequence Variation and DNA Fingerprinting

Background

Pinus massoniana, an ecologically and economically important conifer, is widespread across central and southern mainland China and Taiwan. In this study, we tested the central–marginal paradigm that predicts that the marginal populations tend to be less polymorphic than the central ones in their genetic composition, and examined a founders'' effect in the island population.

Methodology/Principal Findings

We examined the phylogeography and population structuring of the P. massoniana based on nucleotide sequences of cpDNA atpB-rbcL intergenic spacer, intron regions of the AdhC2 locus, and microsatellite fingerprints. SAMOVA analysis of nucleotide sequences indicated that most genetic variants resided among geographical regions. High levels of genetic diversity in the marginal populations in the south region, a pattern seemingly contradicting the central–marginal paradigm, and the fixation of private haplotypes in most populations indicate that multiple refugia may have existed over the glacial maxima. STRUCTURE analyses on microsatellites revealed that genetic structure of mainland populations was mediated with recent genetic exchanges mostly via pollen flow, and that the genetic composition in east region was intermixed between south and west regions, a pattern likely shaped by gene introgression and maintenance of ancestral polymorphisms. As expected, the small island population in Taiwan was genetically differentiated from mainland populations.

Conclusions/Significance

The marginal populations in south region possessed divergent gene pools, suggesting that the past glaciations might have low impacts on these populations at low latitudes. Estimates of ancestral population sizes interestingly reflect a recent expansion in mainland from a rather smaller population, a pattern that seemingly agrees with the pollen record.     

The strength of genetic interactions scales weakly with mutational effects

Background

Genetic interactions pervade every aspect of biology, from evolutionary theory, where they determine the accessibility of evolutionary paths, to medicine, where they can contribute to complex genetic diseases. Until very recently, studies on epistatic interactions have been based on a handful of mutations, providing at best anecdotal evidence about the frequency and the typical strength of genetic interactions. In this study, we analyze a publicly available dataset that contains the growth rates of over five million double knockout mutants of the yeast Saccharomyces cerevisiae.

Results

We discuss a geometric definition of epistasis that reveals a simple and surprisingly weak scaling law for the characteristic strength of genetic interactions as a function of the effects of the mutations being combined. We then utilized this scaling to quantify the roughness of naturally occurring fitness landscapes. Finally, we show how the observed roughness differs from what is predicted by Fisher''s geometric model of epistasis, and discuss the consequences for evolutionary dynamics.

Conclusions

Although epistatic interactions between specific genes remain largely unpredictable, the statistical properties of an ensemble of interactions can display conspicuous regularities and be described by simple mathematical laws. By exploiting the amount of data produced by modern high-throughput techniques, it is now possible to thoroughly test the predictions of theoretical models of genetic interactions and to build informed computational models of evolution on realistic fitness landscapes.     

Using the realized relationship matrix to disentangle confounding factors for the estimation of genetic variance components of complex traits

Background

In the analysis of complex traits, genetic effects can be confounded with non-genetic effects, especially when using full-sib families. Dominance and epistatic effects are typically confounded with additive genetic and non-genetic effects. This confounding may cause the estimated genetic variance components to be inaccurate and biased.

Methods

In this study, we constructed genetic covariance structures from whole-genome marker data, and thus used realized relationship matrices to estimate variance components in a heterogenous population of ~ 2200 mice for which four complex traits were investigated. These mice were genotyped for more than 10,000 single nucleotide polymorphisms (SNP) and the variances due to family, cage and genetic effects were estimated by models based on pedigree information only, aggregate SNP information, and model selection for specific SNP effects.

Results and conclusions

We show that the use of genome-wide SNP information can disentangle confounding factors to estimate genetic variances by separating genetic and non-genetic effects. The estimated variance components using realized relationship were more accurate and less biased, compared to those based on pedigree information only. Models that allow the selection of individual SNP in addition to fitting a relationship matrix are more efficient for traits with a significant dominance variance.     

Single Nucleotide Polymorphism Analysis of European Archaeological M. leprae DNA

Background

Leprosy was common in Europe eight to twelve centuries ago but molecular confirmation of this has been lacking. We have extracted M. leprae ancient DNA (aDNA) from medieval bones and single nucleotide polymorphism (SNP) typed the DNA, this provides insight into the pattern of leprosy transmission in Europe and may assist in the understanding of M. leprae evolution.

Methods and Findings

Skeletons have been exhumed from 3 European countries (the United Kingdom, Denmark and Croatia) and are dated around the medieval period (476 to 1350 A.D.). we tested for the presence of 3 previously identified single nucleotide polymorphisms (SNPs) in 10 aDNA extractions. M. leprae aDNA was extracted from 6 of the 10 bone samples. SNP analysis of these 6 extractions were compared to previously analysed European SNP data using the same PCR assays and were found to be the same. Testing for the presence of SNPs in M. leprae DNA extracted from ancient bone samples is a novel approach to analysing European M. leprae DNA and the findings concur with the previously published data that European M. leprae strains fall in to one group (SNP group 3).

Conclusions

These findings support the suggestion that the M. leprae genome is extremely stable and show that archaeological M. leprae DNA can be analysed to gain detailed information about the genotypic make-up of European leprosy, which may assist in the understanding of leprosy transmission worldwide.     

A phasing and imputation method for pedigreed populations that results in a single-stage genomic evaluation

Background

Efficient, robust, and accurate genotype imputation algorithms make large-scale application of genomic selection cost effective. An algorithm that imputes alleles or allele probabilities for all animals in the pedigree and for all genotyped single nucleotide polymorphisms (SNP) provides a framework to combine all pedigree, genomic, and phenotypic information into a single-stage genomic evaluation.

Methods

An algorithm was developed for imputation of genotypes in pedigreed populations that allows imputation for completely ungenotyped animals and for low-density genotyped animals, accommodates a wide variety of pedigree structures for genotyped animals, imputes unmapped SNP, and works for large datasets. The method involves simple phasing rules, long-range phasing and haplotype library imputation and segregation analysis.

Results

Imputation accuracy was high and computational cost was feasible for datasets with pedigrees of up to 25 000 animals. The resulting single-stage genomic evaluation increased the accuracy of estimated genomic breeding values compared to a scenario in which phenotypes on relatives that were not genotyped were ignored.

Conclusions

The developed imputation algorithm and software and the resulting single-stage genomic evaluation method provide powerful new ways to exploit imputation and to obtain more accurate genetic evaluations.     

Genomic prediction of breeding values using previously estimated SNP variances

Background

Genomic prediction requires estimation of variances of effects of single nucleotide polymorphisms (SNPs), which is computationally demanding, and uses these variances for prediction. We have developed models with separate estimation of SNP variances, which can be applied infrequently, and genomic prediction, which can be applied routinely.

Methods

SNP variances were estimated with Bayes Stochastic Search Variable Selection (BSSVS) and BayesC. Genome-enhanced breeding values (GEBV) were estimated with RR-BLUP (ridge regression best linear unbiased prediction), using either variances obtained from BSSVS (BLUP-SSVS) or BayesC (BLUP-C), or assuming equal variances for each SNP. Datasets used to estimate SNP variances comprised (1) all animals, (2) 50% random animals (RAN50), (3) 50% best animals (TOP50), or (4) 50% worst animals (BOT50). Traits analysed were protein yield, udder depth, somatic cell score, interval between first and last insemination, direct longevity, and longevity including information from predictors.

Results

BLUP-SSVS and BLUP-C yielded similar GEBV as the equivalent Bayesian models that simultaneously estimated SNP variances. Reliabilities of these GEBV were consistently higher than from RR-BLUP, although only significantly for direct longevity. Across scenarios that used data subsets to estimate GEBV, observed reliabilities were generally higher for TOP50 than for RAN50, and much higher than for BOT50. Reliabilities of TOP50 were higher because the training data contained more ancestors of selection candidates. Using estimated SNP variances based on random or non-random subsets of the data, while using all data to estimate GEBV, did not affect reliabilities of the BLUP models. A convergence criterion of 10⁻⁸ instead of 10⁻¹⁰ for BLUP models yielded similar GEBV, while the required number of iterations decreased by 71 to 90%. Including a separate polygenic effect consistently improved reliabilities of the GEBV, but also substantially increased the required number of iterations to reach convergence with RR-BLUP. SNP variances converged faster for BayesC than for BSSVS.

Conclusions

Combining Bayesian variable selection models to re-estimate SNP variances and BLUP models that use those SNP variances, yields GEBV that are similar to those from full Bayesian models. Moreover, these combined models yield predictions with higher reliability and less bias than the commonly used RR-BLUP model.

Electronic supplementary material

The online version of this article (doi:10.1186/s12711-014-0052-x) contains supplementary material, which is available to authorized users.     

Cuckoo search epistasis: a new method for exploring significant genetic interactions

The advent of high-throughput sequencing technology has resulted in the ability to measure millions of single-nucleotide polymorphisms (SNPs) from thousands of individuals. Although these high-dimensional data have paved the way for better understanding of the genetic architecture of common diseases, they have also given rise to challenges in developing computational methods for learning epistatic relationships among genetic markers. We propose a new method, named cuckoo search epistasis (CSE) for identifying significant epistatic interactions in population-based association studies with a case–control design. This method combines a computationally efficient Bayesian scoring function with an evolutionary-based heuristic search algorithm, and can be efficiently applied to high-dimensional genome-wide SNP data. The experimental results from synthetic data sets show that CSE outperforms existing methods including multifactorial dimensionality reduction and Bayesian epistasis association mapping. In addition, on a real genome-wide data set related to Alzheimer''s disease, CSE identified SNPs that are consistent with previously reported results, and show the utility of CSE for application to genome-wide data.