Brassica oleracea var. botrytis) by combining 174 randomly selected cauliflower gene bank accessions from two different gene banks. The collection was genotyped with genotyping-by-sequencing (GBS) and phenotyped for six curd-related traits at two locations and three growing seasons. A GWAS analysis based on 120,693 single-nucleotide polymorphisms identified a total of 24 significant associations for curd-related traits. The potential for genomic prediction was assessed with a genomic best linear unbiased prediction model and BayesB. Prediction abilities ranged from 0.10 to 0.66 for different traits and did not differ between prediction methods. Imputation of missing genotypes only slightly improved prediction ability. Our results demonstrate that GWAS and genomic prediction in combination with GBS and phenotyping of highly heritable traits can be used to identify useful quantitative trait loci and genotypes among genetically diverse gene bank material for subsequent utilization as genetic resources in cauliflower breeding.Genetic resources are an important source of genetic variation for plant breeding. Genome-wide association studies (GWAS) and genomic prediction greatly facilitate the analysis and utilization of useful genetic diversity for improving complex phenotypic traits in crop plants. We explored the potential of GWAS and genomic prediction for improving curd-related traits in cauliflower ( Adaptation to unfavorable environmental conditions, disease resistance, and nutritional value are traits for which new alleles can be found in genetic resources  is an important vegetable crop, owing to its high nutritional value (http://faostat.fao.org/), cauliflower is of great economic importance, particularly in Asia. The most important trait and yield determinant is the cauliflower curd  to dissect the genetic basis of disease resistance  gene in cauliflower, whose overexpression increased curd yield (Genome-wide association studies (GWAS) have been carried out in major cereal crops, including maize  from large and diverse germplasm collections , althougex situ gene banks, and (3) to evaluate the effect of data imputation on association mapping and genomic prediction. We show that GWAS identifies genomic regions harboring potentially useful variation and that genetic resources are suitable for genomic prediction of phenotypic variation in highly heritable traits.In this study, we combined GBS with a phenotypic analysis of cauliflower genetic resources to investigate the potential of GWAS for the identification and genomic prediction for the selection of useful genetic variation in cauliflower breeding. More specifically, the main objectives of this study were (1) to identify SNP markers that are associated with phenotypic variation in curd-related traits using GWAS, (2) to quantify the predictive ability of genomic prediction models for curd-related traits in diverse cauliflower genotypes obtained from File S1. All accessions were phenotyped for curd-related traits in replicated field trials at two locations , for three successive growing seasons . The field experiment was conducted in randomized complete block design with two replications  and from the Leibniz-Institut für Pflanzengenetik und Kulturpflanzenforschung (IPK) Gatersleben, Germany. Detailed information about accessions is given in Supplemental Material, Table S1 in Curd width (cm): width of the curd.Cluster width (cm): width of the largest floral cluster.Number of branches: number of branches within the curd that originated from the main stem.Apical shoot length (cm): stem length from the apical meristem to where the closest first-rank branch originated from the main stem.Nearest branch length (cm): length of the branch that is nearest to the apical meristem.Days to budding: number of days from planting to appearance of the first floral bud.ApekI restriction enzyme (http://www.bioinformatics.babraham.ac.uk/projects/fastqc/). Eighteen genotypes with <300,000 reads were excluded from further analyses, which resulted in a total sample of 174 accessions for further analyses. The preprocessed reads were aligned to the genome of B. oleracea sp. capitata (File S2).We genotyped the material with the original GBS protocol using the n enzyme  and Fastcapitata , bcfutilWe imputed missing genotypes with fastPHASE  and BEAGastPHASE  and markBEAGLE 4  and markm is the overall mean, r is the number of replications, and e is the number of environments. Best linear unbiased predictors (BLUPs) for the genotypic effects were extracted from model (1) and used to calculate the genetic correlation (The effects of the genotype and environment (environment was treated as the combination of location and season) and their interactions with phenotypic variation were evaluated using analysis of variance with the aov function of R . Detailsa at one locus and allele b at the other locus  to infer clusters of genetically related individuals by using a k-means algorithm as implemented by er locus . The exter locus . Additiohttps://github.com/Gregor-Mendel-Institute/mlmm. EMMAX is a method that uses a linear model in combination with a marker-derived relationship matrix to correct for population structure. The linear model has the form:GWAS was performed with the R  implemenFollowing z is the number of predictors (number of significant SNPs in GWAS), and N is the number of observations. The proportion of genotypic variance explained was calculated as:P-values. The FDR was set to 0.2 for all data sets.Confounding effects due to population structure were evaluated with the inflation factor λ, which is the ratio of the observed median to the expected median of a test statistic distribution . Values n × 1 vector of random effects and We evaluated three different genomic prediction methods, namely genomic BLUP (GBLUP), ridge regression BLUP (RRBLUP), and BayesB. The GBLUP model uses a realized relationship calculated from genetic markers  of phenotypic data are provided as supplementary material (File S2).Raw sequence data have been submitted to the Sequence Read Archive under accession number PRJEB8701. SNP calls are available on figshare at File S1). Analysis of variance showed that all traits were strongly affected by genotype (G), environment (E) and genotype by environment interaction , as did apical length and nearest branch length . The clusters are differentiated by geographic origin and flowering time. Cluster 1 (n = 25) consists of geographically diverse accessions (Table S4 in File S1) without a distinct geographic origin, but differs from the other clusters by its high average time to flowering (n = 56) and 4 (n = 40) consist of predominately European accessions that differ by their mean time to budding. Clusters 3 (n = 24) and 5 (n = 22) consist mainly of Asian accessions that also differ by mean time to budding.We inferred five genetic clusters  by k-mealowering . ClusterWe next tested whether the five clusters also differ by the extent of genome-wide LD, which may reflect differences in the breeding history. Based on the method described by ∼151 kbp . The ext ∼41 kbp . ClusterFile S1), indicating a stronger differentiation between those clusters.The average persistence of linkage phase is moderate between all clusters except for cluster 5, which reaches the expectation value of independent segregation (50%) for unlinked markers between clusters already at close distances in comparison with cluster 2 and cluster 4 , which shows that the two methods account sufficiently well for population structure.Since the accessions show a strong population structure, we conducted a GWAS with models that correct for population structure and used the λ parameter to assess how well a correction was achieved. Overall, both GWAS methods showed λ values close to 1 (reflecting a good correction) for all traits and data  was associated with both curd width and cluster width. Another SNP (C07:41524584) was associated with number of days to budding and number of branches . We idenFile S1). For the traits of curd width and cluster width, no significant SNP detected by the GWAS was linked to a SNP with a high DAPC loading , but for number of days to budding the significant association detected on chromosome O6 is located close to SNPs with high DAPC loadings . This suggests that SNPs linked with flowering time variation also contribute to population differentiation.Further, we tested whether SNPs identified as significantly associated with phenotypic variation also contribute to population structure .Finally, we tested whether genomic prediction of phenotypic traits can be carried out with genetically diverse gene bank accessions to select new genetic resources for breeding purposes. The average prediction ability for each trait was calculated using five cross-validations with 10 replications; it ranged from 0.13 to 0.65 with GBLUP  and fromP-values in the GWAS . According to this analysis, population structure had a strong effect on the genomic prediction ability of cluster width , curd width , and number of days to budding . The variance explained by principal components was marginal for the other traits.We assessed the influence of population structure on prediction ability using cross-validation. A correction for population structure resulted in a minor decrease in prediction ability for most traits, except curd width. The decrease in prediction ability was substantial for number of days to budding  cluster with the European accessions from IPK and the remaining 25 (51%) are distributed between cluster 1  and cluster 5 (predominately Asian accessions). This is unexpected under the assumption of a strong correlation between geographic origin and genetic relationship, but may be explained by incomplete passport data. Data about the seed donor but not the collection site were available for 79 of 93 USDA accessions (85%), and in these cases the true geographic origin could not be verified. For this reason, the analysis of genetic relationship allows a putative geographic origin of accessions to be assigned and can be used to complement missing passport data.Genome-wide LD levels in the complete sample, which we measured as LD decay, were fairly high for an outcrossing species. The maximum physical distance for genetic linkage is reached at 151 kbp using the whole population. This value is comparable with that of self-fertilizing species, but lower than a previous estimate for cauliflower of up to 400 kbp . This chromosome harbors multiple paralogs of the File S1). The proportion of markers in the same linkage phase was moderate between most clusters, but slightly lower between clusters 2 and 5 and clusters 4 and 5, which indicates that genomic prediction ability is mainly influenced by the genetic relationship of individuals and not by a persistent linkage of marker alleles with causal QTL in different clusters.Finally, we compared the persistence of linkage phase between clusters  coincide well with QTL regions identified in previous studies. For example, a SNP on chromosome O6 explained 26.8% of variation and was close to a QTL detected by A. thaliana Flowering Locus C (FLC) gene, which controls vernalization and has a major influence on flowering time.The phenotypic differences in flowering time and curd width between genetic clusters suggest a genetic basis for these differences. We used two GWAS methods for the imputed and unimputed SNP data to map QTL controlling these traits and identified 24 SNPs that were associated with at least one of the six phenotypic traits. The genomic locations of SNPs associated with flowering time . The SNPs explain between 27.4 and 34.1% of the genetic variation and therefore seem to be linked to a major QTL. These SNPs are located in genes whose A. thaliana orthologs regulate response to heat stress, which is consistent with the observation that temperature has a strong effect on cauliflower curd development  may result from the small sample size. Sample size has a great influence on detection power for complex traits in GWAS . HoweverGenomic prediction is a useful method for characterizing gene bank accessions, because it may allow phenotyping to be restricted to a subset of accessions in order to predict trait values for the complete collection. We used GBLUP and BayesB for prediction, because these models have a good performance, stable prediction ability, and are suited for different genetic architectures . In addiBrassica species. Prediction abilities for number of days to budding and curd width are similar to those for flowering time (0.70) and grain yield (0.50) in rapeseed (B. napus)  and are close to SNPs linked to flowering time QTL in the GWAS. This indicates that selection for different flowering time or adaption to different areas contributed to the genetic population structure . However, imputation may improve the power of GWAS because in the imputed data only we identified one additional QTL for flowering time on chromosome O6, which was also found by P-values in GWAS may be too conservative and result in a high proportion of false negatives , and Q is the FDR  with the imputed data than with unimputed data (14; Figure S3 in egatives . Therefo the FDR . We used debated . Thus, aThe difference in the number of significant associations between the unimputed and imputed data sets is also influenced by the imputation method. The fastPHASE method is not well suited for GBS data, because a parameter vector of allele frequencies has to be estimated for each SNP. As fastPHASE performs best with SNPs genotyped in many individuals , the higThe imputation of missing markers slightly improved prediction ability for most traits, consistent with previous studies that revealed only minor advantages of imputation, particularly in self-fertilizing crops with a slow LD decay (B. oleracea (In summary, there was only a minor advantage of imputation for GWAS and genomic prediction with our sample. However, the rapid development of genome sequencing technologies and rapidly decreasing costs will alleviate the problem of missing data for genomic prediction, as genome resequencing will uncover most genetic variation, in particular for crops with small genome sizes such as ex situ conserved gene bank accessions. Our sample was randomly selected and represents a broad genetic and geographic diversity. We achieved reasonable genomic prediction abilities, although genetic clustering inflates prediction ability if the cluster structure is correlated with trait distribution. For this reason, genotyping whole collections of gene bank accessions and the phenotyping of a sufficiently large subset allows the prediction of relevant phenotypic traits in the whole collection and the subsequent selection of accessions for further use as genetic resources. This will contribute to an efficient description and utilization of ex situ conserved germplasm resources.Breeding populations of cauliflower are characterized by a low genetic diversity (www.g3journal.org/lookup/suppl/doi:10.1534/g3.117.300199/-/DC1.Supplemental material is available online at Click here for additional data file.Click here for additional data file.


Tumor necrosis factor alpha-induced protein 3 (TNFAIP3) is an anti-inflammatory protein implicated in multiple autoimmune and rheumatologic conditions. We hypothesized that lower levels of TNFAIP3 contributes to excessive cytokine production in response to inflammatory stimuli in axial spondyloarthritis (AxSpA). A further aim was to determine the immune signaling and genetic variation regulating TNFAIP3 expression in individual subjects.TNFAIP3 gene and other auto-inflammation-implicated genes were sequenced by next-generation sequencing and variants identified.Blood-derived macrophages from 50 AxSpA subjects and 30 healthy controls were assessed for TNFAIP3 expression. Cell lysates were also analyzed for NF-κB, mitogen-activated protein (MAP) kinase and STAT3 phosphorylation, and supernatants for cytokine production. Coding and regulatory regions in the p = 0.0085). Spondyloarthritis subject macrophages correspondingly produced more TNF-α in response to lipopolysaccharide . Subjects with the highest TNFAIP3 produced significantly less TNF-α in response to LPS (p = 0.0023). Within AxSpA subjects, those on TNF blockers or with shorter duration of disease expressed lower levels of TNFAIP3 . TNFAIP3 expression correlated positively with phosphorylated IκBα, phosphorylated MAP kinases, and unstimulated phosphorylated STAT3, but negatively with LPS or TNF-α-stimulated fold induction of phosphorylated STAT3. Further, subjects with specific groups of variants within TNFAIP3 displayed differences in TNFAIP3 (p = 0.03–0.004). Nominal pQTL associations with genetic variants outside TNFAIP3 were identified.Mean TNFAIP3 was significantly lower in spondyloarthritis macrophages than controls (Our results suggest that both immune functional and genetic variations contribute to the regulation of TNFAIP3 levels in individual subjects. Decreased expression of TNFAIP3 in AxSpA macrophages correlated with increased LPS-induced TNF-α, and thus, TNFAIP3 dysregulation may be a contributor to excessive inflammatory responses in spondyloarthritis subjects. TNFAIP3 gene have been identified in genome-wide association studies (GWAS) in systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), type I diabetes, Crohn’s disease, celiac disease, primary biliary cirrhosis, systemic sclerosis, and psoriasis  is an anti-inflammatory ubiquitin modifying enzyme implicated in multiple autoimmune and autoinflammatory disorders . Diseasesoriasis , 2. More0 is an aTNFAIP3 encodes an 89.6-kDa cytosolic protein with a deubiquitinating OTU (ovarian tumor) domain, and seven zinc-finger domains containing ubiquitin-binding and E3 ubiquitin-ligating activities that modulate multiple proteins within inflammatory signaling cascades. The ubiquitinating region of TNFAIP3 attaches K48-linked polyubiquitin, thus targeting molecules such as receptor-interacting protein (RIP-1) or the E2 ubiquitin-conjugating protein UBCH5C for proteasome destruction. TNFAIP3 also removes K63-linked polyubiquitin chains required for the activity of molecules, such as RIP-1, TNFR-associated factor 6, and Tank-binding kinase (TBK1) upstream of NF-κB activation. TNFAIP3 thus antagonizes signaling downstream of pattern recognition receptors (PRRs) such as toll-like receptors (TLRs) and NOD-like receptors, as well as cytokine receptors . Human monocytes were purified using the human monocyte isolation kit II (Miltenyi Biotec) according to the manufacturer’s instructions. Purified monocytes were plated in RPMI 1.5–2 h and then non-adherent cells removed. Adherent cells were subsequently incubated in complete RPMI 1640 medium (RPMI 1640 with 10% FBS (HyClone), 4 mM rophages .Cells were lysed in Bio-Rad lysis buffer, sonicated 30 s, and stored at −80°C until analysis. TNFAIP3 and CARD9 levels were quantified by ELISA (MyBioSource) with normalization to lysate protein concentration as determined by bicinchoninic assay (Thermo Scientific).On day 5 post isolation, cells were stimulated with 10 ng/mL LPS, 100 nM PGE2, or both for 24 h. Supernatants were assayed for IL-23 and TNF-α concentration by ELISA (eBioscience) and IL-6, IL-8, and IL-12p70 by Luminex (eBioscience). After supernatants were removed, the cells were lysed in 100 µL type lysis buffer for determination of cellular protein concentration as a cell number surrogate.Macrophages were stimulated with 10 ng/mL LPS, 1 ng/mL TNF-α, 100 µg/mL curdlan, or 200 ng/mL IL-23 for 30 min and then cells were lysed in 1× lysis buffer (Bio-Rad luminex kit). pATF2, pJNK, p38, pNF-κB p65, pERK, and pSTAT3 were analyzed using a multiplex luminex assay (Bio-rad Pro Phosphoprotein magnetic 6-plex) and pIκBα was assayed using the MILLIPLEX MAP Phospho IκBα (Ser32) Magnetic Bead MAPmate (Millipore). Phosphoproteins were detected on a Luminex 100 system machine. Cytokine and cell signaling results were all normalized to cellular protein concentration. One AxSpA biochemistry sample had much lower protein amounts (<10% on average compared to other samples) and was discarded from the correlational analysis of signaling events.W test was used to test protein expression data for normality. Significant departures from a Gaussian model for the protein-adjusted TNFAIP3 ratios were treated by normalizing via a Box–Cox transformation, better enabling the use of linear regression approaches. Comparisons between mean protein expression levels in dichotomous outcomes were made using a T-statistic and 1 M permutations to obtain a p-value. To test correlation patterns for continuous outcomes, Spearman’s rs correlation coefficients were calculated and corresponding p-values testing departure from rs = 0 are presented. To test for clustering patterns in TNFAIP3 protein levels across AxSpA samples in an exploratory fashion, both K-means (varying k) and UPGMA clustering methods were applied to examine the data visually for separation between AxSpA cases. Experiment-wise significance levels were determined using a Bonferroni approach.A Shapiro–Wilk p < 1E−05 were considered potentially problematic and excluded from analyses of the endpoints. To test the null hypothesis of independence between genotypes at each variant and case/control status, a logistic regression model was constructed under additivity of genetic effects, adjusted for age and sex covariates. HWE, and logistic and linear regression analyses were performed in the R programming language using existing statistical routines. Haplotype analyses for variants segregating at the TNFAIP3 gene region utilized a Gibbs sampling algorithm to estimate phase. Pairwise linkage disequilibrium calculations were performed using the NCI LDlink tool and comparisons were made to the CEU and GRB HapMap sample sets using r2. To test for differences in the distributions of variants in dichotomous outcomes, a Kolmogorov–Smirnov test was used. Experiment-wise significance levels were determined using a Bonferroni approach.For the purposes of quality control, an exact test of Hardy–Weinberg equilibrium (HWE) was applied to genotype data at each variant and performed separately for cases and controls. Variants exhibiting HWE p-values. To verify the p-values generated for the top 30 findings, a permutation routine was run to obtain permuted p-values under the same model.To test the null hypothesis of independence between TNFAIP3/total protein values and genetic variants, a linear regression model was used, also adjusted for age and sex. These pQTL analyses were performed separately for cases, controls, and the combined group of all individuals. For computational efficiency, both the logistic regression and linear regression models used asymptotic null distributions for the calculation of T-statistic was calculated for each permuted iteration and compared to the T-statistic calculated for the observed data. A permuted p-value was obtained by calculating the frequency of permuted runs that exceeded the observed T-statistic. Given that the permuted p-value is binomially distributed, one million iterations was deemed sufficient in producing highly stable p-value estimates for these data given that the 95% confidence interval for a p-value of 0.0001 is , for a p-value of 0.001 is , and for a p-value of 0.01 is . For the test of TNFAIP3/protein levels vs. AxSpA/Control endpoint, we also calculated the Mann–Whitney U test for the purposes of comparison with the permuted results.The permutation routine was written in the XLISP-STAT programming language to test the null hypothesis of exchangeability between case/control statuses in analyses of dichotomous outcomes. In each permutation, the case/control status variable was randomized by assignment to a uniformly distributed random variable and sorted. A Following the ASAS classification criteria introduced in 2009, “ankylosing spondylitis” was subsumed under the classification rubric of “axial spondyloarthritis” . This brWe focused on blood-derived macrophages for multiple reasons: macrophages are abundant in histologic sections from inflamed enthesitis and sacroiliac joints in AS , 40. In p = 0.0085; Mann–Whitney U test p = 0.019) for control and median AxSpA TNFAIP3 was 77.8 vs. 113 in controls. By contrast, in the same lysates, CARD9 expression did not differ significantly and exhibited similar distributions  and disease duration . Subjects on TNF blockers or those with disease onset after the median of age 26 almost exclusively had lower TNFAIP3 levels. There were no significant differences in TNFAIP3 levels between those on antibody type anti-TNF medication  and those taking TNF soluble receptors such as etanercept . Thus, analysis by TNF blocker, age of onset, and TNFAIP3 levels revealed at least three distinct subgroups within “axial spondyloarthritis.”Although there was overlap between controls and AxSpA patients, over 40% of the AxSpA patients expressed TNFAIP3 below the control 25th percentile and none above the control 75th percentile. Thus there was a markedly skewed distribution in AxSpA subjects, with over representation of low TNFAIP3 values and no patients with elevated levels. Mean expression for AxSpA TNFAIP3 was 138.0  vs. 255.4   kinase activation , 43. ActTNFAIP3 gene itself in the cultured macrophages. Regarding events downstream of TNFAIP3, we observed correlations with increased PGE2-induced IL-6, but decreased LPS-stimulated TNF-α  to produce greater TNF-α in response to LPS as compared to those not on TNF blockers . TNFAIP3 levels also negatively correlated with IL-12p70 production (p < 2 × 10−5), though IL-12 was only detected at low levels . The correlation between TNFAIP3 and pNF-κB/other cytokine induction was weaker (Rho between −0.3 and −0.4) but generally in the negative direction. For instance, the correlation between TNFAIP3 and LPS-induced fold increase in phospho-p65 (NF-κB) was −0.36 (p = 0.001), and TNFAIP3 and LPS-induced fold increase in IL-6 was −0.33 (p = 0.003). The negative correlation between TNFAIP3 and LPS-induced cytokine production, are consistent with known suppression of LPS and TNF-α signaling by TNFAIP3 . The correlations with STAT3 were more complex, in that TNFAIP3 correlated with elevated pSTAT3 under certain conditions [e.g., baseline NT  rarely occurred in subjects with low TNFAIP3. These intronic variants displayed high linkage disequilibrium. Two tightly linked variants, rs719149 and rs719150, associated with lower levels of TNFAIP3 in AxSpA cases only but not controls (p = 0.016 for SpA status). Variants rs5029937, rs5029939, and F127C have previously been reported to associate with RA and SLE and showed a trend toward lower levels in this study (T-test (1 M iterations) yielded a p-value of 0.641 and Kolmogorov–Smirnov test of distributional differences gave a p-value of 0.09 (no significant difference).Within is study , 46. HowTNFAIP3 variants present in our samples, we noted interesting patterns .Upon examination of the linkage disequilibrium structure among individual TNFAIP3, a pQTL analysis was performed on the other autoimmunity/spondyloarthropathy implicated genes selected for NGS  which resides approximately 29 and 22 kbp 3′ of PTPN2 isoform 1 and isoform 2, respectively. Several additional variants in this targeted region, such as the PTPN2 intronic variants rs592390, rs2542162, and rs12971201, also exhibited nominally significant correlation with normalized TNFAIP3 levels  at rs78943928, the minor allele , was positively correlated with increased normalized TNFAIP3 levels in AxSpA subjects. The allele frequency was consistent with that observed in CEU samples (freq G = 0.058) and the phase 3 1000 Genomes European sample set (freq G = 0.0726). Neither AxSpA samples nor controls exhibited a significant departure from HWE.To assess associations between TNFAIP3 protein levels and genetic variants outside via the pro-inflammatory cellular stress response known as the unfolded protein response, but not all spondyloarthritis patients are HLA-B27 positive . However, macrophages from subjects on TNF blockers tended to produce higher levels of TNF-α, though numbers were not sufficient to detect a significant difference. Similarly, another study by Gibellini et al. reported that PBMC from psoriatic responders to adalimumab and etanercept produced greater levels of TNF-α in vitro  regulation. GWAS have identified  Chinese , 57. Thunaling 3 . Yet mye17 genes . Thus, e17 genes .TNFAIP3 gene at the individual level in groups of AxSpA and controls. Our analysis of TNFAIP3 indicated that most of the variation lies in the intronic regions of TNFAIP3 rather than promoter or coding regions, with similar distributions between cases and controls. In particular, introns 1 and 2 seem most heavily inundated with variation. At first glance, one might think introns would be less subject to purifying selection given the severity of phenotype in knockout mice. However, these two introns appear to be locations of enhancer histone marks and transcription factor consensus-binding sites. Thus, variation in this region might be expected to provide more subtle differences in gene regulation than, for instance, a promoter variant.In this study, we provided a detailed snapshot of genetic variation within the TNFAIP3 variants found in our population have been reported in other diseases: rs5029937 and F127C with RA and SLE, rs5029939 with SLE and systemic sclerosis, and F127C and rs610604 with psoriasis , including a SNP not identified by other GWAS.In summary, although much has been learned about how TNFAIP3 shapes immune responses in mice, and GWAS have picked up multiple TNFAIP3 SNP disease associations, very little is known regarding how TNFAIP3 is regulated or how it shapes immune function within human subjects. In particular, it has been unclear how individual SNPs relate to each other or to TNFAIP3 protein levels. In this study, we sought to bring together genetics and immune function in a synthetic approach to elucidate TNFAIP3 regulation in AxSpA. Herein, we found decreased levels of the anti-inflammatory protein TNFAIP3 in M-CSF-derived macrophages from subjects with AxSpA, constituting a potential contributor to cytokine dysregulation in this arthritic disease. More specifically, based on functional correlations, the lower levels of TNFAIP3 in AxSpA subjects may predispose toward increased fold induction of pSTAT3, p65 NF-κB, and TNF-α in response to PRR agonists such as LPS. Our novel open-ended approach to variant discovery Although GWAS have pointed to associations between genetic variants and disease, the genetic architecture within individuals that conspires to produce disease remains mysterious. Along these lines, we are only beginning to scratch the surface of how these genetic variants orchestrate subtle changes in immune function within individuals. This type of knowledge may only come about through detailed functional and genetic analysis at the individual subject level, as performed here, but in large numbers of subjects. Analyses of individual genes will also have to be integrated into more global genetic, epigenetic, and functional networks to provide insight into net immune function.The study was carried out in accordance with the ethical principles outlined in the Belmont report and Common Rule, with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the Marshfield Clinic Institutional Review Board.All authors listed have read the manuscript except XL. She has returned to China without leaving a forwarding email address and is not reachable. YL—conducting experiments and manuscript writing; ZY and XL—data analysis; JA—data analysis and manuscript writing; MK—conducting experiments; DD—experimental design, data acquisition, and conducting experiments; MB—conducting experiments; DW and VB—data acquisition; LI—conducting experiments; SS and JS—funding, experimental design, data analysis, and manuscript writing.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


By testing marginal epistatic effects, we can identify candidate variants that are involved in epistasis without the need to identify the exact partners with which the variants interact, thus potentially alleviating much of the statistical and computational burden associated with standard epistatic mapping procedures. Our method is based on a variance component model, and relies on a recently developed variance component estimation method for efficient parameter inference and p-value computation. We refer to our method as the “MArginal ePIstasis Test”, or MAPIT. With simulations, we show how MAPIT can be used to estimate and test marginal epistatic effects, produce calibrated test statistics under the null, and facilitate the detection of pairwise epistatic interactions. We further illustrate the benefits of MAPIT in a QTL mapping study by analyzing the gene expression data of over 400 individuals from the GEUVADIS consortium.Epistasis, commonly defined as the interaction between multiple genes, is an important genetic component underlying phenotypic variation. Many statistical methods have been developed to model and identify epistatic interactions between genetic variants. However, because of the large combinatorial search space of interactions, most epistasis mapping methods face enormous computational challenges and often suffer from low statistical power due to multiple test correction. Here, we present a novel, alternative strategy for mapping epistasis: instead of directly identifying individual pairwise or higher-order interactions, we focus on mapping variants that have non-zero  marginal epistatic effect—the combined pairwise interaction effects between a given variant and all other variants. By testing for marginal epistatic effects, we can identify variants that are involved in epistasis without the need of explicitly searching for interactions. Our method also relies on a recently developed variance component estimation method for efficient and robust parameter inference, and accurate p-value computation. We illustrate the benefits of our method using simulations and real data applications.Epistasis is an important genetic component that underlies phenotypic variation and is also a key mechanism that accounts for missing heritability. Identifying epistatic interactions in genetic association studies can help us better understand the genetic architecture of complex traits and diseases. However, the ability to identify epistatic interactions in practice faces important statistical and computational challenges. Standard statistical methods scan through all-pairs  of interactions, and the large number of interaction combinations results in slow computation time and low statistical power. We propose an alternative mapping strategy and a new variance component method for identifying epistasis. Our method examines one variant at a time, and estimates and tests its  Genetic mapping studies, in the form of genome-wide association studies (GWASs)  and molep(p − 1)/2 pairwise combinations for p variants), these methods often suffer from heavy computational burden and low statistical power. Despite various efficient computational implementations  with 1n denoting an n-vector of ones. Thus, Mk is a variant specific projection matrix onto both the null space of the intercept and the corresponding genotypic vector xk. By multiplying Mk, we obtain the following simplified modeling specificationk that is considered.To estimate the variance components with MQS, we first multiply a projection matrix δ =  to denote the variance components. Next, we use the notation i, j, l ∈ {1, 2, 3} to represent the corresponding variance component or covariance matrix. Given estimates Sk is a 3 × 3 matrix in which i, j, l = 1, 2, 3.To simplify notation, we use MAPIT provides two options to compute p-values. The first option is approximate, and is based on a normal test that only requires the variance component estimate y* is assumed to follow a multivariate normal distribution under the modeling assumptions. In particular, 1, …, λn) are the corresponding eigenvalues of the matrixω2, τ2) under the null hypothesis. We can then use the Davies method . In the current study, with i = 1, …, 3. We specifically calculate the pPVEs corresponding to the random effect variance terms -vc argument within the GEMMA software. We also use the standard output (i.e. point estimate and standard error) to conduct an asymptotic normal test to assess the power of this approach.We apply the first procedure to simulations, and the second procedure to both the simulations and real data analyses. In either case, our goal is to estimate the influence of the total contribution across pairwise epistatic effects have on the phenotype. We quantify these contributions by examining the proportion of phenotypic variance explained (pPVE) using the following equation defined in , 77 for https://github.com/lorinanthony/MAPIT. We use the CompQuadForm R package to compute p-values from the Davies method. The Davies method can sometimes yield a p-value equal exactly to 0 when the true p-value is extremely small [P ≈ 0. If this is of concern, one can compute the p-values for MAPIT using Kuonen’s saddlepoint method [The software implementing MAPIT is freely available at ly small . In thist method , 86 or St method .http://www.wtccc.org.uk/), which consists of 2,938 individuals with 458,868 SNPs following the quality control steps described in detail in a previous study [In the present study, we utilize two real data sets: one from the Wellcome Trust Case Control Consortium (WTCCC), and the other from the GEUVADIS Consortium Project. For the first, we specifically used the control samples from the WTCCC 1 study  (http://us study .http://www.geuvadis.org) which contains gene expression measurements for 462 individuals from five different populations: CEPH (CEU), Finns (FIN), British (GBR), Toscani (TSI) and Yoruba (YRI). Following previous studies [cis-SNPs that are located within either 100 kb upstream of the transcription start site (TSS) or 100 kb downstream of the transcription end site (TES), resulting in a total of 2,735,891 unique SNP-gene combinations with an average of 175 cis-SNPs per gene.For the second, we obtained the GEUVADIS data   a standard model with y = βX + ε, and (ii) a population stratification model with y = Zu + βX + ε, where X is the genotype matrix, Z contains covariates representing population structure, and u are fixed effects. Under the first model, we simulate both the additive effect sizes of each causal SNP and the random noise term from a standard normal distribution, and then we scale the two terms further to ensure a narrow-sense heritability of 60%. In the second model, we introduce population stratification effects into the simulations by allowing the top 5 and 10 genotype principal components (PCs) to make up 10% of the overall phenotypic variance (i.e. through the Zu term). These population stratification effect sizes are also drawn from a standard normal distribution. Note that, for both settings, the idea of the null model holds because there are no interaction effects, and MAPIT solely searches for significant marginal epistatic effects that are a summation of pairwise interactions. Furthermore, in the cases in which simulations were conducted under model (ii), the genotype PCs were not included while running MAPIT, and no other preprocessing normalization procedures were carried out to account for the added population structure. All evaluations of calibration and type 1 error are strictly based on the linear mixed model presented in In order to investigate the type I error control, we first subsample from the genotypes for n. α = 0.05, 0.01, and 0.001, respectively, for simulations under model (i). Again, similar tables for data simulated under mode (ii) can be found in Supporting Information  [nd chromosome of all control cases from the WTCCC 1 study X  to simulate continuous phenotypes that mirror genetic architectures affected by a combination of additive and pairwise epistatic effects. Specifically, we randomly choose 1,000 causal SNPs to directly affect the phenotype and classify the causal variants into three groups: (1) a small set of interaction SNPs, (2) a larger set of interaction SNPs, and (3) a large set of additive SNPs. In the simulations carried out in this study, SNPs interact between sets, so that SNPs in the first group interact with SNPs in the second group, but do not interact with variants in their own group (the same rule applies to the second group). One may view the SNPs in the first set as the “hubs” in an interaction map. We are reminded that interaction (epistatic) effects are different from additive effects. All causal SNPs in both the first and second groups have additive effects and are involved in pairwise interactions, while causal SNPs in the third set only have additive effects.To test the power of MAPIT, we again consider simulation designs similar to those proposed by previous epistatic analysis studies . First, 2 = 0.6) , 88, 93.β ∼ MVN. Next, we create a separate matrix W which holds the pairwise interactions of all the causal SNPs between groups 1 and 2. These SNPs have effect sizes also drawn as α ∼ MVN. We scale both the additive and pairwise genetic effects so that collectively they explain a fixed proportion of genetic variance. Namely, the additive effects make up ρ%, while the pairwise interactions make up the remaining (1 − ρ)%. Once we obtain the final effect sizes for all causal SNPs, we draw errors to achieve the target H2. The phenotypes are then created by summing all effects using two simulation models: (i) y = Xβ + Wα + ε and (ii) y = Zu + Xβ + Wα + ε, where Zu again represents population stratification. In the latter model, population stratification effects are introduced into the simulations by allowing the top 5 and 10 genotype principal components (PCs) Z to make up 10% of the overall variation in the trait. The effect sizes for these stratification effects are also drawn as u ∼ MVN.The additive effect sizes of all causal SNPs again come from a standard normal distribution or We consider a few scenarios that depend on two parameters:ρ), which measures the portion of H2 that is contributed by the interaction effects of the first and second groups of causal SNPs. Specifically, the phenotypic variance explained (PVE) by the additive genetic effects is said to be V(βX) = ρH2, while the PVE of the pairwise epistatic genetic effects is given as V(Wα) = (1 − ρ)H2., 10/20/970 (scenario II), 10/50/940 (scenario III), and 10/100/890 (scenario IV). Note that scenarios III and IV assume a larger number of interactions than scenario I and II do, and are thus likely to be closer to reality. The particular case where ρ = 0.5, the additive and epistatic effects are assumed to equally contribute to the broad-sense heritability of the simulated phenotypes. The alternative case in which ρ = 0.8 is a case where the PVE of the simulated complex traits are dominated by additive effects. We analyze 100 different simulated datasets for each value of ρ, across each of the four scenarios. All of the results described in this section are based on the cases in which phenotypes were simulated under model (i) with ρ = 0.8, as this case is a more realistic setting for human traits where epistatic effects only make up a small percentage of the broad-sense heritability. The results for ρ = 0.5 can be found in Supporting Information /p1 = 1.2% of the true interaction PVE since in every scenario p1 = 10. In these situations, the cumulative PVE of these markers is great and MAPIT’s power is large for all four scenarios (approximately 30% power). Note that this power is similar to MAPIT’s ability to detect the group 2 causal markers under Scenario I (i.e. p2 = 10), where each epistatic variant is also expected to explain V(Wα)/p2 = 1.2% of the interaction PVE. Alternatively, MAPIT exhibits half of the power when detecting the group 2 SNPs in the case of Scenario II (i.e. p2 = 20), as each SNP explains only V(Wα)/p2 = 0.6% of the PVE (approximately 15% power). In addition, MAPIT’s power to identify group 1 variants is independent of the number of variants in group 2 (i.e. p2), suggesting that MAPIT’s power depends on the total interaction effects, rather than individual pairwise effects or the number of interacting pairs. The results based on the genome-wide significance threshold are similar and can be found in Supporting Information αij+ε and test H0: αij = 0 for every marker combination of i and j in turn [xi ∘ xj denotes element-wise multiplication between genotypes i and j, and αij represents the effect size of their interaction. Note that the exhaustive search procedure is computationally feasible within PLINK because we only have p ≈ 6,000 markers in the simulations.Here, we compare the performance of MAPIT with a standard exhaustive search procedure that examines all pairwise interactions to explicitly identify the exact pairs of variants involved in epistatic interactions , 56. Spe in turn . KeepingIt is helpful to point out here that the purpose of this comparison is to depict MAPIT as a viable alternative for the exhaustive search procedure. We will show that MAPIT not only can perform a significance test to detect variants involved in epistasis, but also can be used to obtain a prioritized set of variants that are further used to identify pairwise interactions. Our simulation comparisons are thus targeted to illustrate how MAPIT can be used in these two tasks, and how its performance differs from the exhaustive search procedure in different scenarios.αij, while the power of MAPIT, as we have shown in the previous section, depends on the marginal epistatic effects—the summation of interaction effects. Therefore, we would expect MAPIT and the exhaustive search method to be advantageous in different situations . In particular, we would expect the exhaustive search method to be more powerful in scenario I (and II) where each individual interaction effect is large, and MAPIT to be more powerful in scenario (III and) IV where each individual interaction effect is small but the marginal epistatic effect remains large. Furthermore, MAPIT can naturally account for population stratification via the included genetic relatedness matrix, while the exhaustive search method requires including genotype PCs as covariates to control for such confounding effects. Therefore, we would also expect MAPIT to be robustly more powerful when there are confounding population stratification effects that are not explicitly taken into account. To validate our expectations, we again generate continuous outcomes using the same two previously described simulation schemes: (i) y = Xβ + Wα + ε and (ii) y = Zu + Xβ + Wα + ε. Once again, all results described in the main text are based on model (i) with ρ = 0.8, while all other results can be found in Supporting Information  with the rate at which true variants are identified for each model (TPR). ρ) is small , its power quickly decays in the more polygenic scenario where there is a large number of interactions, each with a small effect size (e.g. scenarios III and IV). MAPIT is able to perform well in the more realistic polygenic scenarios (III and IV) by modeling the marginal epistatic effects of each variant, allowing the detection of epistatic variants not to be dependent on the individual pairwise interaction effect size. Importantly, MAPIT remains powerful even in the presence of population stratification, as it can effectively control for population stratification with the included genetic relatedness matrix. In contrast, the exhaustive search approach in PLINK does not explicitly control for population stratification, and can suffer from power loss in the presence of stratification especially when the total epistatic contribution  epistatic interactions. In addition to comparing MAPIT with the exhaustive search method from PLINK, we also consider another common approach for identifying epistatic pairs—a two-step filtering association mapping procedure , 55, 58.2 interactions to assess pairwise power.In this set of simulations, we utilize the same subset of real genotypes used for the marginal epistatic simulations in the last section , and aga2 = 0.6. As in previous sections, all results described in this section are based on model (i) with ρ = 0.8, and all other results can be found in Supporting Information (see ρ = 0.8), using MAPIT as the initial filtration procedure (as opposed to the single-SNP additive linear model) provides more power for finding exact causal epistatic pairs. This improvement comes from the fact that MAPIT allows the ranking of variants to be based on their marginal epistatic effects, rather than their marginal additive effects. Therefore, the set of SNPs identified by MAPIT in the first step already contains variants that capture epistatic effects, thus resulting in higher power in the second step to identify epistatic interaction pairs. In addition, similar to the simulation comparison in the previous subsection, MAPIT and the exhaustive search procedure are advantageous in different settings: the exhaustive search procedure is again more powerful in the sparse setting where each individual pairwise interaction is large (i.e. scenarios I and II) while MAPIT gains an advantage in the polygenic setting where there a large number of interactions each with small effects (i.e. scenarios III and IV). Again, in the presence of population stratification, MAPIT remains powerful while the exhaustive search procedure suffers from substantial power loss  association mapping study for gene expression levels (i.e. eQTL study). Often times, eQTL studies deal with SNP effect sizes (on gene expression levels) that are orders of magnitude larger than that (on organism-level traits) from GWASs –5, thus cis-acting QTL, which are more readily identifiable in small sample sizes than trans-QTL [The specific data set that we consider in this section features 462 individuals from five different populations whose gene expression data was collected by the GEUVADIS consortium . In orderans-QTL . OverallKcis, where for the expression of each gene Kcis was computed using only the corresponding cis-SNPs. While using Kcis, MAPIT tests the summed epistatic effects between a given cis-SNP and all other cis-SNPs within the same gene. The primary reason that we present the main results based on Kcis is to allow for a fair comparison with the exhaustive search method (details below)—which, due to computational reasons, can only be applied to examine all cis-pairs. To assess whether or not these initial results are sensitive to the choice of covariance matrix, we also implement MAPIT using a genetic relatedness matrix Ktrans, where for the expression of each gene Ktrans was computed using only the corresponding trans-SNPs located outside the cis-window . Using MAPIT with Ktrans assesses the summed epistatic effects between a given cis-SNP and all other trans-SNPs. Lastly, we consider the implementation of MAPIT with a genome-wide genetic relatedness matrix KGW, where KGW was computed using all SNPs in the study . Here, using MAPIT with KGW tests the summed epistatic effects between a given cis-SNP and all SNPs genome-wide. Intuitively, using Kcis will be more powerful than using either Ktrans or KGW if epistatic interactions are more likely to happen between cis-SNP pairs, rather than between cis-SNP and genome-wide SNP pairs—however, less powerful otherwise. In addition to these three sets of analyses, to guard against any potential residual population stratification, we also removed the effects of the top 10 genotype principal components and used the residual expression data together with a KPop computed using the genome-wide residual genotype data for a further analysis. The purpose of the additional analyses is to highlight the robustness of the results found using MAPIT.To remove population stratification and other confounding effects, we have removed top factors from the gene expression matrix and normalized the gene expression data within each of the five populations separately—all before performing a final joint normalization  (detailsmepiQTL), the QTL detected by GEMMA as the more conventional expression QTL (eQTL), and the QTL found by PLINK as epistatic QTL (epiQTL). Similarly, we will refer to genes that have at least one mepiQTL as mepiGenes, genes that have at least one eQTL as eGenes, and genes that have at least one epiQTL as epiGenes.To contrast MAPIT’s marginal association findings, we also directly compare results from the single-SNP additive model via GEMMA and the fully exhaustive search model in PLINK. From this point forward, we will refer to QTL identified by MAPIT as marginally epistatic QTL . While using the genetic relatedness matrix Kcis, MAPIT identified a total of 3,434 mepiQTL across 228 different mepiGenes that satisfied this marginal significance rule. Additionally, while using the covariance matrix Ktrans, MAPIT detected a total of 2,160 across 130 mepiGenes. Similarly, MAPIT also identified a total of 2,160 mepiQTL across 130 mepiGenes when using KGW , and this number changed to 3,056 mepiQTL across 184 different mepiGenes after correcting for residual population stratification and using KPop. GEMMA, on the other hand, found 55,645 significant eQTL across 1,417 different eGenes, and no significant eQTL or eGenes after correction for potential residual population stratification. Note that the former number of eGenes as detected by GEMMA is similar to that from the original research [In this analysis, a significant marginal association for a particular SNP identified by MAPIT or GEMMA was determined by using a gene specific Bonferroni-corrected significance p-value threshold Kcis, is presented in 10 p-values presented in Supporting Information  and the gene transcription end site (TES), is depicted in The histogram of the MAPIT p-values for all SNP-gene combinations, while using tion see . Both oftion see  Figs. S6P = 1.828 × 10−8). Figures depicting the genome-wide epistatic scans of the other chromosomes can be found in Supporting Information /2), where qi is the number of top variants (among the top v SNPs) located in the cis-window of gene i. Once again, we applied the fully exhaustive search model in PLINK as a baseline power comparison, in which we examined all of the cis-SNP pairs for each gene. Note that for PLINK we only consider cis-SNP combinations as it was not computationally feasible to perform an absolute complete exhaustive search . K matrices) and GEMMA when searching between the top v = {1000, 2500, 5000, 7500, 10000, 15000, 20000} marginally associated variants. Altogether, the exhaustive search method in PLINK identified 7,361 significant epistatic pairs before the correction of residual confounding effects, and 8,643 significant pairwise interactions after the correction. These benchmarks are represented by the dotted lines in In order to search for exact epistatic pairs among cis-SNPs through the filtering approaches, we took all significant mepiQTL and eQTL, and analyzed the pairwise interactions between them. This comparison allows us to assess the power of MAPIT and GEMMA as filtering approaches within the context of real data. Similar to what was done in the simulation studies, both filtering procedures were carried out by first ranking SNPs by either their mepiQTL or eQTL p-values, and then searching for associated epistatic pairs between the top C16orf88, the SNP rs11645910 (MAPIT P ≈ 0) is a member of many of the top significant epistatic pairs. We also note that 36 of the 228 epistatic associated genes identified by MAPIT with Kcis have been verified in previous analyses on a different RNAseq data set from the TwinsUK cohort [Ktrans and KGW, and 35 of the 184 mepiGenes discovered by MAPIT with KPop after correction for residual confounders, have been verified in the same study.As demonstrated in the numerical experiments, using MAPIT as the initial filtration procedure (as opposed to the single-SNP additive model) efficiently provides more power to finding significant epistatic pairs. Moreover, considering interactions amongst just the top 2,500 mepiQTL (in any of the considered settings for MAPIT) almost results in the same total number of significant epistatic pairs that is to be discovered by the fully exhaustive search model from PLINK. As previously shown, these results may be due to MAPIT’s ability to marginally detect the “hub” SNPs of interactions. For example, under the expression for gene K cohort . SimilarC16orf88, pairwise epistatic effects are estimated to explain approximately 5% of the PVE, while additive effects are estimated to only account for 3 × 10−3%. In fact, the pairwise order component actually explains a larger proportion of phenotypic variance than the linear component in the expression of 7,704 out of 15,607 genes.In order to better explain why MAPIT was able to identify significant epistatic pairs in this study, we refer back to the variance component modeling approach , 83, 84 Finally, we also want to point out one important caveat for mapping epistasis in real data: in the analyses of genetic mapping studies, apparent epistasis inferred by any epistatic mapping methods can sometimes be explained by same-locus additive effects . This meWe have presented MAPIT, a novel method and strategy for detecting variants that are involved in epistasis in genetic mapping studies. For each variant in turn, MAPIT estimates and tests its marginal epistatic effect—the combined epistatic effect between the examined variant and all other variants. By modeling and inferring the marginal epistatic effects, MAPIT can identify variants that exhibit non-zero epistatic interactions with any other variant without the need to identify the specific marker combinations that drive the epistatic association. Therefore, MAPIT represents an attractive alternative to standard methods –56, 63 fIn the present study, we have focused on estimating and testing marginal epistatic effects in the presence of pairwise interactions with MAPIT. MAPIT can also be easily extended to detect variants that are involved in higher-order interactions. Specifically, in the presence of higher-order interactions, we can introduce extra random effects terms to represent the combined higher-order interaction effects between the examined variant and all other variants—this would simply mean adding an extra random effects term for each extra higher-order of interactions. Under the normality assumption of the interaction effect sizes, the introduced random effects terms would all follow multivariate normal distributions, with the covariance matrices determined as a function of the Hadamard product of the additive genetic relatedness matrix , 84, 97.We have focused on mapping epistasis for quantitative traits. For case-control studies, one may be tempted to follow previous approximate approaches of treating binary phenotypes as continuous traits and apply MAPIT directly , 98. Howa priori. Alternatively, we can use the recently developed hybrid effect size prior that has been shown to work well under a variety of effect size distributions [In its current form, we have focused on demonstrating MAPIT with a variance component model. The variance component model in MAPIT effectively assumes that the interaction effect between the examined variant and every other variant follows a normal distribution. This normality assumption and the resulting variance component model have been widely used in many areas of genetics. For example, variance component models are used in rare variant tests to combine the additive effects of multiple rare variants to improve association mapping power , 65. Simibutions . DiffereWe have only compared MAPIT with two commonly used epistatic mapping methods that include an exhaustive search method and an additive effect prioritization method. There are many other novel methods that have been developed recently , 60–62. There are many other potential extensions of MAPIT. We have only focused on analyzing one phenotype at a time in this study. However, it has been extensively shown that modeling multiple phenotypes can often dramatically increase power , 74. Thead hoc epistasis association mapping procedure. First, we identify individual SNP associations with MAPIT. Then, we focus on the most significant associations from the first step to further test all of the pairwise interactions among them in order to identify specific epistatic interactions. Unlike the previous filtering strategies that are commonly used in epistatic mapping, our two-step procedure is unique in the sense that the SNP set identified in our first step contains SNPs that already display strong epistatic effects with other variants. Therefore, our two-step procedure outperforms alternative filtering strategies in simulations and real data applications. Nonetheless, we caution that the two-step procedure is still ad hoc in nature and could miss important epistatic associations. Therefore, exploring statistical approaches that can unify the two steps would be an interesting area for future research. Besides this main limitation, we also note that MAPIT can be computationally expensive. MAPIT requires fitting a variance component model for every SNP in turn, and fitting variance component models are known to be computationally challenging [MAPIT is not without its limitations. Perhaps the most noticeable limitation is that MAPIT cannot be used to directly identify the interaction pairs that drive individual variant association. In particular, after identifying a variant involved in epistasis, it is still unclear which variants it interacts with. Thus, despite being able to identify SNPs that are involved in epistasis, MAPIT is unable to directly identify detailed interaction pairs. However, we argue that being able to identify variants that are involved in epistasis is often an important first step towards identifying and understanding detailed epistatic associations. In addition, being able to identify SNPs involved in epistasis allows us to come up with an initial likely set of variants that are worth further exploration. Indeed, we advertise a two-step llenging , 68. In llenging —a properS1 FigThe QQ plots applying MAPIT to 100 simulated null datasets assuming sample sizes: 1,000 , 1,750 , and 2,500 . These results are based on using simulation model (ii). (A)-(C) use the top 5 genotype PCs, while (D)-(F) use the top 10 genotypes PCs. Blue dots are p-values produced by under the normal test (or z-test), while the black dots represent p-values tested using the Davies method via a mixture of chi-square distributions. The 95% confidence intervals for the null hypothesis of no association are shown in grey.(PDF)Click here for additional data file.S2 Fig2 = 0.6 and parameter ρ = 0.5, estimated with 100 replicates. Here, ρ = 0.5 was used to determine the portion of broad-sense heritability contributed by interaction effects. (A) shows the power of MAPIT to identify SNPs in each causal group under significance level α = 0.05. The lines represent 95% variability due to resampling error. (B) shows boxplots of the marginal PVE estimates for the group 1 and 2 causal SNPs from MAPIT for the four simulation scenarios. The true PVEs per causal SNP  are shown as dashed grey horizontal lines.Groups 1 and 2 causal markers are colored in light red and light blue, respectively. These figures are based on a broad-sense heritability level of H(PDF)Click here for additional data file.S3 Fig2 = 0.6 and parameters ρ = 0.5  and ρ = 0.8 , respectively. These results are estimated with 100 data replicates under simulation model (ii) with the top 5 genotype PCs. Here, ρ = {0.5, 0.8} was used to determine the portion of broad-sense heritability contributed by interaction effects. (A) and (C) show the power of MAPIT to identify SNPs in each causal group under significance level α = 0.05. The lines represent 95% variability due to resampling error. (B) and (D) show boxplots of the marginal PVE estimates for the group 1 and 2 causal SNPs from MAPIT for the four simulation scenarios. The true PVEs per causal SNP are shown as dashed grey horizontal lines. When ρ = 0.05, the true PVEs per causal SNP are: 0.03 for the group 1 SNPs; and 0.03, 0.015, 0.006, and 0.003 for the group 2 SNPs. When ρ = 0.08, the true PVEs per causal SNP are: 0.012 for the group 1 SNPs; and 0.012, 0.006, 0.0024, and 0.0012 for the Group 2 SNPs.Groups 1 and 2 causal markers are colored in light red and light blue, respectively. These figures are based on a broad-sense heritability level of H(PDF)Click here for additional data file.S4 Fig2 = 0.6 and parameters ρ = 0.5  and ρ = 0.8 , respectively. These results are estimated with 100 data replicates under simulation model (ii) with the top 10 genotype PCs. Here, ρ = {0.5, 0.8} was used to determine the portion of broad-sense heritability contributed by interaction effects. (A) and (C) show the power of MAPIT to identify SNPs in each causal group under significance level α = 0.05. The lines represent 95% variability due to resampling error. (B) and (D) show boxplots of the marginal PVE estimates for the group 1 and 2 causal SNPs from MAPIT for the four simulation scenarios. The true PVEs per causal SNP are shown as dashed grey horizontal lines. When ρ = 0.05, the true PVEs per causal SNP are: 0.03 for the group 1 SNPs; and 0.03, 0.015, 0.006, and 0.003 for the group 2 SNPs. When ρ = 0.08, the true PVEs per causal SNP are: 0.012 for the group 1 SNPs; and 0.012, 0.006, 0.0024, and 0.0012 for the Group 2 SNPs.Groups 1 and 2 causal markers are colored in light red and light blue, respectively. These figures are based on a broad-sense heritability level of H(PDF)Click here for additional data file.S5 Figα = 8.3 × 10−6. Groups 1 and 2 causal markers are colored in light red and light blue, respectively. These figures are based on a broad-sense heritability level of H2 = 0.6, and parameters ρ = 0.5 (A) and ρ = 0.8 (B)—estimated with 100 replicates. Here, ρ was used to determine the portion of broad-sense heritability contributed by interaction effects. The lines represent 95% variability due to resampling error.(A) and (B) show the power of MAPIT to identify SNPs in each causal group under the Bonferroni-corrected genome-wide significance level (PDF)Click here for additional data file.S6 Figα = 8.3 × 10−6. These results are estimated with 100 data replicates under simulation model (ii). (A) and (B) use the top 5 genotype PCs. (C) and (D) use the top 10 genotype PCs. Groups 1 and 2 causal markers are colored in light red and light blue, respectively. These figures are based on a broad-sense heritability level of H2 = 0.6, and parameters ρ = 0.5  and ρ = 0.8 . Here, ρ was used to determine the portion of broad-sense heritability contributed by interaction effects. The lines represent 95% variability due to resampling error.All Figures show the power of MAPIT to identify SNPs in each causal group under the Bonferroni-corrected genome-wide significance level (PDF)Click here for additional data file.S7 Fig2 = 0.6, and the parameters ρ = 0.5 (A) and ρ = 0.8 (B). Here, ρ was used to determine the portion of broad-sense heritability contributed by interaction effects. In (A), the true epistatic PVE is 0.3. In (B), the true epistatic PVE is 0.12. In both cases, the true PVE is shown as the grey horizontal line.Compared here are the epistatic PVE estimates computed by the standard variance component model. Each simulation scenario is represented by a different color, with each of the three simulation schemes being labeled on the x-axis. These figures are based on 100 simulations where the overall broad-sense heritability level is H(PDF)Click here for additional data file.S8 Figα = 0.05 under a standard asymptotic normal test. Each simulation scenario is represented by a different color, with each of the three simulation schemes being labeled on the x-axis. These figures are based on 100 simulations where the overall broad-sense heritability level is H2 = 0.6, and the parameters ρ = 0.5 (A) and ρ = 0.8 (B). Here, ρ was used to determine the portion of broad-sense heritability contributed by interaction effects.Compared here is the power of the standard variance component model to estimate the true non-zero pairwise epistatic PVE at the significance level of (PDF)Click here for additional data file.S9 Fig2 = 0.6 and ρ = 0.5. Here, ρ = 0.5 was used to determine the portion of broad-sense heritability contributed by interaction effects. Group 1 (light red) and group 2 (light blue) causal SNPs. The x-axis shows the false positive rate, while the y-axis gives the rate at which true causal variants were identified. Results are based on 100 replicates in each case.We compare the mapping abilities of MAPIT (solid line) to the exhaustive search procedure in PLINK (dotted line) in scenarios I (A), II (B), III (C), and IV (D), under broad-sense heritability level H(PDF)Click here for additional data file.S10 Fig2 = 0.6 and ρ = 0.5. Here, ρ = 0.5 was used to determine the portion of broad-sense heritability contributed by interaction effects. Group 1 (light red) and group 2 (light blue) causal SNPs. The x-axis shows the false positive rate, while the y-axis gives the rate at which true causal variants were identified. Results are based on 100 replicates in each case, where the data was created under simulation model (ii) with the top 5 genotype PCs.We compare the mapping abilities of MAPIT (solid line) to the exhaustive search procedure in PLINK (dotted line) in scenarios I (A), II (B), III (C), and IV (D), under broad-sense heritability level H(PDF)Click here for additional data file.S11 Fig2 = 0.6 and ρ = 0.8. Here, ρ = 0.8 was used to determine the portion of broad-sense heritability contributed by interaction effects. Group 1 (light red) and group 2 (light blue) causal SNPs. The x-axis shows the false positive rate, while the y-axis gives the rate at which true causal variants were identified. Results are based on 100 replicates in each case, where the data was created under simulation model (ii) with the top 5 genotype PCs.We compare the mapping abilities of MAPIT (solid line) to the exhaustive search procedure in PLINK (dotted line) in scenarios I (A), II (B), III (C), and IV (D), under broad-sense heritability level H(PDF)Click here for additional data file.S12 Fig2 = 0.6 and ρ = 0.5. Here, ρ = 0.5 was used to determine the portion of broad-sense heritability contributed by interaction effects. Group 1 (light red) and group 2 (light blue) causal SNPs. The x-axis shows the false positive rate, while the y-axis gives the rate at which true causal variants were identified. Results are based on 100 replicates in each case, where the data was created under simulation model (ii) with the top 10 genotype PCs.We compare the mapping abilities of MAPIT (solid line) to the exhaustive search procedure in PLINK (dotted line) in scenarios I (A), II (B), III (C), and IV (D), under broad-sense heritability level H(PDF)Click here for additional data file.S13 Fig2 = 0.6 and ρ = 0.8. Here, ρ = 0.8 was used to determine the portion of broad-sense heritability contributed by interaction effects. Group 1 (light red) and group 2 (light blue) causal SNPs. The x-axis shows the false positive rate, while the y-axis gives the rate at which true causal variants were identified. Results are based on 100 replicates in each case, where the data was created under simulation model (ii) with the top 10 genotype PCs.We compare the mapping abilities of MAPIT (solid line) to the exhaustive search procedure in PLINK (dotted line) in scenarios I (A), II (B), III (C), and IV (D), under broad-sense heritability level H(PDF)Click here for additional data file.S14 Fig2 = 0.6. Here, ρ = 0.5 was used to determine the portion of broad-sense heritability contributed by interaction effects. The y-axis gives the rate at which true causal epistatic pairs were identified. Results are based on 100 replicates in each case. The lines represent 95% variability due to resampling error.Here, the effectiveness of MAPIT (green) as an initial step in a pairwise detection filtration process is compared against the more conventional single-SNP testing procedure, which is carried out via GEMMA (purple). In both cases, the search for epistatic pairs occurs between the top 100 significant marginally associated SNPs are considered. We use the fully exhaustive search model in PLINK (orange) as a baseline comparison. We compare the three methods in all scenarios (x-axis), under broad-sense heritability level H(PDF)Click here for additional data file.S15 Fig2 = 0.6. Here, ρ = 0.5  and ρ = 0.8  were used to determine the portion of broad-sense heritability contributed by interaction effects. The y-axis gives the rate at which true causal epistatic pairs were identified. Results are based on 100 replicates in each case, where the data was created under simulation model (ii). (A) and (B) use the top 5 genotype PCs, while (C) and (D) use the top 10 genotypes PCs. The lines represent 95% variability due to resampling error.Here, the effectiveness of MAPIT (green) as an initial step in a pairwise detection filtration process is compared against the more conventional single-SNP testing procedure, which is carried out via GEMMA (purple). In both cases, the search for epistatic pairs occurs between the top 100 significant marginally associated SNPs are considered. We use the fully exhaustive search model in PLINK (orange) as a baseline comparison. We compare the three methods in all scenarios (x-axis), under broad-sense heritability level H(PDF)Click here for additional data file.S16 FigKcis, where for the expression of each gene Kcis was computed using only the corresponding cis-SNPs. (B) corresponds to using MAPIT with a genetic relatedness matrix Ktrans, where for the expression of each gene Ktrans was computed using SNPs outside of the corresponding cis-window. (C) corresponds to using MAPIT with a genome-wide genetic relatedness matrix KGW, where KGW was computed using all SNPs in the study. (D) illustrates results from using MAPIT with KPop, which was computed after we first controlled for residual population stratification effects.(A) corresponds to using MAPIT with a genetic relatedness matrix (PDF)Click here for additional data file.S17 FigKtrans (A), KGW (B), and KPop (C), respectively. The horizontal red line corresponds to a uniform distribution of p-values. (D)-(F) show the number of significant pairwise interactions (y-axis) identified by MAPIT (green) and GEMMA (purple) when searching between the top v = {1000, 2500, 5000, 7500, 10000, 15000, 20000} marginally associated variants (x-axis). We use the number of significant pairs identified by fully exhaustive search model in PLINK as a baseline comparison (orange dotted line). Note that PLINK only analyzes cis-SNPs pairs, while MAPIT with Ktrans (D), KGW (E), and KPop (F) effectively analyzes the marginal epistatic effects of cis-SNPs with all genome-wide SNPs. This image shows the distributions of genome-wide significant epistatic pairs as found by each method. An interaction for MAPIT and GEMMA was deemed signifiant if it had a joint p-value below the threshold P = 0.05/(∑iqi(qi − 1)/2), where qi is the number of top variants located in the cis-window of gene i. In the case of PLINK, we consider two variants to be a significantly associated epistatic pair if they have a joint p-value below the threshold P = 1.09 × 10−10, which corresponds to the Bonferroni-correction that would be used if we examined all possible genome-wide SNP pairs across all genes in the final data set. Overall, PLINK detected 7,361 , and 8,643 (F) significant pairwise interactions.(A)-(C) show a histograms of the MAPIT p-values for all variants in the GEUVADIS data set using the genome-wide genetic relatedness matrix (PDF)Click here for additional data file.S18 FigKtrans. (B) displays the marginally epistatic QTL (mepiQTL) detected by MAPIT using the genetic relatedness matrix KGW. (C) corresponds to the mepiQTL identified by MAPIT using KPop. The x-axis of each plot divides a typical cis-candidate region into a series of bins. The y-axis plots the number of SNPs in each bin that have a p-value less than a gene specific Bonferroni-corrected significance p-value threshold P = 0.05/∑isi, where si is the number of cis-SNPs for gene i, divided by the total number of SNPs in that bin. Bars in green denote the region bounded by the TSS and TES, with gene lengths divided into 20 bins for visibility—because the gene body is thus artificially enlarged, SNP density within genes cannot be directly compared with SNP density outside of genes.Shown here are the distribution of locations for significant SNPs, relative to the 5′ most gene transcription start site (TSS) and the 3′ most gene transcription end site (TES). (A) displays the marginally epistatic QTL (mepiQTL) detected by MAPIT using the genetic relatedness matrix (PDF)Click here for additional data file.S19 Fig10(P) transformed MAPIT p-values of quality-control-positive cis-SNPs plotted against their genomic position in chromosomes (A) 2, (B) 3, and (C) 4, respectively. Note that MAPIT was implemented with Kcis. Here, the epistatic associated genes are labeled (blue). The (red) horizontal line indicates a genome-wide significance threshold (P = 1.828 × 10−8). Note that all panels are truncated at −log10(P) = 10 for consistency and presentation, although for some genes there are strongly marginally epistatic associated markers with p-values P ≈ 0.Depicted are the −log(PDF)Click here for additional data file.S20 Fig10(P) transformed MAPIT p-values of quality-control-positive cis-SNPs plotted against their genomic position in chromosomes (A) 5, (B) 7, and (C) 8, respectively. Note that MAPIT was implemented with Kcis. Here, the epistatic associated genes are labeled (blue). The (red) horizontal line indicates a genome-wide significance threshold (P = 1.828 × 10−8). Note that all panels are truncated at −log10(P) = 10 for consistency and presentation, although for some genes there are strongly marginally epistatic associated markers with p-values P ≈ 0.Depicted are the −log(PDF)Click here for additional data file.S21 Fig10(P) transformed MAPIT p-values of quality-control-positive cis-SNPs plotted against their genomic position in chromosomes (A) 9, (B) 10, and (C) 11, respectively. Note that MAPIT was implemented with Kcis. Here, the epistatic associated genes are labeled (blue). The (red) horizontal line indicates a genome-wide significance threshold (P = 1.828 × 10−8). Note that all panels are truncated at −log10(P) = 10 for consistency and presentation, although for some genes there are strongly marginally epistatic associated markers with p-values P ≈ 0.Depicted are the −log(PDF)Click here for additional data file.S22 Fig10(P) transformed MAPIT p-values of quality-control-positive cis-SNPs plotted against their genomic position in chromosomes (A) 12, (B) 13, and (C) 14, respectively. Note that MAPIT was implemented with Kcis. Here, the epistatic associated genes are labeled (blue). The (red) horizontal line indicates a genome-wide significance threshold (P = 1.828 × 10−8). Note that all panels are truncated at −log10(P) = 10 for consistency and presentation, although for some genes there are strongly marginally epistatic associated markers with p-values P ≈ 0.Depicted are the −log(PDF)Click here for additional data file.S23 Fig10(P) transformed MAPIT p-values of quality-control-positive cis-SNPs plotted against their genomic position in chromosomes (A) 15, (B) 16, and (C) 17, respectively. Note that MAPIT was implemented with Kcis. Here, the epistatic associated genes are labeled (blue). The (red) horizontal line indicates a genome-wide significance threshold (P = 1.828 × 10−8). Note that all panels are truncated at −log10(P) = 10 for consistency and presentation, although for some genes there are strongly marginally epistatic associated markers with p-values P ≈ 0.Depicted are the −log(PDF)Click here for additional data file.S24 Fig10(P) transformed MAPIT p-values of quality-control-positive cis-SNPs plotted against their genomic position in chromosomes (A) 18, (B) 19, (C) 20, and (D) 21 respectively. Note that MAPIT was implemented with Kcis. Here, the epistatic associated genes are labeled (blue). The (red) horizontal line indicates a genome-wide significance threshold (P = 1.828 × 10−8). Note that all panels are truncated at −log10(P) = 10 for consistency and presentation, although for some genes there are strongly marginally epistatic associated markers with p-values P ≈ 0.Depicted are the −log(PDF)Click here for additional data file.S25 FigK and K2, respectively. Note that K2 = K ∘ K is obtained by using the Hadamard product (i.e. the squaring of each element) of the matrix K. See Methods and Material for details.Estimates of the pPVE on the y-axis were calculated by using variance component models, where each of the components represent for additive effects (grey) and pairwise epistasis (green). More specifically, the variance components correspond to additive and pairwise epistatic covariance matrices (PDF)Click here for additional data file.S1 Table3, 1 × 104, 5 × 104, and 1 × 105 genetic markers, respectively. Sample sizes were set to 1,000, 2,500, and 5,000. Values in the parentheses are the standard deviations of the estimates.Each entry represents the mean computation time (in minutes) it takes to run MAPIT under different hypothesis testing strategies. These tests are the normal test, and the Davies method for approximating a mixture of chi-squares. Computations were performed using 32 cores on Duke University’s Center for Genomic and Computational Biology HARDAC Cluster. To create genetic data for these simulations, we generated 5 × 10(PDF)Click here for additional data file.S2 Tableα = 0.05, 0.01, and 0.001. Sample sizes were set to 1,000, 1,750, and 2,500. Values in the parentheses are the standard deviations of the estimates.Each entry represents type I error rate estimates as the proportion of p-values a under the null hypothesis based on 100 simulated continuous phenotypes for the normal test (or z-test) and the Davies method. These results are based on 100 simulated data sets using simulation model (ii) with the top 5 genotype PCs. Recall that model (ii) is used to evaluate the type I error control of MAPIT when there is population stratification. Empirical size for the analyses used significance thresholds of (PDF)Click here for additional data file.S3 Tableα = 0.05, 0.01, and 0.001. Sample sizes were set to 1,000, 1,750, and 2,500. Values in the parentheses are the standard deviations of the estimates.Each entry represents type I error rate estimates as the proportion of p-values a under the null hypothesis based on 100 simulated continuous phenotypes for the normal test (or z-test) and the Davies method. These results are based on 100 simulated data sets using simulation model (ii) with the top 10 genotype PCs. Recall that model (ii) is used to evaluate the type I error control of MAPIT when there is population stratification. Empirical size for the analyses used significance thresholds of (PDF)Click here for additional data file.S4 Tablej that were also identified by column k.Coverage was computed as the proportion of significant QTL detected by row (XLSX)Click here for additional data file.S5 Tablej that were also identified by column k.Coverage was computed as the proportion of significant genes detected by row (XLSX)Click here for additional data file.S6 TableP = 0.05/∑isi, where si is the number of cis-SNPs for gene i. Also listed are the corresponding genes whose expressions are associated.Strong significance of association for a particular SNP or locus was determined by using a gene specific Bonferroni-corrected significance p-value threshold (XLSX)Click here for additional data file.S7 TableP = 0.05/∑isi, where si is the number of cis-SNPs for gene i. Also listed are the corresponding genes whose expressions are associated.Strong significance of association for a particular SNP or locus was determined by using a gene specific Bonferroni-corrected significance p-value threshold (XLSX)Click here for additional data file.S8 TableP = 0.05/∑isi, where si is the number of cis-SNPs for gene i. Also listed are the corresponding genes whose expressions are associated.Strong significance of association for a particular SNP or locus was determined by using a gene specific Bonferroni-corrected significance p-value threshold (XLSX)Click here for additional data file.S9 TableP = 0.05/∑isi, where si is the number of cis-SNPs for gene i. Also listed are the corresponding genes whose expressions are associated.Strong significance of association for a particular SNP or locus was determined by using a gene specific Bonferroni-corrected significance p-value threshold (XLSX)Click here for additional data file.