Oreochromis niloticus (Nile tilapia) is principally determined by an XX/XY locus but other genetic and environmental factors also influence sex ratio. Restriction Associated DNA (RAD) sequencing was used in two families derived from crossing XY males with females from an isogenic clonal line, in order to identify Single Nucleotide Polymorphisms (SNPs) and map the sex-determining region(s). We constructed a linkage map with 3,802 SNPs, which corresponded to 3,280 informative markers, and identified a major sex-determining region on linkage group 1, explaining nearly 96% of the phenotypic variance. This sex-determining region was mapped in a 2 cM interval, corresponding to approximately 1.2 Mb in the O. niloticus draft genome. In order to validate this, a diverse family  and population  test panel were genotyped for five of the SNPs showing the highest association with phenotypic sex. From the expanded data set, SNPs Oni23063 and Oni28137 showed the highest association, which persisted both in the case of family and population data. Across the entire dataset all females were found to be homozygous for these two SNPs. Males were heterozygous, with the exception of five individuals in the population and two in the family dataset. These fish possessed the homozygous genotype expected of females. Progeny sex ratios  from two of the males with the “female” genotype indicated that they were neomales . Sex reversal induced by elevated temperature during sexual differentiation also resulted in phenotypic males with the “female” genotype. This study narrows down the region containing the main sex-determining locus, and provides genetic markers tightly linked to this locus, with an association that persisted across the population. These markers will be of use in refining the production of genetically male O. niloticus for aquaculture.Sex in  DMY/dmrt1bY in Oryzias latipes (medaka) Gsdf(Y) in Oryzias luzonensis (Luzon ricefish) amhy in Odontesthes hatcheri (Patagonian pejerrey) Amhr2 in Takifugu rubripes (tiger pufferfish) sdY in Oncorhynchus mykiss (rainbow trout) sdY protein in O. mykiss is similar to part of the interferon regulatory factor 9). In all of these species the sex determination system is principally XX/XY, but mismatches between sexual genotype and phenotype are not uncommon Patterns of sex determination and differentiation in fish are very varied, with a wide range of gonochoristic and hermaphroditic species. Among the gonochoristic species, genetic and/or environmental factors determine sex Oreochromis niloticus (Nile tilapia) is one of the most important farmed species with a production exceeding 2.8 million metric tonnes in 2010 Since many farmed species of fish exhibit sexual dimorphism in a range of traits of interest like growth or age at maturity, clarification of the sex-determining system of such fish is beneficial for the aquaculture industry towards the production of mono-sex stocks. O. niloticus and Oreochromis mossambicus (Mozambique tilapia), sex is primarily determined by an XX/XY system on linkage group (LG) 1, whereas in others, for example Oreochromis aureus (blue tilapia), sex is primarily determined by a WZ/ZZ system on LG 3 O. niloticus, genes on LG 3 O. niloticus have been carried out on fish derived from Lake Manzala in Egypt, the subject of the present study, and it is clear that both non-LG 1 genes and temperature affect sex ratios in at least some families in this population.In tilapias, evidence so far suggests the existence of two different major sex-determining systems. In some tilapia species, including O. niloticus is based on more than 500 markers, mostly microsatellites UNH995 on LG 1 1b and cyp19a, but further mapping ruled these out as candidates for the major sex-determining locus The current linkage map for in vitro. Eggs were incubated in downwelling incubators until the larvae had absorbed the yolk sac. Fry from families 1–6 . All working procedures complied with the Animals Scientific Procedures Act lies 1–6  were theUNH995 marker) were used to prepare RAD Libraries  and broodstock  with dams from an isogenic XX clonal line and XY sires  and treated with RNase to remove residual RNA from the sample. Each sample was quantified by spectrophotometry (Nanodrop) and quality assessed by agarose gel electrophoresis, and was finally diluted to a concentration of 50 ng/µL in 5 mmol/L Tris, pH 8.5. The RAD library preparation protocol followed essentially the methodology originally described in Baird et al. SbfI (recognising the CCTGCA|GG motif) high fidelity restriction enzyme  using 6 U SbfI per µg genomic DNA in 1× Reaction Buffer 4 (NEB) at a final concentration of c. 1 µg DNA per 50 µL reaction volume. The reactions  were then heat inactivated at 65°C for 20 minutes. Individual specific P1 adapters, each with a unique 5 bp barcode , 0.75/0.25 µL 10× Reaction Buffer 2 (NEB), 0.36/0.12 µL T4 ligase  and reaction volumes made up to 45/15 µL with nuclease-free water for each parental/offspring sample. Following heat inactivation at 65°C for 20 minutes, the ligation reactions were slowly cooled to room temperature (over 1 hour) then combined in appropriate multiplex pools  was digested at 37°C for 40 minutes with  barcode , were liex pools . ShearinReads of low quality , missing the restriction site or with ambiguous barcodes were discarded. Retained reads were sorted into loci and genotyped using Stacks software 0.9995 The genetic map was constructed using R/Onemap scanone). The model used for the analysis was based on interval mapping. The algorithm used considers the phenotype to follow a mixture of Bernoulli distributions and uses a form of the expectation-maximisation algorithm for obtaining maximum likelihood estimates makeqtl, addqtl, scantwo, fitqtl, stepwiseqtl). With this approach greater power can be achieved in the analysis allowing for detection of QTLs that would be remained undetected in the one-dimensional approach above. Approximate Bayesian 95% density intervals were calculated. An approximate estimate of the phenotypic variance explained by the QTL is obtained from the following equation: 1–10−2LOD/n. It has to be stressed that while the estimated variance may be reasonable for additive QTL, problems can be caused in the case of linked QTL The QTL analysis was performed using R/qtl Oni20117, Oni61067, Oni23063, Oni28137, Oni22734, NCBI dbSNP accession 748775078, 748775079, 748775085, 748775081 and 748775082 respectively; We designed SNP assays using the KASP genotyping system (KBioscience UK Ltd) for five SNPs (association). Both the Bonferroni and permutation tests  were used in order to correct for multiple testing.Family data  and 40 unrelated broodstocks  were genTwo crosses with 68 and 20 offspring and their parents  were sampled . The samIn order to maximise the number of informative markers and minimise the amount of missing or erroneous data, we used SNP markers retrieved in at least 75% of the samples in each family, and carrying one or two SNPs. Since Family 2 had only 20 offspring, the genetic map was constructed with the Family 1 data only (68 offspring), while Family 2 was used to validate this. The sire-based map consists of 3,802 SNP markers that were grouped in 23 linkage groups, with an average spacing of 0.7 cM and spanning a total distance of 1,176 cM  & S2. A α = 0.001) was 3.89 as calculated from permutation tests . The highest LOD score was observed at the 28.5th cM of LG 1. Two adjacent SNPs were located in this position . Only Oni23063 was analysed subsequently. The two-QTL model did not reveal any significant additional QTL or any evidence for epistasis. Even though models that take into account the existence of a major QTL (as in this study) or ones that test for existence of multiple QTLs simultaneously reduce the residual variation , no additional QTLs were detected. The calculated 95% Bayesian Density Intervals for the QTL location spanned a region of 2 cM (28–30 cM in LG 1), corresponding to approximately 1.2 Mb in the O. niloticus genome. The phenotypic variance explained by the QTL was 96%.The results from the single-QTL model for binary traits provided evidence for the existence of a major QTL in LG 1 for both families . The higp-value thresholds  for permutation and the Bonferroni correction tests were 0.016 and 0.01 respectively. All five SNP markers were found to be significantly associated with sex in the family data both when tested in each family separately and across all families simultaneously . Oni23063 and Oni28137 showed the highest association with phenotypic sex for both the population and family data . Females were homozygous and males heterozygous for those two SNPs. The only exceptions from the above pattern were found for one male progeny from the four tested families and five male broodstock fish  located at the position of Oni23063 . While these showed highly significant association (p = 4.05×10−14 for both markers) in the control group, in the temperature treated group neither marker was significantly associated after correction for multiple testing (p = 0.039 for both markers). Five phenotypic males were found to deviate from the expected association in the control group, while in the treated group 28 phenotypic males deviated from the expected association for Oni23063 and Oni28137  females were homozygous for the same allele, while males were heterozygous, apart from two males (one each from Families 1 and 4) that were homozygous for the allele found in females. The results from the unrelated adult individuals showed again the same pattern, with the exception of five males that were homozygous for these two SNPs. Of these five, two were shown to give >95% female progeny in crosses to normal females (while no progeny testing data was available for the other three). No phenotypic female was mis-assigned in our entire dataset. Our data support the hypothesis that the mis-assigned (homozygous) males were in fact neomales, genetically female fish (as defined by the LG1 sex-determining locus) that have undergone sex reversal due to unknown genetic or environmental factor(s). The highly significant population-based linkage disequilibrium observed strongly supports the view that these two SNP markers are in very close proximity to the causative locus.In all tested families, at each of the two loci  results in significant masculinisation in some progenies if started around 10 days post fertilisation and applied for at least 10 days When a family responsive to sex reversal by exposure to elevated temperature was genotyped for O. mykiss, a gene associated with immune-related functions in other organisms was found to be its master sex-determining gene O. latipesO. mykissThe genomic region, which was derived from the calculated density interval, includes 10 identified genes, none of which have yet been identified as the major sex-determining gene of any species. Nevertheless, it would not be prudent to exclude any of these as candidates at this time. A diversity of sex-determining systems has been documented in fish, implicating a variety of different, and in some cases unexpected, genes. For example, in This study did not address the reasons why YY × XX crosses yield varying proportions of females. However, the SNP markers developed will help to tackle this issue, a key constraint on the commercial development of this technique.O. niloticus genome that is several-fold denser than the existing one, a reduced candidate region for the sex-determining gene(s) and a set of tightly sex-linked SNP markers. Although we could not identify the causative gene(s), the fact that no female was mis-assigned using our sex-associated SNPs means that those SNPs could be also of high practical value towards the production of all male stocks for the O. niloticus aquaculture industry.This study provides a linkage map of the Table S1Sample origins and RAD barcodes. Details each sample used: sample ID, family, gender, RAD barcode (index) used, number of raw reads (paired-ended or single-ended) and number of RAD-tags.(CSV)Click here for additional data file.Table S2Genetic maps. Ordered markers: marker ID, linkage group and position (cM).(CSV)Click here for additional data file.Table S3KASP assay primer sequences. List of the allele-specific primers and common primer designed for the allele-specific PCR genotyping assay of the five markers as well as their NCBI dbSNP accession numbers.(CSV)Click here for additional data file.Table S4Details of the KASP assay results. Genotypes of the 280 assays.(CSV)Click here for additional data file.Data S1Marker sequences. Details of SNP alleles and RAD-tag allele sequences of the five markers. (FASTA format)(TXT)Click here for additional data file.Data S2Details of the physical location of the markers and the neighbouring annotated genes. (GFF3 format)(TXT)Click here for additional data file.


The relative importance between additive and non-additive genetic variance has been widely argued in quantitative genetics. By approaching this question from an evolutionary perspective we show that, while additive variance can be maintained under selection at a low level for some patterns of epistasis, the majority of the genetic variance that will persist is actually non-additive. We propose that one reason that the problem of the “missing heritability” arises is because the additive genetic variation that is estimated to be contributing to the variance of a trait will most likely be an artefact of the non-additive variance that can be maintained over evolutionary time. In addition, it can be shown that even a small reduction in linkage disequilibrium between causal variants and observed SNPs rapidly erodes estimates of epistatic variance, leading to an inflation in the perceived importance of additive effects. We demonstrate that the perception of independent additive effects comprising the majority of the genetic architecture of complex traits is biased upwards and that the search for causal variants in complex traits under selection is potentially underpowered by parameterising for additive effects alone. Given dense SNP panels the detection of causal variants through genome-wide association studies may be improved by searching for epistatic effects explicitly. In this study we have shown that two independent problems may have a common cause. Why do traits under selection exhibit additive genetic variance, and why is the proportion of the heritability explained by additive effects much smaller than the total heritability estimated to exist? Our results indicate that epistatic interactions can allow deleterious mutations to persist under selection and that these interactions can abate the depletion of additive genetic variation. Furthermore, a much larger element of non-additive genetic variance is maintained, which supports the notion that the heritability estimated from family studies could be a mixture of both additive and non-additive components. We show that searching directly for epistatic effects greatly improves the discovery of variants under selection, despite the multiple testing penalty being much larger. Finally, we demonstrate that common practices in genome-wide association studies could lead to both an ascertainment bias in detecting additive effects and a confirmation bias in perceiving that most of the genetic variance is additive. There exists a paradox in evolutionary biology. Despite a near-ubiquitous abundance of genetic variation e.g.e.g.With respect to the fields of both the aforementioned issues, it is typical to model genetic variation using an additive framework, such that each allele affecting a trait acts in an independent, linear, cumulative manner. For many practical applications this is a very useful approach e.g., but theThe importance of epistasis in complex traits has proven to be a particularly divisive issue throughout the history of quantitative genetics. Recently it has been suggested that epistasis might form part of the answer to the ‘missing heritability’ e.g.e.g.Homo sapiensGallus gallusDrosophila melanogasterSaccharomyces cerevisiaeArabidopsis thalianaBeyond the realm of complex trait genetics it appears that epistasis does appear to be common. For example in molecular studies it is routine to observe ‘phenotypic rescue’ where the phenotypic effect of a gene knockout can be masked by a second knockout e.g.. Anotheri.e. non-additive variation cannot be estimated, thus SNPs are not modelled to have non-additive effects). But whether the phenomenon of stasis can accommodate a purely additive genetic model remains an open question.At the statistical level, for a pair of single nucleotide polymorphisms (SNPs) that exhibit epistasis, in addition to interaction terms between the two loci, the total genetic effect is likely to also include marginal additive or dominance effects at each locus The premise of this study is centred around finding common ground between the problems of stasis and the missing heritability. Given that fitness related traits often exhibit stasis then the underlying genetic architecture may not solely comprise independent additive effects. Through theory and simulations we demonstrate that epistasis will maintain additive genetic variation under selection at higher levels than independent additive effects, and that by extending GWA studies to search for epistasis directly we could improve statistical power to detect additive genetic variation.Selection rapidly drives deleterious additive effects to fixation, but how effective is selection at purging deleterious, non-additive effects? We simulated 56 G-P maps  rapidly haemorrhage genetic variance see , such thSecondly, with the patterns of canalisation (rows 1–2), as LD reduces although some genetic variance is maintained, the G-P map appears entirely additive. Thus functional maps that confer epistatic effects that can be detected at relatively low LD are likely to be interpreted as being entirely additive. Thus, researchers who attempt to quantify the contribution of non-additive variance from SNPs associated with a trait are liable to incorrectly confirm that most variants act additively.Typically GWA studies test each SNP one at a time for additive effects. To explicitly include interaction terms in the search this approach can be extended from one dimension (1D) to two dimensions (2D), where every pair of SNPs is tested jointly for an association Given that we know the trajectory of allele frequencies under selection, it is possible to ask what the best GWA strategy for detecting evolutionarily likely variants might be. Two main search methods were tested, 1D scans , and exhaustive 2D scans , a strong advantage in power to detect variants at evolutionarily likely frequencies can be conferred by using exhaustive two-dimensional scans and modelling whole genotype effects (8 d.f. test).Broadly, the results show two important points. Firstly, there is no single method that is always superior under the conditions that were tested. Secondly, it is very rare that parameterising for additive effects is the most powerful method . Rather,A more detailed view of this relationship between LD and detectability is shown in It may seem surprising that despite the much larger multiple testing penalty, the 2D scans perform well in terms of power. But there exists a trade-off between the extra variance explained by extending the search into higher dimensions, and the amount of variance required to be detected in order to overcome the multiple testing correction. The results show that because non-additive variance components can be maintained under selection the 2D strategy is conferred an advantage in this trade-off.The architecture of genetic variation must be understood if we are to make progress in fields such as disease risk prediction, personalised medicine, and animal and crop breeding. This study sought to examine the potential for epistasis to maintain genetic variation under selection, and thus to inform GWA strategies based on these results.We investigated to what extent deleterious mutations could be maintained as common polymorphisms under selection. A large sample of potential G-P maps were assayed The results suggest that we should expect significant levels of non-additive variation to be maintained in fitness-related traits. While non-additive variance components are often considered to be nuisance terms in quantitative genetics e.g. patterns 45, 47, 53) could destabilise the equilibrium and lead to eventual fixation.Although the intention behind the use of the genetic algorithm in this study was to explore the potential for a two-locus system to maintain additive variance, rather than to necessarily identify biologically feasible maps, those maps that emerged did not appear biologically untenable. In fact they can be supported by reports in the literature due to their tendencies for exhibiting heterozygote advantage It is important to note that the processes underlying stasis and missing heritability are unlikely to be caused by any single factor. For example, a compelling argument is that though most traits exhibit genetic variation, selection acts upon multidimensional trait space in which there is no genetic variation e.g.Occam's razor can be invoked to justify the additive paradigm used in GWA studies We were interested in simulating the behaviour of epistatic interactions under selection in order to ask the questions i) for how long and at which frequencies are deleterious mutations maintained under selection, ii) how much additive variance can this produce, and iii) what is the best strategy to identify evolutionarily persistent variation. We approached this problem through two methods, using stochastic simulations and by calculating the expected trajectories deterministically, and overall a range of different epistatic and dominant G-P maps were assessed. In addition, we heuristically searched the two-locus genotype-phenotype parameter space using a genetic algorithm to assess what the upper limit on how much additive genetic variation can be maintained under selection.The evolutionary fate of an arbitrary two-locus epistatic fitness pattern can be characterised by the allele frequencies and recombination fraction of the two loci as a Markovian process. Therefore it is straightforward to calculate the trajectory of allele frequencies over evolutionary time for a wide range of epistatic patterns. For each G-P map, deterministic simulations were performed with varying conditions for initial allele frequencies Click here for additional data file.Figure S2Deterministic trajectory of allele frequencies as in (TIF)Click here for additional data file.Figure S3Simulated trajectory of allele frequencies as in (TIF)Click here for additional data file.Figure S4Quasi-LD generated by selection. For the 25 deterministic simulations the expected quasi-LD between the physically unlinked causal SNPs was calculated. It can be seen that significant levels are generated, such that orthogonal standard parameterisation methods would violate assumptions of independence. Boxes represent different G-P maps from (TIF)Click here for additional data file.Figure S5Deterministic change in genetic variance for loci under selection exhibiting various epistatic patterns , when LD(TIF)Click here for additional data file.Figure S6As in (TIF)Click here for additional data file.Figure S7As in (TIF)Click here for additional data file.Figure S8Relationship between genetic variance of observed SNPs ((TIF)Click here for additional data file.


Molecular and epidemiological evidence demonstrate that altered gene expression and single nucleotide polymorphisms in the apoptotic pathway are linked to many cancers. Yet, few studies emphasize the interaction of variant apoptotic genes and their joint modifying effects on prostate cancer (PCA) outcomes. An exhaustive assessment of all the possible two-, three- and four-way gene-gene interactions is computationally burdensome. This statistical conundrum stems from the prohibitive amount of data needed to account for multiple hypothesis testing.To address this issue, we systematically prioritized and evaluated individual effects and complex interactions among 172 apoptotic SNPs in relation to PCA risk and aggressive disease . Single and joint modifying effects on PCA outcomes among European-American men were analyzed using statistical epistasis networks coupled with multi-factor dimensionality reduction (SEN-guided MDR). The case-control study design included 1,175 incident PCA cases and 1,111 controls from the prostate, lung, colo-rectal, and ovarian (PLCO) cancer screening trial. Moreover, a subset analysis of PCA cases consisted of 688 aggressive and 488 non-aggressive PCA cases. SNP profiles were obtained using the NCI Cancer Genetic Markers of Susceptibility (CGEMS) data portal. Main effects were assessed using logistic regression (LR) models. Prior to modeling interactions, SEN was used to pre-process our genetic data. SEN used network science to reduce our analysis from > 36 million to < 13,000 SNP interactions. Interactions were visualized, evaluated, and validated using entropy-based MDR. All parametric and non-parametric models were adjusted for age, family history of PCA, and multiple hypothesis testing.AKT3 rs2125230-PRKCQ rs571715 and disease aggressiveness using SEN-guided MDR (p = 0.011).Following LR modeling, eleven and thirteen sequence variants were associated with PCA risk and aggressive disease, respectively. However, none of these markers remained significant after we adjusted for multiple comparisons. Nevertheless, we detected a modest synergistic interaction between AKT3-PRKCQ and aggressive PCA requires further validation using independent observational studies.In summary, entropy-based SEN-guided MDR facilitated the logical prioritization and evaluation of apoptotic SNPs in relation to aggressive PCA. The suggestive interaction between  Men with aggressive PCA had both a Gleason score ≥ 7 and tumor stage III/IV. Although non-aggressive PCA cases primarily had a Gleason score < 7 and tumor stage I/II, a small percentage (1.8%) of them had a Gleason score > 6 and a tumor stage I/II. Among cases, there were no significant differences in family history of disease or PSA levels between men diagnosed comparing men with aggressive and non-aggressive disease (data not shown). The vast majority of subjects with aggressive PCA had higher Gleason scores than subjects with non-aggressive PCA, although 9 of the 488 non-aggressive cases (1.08%) had a Gleason score greater than 6.TNFRSF10B rs1001793 or TNFSF10 rs4894559 A alleles was nominally associated with a 1.23-1.38 fold increase in PCA risk (p ≤ 0.039), as shown in Table BIK rs4988366 AG & AG + GG; BNIP3L rs10503786 TT & TC + TT; CASP9 rs1052571 TT; IKBKE rs1539243 TC & TC + TT; PRKCE rs608139 CC; PRKCE rs935673 GG & AG + GG; TNFRSF1A rs4149576 AG, GG, & AG + GG; and TNFRSF1A rs4149577 TC & TC + CC] (p ≤ 0.043). However, after applying Bonferonni correction, none of these findings remained statistically significant under the per-allele, dominant and recessive genetic models.We examined 172 apoptosis-related sequence variants in relation to PCA risk and disease aggressiveness, as shown in Tables AKT3 rs10157763 TC & TC + TT; AKT3 rs10927067 AG & AG + AA; AKT3 rs12031994 TC & TC + CC;AKT3 rs2125230 AG & AG + AA; AKT3 rs2125231 AG + AA; AKT3 rs2345994 TC & TC + CC; AKT3 rs4132509 AC & AC + AA; BCL2L14 rs885720 AG & AG + AA; CARD8 rs10405717 TC & TC + TT; IKBKE rs11578093 GG & TG + GG; and RAF1 rs13060691 TG] (p ≤ 0.031), as summarized in Table IKBKE rs1539243 TT and PIK3CB rs500687 CC genotypes were moderately linked with a 44-56% reduction in aggressive PCA susceptibility (p ≤ 0.019). However, none of these loci remained significant after adjusting for multiple comparison bias.In terms of disease progression, eleven apoptosis SNPs were modestly associated with a 1.28-1.81 fold increase in the risk of developing aggressive PCA . These apoptosis-related SNPs, after adjusting for confounders, were modestly associated with PCA risk and/or aggressive disease. Yet, these findings lost statistical significance after adjusting for multiple hypothesis testing. Main effects were not observed for AKT3 rs2125230 and PRKCQ rs571715 in relation to PCA risk or disease progression in our study set. Wang and co-workers (2009) evaluated interactions among 5 apoptosis-related SNPs, including death receptor 4 (DR4), and pack-years of smoking in relation to bladder cancer using entropy-based MDR  was selected as the best predictor of disease outcome. Accuracy is a function of the percentage of true positives (TP), true negatives (TN), false positives (FP), and false negatives (FN) as defined as (TP + TN)/(TP + TN + FP + FN). ATAs are averaged across all 10 pieces of the data, in order to provide an estimate of the predictive ability of the loci in relation to the outcome of interest. We used cross-validation consistency (CVC) to measure the degree to which the same best MDR model was selected across the 10 divisions of the data. Models with a CVC of ≥ 8/10 using a 10-fold cross-validation were considered more carefully. If the MDR model met the CVC criteria, we selected models that had the highest ATAs. The combination of CVC and permutation testing were used to control for multiple hypothesis testing. Permutation testing results were statistically significant at the ≤ 0.05 level.The current version of MDR used in this study enabled the incorporation and adjustment of multiple covariates . To remo1, SNP2; disease status)] was greater than the total mutual information of each individual locus considered separately [I  + I ]. Interactions were further visualized using an interaction entropy graph, which uses a color-coding scheme to interpret interactions. Strong interacting factors, coded either red or orange, indicated high and medium levels of synergistic effects on outcomes, respectively. Weak interacting factors, coded either blue or green, denoted high or modest levels of redundancy between markers, respectively. Gold depicted independence and a midway point between synergy and redundancy. Design of interaction entropy graphs was accomplished using the Orange software [The interaction entropy algorithm, based on information theory, is a method to verify, visualize, and interpret combination effects identified by parametric  and non-parametric  statistical test,71-74. Jsoftware .1, SNP2, and a class variable . Thus, it describes the pairwise interactive effect on a discrete outcome. An epistasis network, or graph, consists of a set of vertices  and edges (pairwise interactions) that attach the vertices. In the current study, the statistical epistasis networks (SEN) were built by incrementally adding edges if their strengths were greater than a given threshold. Each vertex and each edge connecting two vertices were assigned a weight commensurate with the strength of main and interactive effects, respectively. The weight of a vertex is depicted by its size; whereby, a larger size is indicative of a higher main effect. Similarly, the thickness of the line between SNP pairs is directly proportional to the strength of their interaction.An important limitation of any gene-gene interaction analysis method is the combinatorial nature of the problem. Exhaustive analysis of all possible two-, three-, four-way combinations of SNPs creates a computational burden and significant multiple testing problems. We addressed this issue by pre-processing the data using statistical epistasis network (SEN) modeling, which has been described elsewhere . BrieflyWe used SEN to visually summarize the strongest individual SNP effects and SNP-pairwise interactions. The topology of the graph, consisting of SNPs and their pairwise interactions, was used to guide MDR modeling. This resulted in a reduction in the total number of SNP combinations. For instance, we reduced the gene-gene interaction analysis from 172 to 24 SNPs that resided within the major connected component with the largest number of vertices . The derived major component plot was validated by comparing: (1) the number of vertices and edges among the various connected "sub-networks"; and (2) the size of the major component plot of real data versus randomized data that underwent 1000 permutations. The latter compared data using a pairwise interaction strength cut-off of 1% and significance level of 0.05. To ensure that no significant interactions were identified, non-informative SNPs outside the major component plot were also analyzed by MDR. In essence, SEN-guided MDR facilitated logical prioritization of SNPs for gene-gene interaction analysis in relation to PCA outcomes.PCA: (PCA); SNP: (single nucleotide polymorphism); MDR: ; SEN: .The authors declare that they have no competing interests.NAL: conceptualized the project, conducted the statistical analysis and initial MDR modeling, interpreted study results, and composed the initial manuscript draft. ENR, SY, LRK: Intellectually contributed toward the introduction and/or discussion. TH: performed statistical epistasis network modeling. JZ and JR: conducted MDR modeling and/or SEN-guided MDR analysis. GNB & LRK: co-supervised data-management and statistical/bioinformatics analyses. LRK, DWH, GNB, JHM, KSK: served as mentors in the study design and implementation as well as data interpretation. All authors contributed to draft reviewing, editing, and approving the final manuscript draft.The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1755-8794/5/11/prepubTable S1. Corresponding Gene and dbSNP IDs for apoptosis-related sequence variants depicted in the Statistical Epistasis Network Modeling Graph, presented in Figure Click here for fileTable S2. Functional consequence of selected apoptosis-related Polymorphisms.Click here for file


FAM78B, contains three binding sites for the transcription factor PPARG and two binding sites for HNF1A, both previously implicated in the pathology of type 2 diabetes. The fact that both loci showed ancestry effects may provide novel insight into the genetic architecture of fasting plasma glucose in individuals of African ancestry.For samples of admixed individuals, it is possible to test for both ancestry effects via admixture mapping and genotype effects via association mapping. Here, we describe a joint test called BMIX that combines admixture and association statistics at single markers. We first perform high-density admixture mapping using local ancestry. We then perform association mapping using stratified regression, wherein for each marker genotypes are stratified by local ancestry. In both stages, we use generalized linear models, providing the advantage that the joint test can be used with any phenotype distribution with an appropriate link function. To define the alternative densities for admixture mapping and association mapping, we describe a method based on autocorrelation to empirically estimate the testing burdens of admixture mapping and association mapping. We then describe a joint test that uses the posterior probabilities from admixture mapping as prior probabilities for association mapping, capitalizing on the reduced testing burden of admixture mapping relative to association mapping. By simulation, we show that BMIX is potentially orders-of-magnitude more powerful than the MIX score, which is currently the most powerful frequentist joint test. We illustrate the gain in power through analysis of fasting plasma glucose among 922 unrelated, non-diabetic, admixed African Americans from the Howard University Family Study. We detected loci at 1q24 and 6q26 as genome-wide significant via admixture mapping; both loci have been independently reported from linkage analysis. Using the association data, we resolved the 1q24 signal into two regions. One region, upstream of the gene  Most genome-wide association studies performed to date have focused on individuals with European ancestry. Admixed African Americans tend to have disproportionately higher risk for many common, complex diseases. Disease or trait mapping in admixed individuals can benefit from joint analysis of ancestry and genotype effects. We developed a joint test that is more powerful than either admixture mapping of ancestry effects or association mapping of genotype effects performed separately. Our joint test fully capitalizes on the reduced testing burden of admixture mapping relative to association mapping. The test is based on generalized linear models and can be performed using standard statistical software. We illustrate the increased power of the joint test by detecting two loci for fasting plasma glucose in a sample of unrelated African American individuals, neither of which loci was detected as significant by traditional association analysis. Tang We illustrate application of the joint test by analyzing fasting plasma glucose among 922 non-diabetic, admixed African Americans from the Howard University Family Study (HUFS) conducted in the Washington, D.C metropolitan area. The prevalence of type 2 diabetes (diagnosed mainly on the basis of elevated fasting plasma glucose levels) among adults in the USA is currently 11.3%, ranging from 10.2% among European Americans to 18.7% among African Americans We first describe the characterization of local ancestry for the 922 admixed African Americans using 797,831 autosomal SNPs. The mean proportion of African ancestry was 0.797  and account for correlation for all markers chromosome-wide.To empirically estimate the testing burdens of admixture mapping and association mapping, we fit autoregressive models and estimated the effective number of tests based on autocorrelation. For example, for the first individual in our sample, there were five ancestry switches along chromosome 22  and the et al.et al.Adjusting for global ancestry will not completely control confounding due to local ancestry in association mapping i.e., p-values from admixture mapping while maintaining power and the genome-wide significance level for association. As expected, a large p-value from admixture mapping implies that the locus is less likely to affect the phenotype, thereby increasing the sample size necessary for association to reach genome-wide significance . Given that the ratio of the testing burdens for association mapping to admixture mapping for chromosome 22 is smaller than the ratio genome-wide, the gain in power demonstrated by these simulations underestimates the gain in power of BMIX over MIX at the genome-wide scale.We also compared the average power of our joint test to the MIX score We performed admixture mapping for fasting plasma glucose by linearly regressing fasting plasma glucose on local ancestry, adjusted for age, global ancestry, and sex. We detected two genome-wide significant loci , one at We performed association mapping for fasting plasma glucose by linearly regressing fasting plasma glucose on genotype stratified by local ancestry, assuming an additive genotype model, adjusted for age, global ancestry, and sex. The genomic control inflation factor was 1.009  and two binding sites for the transcription factor HNF1A  have been identified , East Asian ancestry , and Native American ancestry (Pima Indians) By sequentially updating the probability that a locus is a trait locus based on ancestry with the probability that the locus is a trait locus based on genotypic association conditional on ancestry, our procedure estimates the joint probability that a locus has ancestry and association effects. At chromosome 1q24, association mapping resolved the admixture signal into two regions, vs. individuals of African ancestry.In summary, we describe a joint test of ancestry and association for mapping disease susceptibility loci and trait loci in admixed individuals. Key properties of our test are that it maintains conditional independence of genotype and local ancestry and that it fully capitalizes on the reduced testing burden of admixture mapping relative to association mapping, making it more powerful than all existing joint tests. Upon application to fasting plasma glucose in African Americans, we identified two loci at genome-wide significance levels, whereas conventional association mapping yielded no new discoveries. Both loci have been identified previously by genome-wide linkage analysis, providing evidence of replication and indicating that linkage analysis, admixture mapping, and association mapping are all converging on the same loci. By taking advantage of fine-mapping afforded by association mapping and background linkage disequilibrium, we resolved one locus into two separate intervals. One of these intervals contains a promoter with multiple binding sites for transcription factors previously implicated in type 2 diabetes. The fact that both loci were discovered via admixture mapping directly implies that the genetic architecture of fasting plasma glucose is different in individuals of European ancestry First, we briefly review Bayes' Theorem p-values that can be transformed using quantile functions. Given a type I error rate i.e., both type I error rates are partially Bonferroni-corrected). We therefore need estimates of the effective number of tests for both admixture mapping and association mapping, which we obtain based on autocorrelation. For admixture mapping, we first estimate the effective number of tests for each chromosome for each individual by fitting an autoregressive model to the vector of local ancestries  and evaluating the spectral density at frequency zero Let the likelihood function p-values is that the latter accounts only for the density under the null hypothesis whereas the former also accounts for the density under the alternative hypothesis. On the other hand, a disadvantage of Bayes factors is that they, like p-values, reflect the probability of the data rather than the probability of a hypothesis. In contrast, posterior probabilities directly measure the probability of a hypothesis. A natural, objective threshold of posterior probabilities is 0.5, which is the point at which the hypothesis favored by the posterior odds switches.Two main quantities in Bayesian inference are Bayes factors and posterior probabilities. One advantage of Bayes factors over The algorithm consists of six steps.ith of individual, ith individual at the jth marker , and ith individual . We require the p-value from the test of Using generalized linear regression, perform admixture mapping by regressing phenotype on local ancestry, adjusting for global ancestry (and other covariates as appropriate). For example, let p-values from Step 1 into posterior probabilities. First, transform the p-values from admixture mapping into Convert the ith individual in the kth stratum, ith individual in the kth stratum at the jth marker , and Using generalized linear regression, perform association mapping by regressing phenotype on genotype, stratified by local ancestry, adjusting for global ancestry (and other covariates as appropriate). For example, let Combine the regression coefficients for genotype for the strata of local ancestry using inverse variance-weighted fixed effects. The pooled estimate of the genotype effect is given by p-values for the pooled estimates of the genotype effects combined over strata. The association test statistic Obtain association p-values into posterior probabilities using posterior probabilities from admixture mapping as prior probabilities. First, transform the p-values from association mapping into Convert the association All calculations were performed in R STF of 0.12, mimicking the amount of population differentiation between the African and European ancestors of African Americans. A sample of admixed individuals was generated with an average of 80% of the genome inherited from the first parental population, mimicking the amount of African ancestry in African Americans. For each marker and individual, the genotype was coded as 0, 1, or 2 copies of the derived allele and local ancestry was coded as 0, 1, or 2 copies inherited from the first parental population.The procedure to simulate admixed data under a vicariance model has been detailed previously To investigate whether adjusting for local ancestry is sufficient to control confounding due to global ancestry, we simulated two independent SNPs for a sample of 1,000 admixed individuals. The first SNP was the test SNP and the second SNP was untested. We estimated global ancestry by averaging local ancestries.Ethical approval was obtained from the Howard University Institutional Review Board and written informed consent was obtained from each participant.http://hapmap.ncbi.nlm.nih.gov/downloads/frequencies/2010-08_phaseIIIII/). We note in passing that we did not include imputation in our study because there is no agreed-upon standard approach to perform imputation in admixed samples at this time. Admixture mapping was performed by linearly regressing fasting plasma glucose on local ancestry, adjusted for age, global ancestry , and sex. Association mapping was performed assuming an additive genetic model by linearly regressing fasting plasma glucose on genotype stratified by local ancestry, adjusted for age, global ancestry, and sex.We used BMIX to analyze fasting plasma glucose among 922 non-diabetic, unrelated African Americans from the HUFS Click here for additional data file.Figure S2p-values.Quantile-quantile plot for association (EPS)Click here for additional data file.Table S1Adjusting for local ancestry does not control confounding due to global ancestry.(DOC)Click here for additional data file.Table S2Association results for 1q24 stratified by local ancestry.(DOC)Click here for additional data file.Table S3Clinical characteristics of the 922 participants.(DOC)Click here for additional data file.Text S1R code implementing the BMIX joint test.(TXT)Click here for additional data file.


Drosophila model in which high-sucrose feeding induces phenotypes similar to T2D to assess orthologs of human GWAS-identified candidate genes for risk of T2D and related traits.Genome-wide association studies (GWAS) identify regions of the genome that are associated with particular traits, but do not typically identify specific causative genetic elements. For example, while a large number of single nucleotide polymorphisms associated with type 2 diabetes (T2D) and related traits have been identified by human GWAS, only a few genes have functional evidence to support or to rule out a role in cellular metabolism or dietary interactions. Here, we use a recently developed HHEX, THADA, PPARG, KCNJ11) led to sucrose-dependent toxicity. Tissue-specific knockdown of the HHEX ortholog dHHEX (CG7056) directed metabolic defects and enhanced lethality; for example, fat-body-specific loss of dHHEX led to increased hemolymph glucose and reduced insulin sensitivity.Disrupting orthologs of certain T2D candidate genes (Drosophila approach. To our knowledge, this is the first large-scale effort to study the functional interaction between GWAS-identified candidate genes and an environmental risk factor such as diet in a model organism system.Candidate genes identified in human genetic studies of metabolic traits can be prioritized and functionally characterized using a simple  Drosophila melanogaster. In this study, we used Drosophila to screen candidate genes identified in human genome-wide scans as associated with risk of metabolic abnormalities such as type 2 diabetes. We show that a number of human candidate genes have fly orthologs that play an important role in Drosophila tolerance to high dietary sucrose. We further explored some of the specific metabolic abnormalities that can result when these genes’ activities are reduced in flies, focusing on a gene we call dHHEX (CG7056), the fly ortholog of human HHEX.The search for genetic risk factors for common human diseases often relies on the use of linkage and association studies to establish correlation between genomic markers and disease risk. These studies require additional functional evaluation of candidate genes, including their possible interaction with diet and environment. The number of candidate genes is typically large and the development of appropriate genetic tools in mammalian systems is slow. By contrast, large-scale genetic screens, using widely available genetic tools, are routinely conducted in the fruit fly Type 2 diabetes (T2D), a disease state characterized by impaired insulin sensitivity and hyperglycemia, is one of the world’s leading causes of mortality and morbidity -3. In reC. elegans and Drosophila to rodents and humans ,f Bodmer , snsGCN-n Abmayr , srp.HemBrückner , byn-GALtenstein ,54, and Drosophila semi-defined medium [We modified a commonly used d medium  as previd medium . BrieflytubP-GAL4, byn-GAL4, and snsGCN-GAL4 studies, flies carrying a GAL4-encoding transgene and a balancer as the homologous chromosome were crossed to flies carrying a RNAi-encoding transgene, and survival to pupariation was scored by counting non-tubby (driver>RNAi) and tubby  balancer) pupae, except for a small number of exceptions, where survival to adulthood of non-curly (tubP>RNAi) compared to curly  or non-stubble (tubP>RNAi) compared to stubble  animals was scored instead. In studies of other drivers, either a similar cross was performed and survival to adulthood was scored by counting non-curly (driver>RNAi) and curly  animals, or else rates of eclosion were compared for a fixed number of knockdown embryos compared to a fixed number of control embryos possessing the GAL4 insertion and the proper genetic background, but lacking the RNAi-encoding insertion. Counts that were extremely different from experimental replicates were excluded from analysis (3 out of over 800 replicates were excluded in this way). If fewer than 5 knockdown animals survived in all experimental replicates for a given comparison, then we considered the knockdown to be generally toxic and did not assess sucrose intolerance.In –4, corresponding to 113 crosses tested . For the diet survey, this threshold was 4.17 × 10–3, corresponding to 12 diets tested. For the driver survey, this threshold was 4.55 × 10–3, corresponding to 11 driver-phenotype pairs tested. We used confidence intervals for hypothesis testing; they could in principle also be used for effect-size comparison and equivalence testing.For each comparison, we used Fisher’s exact test to assess whether our data were consistent with the null hypothesis that relative survival of knockdown flies was the same on high- and low-sucrose feeding, as well as to compute point estimates and confidence intervals for the natural logarithm of the odds ratio (ln(OR)) for survival of the knockdown and control genotypes on high and low sucrose. We considered crosses to be hits when statistically significant with a 0.05 threshold, and we considered crosses to be strong hits when statistically significant with a Bonferroni-adjusted threshold. For the RNAi screen for sucrose sensitivity, this threshold was 4.42 × 10t-tests without assuming equal variances.Metabolic parameters were comparing using two-sided unpaired Computations were performed in R, a language and environment for statistical computing, version 2.15.1. Plots were generated in R, some using the ggplot2 package. Some tables were constructed using XeLaTeX and the longtable and booktabs packages.Hemolymph glucose and whole-animal triglycerides were measured as previously described . BrieflyGWAS: Genome-wide association study; HBP: Hexosamine biosynthesis pathway; HDL: High-density lipoprotein; LDL: Low-density lipoprotein; QT: Quantitative trait; SNP: Single nucleotide polymorphism; T2D: Type 2 diabetes.RLC and TJB are co-founders of Medros, Inc., which uses models of human disease for drug development.RLC, TJB, and FSC conceived of the project, and NN and FSC identified human and fly genes of interest. All authors contributed to the design of the experiments. PVR conducted hemolymph glucose measurements, JLF conducted mass and triglyceride measurements, and JP and JN conducted all other experiments. JP designed and conducted the statistical analysis. JP, PVR, NN, and TJB wrote this manuscript, all authors contributed to completing and revising it, and all authors read and approved the final manuscript.Includes Figure S1 and Tables S1–S8.Click here for file


To detect rare variants associated with a phenotype, we develop a novel statistical method that can use both family and unrelated case-control data. Unlike the currently existing methods, we first use family data to calculate weights to be given to rare variants, differentiating between concordantly affected and discordant sib pairs. These weights are then used in an association test applied to the unrelated case-control data. We applied the proposed method to the simulated sequencing data in Genetic Analysis Workshop 17 and identified two genes associated with the disease. Genome-wide association studies, which are based on the common disease/common variants assumption, have successfully identified susceptibility loci for complex traits. However, the variants discovered through these studies explain only a modest portion of the trait variability . With thBodmer and Tomlinson  suggesteith individual Madsen and Browning [Briefly, for the Browning  define aL is the number of variants, ijg is the genotypic score, and jw is the weight for the jth single-nucleotide polymorphism (SNP). The weight jw is defined as the inverse of the jth SNP’s standard deviation estimated in control subjects when the corresponding MAF is less than α (such as 0.02) and 0 otherwise. Then the Wilcoxon rank sum test is applied to do the association test. Madsen and Browning rank the genetic scores, calculate the sum of the ranks for case subjects as:where p-value using a permutation strategy. That is, they permute disease status among individuals 1,000 times to compute 1,000 statistics X, denoted and calculate the which follows approximately a standard normal distribution under the null hypothesis. Madsen and Browning  demonstrRecently, we have demonstrated that family data are useful for searching for rare variants ,8, becauL variants belonging to a group . We have shown that family data, such as affected sib pairs, have enriched information for detecting rare disease-associated variants because the same disease variants are more likely to segregate within a family [We start by assuming that we have a family . Thus eaA and a, where A always refers to the minor allele. For the ith sib pair and the jth SNP, we define a genotype score α be a predefined threshold. We always let α. For those SNPs with MAF ≤ α , we define A, A, and A and the other does not, where K is the number of other SNPs in the region with MAF <α carried by the other sib. For discordant sib pairs, A and the unaffected sib does not, A, and A, where K is the number of alleles with MAF <α present at the other SNPs carried by the affected sib.Assume that a SNP has two alleles Let:Nsib is the number of sib pairs. For the jth SNP, define:where jp is the MAF of the SNP, estimated from the case and control subjects combined. We rank the jb in descending order and give the jth SNP weight jw = jb if jb falls in the top quartile and weight jw = 0 if not. The proposed weight incorporates information about the variants shared (not shared) by affected (discordant) sib pairs.where DN unrelated case subjects and CN unrelated control subjects. Let k be the kth unrelated individual. For each SNP j , we let jw be the weight as found earlier using the sib pairs. We use the jw to calculate the kth individual’s genetic score, similar to the idea of Madsen and Browning [After defining the weights for individual SNPs, using either affected or discordant sib pairs, we use the weights to test for association between the phenotype and each set of variants in a group. We assume that we have Browning ; that iskjg is the number of minor alleles in SNP j for individual k. We then define:where where the summation is over the unrelated case subjects. Similarly, we define:calculated for the unrelated control subjects. Our null hypothesis is that no marker is associated with the phenotype; that is, we have where The Genetic Analysis Workshop 17 (GAW17) simulated sequence data set includes both family and unrelated individuals data, which is ideal for the proposed method. Each replicate is composed of 697 individuals in the family data set and 697 individuals in the unrelated individuals data set. There are 200 replicates in total, all with the same genotype data but with phenotype data independently simulated across the replicates.α = 0.01 as the MAF cutoff to define the rare variants and calculated weights based on the identified 38 affected sib pairs using the Eq. (4-5).We first performed an analysis using only one replicate, which was selected to be the 82nd replicate. To calculate the weights, we clustered the sib pairs into affected and discordant sib pairs. Based on the 82nd phenotype replicate, we identified 38 affected and 22 discordant sib pairs. We then set The 82nd phenotype replicate includes 209 unrelated case subjects and 488 unrelated control subjects. This data set was used to test for association in each of 3,205 genes.α = 0.01 was used to define rare variants for Madsen and Browning’s method.We compared the power of the proposed method with Madsen and Browning’s method using the same unrelated case-control data. The same MAF threshold of We expect there to be little or no power for detecting rare variants using a single replicate because of the small sample size. We therefore included additional replicates until we reached a sample size of 400 affected sib pairs and 2,400 case subjects and 2,400 control subjects. We used 400 affected sib pairs, which was suggested by our previous study . AlthougWe applied the proposed method and Madsen and Browning’s method to 3,205 genes using the 82nd replicate. As expected, we found virtually no power for either method.We next increased the sample size to 400 affected sib pairs to calculate the weights and an additional 2,000 case subjects and 2,000 control subjects for the association test using our proposed method. For comparison, we used 2,400 case subjects and 2,400 control subjects for Madsen and Browning’s method. Thus the total sample size is the same for both methods. Figure PICK3C2B, but our proposed method resulted in a much smaller p-value (8.67 × 10−10 vs. 1.48 × 10−5). Furthermore, the proposed method identified HSP90AA1 (p = 8.63 × 10−6), which was missed by Madsen and Browning’s method.We next examined the 15 causal genes generated in the simulations (Table HSP90AA1, which was missed by Madsen and Browning’s method. Our method demonstrates that incorporating family data can potentially improve statistical power to detect rare variants in an association analysis, which is consistent with the result of Zhu et al. [In this paper, we propose a novel method to analyze the GAW17 data set. Unlike the existing methods, the proposed method calculates the weights using either affected or discordant sib pairs. The proposed method requires that both the case and control groups and the family members are genotyped for the same set of SNPs or are resequenced in the same region. Compared with Madsen and Browning’s method, the proposed method detects the true causal gene The authors declare that there are no competing interests.XZ designed the study. TF performed the data analysis. TF and XZ drafted the manuscript. RCE revised the manuscript. All authors read and approved the final manuscript.


We conducted genetic association tests on 7,087 nonsynonymous SNPs in three GAW17 family replicates for Affected status with the β coefficient fixed for three quantitative phenotypes and compared these to an association model where the β coefficient was allowed to vary. Bivariate environmental correlations were 0.64 (± 0.09) for Q1, 0.798 (± 0.076) for Q2, and −0.169 (± 0.18) for Q4. Heritability of Affected status improved in each univariate model where a constrained β coefficient was used to account for stochastic environmental effects. No genome-wide significant associations were identified for either method but we demonstrated that constraining β for covariates slightly improved the genetic signal for Affected status. This environmental regression approach allows for increased heritability when the β coefficient for a highly correlated quantitative covariate is constrained and increases the genetic signal for the discrete trait.Joint analyses of correlated phenotypes in genetic epidemiology studies are common. However, these analyses primarily focus on genetic correlation between traits and do not take into account environmental correlation. We describe a method that optimizes the genetic signal by accounting for stochastic environmental noise through joint analysis of a discrete trait and a correlated quantitative marker. We conducted bivariate analyses where heritability and the environmental correlation between the discrete and quantitative traits were calculated using Genetic Analysis Workshop 17 (GAW17) family data. The resulting inverse value of the environmental correlation between these traits was then used to determine a new  The current availability of groups of correlated phenotypes for several common complex chronic diseases can aid in the study of these traits by providing data beyond what is contained in the phenotypes individually. Several earlier statistical genetic studies have shown that when correlations between phenotypes are explicitly modeled, they provide greater power than that provided by univariate analyses of individual traits -6. Jointβ coefficient for the quantitative trait, which was constrained to this value in a univariate analysis of affection status with the quantitative phenotype included as a covariate. Next, we compared the resulting model to a univariate analysis of affection status in which the quantitative trait was included as an unmodified covariate. Finally, we conducted genetic association tests using measured genotype analysis for affection status with each quantitative phenotype included as a covariate in two models: (1) a model in which the β coefficient was allowed to fluctuate and (2) a model in which the β coefficient was constrained. We used only the first three replicates of the GAW17 family data set to determine whether this method maximized the genetic signal for the true known genetic variants.Toward this end, we present a novel statistical genetics regression method that accounts for a portion of the environmental component using the Genetic Analysis Workshop 17 (GAW17) 1000 Genomes Project simulated family data between the discrete trait (Affected) and quantitative phenotypes Q1, Q2, and Q4 over all 200 replicates. We conducted bivariate polygenic analyses of the discrete trait with each of the three quantitative traits. We then used the resulting data from these analyses to calculate a new The GAW17 family data set contains 697 individuals divided into 194 nuclear families in 8 pedigrees with 202 founders from the 1000 Genomes Project. These family data include 13,875 autosomal single-nucleotide polymorphisms (SNPs) from 3,205 genes, with 7,087 of these genotyped SNPs in 1,890 genes being nonsynonymous. Each of the 200 simulated data sets includes the following information for each individual: affection status, three continuous quantitative traits , age, smoking status, and sex [β coefficient for the quantitative trait using the equation:For the environmental regression, we used maximum-likelihood methods, taking into account relationships among family members, to determine heritability for Affected status and each of the three quantitative traits in a bivariate polygenic model using the computer program Sequential Oligogenic Linkage Analysis Routines (SOLAR) . This biwhere:eρ is the environmental correlation between the discrete trait and the quantitative trait.β coefficient for the quantitative trait and constrained it in a univariate polygenic model, using the discrete phenotype as the trait and the quantitative variable as a covariate. This resulted in a new heritability, calculated by:Next, we used the inverse of the resulting value as the eβ is the constrained β coefficient, gρ is the genetic correlation between traits, Qh is the square root of Dh is the square root of β coefficient was allowed to fluctuate.where p-value for association using Affected status as the trait and Age, Sex, and Smoking as the covariates. To control for potential population stratification, we performed principal components analysis on genotype scores for 6,178 polymorphic synonymous SNPs in the 202 founders using the prcomp routine available in the R statistical package (http://www.r-project.org) [For the association analysis we conducted a measured genotype analysis on each of the 7,087 nonsynonymous SNPs to calculate a nominal ect.org) . We inclβ coefficient for the quantitative trait constrained in order to determine whether this method improved power to detect association. Because of issues of multiple testing, we initially used a highly conservative Bonferroni correction of 7.05 × 10−6 for genome-wide significance based on the GAW17 family data. However, as a result of linkage disequilibrium patterns in these data, it is likely that the total number of effective SNPs is lower than the total 7,087 SNPs used in the study. Therefore we calculated the effective number of SNPs using Moskvina and Schmidt’s method implemented in SOLAR [p-value and the effective number of SNPs to determine an adjusted p-value for each gene to be used in multiple testing. This p-value was calculated using the equation:We conducted measured genotype analysis for each polymorphic SNP. The number of minor alleles was added to the quantitative polygenic genetic model as a covariate to assess the effect of the SNP genotype on the mean of the trait. This model was fitted to the data and compared with the null model of no difference in trait mean by genotype using a likelihood-ratio test. Twice the difference in log-likelihoods of these models was distributed as a chi-square random variable with 1 degree of freedom. The resulting likelihood-ratio test statistic was recorded for each nonsynonymous SNP. We then repeated this measured genotype association analysis with the p-value, “nominal” is the uncorrected p-value, and “effective” is the effective number of SNPs. This approach allows for nonindependence among family members and accounts for effects of other potential covariates [where “corrected” is the corrected variates .For the environmental regression analysis, Table β coefficient was calculated for all three quantitative phenotypes , and the inverse value was constrained in a univariate polygenic model, for affection status, as a covariate along with Age, Sex, and Smoking. This was then compared to a polygenic model for affection status where the quantitative phenotype was not constrained but included as a covariate. Overall, constraining the β coefficient improved the heritability of affection status through accounting for environmental correlation with each of the three quantitative phenotypes. Q2 demonstrated the greatest change in heritability for affection status with an average increase of 0.118  were found in these family data.We conducted the genetic association analysis on affection status adjusting for all three quantitative phenotypes in the first three replicates of the data set. We compared a measured genotype association analysis of affection status in which the β coefficient, we also found a slight increase in the average chi-square differences  for SNPs truly associated with affection status in these family data. Although there is only a slight increase in chi-square, there are only 12 SNPs  that are truly associated with affection status in the GAW17 family data. Of these 12 SNPs, only 5  are present in more than five individuals, indicating that we may have limited power to accurately detect genome-wide significance in these data.No genetic association that met our conservative criteria for genome-wide significance was detected for either the free association or the environmental regression association model. This lack of significant association may be due to the small sample size and the limited number of “true” Affected variants 12 SNPs) within these family data. Therefore we investigated the average differences in chi-square values for association tests in three different data sets under the assumption that an improvement in heritability would improve the genetic signal associated with affection status while decreasing the overall signal for nontrue variants (Table  SNPs witβ coefficient for our quantitative trait. We found that this increased our average heritability when the β coefficient for the quantitative trait was constrained. We then compared two measured genotype association analyses, one in which the β coefficient was constrained for the quantitative trait to account for environmental correlations and the other in which the β coefficient was allowed to vary. Neither method identified any true associated variants in the GAW17 family dataset when a strict correction for multiple testing was used, but the novel environmental regression method did allow for an increase in the chi-square value for SNPs known to be associated with affection status, particularly in replicates in which the heritability was improved.As next-generation sequencing data become more available, an important consideration will be to maximize the ability to detect rare variants that have a large effect on chronic disease. The easiest way to detect these rare variants will be through large pedigrees, because rare variants will be amplified in families. Our results suggest that by controlling for some of the stochastic environmental noise between two highly correlated traits, we can improve the ability to identify genetic variants in pedigrees through an increase in heritability. For the current study, we proceeded with a two-step process. The first step was to conduct a bivariate polygenic analysis between a discrete trait and a quantitative trait to calculate a The authors declare that there are no competing interests.PEM carried out the statistical analysis, participated in the study design and drafted the manuscript. JWK aided in the statistical analysis and participated in the study design. TDD participated in the study design and statistical analysis. LA aided in the study design and helped draft the manuscript. JB conceived of the study and participated in its design and coordination.


The advent of affinity-based proteomics technologies for global protein profiling provides the prospect of finding new molecular biomarkers for common, multifactorial disorders. The molecular phenotypes obtained from studies on such platforms are driven by multiple sources, including genetic, environmental, and experimental components. In characterizing the contribution of different sources of variation to the measured phenotypes, the aim is to facilitate the design and interpretation of future biomedical studies employing exploratory and multiplexed technologies. Thus, biometrical genetic modelling of twin or other family data can be used to decompose the variation underlying a phenotype into biological and experimental components.Using antibody suspension bead arrays and antibodies from the Human Protein Atlas, we study unfractionated serum from a longitudinal study on 154 twins. In this study, we provide a detailed description of how the variation in a molecular phenotype in terms of protein profile can be decomposed into familial i.e. genetic and common environmental; individual environmental, short-term biological and experimental components. The results show that across 69 antibodies analyzed in the study, the median proportion of the total variation explained by familial sources is 12% (IQR 1-22%), and the median proportion of the total variation attributable to experimental sources is 63% (IQR 53-72%).The variability analysis of antibody arrays highlights the importance to consider variability components and their relative contributions when designing and evaluating studies for biomarker discoveries with exploratory, high-throughput and multiplexed methods. There is an enormous unmet need for biomarkers to characterize disease type, status, progression, and response to therapy. A biomarker, which can be defined as a physical sign or laboratory measurement that serves as an indicator for biological processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention ,2, can tProteomics, the large-scale study of the protein content of cells, organs or organisms, offers the potential to evaluate global changes in protein expression, protein interaction patterns and their post-translational modifications that take place in response to normal or pathological stimuli. The availability of DNA microarray analysis permits expression of thousands of genes to be monitored simultaneously, but RNA expression has been found to correlate significantly to only one third with the corresponding actual protein content . TherefoRecent technological advances in the field of genomics and proteomics have also brought about a new statistical research area, the analysis of data from high-throughput screening experiments. Using protein microarray technology, the profiles of thousands of proteins can be monitored in a high-throughput manner with the aim of selecting a subset of proteins that could be characterised as potential biomarkers creating possibilities for diagnostic, prognostic and disease progression monitoring . When prin utero, dietary and socio-economic effects due to common upbringing. Identical/monozygotic (MZ) twins derive from a single fertilized egg and therefore inherit identical genetic material while non identical/dizygotic (DZ) twins share 50% of their genetic material. In a classical twin study the assumption is that MZ and DZ twins share the same degree of similarity in their environments and therefore one compares phenotypic concordance within MZ twin pairs to the concordance within DZ twin pairs. Comparing the resemblance of MZ twins for a trait or disease with the resemblance of DZ twins offers the first estimate of the extent to which genetic variation determines phenotypic variation of the trait or disease. The sources of variation commonly considered in genetics are additive genetic influences , dominant genetic influences , common environment (influences shared by family members e.g. socio-economic status) and individual environment  and common environmental effects.The phenotype of an individual might change as a result of complex, dynamic interactions between an individual's genome and environmental factors. To characterize and quantify the contributions that genes, the shared and the individual-specific environment and the interactions of these make to human complex traits and phenotypes, we use data from relatives who grow up in similar environments but are of differing genetic relatedness . For a long time, twin studies  have beeIn the following, we have investigated the variance of exploratory affinity arrays using longitudinal twin study.Important attributes of discovered biomarkers, in addition to being associated with a disease, are that they can be measured with precision (low variance) and exhibit relatively low amounts of short-term variability relative to the effect size of the difference between healthy and diseased individuals . For antFor this study the measured relative quantity of interest is the intensity of fluorescence emitted and measured when antibodies immobilized onto beads capture their target protein from a sample . To asseUsing singular value decomposition (SVD)  we projePlots of the data after normalization, removal of outliers and Box-Cox transformations are presented in Figure For each antibody the percentage of total variance attributable to familiality (fam), individual environment (env), common visit (cv), individual visit (iv) and residual experimental effects (exp) each antibody is presented in Table Figure In what follows, we present summaries of the proportion of non-experimental variance attributable to familiality, individual environment, common visit and individual visit. The boxplots in Figure Highlighting those HPA antibodies with most preferred characteristics, we identified five interesting antibodies where more than 50% of the total phenotypic variance is attributable to stable biological  variability. Among these target proteins were interleukin 12 (il12a), a heterodimeric 70 kDa glycoprotein with implications in cell-mediated immunity  targetedThe results suggest that some antibodies are more suitable and promising than others and that they can be potential candidates to be used further in biomarker discovery studies. Among these, HPA006279 has been shown to reveal interesting differences in plasma protein profiles in Metabolic syndrome cases and controls . The ideIn this paper we use a linear mixed-effects model in a unique twin design with duplicated repeated measurements to apportion the total variation of molecular phenotypes (protein profiles) into biological and experimental  variation. Understanding the sources of variation  inherent in the measurement of a molecular phenotype is a key step in assessing the potential for stable, informative biomarkers. We observed that across the 69 antibodies the median proportion of total variation attributable to familial sources was 12%. This familial component is consistent with protein profiles having the potential to reflect the polygenic basis of complex disease. Further, across the 66 HPA antibodies, the median proportion of total variation explained by stable sources  was 25%. Stable variation in the current setting comprises that a protein profile remains constant within an individual over the course of the sampling period. A small proportion of variation originated from the short-term biological component, individual visit (median proportion 6%). Common visit represented an inconsiderable amount of variation. Most of the variation originated from experimental sources (median proportion 63%). To our current knowledge, the present study is the first to address the key issue of investigating sources of variation in data generated by exploratory antibody microarrays. It should provide important information when aiming at designing and utilizing such assays and be valuable for multiplexed and quality controlled assays [Ultimately, diagnostic tools built on markers discovered via these screening approaches could become valuable approaches to predict disease state and progression. As an example, antibodies that allow the comparison of individuals that are discordant for diabetes and diabetes-related clinical traits would be useful for identifying individuals likely to suffer from diabetes in the future, long before conventional diagnostic techniques can prove effective. In this way these affinity-based proteomics discoveries would become useful in clinical settings.However, most antibodies used in this screening method have a large residual variance suggesting that a large proportion of variation in the data is experimentally derived. Potential (and non-separable) sources of this experimental variation, which exclude sample collection, preparation and storage, are the:(i) complexity and composition of the serum samples which has an effect on the assays;(ii) biotin modification of samples with regard to the numbers and variability of modifications introduced per molecule and sample;(iii) sample treatment in terms of liquid transfers, heating, and assay buffer dilution;(iv) assay procedure with immobilized antibodies selectively capturing aggregated or free molecules from the surrounding solution;(v) fluorescence-based read-out being influenced by bleaching and dye incorporation onto the target molecules.(vi) specificity of antibody binding events.Addressing these issues would lead to a reduction in the proportion of phenotypic variation arising from experimental sources. This would in turn reduce the sample sizes  required to detect epidemiological effects of interest. A reduction of the experimental variability, possible to achieve by using two antibodies to detect a target protein, would ensure that the experimental noise does not swamp biological signals of interest. The technical precision of such a measurement and of other antibodies can be improved, either by addressing the issues outlined above, or, in the short term, by assaying samples in technical replicate.Research in the field of proteomics is advancing, with affinity-based approaches emerging alongside classical mass spectrometric approaches. With array-based proteomics becoming a promising area in the field of biomedical research, decomposition of the underlying variation in protein profiles into biological  and experimental components is an important and useful step in exploring the applicability of antibody arrays for the exploration of the proteome. Ultimately, such proteomic strategies may lead to new disease markers and drug targets can be identified, benefitting from the possibilities offered by the versatility of both the employed affinity reagents and multiplexed techniques.In this paper we longitudinally collect serum samples from a cohort of 77 twins (56 MZ pairs and 21 DZ pairs) to explore the sources of variation underlying antibody array-based protein phenotypes with the aim of aiding the design and interpretation of future proteomic research. We use a mixed-effects modelling approach to obtain estimates of variance components.familiality (the combined effects of genetic and common environment) and individual environment, both of which are longitudinally stable biological components. The two short-term biological components are common visit and individual visit, which respectively measure the amount of shared (by twins within a pair) and non-shared longitudinal variation observed over the sampling period of the present study .This is a longitudinal family study whose design involves duplicate measurements over time in a sample that includes related individuals (twins). Consequently it combines the features of a longitudinal study (the power to study the pattern of changes in a trait over time) with the features of a cross-sectional twin study .). The study design allows us to break down the observed molecular phenotypic variance into four biological components. These are http://www.twinsUK.ac.uk, and invited to participate in this study. Recruitment of the twins was as follows: eligible twins were sent an information sheet containing details of the study as well as two consent forms. If the twins agreed to participate they signed and sent one copy of their consent forms to the administration team at the Department of Twin Research and genetic epidemiology (DTR), King's College London. Once a consent form was received, a member of the administration team would contact the twins by letter and phone to book their appointment. In addition, 68 twins (34 MZ pairs) were asked to re-attend once they had successfully completed the first visit with the time between the two visits ranging from 63 to 99 days (26 twins), 104 to 140 days (34 twins) and 150 to 216 days (8 twins). At each visit to the clinic, the twins were in pairs.A total of 154 healthy, postmenopausal, female twins, comprising of 56 MZ and 21 DZ pairs, were ascertained from the TwinsUK database at St. Thomas' Hospital Fasting blood samples were collected from all selected twins from one or both visits rendering a total of 222 samples with samples from individuals of a twin pair taken on the same day. These were to be used for the study of biological and technical variability in the various molecular phenotyping platforms, focusing on the unique opportunities afforded by studies in a large set of clinically well characterised monozygotic and dizygotic twins. These studies were all part of the Molecular Phenotyping to Accelerate Genomic Epidemiology (MolPAGE) project. For the MolPAGE project, eligible volunteers were healthy, Caucasian females of North Europe descent, aged between 45-76 years old. The study was approved by St. Thomas' Hospital Research Ethics Committee (EC04/015 Twins UK). The experiments and subsequent analyses presented in this paper are based on serum samples extracted from the fasting blood samples.Protocols for antigen selection, cloning, protein expression, immunization of rabbits, and affinity purification to yield polyclonal antibodies were performed as described previously ,27. All 6 beads in a 96-well half-area microtiter plate (Greiner BioOne) and beads were allowed to sediment for 30 s on a magnetic bead separator  prior to the removal of supernatants. For an albumin binding Affibody® molecule, 4 μg were coupled. Beads were stored in a protein-containing buffer  with NaN3. All coupled beads were re-suspended with sonication in an ultrasonic cleaner (Branson Ultrasonic Corporation) for 5 min prior to storage at 4°C. All antibody-coupled beads were counted using the Luminex LX200 instrument and the coupling efficiency for each antibody was determined via R-Phycoerythrin labeled anti-rabbit IgG antibody (Jackson ImmunoResearch). A bead mixture was created in solution, and optimized as previously described [Antibodies were coupled to magnetic carboxylated beads  in accordance to the manufacturer's protocol with minor modifications. For each antibody, 3.2 μg were coupled to 10escribed .Protocols for sample labelling and assay procedure were based on earlier work . At firsAll samples were utilized without removing unincorporated biotin and diluted 1/50 utilizing a liquid handler in a assay buffer composed of 0.5% (w/v) polyvinylalcohol and 0.8% (w/v) polyvinylpyrrolidone (Sigma) in 0.1% casein in PBS (PVXC) supplemented with 0.5 mg/ml non-specific rabbit IgG (Bethyl). A second heat treatment was performed as above and 45 μl sample were added to 5 μl of bead mixtures in a microtiter plate (Greiner BioOne). Incubation took place over night on a shaker at an ambient temperature. Beads were washed in wells with 3 × 50 μl PBST  on a magnetic bead separator with a liquid handling system followed 10 min with 50 μl of a stop solution containing 0.1% paraformaldehyde in PBS. Beads were washed 1 × 50 μl PBST and 30 μl of 0.5 μg/ml R-Phycoerythrin labeled streptavidin (Invitrogen) in PBST were added and incubated for 20 min. Finally, beads were washed 3 × 50 μl and measured in 100 μl PBST. Measurements were performed using a Luminex LX200 instrument with Luminex xPONENT software and counting at least 50 events per bead ID, displaying binding events as median fluorescence intensity. A summary of the experimental work flow is presented in Figure Of the 222 serum samples obtained from fasting blood, 48 samples from 24 MZ twin pairs were split into two aliquots  rendering an additional 48 sample aliquots. The resulting 270 sample aliquots were then randomized and placed onto three 96-well plates, where each plate contained an extra 6 reference samples. Subsequently a total of 69 antibodies were utilized to render a 270 by 69 matrix of protein (antibody) array data.Probabilistic quotient normalization (PQN)  was usedIntensity distributions of the antibodies after normalization using PQN were investigated to identify samples that were potential outliers. In order to detect potential outliers we used singular value decomposition  to projeAll subsequent analyses were done on data that had been normalized using PQN and had undergone removal of outlying samples. Further, a Box-Cox transformation  was perfFor each molecular phenotype (antibody) we used a statistical model to quantify the biological and experimental variation inherent in the phenotype. As mentioned before, the aim was to partition the total variability in a molecular phenotype into variability that is attributable to familiality , individual environmental, common visit, individual visit and experimental components, respectively. Note that familial and individual environmental variability together make up stable biological variability.ijkl denote the normalized and transformed intensity of the lth aliquot replicate , at the kth visit  of the jth twin  from the ith twin pair . The data for each antibody was modelled using a linear mixed-effects model [As mentioned previously, the measured quantity of interest was the intensity of fluorescence emitted when an immobilised antibody captured an antigen in a sample. For each antibody let Yts model -32:p is the mean intensity for samples on plate p  maps sample aliquots to plates), A is the additive genetic effect, D is the dominant genetic effect, C is the common environment effect, E is the individual or unique environment effect, W is the common visit effect, V is the individual visit effect, and lastly ε represents the residual experimental effects. The plate mean μp is a fixed effect, while A, D, C, E, W, and V are random effects. It is assumed that the random effects are additive and independent. This implies that the total phenotypic variance can be decomposed as:where μThe covariance between phenotypic measurements on a pair of samples gathered at the same visit from monozygotic twins is Var(A) + Var(D) + Var(C) + Var(W), and for dizygotic twins is (1/2)Var(A) + (1/4)Var(D) + Var(C) + Var(W). Familiality (fam) is the proportion of variance attributable to genetic and common environmental effects:For twin data, the variances Var(A), Var(C) and Var(D) are not all identifiable. However familiality is an estimable function of these variance parameters.For each antibody, maximum likelihood (ML) estimates of the variance components were obtained by fitting model (1) using the lmer function from the lme4 package in R  after noSubsequently the familial variance (which represents the combined effects of genetics and common environment) was obtained as the sum of the estimated variances of H and M, i.e familial variance = Var(H) + Var(M).1 and x2 are the phenotype measurements of two monozygotic (MZ) twins then the covariance matrix of the measurements is such that: Var(x1) = Var(x2) = Var(H) + var(M) +Var(E) and covariance = Var(H) + Var(M). Similarly if x1 and x2 are the phenotype measurements of two dizygotic (DZ) twins then covariance matrix of the measurements is such that: Var(x1) = Var(x2) = Var(H) + Var(M) + Var(E) and covariance = Var(H). A similar approach has previously been used and elaborated on metabolomics data [Note that if xics data .The PQN pre-processing procedure that we applied should mitigate any systematic differences between measurements in the different wells introduced by the instrumental time drift between plate well 1 through to plate well 96. However, in order to investigate if there were any substantial significant intensity-drift effects remaining after PQN we also fit a second model (hereafter referred to as model 2) by introducing a linear, plate-specific well location term into model 1, where well location is a number between 1 and 96 representing the position of a sample in the plate wells. That is in model 2, for each antibody we fit a linear mixed-effects model with linear, plate-specific intensity-drift fixed effects and the random effects A, D, C, E, W, and V as before. Subsequently Akaike's information criterion ,36 was uwhere k is the number of parameters in the model, and L is the maximized value of the likelihood function for the estimated model. For a given a data set, several competing models may be ranked according to their AICs and the model with the smallest AIC is chosen as the one that fits the data best. The pre-processed data and R script used to perform the variability analysis can be found as Additional Files HPA: Human Protein Atlas; IQR: Interquartile range; Fam: familial sources; Env: individual environment effects; Cv: common visit effects; Iv: individual visit effects; Exp: experimental effects; MZ: monozygotic; DZ: dizygotic; PQN: probabilistic quotient normalization; AIC: Akaike's information criterion; LOWESS: locally weighted scatterplot smoothing.The authors declare that they have no competing interests.BSK did the data analysis and generated the manuscript, GN provided guidance on the data analysis and helped generate the manuscript, MN has carried out array experiments and participated in data analysis, MR provided guidance on the data pre-processing and analysis, AB was responsible for storage and distribution of the serum samples, CCH supervised aspects of this manuscript, MU supervised aspects of this manuscript, PN has edited the manuscript and supervised the experiments, TDS supervised aspects of this manuscript, JMS generated the manuscript, designed and carried out array experiments and participated in data analysis. All authors read and approved the final manuscript.p proteins, indexed by k ∈ {1,...,p}. Suppose that there are n samples, indexed by i ∈ {1,...,n}, and each is measured in technical duplicate, with duplicates indexed by j ∈ {1, 2}. A model for the observed data is:Consider a proteomics platform, which measures the abundance of where:kth protein as measured in the jth replicate of the ith biological sample• μk)  of the measured abundance of protein k• k in sample i around μk) . It is less appropriate to use the correlation across proteins, s1, as this is affected by the overall scale of the range of measurement. For instance, for the same level of technical variation, s1 can be made arbitrarily large by increasing the range between the expected values of the lowest- and highest-expressed protein levels (i.e. increasing the range of the μk).A different, commonly used (and often misinterpreted) measure of correlation would be calculated as follows. For the pair of replicates of sample 1, form the two vectors Protein profiles before data processing. Profiles from all antibodies across all samples are shown before any data processing, with the red line indicating the locally weighted scatterplot smoothing (LOWESS).Click here for fileProtein profiles after data processing. Profiles from all antibodies across all samples are shown after any data processing, with the red line indicating the locally weighted scatterplot smoothing (LOWESS).Click here for filePre-processed data. The csv file contains pre-processed intensity values for all antibodies across all samples.Click here for fileR script for variability analysis. The R script can be used to perform the variability analysis with the pre-processed data from Additional File Click here for file