Typically, a marker-based matrix of genomic similarities among individuals (G) is constructed, to account more properly for the covariance structure in the linear regression model used. We show that the generalized least-squares estimator of the regression of phenotype on one or on m markers is invariant with respect to whether or not the marker(s) tested is(are) used for building G, provided variance components are unaffected by exclusion of such marker(s) from G. The result is arrived at by using a matrix expression such that one can find many inverses of genomic relationship, or of phenotypic covariance matrices, stemming from removing markers tested as fixed, but carrying out a single inversion. When eigenvectors of the genomic relationship matrix are used as regressors with fixed regression coefficients, e.g., to account for population stratification, their removal from G does matter. Removal of eigenvectors from G can have a noticeable effect on estimates of genomic and residual variances, so caution is needed. Concepts were illustrated using genomic data on 599 wheat inbred lines, with grain yield as target trait, and on close to 200 Arabidopsis thaliana accessions.Standard genome-wide association studies (GWAS) scan for relationships between each of  The advent of an enormous amount of DNA markers has given impetus to thousands of genome-wide association studies (GWAS) in humans, plants, and livestock . This method was subsequently enhanced by use of mixed linear model methodology, originally developed in animal breeding by A  linear regression of some phenotypic measurement on the number of copies of a reference allele at a single marker locus, ing by A . Given tgenetics . Along tG in order to perform GWAS in some optimal manner, e.g., to account for population stratification, was unclear. Consider the following question: if marker j in a GWAS is tested as a fixed effect in a SMR mixed model that includes G in the covariance structure, should the contribution of such marker to genomic similarity be removed from G? It is well understood  would need to be constructed and inverted . The analysis would be impractical if the number of variants tested is large, as is the case with sequence data. It is fairly obvious that if p is very large, the impact of removing a marker should be nil. However, the question posed above deserves an unambiguous answer.The preceding methods were also adopted and enhanced by human geneticists. od e.g.,  that if G, and regressions on a subset of these were regarded as fixed in a mixed model, but with G used without any modification; G used as covariates in the fixed part of the model are also an implicit part of G. Should G then be left intact? On one hand, the view could be taken that if an eigenvector is used as a covariate with a fixed regression coefficient, its contribution to G should be discounted. On the other hand, removal of the eigenvector could degrade the measure of similarity among individuals. G would provide a solution to the problem  when the aim is to infer marker effects and genomic heritability. However, such attenuation shrinks all regressions on eigenvectors to 0 (to distinct degrees), and shrinkage on regressions on markers with medium or large effect sizes, or on eigenvectors used to account for population stratification, should not be exerted. Under such reasoning, the contribution to G of a marker or of eigenvector(s) associated with fixed regressions, should be discounted if one seeks net effect size estimates and corresponding tests of hypotheses. Another view , with the purpose of accounting for population stratification, with the remaining eigenvectors used to induce similarities among individuals. In particular, we show algebraically that the generalized least-squares estimator of the regression on a marker is invariant with respect to whether or not the marker (or set of markers) treated as fixed is used when building G. It is also shown that removal of eigenvectors does matter. The manuscript is organized as follows. Basic concepts of GWAS conducted with kinship matrices in the model are reviewed in the sections under Standard Approaches Used in GWAS. Next, in Impact of Removing Markers from the G-Matrix, it is shown how inverses of the p needed genomic relationship (or of phenotypic covariance) matrices can be found in a convenient manner, and use the results to prove the invariance indicated above; removal of eigenvectors is also discussed in this section. To illustrate main, as well as related, concepts, data on wheat inbred lines and on A. thaliana were used, as described in Case Studies with Wheat and Arabidopsis Data. Technical details are shown in Appendices to the paper and toy examples are in Supplemental Material, File S1.In this paper, we address the construction of n × p marker matrix be X = {ijx}; its thj column xj  contains marker genotype codes, i denotes individual, and n is sample size. Marker (SNP) genotypes can be coded as 0,1,2 for aa, Aa, AA individuals, respectively, where A is a reference allele; such coding captures additive genetic effects in the main. Markers and phenotypes are typically centered , and most GWAS studies use the SMR modelj carried by e.g., smoking, age, and region) can be included in the model but these are not needed for the purposes of this discussion. y, given marker genotypes, is that of the SNP in question, hopefully flagging some genomic region in an unambiguous manner (the assumption is unlikely to hold for a complex trait).Let the y on the number of copies of allele A isp values must be taken with caution when a complex trait is confronted because of model specification error. Further, family effects or genomic similarities among individuals affect the variance–covariance structure of the observations, and OLS SMR ignores this issue. Because of the assumption of independence of residuals, the SMR approach sees more statistical information in the data set than there actually is.The OLS estimator of the regression of p matrices of order G is positive definite, and that it has rank n. If G does not possess a unique inverse as its rank would be p at most. If p is large, the contribution of marker j to diagonal and off-diagonal elements of G is negligible relative to that made by the other Write the raw marker genotypes as G renders the GWAS model more effective because similarities among individuals are represented in a more informed manner. Here, the regression model (1) is augmented with a random genomic effect i (assumed to vary at random in the population) that is captured by all p markers; An improvement over OLS-SMR uses realized relationships in the regression model, to account for correlations between individuals. With markers, one can observe variable degrees of similarity between full-sibs, that differ from, say, the expected additive relationship of nherited . This feG means that genomic relationships enter into the phenotypic variance–covariance structure and Let standard  represene.g., As pointed out earlier, if a regression on a marker is treated as a fixed effect, it would seem sensible to remove its contribution to on e.g., e.g., a priori. Actually, the Bayesian treatment of a fixed effect  implies an infinite prior variance provided the flat prior is unbounded. Here, we examine the question of whether or not a marker effect declared as fixed can also be allowed to have a random effect, as implied when including the marker in question in the building of G.Conceivably, a marker effect could be modeled as the sum of a fixed and of a random component; the fixed part would index the mean of the distribution, and the random part would contribute to the likelihood only through covariance structure. This view, however, contradicts quantitative genetic theory, where quantitative trait locus (QTL) effects are fixed and genotypes are random , even if n is moderate. However, use of (47) in Appendix A producesp inverses is replaced by one involving a single inversion plus a series of matrix multiplications. Toy examples are in File S1.Let t models . The GLSj is used or excluded when building G? Consider two GLS estimators: one with and the other without marker j included in G. Let these estimators be G. The difference between the two GLS estimators isAppendix B that i.e., exclusion of marker j when forming G does not affect the generalized least-squares estimator. This result holds provided that G is built consistently with the way in which i.e., the Does it make a difference whether or not marker j is treated as fixed. The variance isEven though the GLS estimator can be computed in the usual form, a subtle point is that Appendix A producesG needs to be inverted only once.For model (10), an alternative way of computing j is used when building G. It just remains to see whether or not the same holds for BLUP i.e., without using the mixed model equations) representation of BLUPG. It is shown in Appendix C that As shown earlier, the It is concluded that point estimates and point predictions from GLS m markers X when forming G, and their effects are tested jointly for association. Let m markers is used. ThenAppendix A givesExpressions (14), (15), and (22) generalize to the situation where m markers are left out in the build-up of m), the GLS estimator ism regressions obtained without any modification of the genomic or phenotypic variance-covariance matrices. The variance of the estimator isAssuming that variance components remain unaltered if G (suppose it is positive-definite) producesG and n eigenvalues; note that i.The eigen-decomposition of G. Suppose that the regressions on the first two eigenvectors are treated as fixed to account for some structure; the SMR model becomesPopulation structure is often accounted for by regressing phenotypes on some eigenvectors or on PC of y, and take the variance components as known, so thatAppendix A to (38) producesp phenotypic variance-covariance matrices, one extracts eigenvectors from Let e.g., A publicly available wheat data set was employed to investigate several issues associated with removing markers or eigenvectors from age BGLR ; these dA. thaliana data set described by We also used the vs. GLS in the wheat data at two specified values of the variance ratio or, equivalently, of genomic heritability. Marker genotypes were centered to have a mean of zero, marker by marker, for all 1279 DArT polymorphisms; phenotypes were already standardized to have a null mean and variance 1. For OLS, computation was done using the lm function available in the R package (http://www.r-project.org/). In GLS, the genomic relationship matrix used was as follows: 1) with i and j. 2) We then formed Appendix D.We compared SMR-OLS p values) for OLS, the GLS analyses at Appendix D, one can calculate the GLS statistics employing OLS computations); alternative measures are discussed by The SMR OLS and GLS analyses gave similar inferences in terms of regression coefficients, i.e., failure to account for other variants is one of the most obvious explanations of missing heritability  The MMR estimates were larger in size and more variable (SE not shown) due to the colinearity caused by strong LD between some markers. In theory, SMR may have a larger bias  than MMR, but the latter produces estimates with more variability. The mean-squared error of estimation cannot be evaluated in the absence of knowledge of model parameters; the true marker effect depends on the effects of the QTL affecting the trait, and on the unknown LD relationships between markers and QTL, these being of a multivariate nature in the case of complex traits  to use variance components estimated from an all-markers analysis, unless there are some huge effect variants that would probably be detected anyhow. Since we showed analytically that the GLS estimator is invariant with respect to removing markers from G, it is unnecessary to re-estimate variance parameters, or to modify G at any pass of a SMR GWAS.It is concluded from the preceding that, if the contribution of a marker to G, which is contradictory. To guide the specification of the GWAS model, we searched for genomic structure in the wheat and Arabidopsis genotype matrices using multi-dimensional scaling (MDS).Many GWAS use a SMR model with one or a few regressions on PC of Arabidopsis accessions. There were 179,101 and 19,701 Euclidean distances between rows of X (or of G) in the wheat and Arabidopsis data sets, respectively. In MDS, distances are rotated into a matrix whose eigen-decomposition yields the K-dimensional coordinates, while preserving distances in some best fit sense. There are two types of MDS: classical and nonmetric. In classical MDS, differences and ratios between distances are preserved. In nonmetric scaling, only the order of the distances is relevant. The best fitting K is found at the eigenvalue in which an elbow of an eigenvalue decay plot is observed, or can be derived from a metric called STRESS. Here, squared differences between observed and fitted distances are summed over the two dimensions, and expressed relative to the sum of all observed squared distances. If STRESS (the square root of the preceding quantity) is smaller than 5–10%, the corresponding dimension is deemed to give a satisfactory fit  and Arabidopsis. In wheat, the first coordinate separates lines into two well delineated groups; the second coordinate stretches the lines within groups along the y-axis. A two-dimensional representation seemed insufficient in the Arabidopsis data. Arabidopsis, respectively; save for the first two, there were no clearly dominant values in Arabidopsis. The middle and bottom panels show STRESS (nonmetric MDS) for models of different dimensionality. In the wheat data set, a satisfactory fit , and larger estimates of residual variance. The relationship between G (not shown) In short, if a PC is treated as fixed but not removed from G, the residual variance will be understated, because the fact that such PC also contributes to genomic variance would not be accounted for properly. Genomic heritability should be re-estimated if PCs are removed from G.We examined the effect of removing PC from ticeable : removinArabidopsis, estimates of variance components and of genomic heritability were In G. With that objective, we compared estimates from various analyses of the wheat data: 1) OLS on markers with and without the first PC as a covariate; 2) GLS (using maximum likelihood estimates of variance components) on markers with or without the first PC as covariate; 3) GLS as in (2) but with or without the first PC removed from the G matrix. As expected, G had a negligible impact on inference, as the metrics used in the comparison aligned on a 45° degree line (results not shown).We evaluated the extent to which associations detected by OLS or GLS were affected by accounting for structure, and by whether or not the PC used as regressor was kept as a part of, or excluded from, the genomic relationship matrix Arabidopsis, we fitted a multiple-regression on the first 70 PC; this was done by OLS and by GLS . The support for statistical significance is shown in In Arabidopsis chromosome 2, and used flowering time (the trait with 90% heritability) as a target trait for evaluating alternative GWAS model specifications. Genomic relationship matrices were constructed with all 215,947 markers, and the regression model included the single marker tested, and either zero, one, five, 10, or 50 PC as fixed covariates. x-axis labels effect size estimates (top panel) and statistical support values (bottom panel) for the model without PC in the regression structure. Clearly, accounting for structure had a marked effect on estimates of marker effects, and on statistical support: as the number of PC in the regression increased, effect sizes decreased in absolute value and support for association vanished. While a large number of markers would be declared as associated when population structure is ignored, only a few of these would remain significant after the first PC is fitted; none would be significant if five or more PC are fitted. When the first PC was removed from G, heritability of flowering time dropped from 0.92 to 0.43. When five, 10 or 50 PC were removed, We extracted the first 5000 markers from G was left intact when one, five, 10, or 50 PC were fitted in the regression structure, vs. the corresponding models with G and variance components appropriately modified. As shown in G of the PC tested was taken into consideration. The bottom panel of Finally, effect size estimates and statistical support were compared for the model in which The authors state that all data necessary for confirming the conclusions presented in the article are represented fully within the article.G. We also examined the impact of removing PC from G, and found that it does matter, and importantly so. Further, and unsurprisingly, estimates of genomic and residual variances were found to be sensitive with respect to the structure of G. Concepts were illustrated using publicly available wheat and Arabidopsis data sets.Our study addressed some standing issues in standard GWAS methodology for complex traits, as practiced in animal, human, and plant genetics. We examined the question of how removal of one or more markers from the genomic relationship matrix affects the generalized least-squares estimator  of allelic substitution effects in a SMR. It was shown analytically that, if variance components are kept constant, the GLS estimator and the GBLUP predictor of marker additive genetic values are invariant with respect to whether or not the marker(s) tested for association is(are) included when constructing In conclusion, in a homogeneous population, inferences from a GWAS using GLS where the genomic relationship matrix is constructed using all markers does not present clear pitfalls other than the inability of a SMR model to represent the statistical genetic architecture of a complex trait properly. On the other hand, if one or more PC are used as fixed regressors to account for population stratification, the genomic relationship matrix perhaps should be modified, and variance components re-estimated accordingly. In the absence of knowledge of the state of nature, it is impossible to answer unambiguously the question of which approach is best. It has been argued and shown that statistical significance and predictive ability are not synonymous .


Macaca fuscata (Japanese macaque). In prior studies we have demonstrated that a high fat, caloric dense maternal diet structures the offspring’s epigenome, metabolome, and intestinal microbiome. During the course of this work we have consistently observed that a 36% fat diet leads to obesity in the majority, but not all, of exposed dams. In the current study, we sought to identify the genomic loci rendering resistance to obesity despite chronic consumption of a high fat diet in macaque dams. Through extensive phenotyping together with exon capture array and targeted resequencing, we identified three novel single nucleotide polymorphisms (SNPs), two in apolipoprotein B (APOB) and one in phospholipase A2 (PLA2G4A) that significantly associated with persistent weight stability and insulin sensitivity in lean macaques. By application of explicit orthogonal modeling (NOIA), we estimated the polygenic and interactive nature of these loci against multiple metabolic traits and their measures  which collectively render an obesity resistant phenotype in our adult female dams.Maternal obesity contributes to an increased risk of lifelong morbidity and mortality for both the mother and her offspring. In order to better understand the molecular mechanisms underlying these risks, we previously established and extensively characterized a primate model in  In the last several decades, a global epidemic of increasing rates of obesity in humans has been well described but relatively poorly understood at a genomic leveli.e., diet, exercise, early life exposures, reproductive life-stage, sex, and co-morbid metabolic conditions), identifying clearly defined obese susceptible and resistant genomic variants in humans is exceedingly challenging since it necessitates enormous subject cohorts in ancestrally diverse populations with reliable linked exposure data for fine-mapping of loci.Given such relative rarity  of obese susceptibility variants in the general population, but persistent evidence for heritability16Macaca fuscata (Japanese macaque)1819201819222324252618232627293032de novo SNPs of interest for subsequent validation in an inclusive larger cohort.An alternative to human meta-analyses of GWAS data are strong phenotype-genotype studies in relevant non-human primate models. To this end, we have spent nearly a decade establishing and characterizing the effect of obesity and chronic high fat dietary exposure on adult female dams and their offspring in Macaca fuscata) model20212223242526272829303132Macaca fuscata gene assembly, and subsequent concern for misclassification of whole genome sequencing data which would be inherent to mapping onto a moderate (6–12X) resolution Macaca mulatta rhesus assembly. Genes were selected for inclusion on the array based on a role in obesity, hyperlipidemia, insulin resistance, or lipid metabolism (such as those for cholesterol and triglyceride metabolism). Since the Macaca fuscata genome has not been sequenced, we used the currently available primate genome assemblies, with an emphasis on the rhesus macaque (M. mulatta) genome which diverged from M. fuscata 0.31 to 0.88 million years agoM. fuscata breeding group is a grand mean of 0.01802 .To identify functional and potentially novel SNPs associated with sensitivity or resistance to the development of obesity with high fat diet consumption present in our well characterized Japanese macaque  or sensitive (n = 4) based on mean % bodyweight gain , leptin/body weight ratio , and insulin AUC . Genomic DNA was extracted, hybridized to the array, and sequenced using the 454 FLX Titanium platform. SNPs of potential further interest for validation were first called based on an odds ratio approximating infinity . These criteria were sequentially relaxed to allow for 3 of 4 and 2 of 4 in one cohort, but still absent in the comparison cohort  which only identifies homozygous alternative allele SNPs. Genes were identified for further analysis on Atlas-SNP2 and SNPTools if ssahaSNP made homozygous alternative allele calls in all the samples in one group, but none of the samples in the other group (odds ratio approximating infinity). Among the 1534 SNPs called by all three SNP calling tools, Variant Effect Predictor (VEP)p value < 0.063 in our small discovery cohort) were chosen for further analysis. A SNP in phospholipase A2, group IVA  (PLA2G4A) (p = 0.012) (APOB) (p = 0.061 and p = 0.062)   and two = 0.062)  met thesPLA2G4A and APOB SNPs were further interrogated by two means: functional annotation and validation in an expansive cohort. Functional annotation used a Combined Annotation Dependent Depletion (CADD)PLA2G4A SNP had the highest PHRED scaled C-score (23.6). A PHRED score of ≥20 indicates the SNP is among the 1% of SNPs in the human genome most likely to have a functional effect. The PHRED scores for the APOB chr13:20932165 (9.018) and chr13:20940049 (15.07) approach or surpass a PHRED score ≥10 which indicates they are predicted to be among the 10% most likely SNPS to have a functional effect. Examination of individual constituents of the CADD scores showed that the PLA2G4A and APOB chr2:21235409 loci are highly conserved across primates, including humans.The i.e., exploration of potential mechanisms rendering an association with obesity resistance in our cohort of strictly experimentally defined animals , we took a dual approach. First, we completed expanded phenotyping among a total of 71 animals, inclusive of 43 adult female dams who had been placed on the HFD for at least 3 years and subjected to expansive phenotypic testing and measured analysis . Second, the PLA2G4A and APOB SNPs were assayed by PCR based genotyping in an extended panel among all 43 adult female dams on the HFD for at least 3 years with extensive trait-correlated and trait-independent phenotypic data , age starting diet  nor age at first pregnancy after starting diet , nor initial baseline metabolic phenotyping (p = 0.02).At the time of initial allocation onto the HFD, adult animals subsequently classified as obese resistant and sensitive did not significantly differ by virtue of number of prior pregnancies  association between the classification and the PLA2G4A SNP. PLINK quantitative trait association analysis showed significant (p < 0.05) associations of both APOB SNPs with insulin and glucose AUC after year 3 on the HFD  models across 15 phenotypes enotypes . Of the n = 43 animals). The Genotype  shows the genotypes for each of the loci . Significance of association is annotated by boxing, with the genotypes and allelic variation predicted to associate with the phenotype in a significant manner being outlined with colored boxes. The Genotypic Effects (y-axis) shows the NOIA predicted effect of the genotype on a phenotype, with the value being specific to the phenotype. For example, in panel APOB.1 is demonstrated to be significant in an additive model with a p = 0.035. In contrast, neither APOB.2 nor PLA2G4A demonstrated a significant effect on weight change (one phenotypic characteristic which renders of fails to render obesity). In fact, when examining all six other phenotypic characteristics projected in APOB.1 locus demonstrated an additive effect on weight change percent , we estimated the polygenic and interactive nature of these loci against multiple traits which collectively render an obesity resistant phenotype in our adult female dams.We applied comparative principles and designed an exon capture array of conserved metabolism genes for use in Japanese macaque, and demonstrated the capacity of this technology to identify functional SNPs related to insulin sensitivity and resistance to obesity in a relevant primate model of chronic high fat diet exposure. We discovered that although body weight and body composition traits are quantitative, two loci in Our approach towards identifying obesity resistant loci in adult primates has significant advantages and provides clarity over previous human GWAS analysis seeking to identify susceptibility loci. Recent meta-analyses2212We have overcome these inherent limitations to human GWAS analysis in our well-characterized primate model in three manners. First, we challenged all animals in our analysis to a high fat diet and normalized our trait measures to reproductive life-stage, time of exposure to the diet, and baseline characteristics at the time of initial diet allocation. Second, we estimated association with 37 different trait loci which have both independent and dependent predictive capacity and estimated their interaction. This second manner enabled us to further identify significant associations with multiple additional traits that accompany or lend to the obesity resistant phenotype in an extended panel of all 43 adult female dams on the HFD for at least 3 years with extensive phenotype data. Third, we were thus able to apply multiple previously validated means for fine-mapping of polygenic and interactive loci.APOB C/T SNP at chr13:20932165 coding for glycine or aspartic acid is of particular interest because it is also present in humans as SNP rs142828185. Although little information is presently available regarding the SNP with no minor allele frequency or phenotypic association reported in dbSNP, much is known about the role of APOB as a primary apolipoprotein of LDLs45APOBFrom a translational perspective, the APOB C/T SNP at chr13:20932165 coding for glycine or aspartic acid was associated with multiple traits in addition to levels of serum LDL, the likelihood that these and potentially other variants in humans would culminate in up to one third of adult females being resistant to high fat diet induced obesity is both novel and of particular interest. Such pleiotropy would support a model of gene-by-food environment interactions, whereby the majority of a population cohort are susceptible to HFD with resultant insulin resistance and obesity. To this end, and of particular interest to our study, common coding variants in APOB have recently been suggested to play a role in maternally-derived obesity in young adults. Specifically, Hochner et al. recently demonstrated that a common coding variant in the 4th exon of APOB (rs1367117) demonstrated a significant maternally-derived effect on BMI  and waste circumference p > 0.6). Moreover, these investigators working with 1250 young adults and their parents were able to demonstrate a dominant maternal parent-of-origins effect, suggestive of maternally-derived associations of rs1367117 with elevated fasting glucose  and insulin APOB rs1469513 on obesity-rendering traits, alongside the interaction of APOB rs1469513 and dietary intake on these same traitsp 0.001) and low-density lipoprotein cholesterol (p 0.010), body weight (p 0.048), and body mass index (p 0.029) were significantly different in carriers of the A allele and minor G allele of APOB rs1469513. Among individuals whose fat intake was above the median of the study cohort, the difference for the body mass index across genotypes was 1.14%  and carriers of the minor G allele had increased odds of being obese  compared with homozygotes for the A alleleAPOB gene demonstrating an alternate risk of modifying risk of obesity resistance. What is notable is the concomitant impact of both presumptive maternal parent of origin effect, as well as modifier of dietary impact, in our primate cohort. Taken together, our findings alongside the current collective literature suggests that APOB is a primary determinant of high fat diet induced obesity, and may render multigenerational impact through a maternal parent of origin effect.Because we found that the PLA2G4A is of additional translational interest, although less is known regarding variants in the human population. The PLA2G4A gene encodes a key calcium activated enzyme which catalyzes the hydrolysis of membrane phospholipids to release arachidonic acid, rendering eicosanoids (prostaglandins and leukotrienes) and lysophospholipidsPLA2G4A on plasma triglyceride levels in 208 human subjects, genotype by supplementation interaction effects were observed for 4 SNPs. Specifically, the rs10752979, rs10737277, rs7540602, and rs3820185 in PLA2G4A withstood MIXED procedure testing adjusting for age, sex, BMI and energy intake. NOIA generated four models showing an association between PLA2G4A genotype and triglyceride levels including two models in which PLA2G4A was dominant (APOB) and central enzymes for mediating eicosanoid-driven inflammation (PLA2G4A) modulate obesity-resistant traits in response to dietary challenge or supplementationdominant . Our finAPOB in humans may render susceptibility to obesity in first generation young adult offspringEqually intriguing are these current findings in context with our prior demonstrations that generally regardless of maternal insulin resistance and obesity status, there is a notable impact of high fat diet feeding during gestation and lactation among offspring. The impact of early in life high fat diet exposure are noteworthy and include non-alcoholic fatty liver disease (NAFLD) with lipid accumulation, pancreatic and immune modulatory dysfunction, thyroid hormone dysregulation, hypertension, and alterations in sirtuins and their regulated pathways1827505130192425The loci identified here as significant represent an experimentally robust, in-depth, fine-mapped genotype-phenotype association analysis in a highly relevant and well-characterized primate model. Future application of our findings into human cohorts are likely to yield important insights into the molecular and physiologic mechanisms leading to obesity and insulin resistance in not only the current generation, but in the generations to come.A total of 783 lipid metabolism, obesity, and fatty acid related genes were selected as targets . Human, Experimental design: The use of M. fuscata by our consortium of investigators has been previously described242526272829303132rd trimester of pregnancy or post lactation/pre-gestation. The area under the curve (AUC) for glucose and insulin were calculated from zero values. Body composition analysis (DXA) was performed in year 3 of diet exposure in the non-pregnant state, and lean and fat mass were calculated with standard measures has been previously described242526272829303132242526272829303132All animal protocol work is approved by and in accordance with the relevant guidelines and regulations as stated by the institutional animal care and use committees (IACUC) at both Baylor College of Medicine (protocol number AN-4752) and the Oregon National Primate Research Center (ONPRC). The full extended trait panel is shown in 20212223242526272829303132i.e., present in all 4 dams of one group, and absent in all of the other) as estimated by ssahaSNP, which only identifies homozygous alternative allele SNPs. In order to further assure high quality and statistically robust SNP identification in an initial small discovery cohort of 8 animals, three tools were used to call SNPs APOB and one PLA2G4A SNPs in association with each of the 37 phenotype measurements with significance defined by probability (p < 0.05) models across 15 phenotypes.Our initial SNP calls were based on infinite odds ratios .Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


G-REMLadp, to estimate the phenotypic variance explained by parent-of-origin effects (POEs) across the genome. Our method uses restricted maximum likelihood analysis of genome-wide genetic relatedness matrices based on individuals’ phased genotypes. Genome-wide SNP data from parent child duos or trios is required to obtain relatedness matrices indexing the parental origin of offspring alleles, as well as offspring phenotype data to partition the trait variation into variance components. To calibrate the power of G-REMLadp to detect non-null POEs when they are present, we provide an analytic approximation derived from Haseman-Elston regression. We also used simulated data to quantify the power and Type I Error rates of G-REMLadp, as well as the sensitivity of its variance component estimates to violations of underlying assumptions. We subsequently applied G-REMLadp to 36 phenotypes in a sample of individuals from the Avon Longitudinal Study of Parents and Children (ALSPAC). We found that the method does not seem to be inherently biased in estimating variance due to POEs, and that substantial correlation between parental genotypes is necessary to generate biased estimates. Our empirical results, power calculations and simulations indicate that sample sizes over 10000 unrelated parent-offspring duos will be necessary to detect POEs explaining < 10% of the variance with moderate power. We conclude that POEs tagged by our genetic relationship matrices are unlikely to explain large proportions of the phenotypic variance (i.e. > 15%) for the 36 traits that we have examined.We propose a new method, The online version of this article (doi:10.1007/s10519-017-9880-0) contains supplementary material, which is available to authorized users. POEs imply that heterozygote individuals have phenotypes which are distributed differently depending upon which of their alleles were maternally and paternally transmitted  to offspring genome-wide genetic relatedness matrices and phenotype data. Our method involves the construction of a genetic relationship matrix indexing the parental origin of offspring alleles using genome-wide SNP data from parent–child duos or trios. The proposed method is an early adaptation to human genetics of procedures developed for animal breeding , dominance effects (βδ) and POEs (βγ), which are assumed to be independently normally distributed with mean 0 and variances that are inversely proportional to the number of markers affecting the phenotype: The mixed model utilizing these codings is given in Eq. mentclass2pt{minimmentclass2pt{minimThe primary concern of this paper is with the partitioning of phenotypic variance components according to Equations The second equality in Eq. The bold-faced Greek characters on the final line of Eq. It is important to note that we have assumed, but not demonstrated an equivalence between the component of variance due to parent-of-origin effects and that due to imprinting defined by classical quantitative genetics  regression framework where each distinct pair of individuals in the sample is used as the unit of analysis . This means that the products of the GRMs This prediction was supported by the empirical analysis, in which the off-diagonal elements of the GRMs were uncorrelated  as a multiple regression, and we can analyze the power of simple regressions but fit multiple components in practice. The Wald test statistic of a variance component, POE for example, is given by r et al. .vech is the operator which transforms a symmetric matrix to a column vector of its lower-diagonal elements (Henderson and Searle Starting with standardized outcomes and predictor [where We derive results for a set of http://cnsgenomics.com/shiny/gctaPower/) to determine the power to detect a variance component of a particular size.The denominator of the Wald  Goddard , in whicFor In our simulations, we used the true G-REMLadp requires a set of phased genotypes, each with parent-of-origin assignments. Mitochondrial DNA and X chromosome SNPs are excluded from analysis. In the empirical analysis, we used a Perl script to assign parent-of-origin to genotypes which had already been phased, as described below. Given a set of phased, parental-origin-assigned SNPs, we first recoded each genotype to the three-term orthogonal coding given in Table MACH’s  by subtracting the paternal minor allele indicator from the maternal indicator and wrote this to an appropriately formatted .mldose.gz file, then generated an .mlinfo.gz file from the relevant sources for the SNP data set. We input the .mldose.gz and .mlinfo.gz files to GCTA’s MACH dosage function (--dosage-mach-gz) to generate the POE GRM. We then input the additive, dominance, and POE GRMs to GCTA, with the phenotype and covariate files, to fit the mixed model and estimate variance components. We chose to estimate the variance components without constraining them to be positive so that the null distribution of test statistics would not be a mixture (Visscher https://github.com/amatrhr/g-remladp); power calculations can be performed using the GCTA-GREML power calculator at (http://cnsgenomics.com/shiny/gctaPower/).Visscher . We alsoG-REMLadp model to: (1) evaluate the predicted statistical power using the Haseman–Elston regression approximation; (2) test the bias and variance of the method in response to violation of its assumptions; and (3) assess computational requirements. In simulation studies, data were simulated according to Eq. GCTA software. The goals were to estimate the bias and variance of the variance component estimators, the agreement between HE and GCTA estimates, and the empirical power and Type I error rates of the HE test.We simulated data according to the odel to:  evaluateG-REMLadp to violations of its assumptions, and as a way of widening the breadth of the simulations. Realistically, most samples in which G-REMLadp could be applied will have filtered SNPs for violations of HWE as part of routine QC  empirical absolute bias, the average difference between the simulated variance component and the value estimated in a replication; (2) empirical sampling variance, the variance of estimated variance components over replications; and (3) power/Type I error rate, the proportion of replications in which the Wald test of a null variance component exceeded the 95% critical value under a simulated non-null/null variance component.In the simulations, we expected power to increase with increasing sample size and variance component size and decreasing number of effective loci (noting that this means a larger effect at each locus for a given variance component size in our design), and expected variance to decrease according to the same pattern. We expected that violation of assumptions would lead to detectable bias.G-REMLadp to a sample of up to 4753 individuals gathered as part of the Avon Longitudinal Study of Parents and Children (ALSPAC), a prospective study of health and development beginning at pregnancy. We considered 36 different phenotypes which had been previously associated with POEs or which were related to body size, development, or social functioning.See the Supplementary Material for further description of the sample, including the phenotyping and quality control procedures that we applied to it. The sample, the longitudinal study and its context, as well as its genotyping, are described in detail in two papers  under violation of HWE due to dependence of parental genotypes.We observed that violating HWE increased the discrepancy between predicted and observed test statistics. However, these results do not indicate whether this was due to increased bias or variance of the estimates, or both. Additionally, because the predicted test statistics were based on many simplifying assumptions, it is possible that the increased discrepancy would not have led to incorrect inference, and it is worth exploring whether violating HWE causes the estimated variance components to be misleading in predictable ways.Results for simulations with truly null variance components are not shown. The absolute bias was under Table Table GCTA and HE estimates tended to differ in the presence of correlation between parental genotypes; in this situation, HE regression estimates of POEs had higher variance (and hence higher mean-squared error) than did GCTA estimates, which is expected to be the case even in additive-only models  with independent parental genotypes to 0.9624 with correlated parents. This was not observed for estimates of the two other types of variance components.The G-REMLadp are given in Supplementary Table III for the 36 phenotypes. Results for a set of five variables with large parent of origin variance component estimates are given in Table Estimates and standard errors of entclass1pt{minimaAcross the 36 phenotypes surveyed, in the aggregate, additive variance components were frequently estimated reliably, positively, and away from 0. In general, if a variance component was detectable, it represented additive variance. POEs had standard errors approximately equal to those of additive variance components, while estimates of dominance variance showed slightly larger standard errors. Further, half of the dominance variance components were negative and half positive. Although the sample size is too small to perform significance tests of differences in heritability estimates across traits, lipid traits tended to have negative dominance components and IQ traits positive ones.G-REMLadp does not seem to be inherently biased in estimating variance due to additive effects, dominance effects, and POEs, and (2) that substantial correlation between parental genotypes is necessary to bias G-REMLadp estimates. We did not investigate the effect that linkage disequilibrium might have on our results, but present the correlations between codings in the Supplementary Material. If local levels of linkage disequilibrium are associated with POE size, an implementation of G-REMLadp using GCTA-LDMS would likely be able to estimate variance components without LD bias, while an LDAK implementation would have estimates at greater risk of bias  Despite the limited power of our analysis, it may be interesting to follow up some of the phenotypes that had high estimates of parent of origin effects in the ALSPAC cohort, like age at menarche [a phenotype known to be influenced by imprinted loci  cannot distinguish POEs from certain patterns of maternal/paternal effects , could’ve resulted in more thorough evaluation of G-REMLadp is not necessarily limited to genome-wide analyses; future work could specifically examine relatedness at known imprinted loci in the construction of GRMs, although this would require revised power calculations to estimate sufficiently large samples to account for the lower degree of tagging of phenotypic variation.A further drawback is that the power calculations which we present are based on the assumption that causal loci are randomly distributed throughout the genome. It is unclear the degree to which parent of origin effects are randomly distributed across the genome in humans vs being clustered at distinct loci. Dissecting the genetic basis of parent of origin effects in humans has been hampered by two factors: (1) GWAS aimed at detecting parent of origin effects have been small meaning that only a small number of common SNPs having relatively large effect have so far been identified; and (2) Many studies have restricted association analyses to regions of the genome known to be imprinted. There are anywhere from 40 to 100 regions known to be imprinted in humans , it is possible to fit G-REMLadp models and detect variance components without bias. The close agreement between GREML and HE regression approaches to estimate variance components suggests that G-REMLadp models can be fit to a good approximation even in very large studies or with limited computational resources, where HE can be up to 50 times faster than GREML


P<5 × 10−8) in combined analyses. A number of these loci contain genes implicated in structure and function of skeletal muscle fibres (ACTG1), neuronal maintenance and signal transduction , or monogenic syndromes with involvement of psychomotor impairment . Mendelian randomization analyses are consistent with a causal effect of higher genetically predicted grip strength on lower fracture risk. In conclusion, our findings provide new biological insight into the mechanistic underpinnings of grip strength and the causal role of muscular strength in age-related morbidities and mortality.Hand grip strength is a widely used proxy of muscular fitness, a marker of frailty, and predictor of a range of morbidities and all-cause mortality. To investigate the genetic determinants of variation in grip strength, we perform a large-scale genetic discovery analysis in a combined sample of 195,180 individuals and identify 16 loci associated with grip strength ( Hand grip strength as a proxy of muscular fitness is a clinical predictor of mortality and morbidity. In a large-scale GWA study, the authors find 16 robustly associated genetic loci that highlight roles in muscle fibre structure and function, neuronal maintenance and nervous system signal transduction. Muscle strength, measured by isometric hand grip strength, is an accessible and widely used proxy of muscular fitness. Lower grip strength is associated with impaired quality of life in older adults, and is an established marker of frailty, predicting physical decline and functional limitation in daily living12478h2=30–65%)10111315Grip strength is highly heritable  cohortP<5 × 10−8) in stage one (P<0.05) in stage two cohorts (P<5 × 10−8) in combined analyses. Effect sizes on grip strength ranged from 0.14 to 0.42 kg per allele under an additive model  in DEC1, and a further common variant falling within the human leukocyte antigen (HLA) region (P<3.13 × 10−3 under a dominance deviation model (see Methods)); at the GBF1 locus, we saw evidence for a dominant effect of the grip strength-raising A allele , but was stronger in men than in women )=0.01 , P=0.75).In stage one analyses, we tested the association of >17 million variants >0.1%, imputation quality >0.4), in 142,035 white European individuals from UK Biobank  with maxtage one , and wertage one  includin cohorts  and 16 lve model . Given t) region . ApproxiACTG1), excitation-contraction coupling (SLC8A1), evidence for neurotrophic roles (TGFA), or involvement in the regulation of neurotransmission (SYT1). ACTG1  encodes a key component of the costamere—a protein complex localized to the Z-disc of skeletal muscle which physically tethers myofibrils to the cell membrane and transmits contractile force generated at the sarcomere to the extracellular matrix via the dystrophin glycoprotein complex (DGC)19Actg1 knockout mice display overt muscle weakness, progressive myopathy and decreased isometric twitch forceSLC8A1 encodes a transmembrane Na+/Ca2+ exchanger which is vital to restoring Ca2+ concentration to pre-excitation levels in excitable cells. Muscle-specific overexpression of SLC8A1 has been shown to induce dystrophy-like skeletal muscle pathologySYT1, is an integral synaptic membrane protein which regulates Ca2+-dependent neurotransmitter release at the presynaptic terminalTGFA encodes transforming growth factor alpha, a well-characterized growth factor which plays a key neurotrophic role in the central and peripheral nervous systems27A number of associated loci contained genes with biologically plausible roles in strength and neuromuscular fitness, through effects on the structure and function of skeletal muscle (Pcombined=9.75 × 10−11) lies 15 kb upstream of LRPPRC (leucine-rich pentacotripeptide-containing), which has been implicated in the French-Canadian variant of Leigh Syndrome (MIM: 220111), a cytochrome C oxidase deficiency with features including developmental delay, hypotonia and weaknessPEX14  (intronic lead variant rs6687430) underlie certain forms of Zellweger Spectrum Peroxisomal Biogenesis Disorder (MIM: 614887), a syndrome characterized by absence of functional peroxisomes and systemic neurological impairmentKANSL1, which has been implicated in the complex impaired-psychomotor phenotype of Koolen-de Vries syndrome (MIM: 610443)KANSL1 is in a large linkage disequilibrium (LD) block also containing MAPT , which encodes the microtubule-associated tau protein. MAPT has been implicated in a suite of so-called tauopathies characterized by progressive neurological deficit, and is also a risk locus for Parkinson’s disease3334β=−0.17 kg, P=3.85 × 10−6), independent of age, sex, height and BMI .Three lead variants for grip strength map in or near genes implicated in monogenic syndromes characterized by neurological and/or psychomotor impairment . rs10186 and BMI . This asIn sensitivity analyses, we re-tested associations of the 16 grip strength variants in UKB after exclusion of up to 8,676 individuals with type 1 diabetes, cancer, or other prevalent disease with potential to influence muscle strength. No loci showed significant attenuation of effect relative to overall analyses .P<0.0056), we observed significant enrichments of associations with grip strength in tissue-specific regulatory regions for a number of tissues, including bone/connective tissue (P=2.03 × 10−10), skeletal muscle (P=1.88 × 10−9) and the CNS (P=7.37 × 10−8). Enrichments at weaker levels of statistical significance were also observed in cardiovascular and gastrointestinal tissue, as well as the adrenal/pancreas axis, and ‘other’ tissues  with transcript levels in brain, tibial nerve and skeletal muscle in GTEx (ACTG1 (rs6565586) was associated with lower expression of ACTG1 in skeletal muscle , counter to directions suggested by actg1 knockout in mouse. At LRPPRC (rs10186876), the strength-increasing allele was associated with higher LRPPRC expression levels in cerebellum  and cerebellar hemisphere , which appears directionally concordant with previously characterized loss of function and otherwise damaging mutations associated with the disease phenotype of French-Canadian Leigh SyndromeERP27 locus), the grip strength-increasing allele was associated with higher levels of MGP expression in tibial nerve . MGP (Matrix Gla Protein) is a well-characterized inhibitor of vascular tissue and cartilage calcification, and consequently acts as a key regulator of bone formationGuided by tissue-specific enrichments, we sought to identify putative effector transcripts underlying these associations by investigating associations of lead SNVs or their proxies ( in GTEx . The griP≤8.37 × 10−6 for α≤0.05), and potential coincidental overlap of eQTL signals with GWAS loci, SMR analyses using whole blood transcriptome dataERP27 (PSMR=2.50 × 10−9) and KANSL1 (PSMR=3.05 × 10−7), both of which are implicated genes from our GWAS analysis.We also performed integrated transcriptome-wide analyses using recently-described MetaXcanLRPPRC, for example, we observed association of higher expression levels across a number of brain tissue types, tibial nerve, whole blood and testis, with higher grip strength. Higher MAPT expression in multiple brain regions known to be implicated in motor coordination  was also associated with higher grip strength.MetaXcan analysis identified 25 protein-coding transcripts implicated in grip strength at Bonferroni-corrected significance in at least one of twelve biologically relevant tissues from the GTEx resource , but not at loci implicated in dystrophic conditions (P=0.47).Hypothesis-free gene set enrichment analysis (GSEA) based on gene-sets of common functional annotation, or belonging to pre-defined canonical pathways , indicatACVR2B and FBXO32) showed a significant association with grip strength , encodes the principal transmembrane receptor of myostatin: the target of BYM338, a monoclonal antibody-based inhibitor of ActRIIB, which has shown early promise in reversing muscle atrophy and promoting hypertrophy in phase I trials45FBXO32 encodes the E3 ubiquitin ligase Atrogin-1/MAFbx, which is recognized as fundamental effector of atrophyMyokine signalling via activin type II receptors (ActRII) has been recognized as a key pathway by which muscle mass might be preserved in many clinical contexts42Nathletes=616, Ncontrols=1,610; see Methods and ACTN3, which encodes the actin-binding protein α-actinin 3 in skeletal muscle, has been associated with elite athlete statusβ=−0.062 kg, P=0.018)   althoughP<3.8 × 10−3), the grip strength-raising allele at TGFA was associated with a lower proportion of type I (slow-twitch oxidative) muscle fibres , and a tendency towards higher proportion of type IIB (fast-twitch glycolytic) muscle fibres   . We acknGiven the roles of sex- and growth hormones and related phenotypes in muscle growth and development484951Using a MR approach, we investigated the potentially causal role of muscular strength in both mortality and disease outcomes, utilizing the 16 replicated loci as an instrumental variable to model genetically determined grip strength as a proxy of wider muscular strength.P=0.265) (P=0.739)  drawn from the EPIC-Norfolk cohort (hazard ratio (HR) per kg higher grip strength (95% CI): 0.96 , P=0.265) . HoweverP=0.739) .P=0.631) or MI (OR (95% CI): 0.98 , P=0.433)  and myocardial infarction  from the CARDIoGRAMplusC4D ConsortiumP=0.433) . This ren cases=20,439; n controls=78,843)   summary statistic MR results for fracture risk from the Genetic Factors for Osteoporosis (GEFOS) consortium  , and 2)  P=0.02; . Summary P=0.02; . However × 10−4) , supportβ=0.072 kg m−2, P=0.074; FMI: β=0.013 kg m−2, P=0.878) , but not FMI  or fat mass index (FMI) (LMI: P=0.878) . A signi not FMI .We have identified 16 loci associated with maximal hand grip strength at genome-wide significance. A number of the lead variants were located within or close to genes implicated in structure and function of skeletal muscle fibres, neuronal maintenance and signal transduction in the central and peripheral nervous systems. Partitioned heritability analyses indicated significant tissue-specific enrichment of skeletal muscle, CNS, connective tissue and bone in the genome-wide grip strength results. We observed evidence of shared genetic aetiology between lean mass and grip strength, while pathway analyses indicated a role for genes involved in regulation of protein catabolism in the aetiology of grip strength.Due to the well-established observational associations of grip strength with mortality and incident CHD it has been hypothesized that improvement of muscle strength might increase longevity and reduce risk of adverse cardiovascular eventsKANSL1, PEX14 and LRPPRC) implicated in rare, severe clinical syndromes characterized by phenotypes of progressive psychomotor impairment, muscle hypotonia and neuropathy29We saw evidence of enrichment of associations with grip strength around genes implicated in myopathies. We also noted three loci with genome-wide significant associations containing genes  analyses comprised participants drawn from the UK Biobank (UKB) studyIndependent lead variants from stage one were followed-up  in an independent sample of up to 53,145 white European individuals drawn from the Cohorts for Heart and Aging Research in Genomic Epidemiology (CHARGE) consortiumHand grip strength at baseline in UKB was measured isometrically using a calibrated Jamar J00105 hydraulic hand dynamometer  adjusted to the individual’s hand size. With the participant seated, one measurement was taken per hand, and maximal grip strength taken as the higher of the two readings. Body mass was assessed using a BC418MA Body Composition Analyser , with the participant dressed in light clothing. Standing height was measured on a rigid stadiometer . Phenotyping details for each of the stage two cohorts are detailed in Our stage one analyses use data from UKB’s imputed interim genotyping release (May 2015), restricted to biallelic SNVs with MAF ≥0.1%. Genotyping and imputation were conducted by UKB using a centralized pipeline, for which detailed protocols are available (see URLs). Briefly, UKB extracted DNA from EDTA buffy coat, before shipping to Affymetrix  for centralized genotyping. Samples were genotyped at >800,000 loci on two custom-designed arrays with 95% common content, designed to optimize quality and quantity of genome-wide imputation: the UK Biobank Axiom array, and the UK BiLEVE Axiom Array. After restriction to biallelic SNVs with MAF≥1% and additional sample genotyping QC, a subset of 641,081 autosomal SNVs from 152,256 samples were available for imputation. SNVs were pre-phased using SHAPEIT3 software and imputed (using a modified version of IMPUTE2 software) to a merged reference panel containing haplotypes from the UK10K Consortium combined with the 1000 Genomes Project reference (see URLs). This approach has previously been shown to provide a high-quality imputation reference in populations of mixed ancestryP<1 × 10−6 were excluded. Surrogate markers were subsequently decoded into the corresponding nine structural haplotypes for analysis. Association of haplotypes  with grip strength was modelled using linear regression adjusted for age, sex, height (m), BMI (kg m−2) and UKB genotype chip in up to 111,860 unrelated genetic white Europeans defined centrally by UKB (see URLs).Nine structural haplotypes previously reported at 17q21.31 were imputed according to previous work3334In UKB, variance component analyses were performed in the subset of individuals of ‘white British’ genetic ancestry using Restricted Estimate Maximum Likelihood (REML) models in BOLT-LMM software (v2.2)n=142,035) were run using a Bayesian linear mixed model (LMM) adjusted for age (years), sex, height (m) and BMI (kg m−2), implemented in BOLT-LMM software (v2.2)142,035 UKB participants had imputed genetic data, grip strength and full covariate availability for genome-wide association analyses; all were of self-identified white ancestry, with the majority (94.6%) reporting as white British. Discovery analyses for maximal grip strength (P≤5 × 10−8). Independent lead variants (n=21) were followed-up in up to 53,145 individuals. In cases where an index variant was not typed or imputed at sufficient quality, appropriate proxies were defined as the variant with the next-lowest P-value within 500 kb of the index .Using genome-wide summary statistics from our UKB phase one analyses, the recently-described LD Score Regression method described by Bulik-Sullivan and colleagues−2) were defined as dual x-ray absorptiometry (DXA)-derived lean mass or fat mass, respectively, divided by the square of DXA-derived height . GWAS were conducted separately in each cohort running a linear mixed model using BOLT-LMMGenetic correlations. Using cross-trait LD Score regression, genome-wide genetic correlations of grip strength were calculated with CHD risk, lean mass index (LMI), fat mass index (FMI) and bone mineral density (BMD) measured at the forearm, femoral neck or lumbar spine. For CHD and BMD we used publicly available GWAS summary statistics form the CARDIoGRAMplusC4D10P-value accounting for eight tests was taken as indicative of statistical significance.Tissue-specific partitioned heritability: Partitioned heritability by LD Score Regression can identify whether certain cell types are enriched for functional gene categories which disproportionately contribute to the heritability of a phenotyper2>0.8) was conducted in skeletal muscle, transformed fibroblasts, nervous system and brain regions in the GTEx resource to identify eQTL associations (see URLs). Variants passing GTEx criteria for tissue-specific eQTL association, and in high LD (r2≥0.8) with the best eQTL for the transcript in question in the tissue of interest were considered significant eQTLs.To explore the potential functional significance of grip strength variants in gene expression, and to prioritize functional genes falling within identified loci, we undertook a number of expression-based analyses. Initially, a look-up of all 16 replicated grip strength variants or their best proxy  were defined from Han et al.Genome-wide discovery results from the UKB cohort were tested for enrichment of pre-specified gene sets based on common functional annotation or known biological pathways in MAGENTA (v2.4)via activin type II receptors  and known atrophy effectors TRIM63 and FBXO32 were identified from literature42Genes involved in myostatin/activin signalling To identify whether grip strength variants were associated with elements of muscle histology, we looked-up each of the 16 replicated loci from combined analyses in a pre-existing GWAS of muscle histology parameters in a sample of 656 men from three independent cohorts of Swedish ancestry (see We performed summary statistic Mendelian randomization (MR)51P-value for association with grip strength within 500 kb of the index in stage one (UKB). All variants included in the analyses are detailed in To infer causality in the association of grip strength with CHD, myocardial infarction (MI), fracture risk, BMD , LMI and FMI, we ran summary statistic MR as described above using the 16 identified loci as instrumental variable for genetically-determined grip strength. For CHD, BMD, LMI and FMI we used the same GWAS summary statistics as we used to test genetic correlations (see above). In addition, we used publicly available MI summary statistics from the CARDIoGRAMplusC4D consortiumn total=21,043, n cases=5,699 cases) based on the number of grip strength-increasing alleles weighted by the effect size from the combined phase one and follow-up analyses. We used effect sizes obtained by fixed-effect inverse variance-weighted meta-analysis of the phase one and two results, excluding EPIC-Norfolk, to generate weights that were independent of EPIC-Norfolk , in line with previous workWe also sought to improve power by using parental lifespans in UKB ; elite African-American  and Jamaican sprint/power athletes , and European athletes   , we asseTo test for departure from additivity, we used a test of dominance deviation, including two terms for best guess genotypes: a term encoding the major homozygotes, heterozygotes and minor allele homozygotes as 0,1,2 and another coding them as 0,1,0, which tests whether the heterozygotes have mean trait values halfway between the homozygote groups and can detect a departure from additivity.Given that observational grip strength is strongly predictive of mortalityhttp://biobank.ctsu.ox.ac.uk/crystal/docs/genotyping_qc.pdf; UK Biobank Phasing and Imputation Protocol; http://biobank.ctsu.ox.ac.uk/crystal/docs/impute_ukb_v1.pdf; MSigDB; http://software.broadinstitute.org/gsea/msigdb; SMR; http://cnsgenomics.com/software/smr; PredictDB Database; http://predictdb.hakyimlab.org; Quanto; http://biostats.usc.edu/Quanto.htmlUK Biobank Genotyping and QC Documentation via the corresponding authors. Pre-defined gene sets (MSigDB), expression data (GTEx) and transcriptome models used by MetaXcan (PredictDB) and SMR methods are available from the listed URLs.Stage one data are from UK Biobank, and can be obtained upon application (ukbiobank.ac.uk). Access to underlying replication and follow-up data including histology and elite athletic performance cohorts may be limited by participant consent and data sharing agreements; requests should be directed in the first instance How to cite this article: Willems, S. M. et al. Large-scale GWAS identifies multiple loci for hand grip strength providing biological insights into muscular fitness. Nat. Commun.8, 16015 doi: 10.1038/ncomms16015 (2017).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Streptococcus pneumoniae and Streptococcus pyogenes, SEER identifies relevant previously characterized resistance determinants for several antibiotics and discovers potential novel factors related to the invasiveness of S. pyogenes. We thus demonstrate that our method can answer important biologically and medically relevant questions.Bacterial genomes vary extensively in terms of both gene content and gene sequence. This plasticity hampers the use of traditional SNP-based methods for identifying all genetic associations with phenotypic variation. Here we introduce a computationally scalable and widely applicable statistical method (SEER) for the identification of sequence elements that are significantly enriched in a phenotype of interest. SEER is applicable to tens of thousands of genomes by counting variable-length k-mers using a distributed string-mining algorithm. Robust options are provided for association analysis that also correct for the clonal population structure of bacteria. Using large collections of genomes of the major human pathogens  Plasticity and clonal population structure in bacterial genomes can hinder traditional SNP-based genetic association studies. Here, Corander and colleagues present a method to identify variable-length sequence elements enriched in a phenotype of interest, and demonstrate its use in human pathogens. The rapidly expanding repositories of genomic data for bacteria hold an enormous and yet largely untapped potential for building a more detailed understanding of the evolutionary responses to changing environmental conditions, such as the widespread use of antibiotics and switches between host-niche as farming practices change.Studies attempting to determine the genetic basis of bacterial traits have traditionally been limited to identifying emerging clones, which are associated with the phenotype of interest, rather than identifying the specific causal genetic elementsFor strongly selected traits caused by highly penetrant variants, such as antimicrobial resistance, scanning for homoplasy (convergent evolution) determined by ancestral state reconstruction has been shown to be successful at identifying the causal variantFor these reasons, genome-wide association studies (GWAS) for bacterial phenotypes have only recently started to appear256765K-mers have been used in bacterial genomics for sequence assembly6de novo assembled contigs or raw read data as input. We apply SEER to both simulated and the real data from large and diverse populations, and show that it can accurately detect associations with antibiotic resistance caused by both presence of a gene and by SNPs in coding regions, as well as discover novel invasiveness factors.Here we present sequence element enrichment analysis (SEER), a method computationally scalable to tens of thousands of genomes, implemented as a stand-alone pipeline that uses either SEER implements and combines three key insights, which we discuss in detail in the methods section: an efficient scan of all possible k-mers with a distributed string mining algorithm, an appropriate alignment-free correction for clonal population structure, and a fast and fully robust association analysis of all counted k-mers.K-mers allow simultaneous discovery of both short genetic variants and entire genes associated with a phenotype. Longer k-mers provide higher specificity, but less sensitivity than shorter k-mers. Rather than arbitrarily selecting a length before analysis or having to count k-mers at multiple lengths and combine the results, we provide an efficient implementation that allows counting and testing simultaneously at all k-mers at lengths over 9 bases long.An association test, using an appropriate correction for the clonal population structure, is performed on the counted k-mers. Those reaching significance are filtered post-association and mapped onto both a well-annotated reference sequence and the annotated draft assemblies to allow discovery of variation in accessory genes not present in the reference strain. The significant k-mers themselves can also be assembled into a longer consensus sequence. Annotating variants by predicted function and effect (against a reference sequence) in the resulting k-mers allows fine-mapping of SNPs and small indels.Meta-analysis of association studies increases sample size, which improves power and reduces false-positive rateshttps://github.com/johnlees/seer as source code, a precompiled binary, and a self-contained virtual machine.SEER is implemented in C++, and available at Streptococcus pneumoniae genomes from the phylogeny observed in a Thai refugee campTo test the power of SEER across different sample sizes, we simulated 3,069 The large k-mer diversity, along with the population stratification of gene loss, makes the simulated estimate of the sample size required to reach the stated power clearly conservative. Convergent evolution along multiple branches of a phylogeny for a real population reacting to selection pressures will reduce the required sample sizeWe also used k-mers counted at constant lengths by DSKThe strong LD caused by the clonal reproduction of bacterial populations means that non-causal k-mers may also appear to be associated. This is well-documented in human genetics; non-causal variants tag the causal variant increasing discovery power, but make it more difficult to fine-map the true link between genotype and phenotypeUsing DSM we counted 68M k-mers which we then tested for association. The 2,639 significant k-mers were mapped to a reference genome, and were found to cover most of the genome with a peak at the causal variant . Mapped cat gene, and tetracycline resistance is conferred by the tetM gene, both carried on the integrative conjugative element (ICE) ICESp23FST81 in the S. pneumoniae ATCC 700669 chromosomeSEER was applied to the sequenced genomes from the study described aboveermB causes resistance by methylating rRNA, whereas mef/mel is an efflux pump systemmel/mef and ermB resistance elements, respectively.Resistance to erythromycin is also conferred by presence of a gene, but there are multiple genes that can be causal for this resistance: folP, prfC and gatA. Macrolide resistance cassettes frequently insert into the ICE in S. pneumoniae, so it is in LD with the genes discussed above. In sulphamethoxazole-resistance folP is modified by small insertions, with which the adjacent permease is in LD with. Finally, prfC and gatA are both involved in translation, so could conceivably contain compensatory mutations when ermB-mediated resistance is present. Further evidence of these compensatory mutations would be required to rule out the k-mers mapping to them simply being false positives driven by population structure.Hits are also found to other sites within the ICE, a permease directly upstream of Some k-mers do not map to the reference, as they are due to lineage specific associations with genetic elements not found in the reference strain. This highlights both the need to map to a close reference or draft assembly to interpret hits, as well as the importance of functional follow-up to validate potential hits from SEER.pbp2x, pbp2b and pbp1a. In this case looking at highest coverage annotations finds these genes, but is not sufficient as so many k-mers are significant—either due to other mechanisms of resistance, physical linkage with causal variants or co-selection for resistance conferring mutations. Instead, selecting the k-mers with the most significant P values gives the top four hit loci as pbp2b (P=10−132), pbp2x (P=10−96), putative RNA pseudouridylate synthase UniParc B8ZPU5 (P=10−92) and pbp1a (P=10−89). The non-pbp hit is a homologue of a gene in linkage disequilibrium with pbp2b, which would suggest mismapping rather than causation of resistance.Multiple mechanisms of resistance to β-lactams are possibleS. pneumoniae is conferred by the SNP I100L in the folA/dyr genedpr and dyr genes, which are adjacent in the genome, have the highest coverage of significant k-mers (Trimethoprim resistance in t k-mers . FollowiWe then compared the results from SEER with the results from two existing methods (see Methods). The first method (implemented using plink) uses mapping of SNPs against a reference, followed by applying the Cochran–Mantel–Haenszel test at every variable siteP values in the causal element, though SEER appears to have a lower false-positive rate. However, as demonstrated by chloramphenicol resistance, if not enough SNP calls are made in the causal gene this hinders fine-mapping. SNP-mediated resistance showed the same pattern since many other SNPs were ranked above the causal variant. In the case of β-lactam resistance both methods seem to perform equally well, likely due to the higher rate of recombination and the creation of mosaic pbp genes.Both SEER and association by core mapping of SNPs (using plink) identified resistances caused by presence of a gene, when it is present in the reference used for mapping . Both prIn addition, as for erythromycin resistance, when an element is not present in the reference it is not detectable in SNP-based association analysis. In such cases, multiple mappings against other reference genomes would have to be made, which is a tedious and computationally costly procedure.Since the k-mer results from SEER are reference-free, the computational cost of mapping reads to different reference genomes is minimized as only the significant k-mers are mapped to all available references. Alternatively, the significant k-mers can be mapped to all draft assemblies in the study, at least one of which is guaranteed to contain the k-mer, to check whether any annotations are overlapped.The small sample, combined with fixed length 31-mer approach (see Methods), did not reach significance for chloramphenicol, tetracycline or trimethoprim as the effect size of any k-mer is too small to be detected in the number of samples accessible by the method. Erythromycin had 19,307 hits, and β-lactams 419 hits, at between 1 and 2% minor allele frequency (MAF), which are all false positives that would likely have been excluded by a fully robust population structure correction method.Streptococcus pyogenes (group A Streptococcus) genomes obtained from population diversity studies for genetic signatures of invasive propensity.Most bacterial GWAS studies to date have searched for genotypic variants that contribute towards or completely explain antibiotic resistance phenotypes. As a proof of principle that SEER can be used for the discovery stage of sequence elements associated with other clinically important phenotypes, we applied our tool to 675 S. pyogenes collected from Fijin=185), and those isolated from throat, skin or urine as non-invasive (n=490). We ran SEER to determine k-mers significantly associated with invasion, followed by a BLAST of the k-mers with the nr/nt database to determine a suitable reference for mapping purposes. After mapping to this reference SNPs were called (see Methods).We sequenced 347 isolates of tetM gene from a conjugative transposon (Tn916) carried by 23% of isolates  with invasive isolates. This could indicate a recombination event, due to the high SNP density and discordance with vertical evolution with respect to the inferred phylogeny23sph) and nrdI (ribonucleotide reductase). In support of these findings, previous work in murine models have found differential expression of sph during invasive disease2526in vitro or within a replication cohort, and functional follow-up such as RNA-seq may also aid in elucidating the role of these genetic variants in S. pyogenes pathogenesis.After applying this correction, we identified two significant hits . The firS. pyogenes population data set found no sites significantly associated with invasiveness. The Cochran–Mantel–Haenszel test (stratified by BAPS cluster) that uses SNPs called against a reference sequence failed to identify the tetM gene and transposon at these elements are not found in the reference sequence. Furthermore, the population structure of this data set is so diverse that 88 different BAPS clusters were found, which overcorrects for population structure when using the DSK method, leaving too few samples within each group to provide the power to discover associations.In contrast, application of the existing association methods described above (plink and DSK) to this SEER is a reference independent, scalable pipeline capable of finding bacterial sequence elements associated with a range of phenotypes, while controlling for clonal population structure. The sequence elements can be interpreted in terms of protein function using sequence databases, and we have shown that even single causal variants can be fine-mapped using the SEER output.Our use of all k-mers 9-100 bases long together with robust regression methods, and the ability to analyse very large sample sizes show improved sensitivity over existing methods. This provides a generic approach capable of analysing the rapidly increasing number of bacterial whole genome sequences linked with a range of different phenotypes. The output can readily be used in a meta-analysis of sequence elements to facilitate the combination of new studies with published data, increasing both discovery power and confirming the significance of results.As with all association methods, our approach is limited by the amount of recombination and convergent evolution that occurs in the observed population, since the discovery of causal sequence elements is principally constrained by the extent of linkage disequilibrium. However, by introducing improved computational scalability and statistical sensitivity SEER significantly pushes the existing boundaries for answering important biologically and medically relevant questions.We offer three different methods to count k-mers in all samples in a study. For very large studies, or for counting directly from reads rather than assemblies, we provide an implementation of distributed string mining (DSM)30N samples, all k-mers over 9 bases long that occur in more than one sample are counted. All non-informative k-mers are omitted from the output; a k-mer Z is not informative if any one base extension to the left (aZ) or right (Za) has exactly the same frequency support vector as Z. The frequency support vector has N entries, each being the number of occurrences of k-mer Z in each sample. Further filtering conditions are explained in the sections below.Over all S. pyogenes genomes this took 3 h 44 min and used 22.3 Gb RAM.DSM30To count single k-mer lengths, an associative array was used to combine the results from DSK in memory. We concatenated results from k-mer lengths of 21, 31 and 41, as in previous studiesP value to reduce false positives from testing underpowered k-mers and reduce computational time.Before testing for association we filter k-mers based on their frequency and unadjusted P value of association in a simple χ2-test (1 d.f.) is <10−5, as in simulations this was true for all true positives, and remove it otherwise. In the case of a continuous phenotype a Welch two-sample t-test is used instead.K-mers are filtered if either they appear in <1% or >99% of samples, or are over 100 bases long. We also test if the P values of the k-mers from the simulated data set against each other . These k-mers are all short words  that appear multiple times per sample, and therefore are of low specificity. Testing the top P value k-mer in this set showed a strong association of the presence/absence vector with three population structure covariates used . Using lasso regression, the first population structure covariate has a higher effect in the model than the k-mer frequency vector  is performed . This is33D, with each element being equal to a sum over all m sampled k-mers:A random sample of between 0.1% and 1% of k-mers appearing in between 5 and 95% of isolates is taken. We then construct a pairwise distance matrix kim is 1 if the mth sampled k-mer is present in sample i, and 0 otherwise. Each element dij is therefore an estimate of the number of non-shared k-mers between a pair of samples i and j. Clustering samples using these distances gives the same results as clustering core alignment SNPs using hierBAPSwhere D, projecting these distances into a reduced number of dimensions. The normalized eigenvectors of each dimension are used as covariates in the regression model. The number of dimensions used is a user-adjustable parameter, and can be evaluated by the goodness-of-fit and the magnitude of the eigenvalues. In species tree with two lineages and 96 isolates, one dimension was sufficient as a population control . Subsequent columns j of X contain the eigenvectors of the MDS projection, user-supplied categorical covariates (dummy encoded), and quantitative covariates . The Broyden–Fletcher–Goldfarb–Shanno algorithm is used to maximize the log likelihood L in terms of the gradient vector β /dβ:where absence and presence for each k-mer are coded as 0 and 1, respectively, in column 2 of the design matrix n Newton–Raphson iterations are applied to β:where sig is the sigmoid function. If this fails to converge, from a starting point using the mean phenotype as the intercept, and the root-mean squared beta from a test of k-mers passing filteringL:which is slower, but has a higher success rate. If this fails to converge due to the observed points being separable, or the s.e. of the slope is >3 , Firth logistic regression is then applied. This adds an adjustment to log using which Newton–Raphson iterations are applied as above.In the case of a continuous phenotype a linear model is fitted:β)The squared distance U to obtain the variance-covariance matrix. The Wald statistic is calculated with the null hypothesis of no association (β1=0):In both cases the s.e. on χ2 distribution with 1 d.f. This is equivalent to the positive tail of a standard normal distribution, the integral of which gives the P value.which is the test statistic of a P<0.05, which in our testing we conservatively Bonferroni corrected to the threshold 1 × 10−8 based on every position in the S. pneumoniae genome having three possible mutationsP value under multiple correlated tests, we observed the distribution of P values from 100 random permutations of phenotype. For the 3,069 Thai genomes setting the family-wise error rate at 0.05 gave a cutoff of 1.4 × 10−8, supporting the above reasoning.For the basal cutoff for significance we use P value cutoff should be chosen in this manner  for each individual study. Association effect size and P value of the MDS components are also included in the output, to compare lineage and variant effects on the phenotype variation.In general, the number of k-mers and the correlations between their frequency vectors will vary depending on the species and specific samples in the study, so the O(N2M) where N is number of samples and M is number of k-mers, but can be parallelized across up to N2 cores.SEER is implemented in C++ using the armadillo linear algebra libraryO(M) and can be parallelized across up to M cores.Processing all 143M informative k-mers as described took 69 min 44 s and 23 MB RAM on 16 cores. This step is On the real data set of full-length genomes the 68M informative k-mers counted was less than the simulated data set above, as the parameters of the simulation created particularly diverse final genomes .β1>0 as a negative effect size does not make biological sense. Remaining k-mers are searched for by exact match in their de novo assemblies, and annotations of features examined for overlap of function. BLATK-mers reaching the threshold for significance are then post-association filtered requiring To better search for gene clusters associated with phenotype, these k-mers are assembled using VelvetSmall k-mers are more likely than full reads to map equally well to multiple places in the reference genome, so reporting both mappings increases the sensitivity. For this data set an average of 21% of k-mers significantly associated with antibiotic resistance report secondary mappings. These k-mers are short (median 15 bp), and therefore have low specificity and high sensitivity as expected.P values from association. High-quality (QUAL>100) SNPs are then annotated for function using SnpEffUsing the BLAT mapping of significant k-mers to a reference sequence, SNPs are called using bcftoolsWe compare with two existing methods. The first uses a core-genome SNP mapping along with population clusters defined from the same alignment to perform a Cochran–Mantel–Haenszel test at every called variant siteStreptococcus pneumoniae ATCC 700669  was set at 50% to represent antibiotic resistance, and a single variant (gene presence/absence or a SNP) was designated as causal. MAF in the population is set from the simulation, and odds ratio (OR) can be varied. The number of cases DE is then the solution to a quadratic equationRatio of cases to controls in the population  and PRJEB3313 (isolates from Kilifi). Results from the S. pyogenes invasiveness GWAS can be found at: http://dx.doi.org/10.6084/m9.figshare.1613851 and can be loaded directly into Phandango (http://jameshadfield.github.io/phandango/) to view the results.How to cite this article: Lees, J. A. et al. Sequence element enrichment analysis to determine the genetic basis of bacterial phenotypes. Nat. Commun. 7:12797 doi: 10.1038/ncomms12797 (2016).Supplementary Figures 1-14, Supplementary Table 1 and Supplementary Methods.