Eqs 6 1 Keygen For 18 Sherlock Expression
A. Original time-course expression of the gene pair RAD51-HST3, where the red cross (green circle) denotes expression levels of RAD51 (HST3). B. Kernelized (using polynomial kernel of degree 2) expression of the gene pair RAD51-HST3.
Eqs 6 1 Keygen For 18 sherlock expression
Székely and colleagues proposed distance correlation (dCor) as a measure of dependence and test for independence between two random vectors [11]. Dcor can be easily implemented in arbitrary dimensions and is widely cited. However, dCor is based on distance covariance, thus it ranges between 0 and 1, i.e., it can not be negative. Chen and colleagues [12] introduced a nonparametric test to detect nonlinear correlations of time-course gene expression data (GED). The maximal local correlation metric was shown to detect the nonlinear association of five time-point GED between rd mice and age-matched wild-type controls, while other correlation methods such as Pearson correlation could not. Later on, an empirical copula-based statistic (CoS) was developed to assess the strength of and test for independence between two random variables [13].
As an important application, the proposed Kc has been demonstrated to uncover known and novel genes involved in the early differentiation of Th17 cells, by revealing genes having a nonlinear correlation with a known marker gene such as IL17A, whose expression is commonly used to assess the Th17 polarization efficiency ([8, 16, 17]). These uncovered genes are likely to be involved with the early Th17 cell differentiation. Thus, Kc is a simple but efficient way to identify genes associated with early Th17 cell differentiation. Aijo and colleagues generated RNA-seq data to measure gene expression during early human T helper 17 (Th17) cell differentiation and T-cell activation (Th0) [8]. They let RNA-seq (count data) of a gene assume a negative binomial distribution with the mean following a Gaussian process at the ith time point of the jth replicate. Further, they employed an MCMC method to identify differential expression dynamics between Th17 and Th0; some selected identified differentially expressed genes were verified by qRT-PCR. The method was called DyNB, which extended maSigPro-GLM [18]. maSigPro-GLM is a package, that takes temporal dimension and correlation of RNA-seq time series into account, to detect differential expression of time-course RNA-seq data with or without replicates.
The time-course expression of IL17A and RORC (ISG20, RAB3, and TIAM1) in Fig 1 (Fig 7) of [8], respectively, show that IL17A has a positive correlation with RORC, ISG20, and RAB3, but it has a negative correlation with TIAM1. These correlations are consistent with the expression (in normalized read counts) of these genes in Th17 cells. Moreover, the CoS test was applied (with 1,000 repeats) to test for the nonlinearity of the four IL17A gene pairs, which were all significant with P equal to 0.014 and 0.000 (rounded to the third digit) for the latter three pairs, respectively. This result justifies that the nonlinear correlations of these pairs exist.
We applied Kc-RBF (with the default γ value) to estimate the nonlinear correlation of similar-patterned (complementary-patterned) gene pairs, e.g., IL17A-ISG20 (IL17A-TIAM1) profiled in Th17 cells [8]. Because the normalized data of these genes in replicate 1 differed much from those of replicate 2 and 3, we set replicate 1 data aside and computed Kc using replicate 2 and 3 data. For genes whose expression of Th0 cells was highly similar to that of Th17 cells, they were not involved in the differentiation of Th17 cells. Thus, to exclude genes irrelevant to immune differentiation, we first computed Kc of MAP1B, RORC, KIF11, IGS20, RAB3 and TIAM1 with themselves in Th17 cells and Th0 cells, e.g., correlation of the expression of MAP1B in Th17 and the expression of MAP1B in Th0 cells. Since self-correlation is similar-patterned, we used Kc-RBF (γ = 0.5), and obtained an averaged self-correlation of MAP1B (KIF11) equal to 0.998 (0.996) with P
Scalable, integrative methods to understand mechanisms that link genetic variants with phenotypes are needed. Here we derive a mathematical expression to compute PrediXcan (a gene mapping approach) results using summary data (S-PrediXcan) and show its accuracy and general robustness to misspecified reference sets. We apply this framework to 44 GTEx tissues and 100+ phenotypes from GWAS and meta-analysis studies, creating a growing public catalog of associations that seeks to capture the effects of gene expression variation on human phenotypes. Replication in an independent cohort is shown. Most of the associations are tissue specific, suggesting context specificity of the trait etiology. Colocalized significant associations in unexpected tissues underscore the need for an agnostic scanning of multiple contexts to improve our ability to detect causal regulatory mechanisms. Monogenic disease genes are enriched among significant associations for related traits, suggesting that smaller alterations of these genes may cause a spectrum of milder phenotypes.
Over the last decade, GWAS have been successful in robustly associating genetic loci to human complex traits. However, the mechanistic understanding of these discoveries is still limited, hampering the translation of the associations into actionable targets. Studies of enrichment of expression quantitative trait loci (eQTLs) among trait-associated variants1,2,3 show the importance of gene expression regulation. Functional class quantification showed that 80% of the common variant contribution to phenotype variability in 12 diseases can be attributed to DNAase I hypersensitivity sites, further highlighting the importance of transcript regulation in determining phenotypes4.
Many transcriptome studies have been conducted where genotypes and expression levels are assayed for a large number of individuals5,6,7,8. The most comprehensive transcriptome dataset, in terms of examined tissues, is the Genotype-Tissue Expression Project (GTEx): a large-scale effort where DNA and RNA were collected from multiple tissue samples from nearly 1000 individuals and sequenced to high coverage9,10. This remarkable resource provides a comprehensive cross-tissue survey of the functional consequences of genetic variation at the transcript level.
To integrate knowledge generated from these large-scale transcriptome studies and shed light on disease biology, we developed PrediXcan11, a gene-level association approach that tests the mediating effects of gene expression levels on phenotypes. PrediXcan is implemented on GWAS or sequencing studies (i.e., studies with genome-wide interrogation of DNA variation and phenotypes). It imputes transcriptome levels with models trained in measured transcriptome datasets (e.g., GTEx). These predicted expression levels are then correlated with the phenotype in a gene association test that addresses some of the key limitations of GWAS11.
Methods similar to PrediXcan that estimate the association between intermediate gene expression levels and phenotypes, but use summary statistics have been reported: TWAS (summary version)15 and Summary Mendelian Randomization (SMR)16. Another class of methods that integrate eQTL information with GWAS results are based on colocalization of eQTL and GWAS signals. Colocalized signals provide evidence of possible causal relationship between the target gene of an eQTL and the complex trait. These include RTC1, Sherlock17, COLOC18, and more recently eCAVIAR19 and ENLOC20.
Here we derive a mathematical expression that allows us to compute the results of PrediXcan without the need to use individual-level data, greatly expanding its applicability. We compare with existing methods and outline a best practices framework to perform integrative gene mapping studies, which we term MetaXcan.
We apply the MetaXcan framework by first training over one million elastic net prediction models of gene expression traits, covering protein coding genes across 44 human tissues from GTEx, and then performing gene-level association tests over 100 phenotypes from 40 large meta-analysis consortia and dbGaP.
We have derived an analytic expression to compute the outcome of PrediXcan using only summary statistics from genetic association studies. Details of the derivation are shown in the Methods section. In Fig. 1a we illustrate the mechanics of Summary-PrediXcan (S-PrediXcan) in relation to traditional GWAS and the individual-level PrediXcan method11.
Figure 4a shows a diagram of S-PrediXcan and S-TWAS. Both use SNP to phenotype associations results (Z X,Y ) and prediction weights (w X,Tg ) to infer the association between the gene expression level (T g ) and phenotype (Y).
Figure 4b compares S-TWAS significance (as reported in ref. 24) to S-PrediXcan significance. The difference between the two approaches is mostly driven by the different prediction models: TWAS uses BSLMM25 whereas PrediXcan uses elastic net26. BSLMM allows two components: one sparse (small set of large effect predictors) and one polygenic (all variants contribute some marginal effect to the prediction). For PrediXcan we have chosen to use a sparse model (elastic net) based on the finding that the genetic component of gene expression levels is mostly sparse27.
Zhu et al. have proposed Summary Mendelian Randomization (SMR)16, a summary data based Mendelian randomization that integrates eQTL results to determine target genes of complex trait-associated GWAS loci. They derive an approximate \(\chi _1^2\) -statistic (Eq 5 in ref. 16) for the mediating effect of the target gene expression on the phenotype. Figure 5a depicts this mechanism.
