Tensor decomposition for multiple-tissue gene expression experiments

Abstract

Genome-wide association studies of gene expression traits and other cellular phenotypes have successfully identified links between genetic variation and biological processes. The majority of discoveries have uncovered cis-expression quantitative trait locus (eQTL) effects via mass univariate testing of SNPs against gene expression in single tissues. Here we present a Bayesian method for multiple-tissue experiments focusing on uncovering gene networks linked to genetic variation. Our method decomposes the 3D array (or tensor) of gene expression measurements into a set of latent components. We identify sparse gene networks that can then be tested for association against genetic variation across the genome. We apply our method to a data set of 845 individuals from the TwinsUK cohort with gene expression measured via RNA-seq analysis in adipose, lymphoblastoid cell lines (LCLs) and skin. We uncover several gene networks with a genetic basis and clear biological and statistical significance. Extensions of this approach will allow integration of different omics, environmental and phenotypic data sets.

Figure 1. Graphical representation of the method.

The gene expression data tensor (top left) is decomposed into the product of an individual scores matrix, a tissue scores matrix and a gene loadings matrix (top right). Columns of the individual scores matrix are then used as phenotypes in a GWAS using SNP genotypes (bottom left) in order to uncover genetic variation correlated with the latent components.

Figure 2. MHC Class II regulation.

Figures a and b shows two components identifying a similar network in different tissues. (Top left) GWAS with the component’s individual scores vector as a phenotype. (Top right) Boxplot of individual scores stratified by genotypes at the lead GWAS SNP. Boxplots show the median, upper and lower quartiles, with whiskers extending to either 1.5 times the interquartile range (IQR), or to the most extreme data point if this is within 1.5 times IQR. (Bottom left) Gene loadings for the component. Only gene loadings with a PIP>0.5 are shown. (Bottom right) Tissue scores vector for the component shown as a barplot.

Figure 3. MHC Class I regulation.

(Top left) GWAS with the component’s individual scores vector as a phenotype. (Top right) Boxplot of individual scores stratified by genotypes at the lead GWAS SNP rs289749. (Bottom left) Gene loadings for the component. Only gene loadings with a PIP>0.5 are shown. (Bottom right) Tissue scores vector for the component shown as a barplot.

Figure 4. Histone RNA processing.

(Top left) GWAS with the component’s individual scores vector as a phenotype. (Top right) Boxplot of individual scores stratified by genotypes at the lead GWAS SNP rs6882616. (Bottom left) Gene loadings for the component. Only gene loadings with a PIP>0.5 are shown. (Bottom right) Tissue scores vector for the component shown as a barplot.

Figure 5. Type I Interferon Response.

(Top left) GWAS with the component’s individual scores vector as a phenotype. (Top right) Boxplot of individual scores stratified by genotypes at the lead GWAS SNP rs2401506. (Bottom left) Gene loadings for the component. Only gene loadings with a PIP>0.5 are shown. (Bottom right) Tissue scores vector for the component shown as a barplot.

Figure 6. Zinc finger gene network.

(Top left) GWAS with the component’s individual scores vector as a phenotype. (Top right) Boxplots of individual scores stratified by genotypes at the lead GWAS SNPs, rs17611866 and rs12630796. (Bottom left) Gene loadings for the component, with zinc finger genes on chr 19 highlighted in purple. Only gene loadings with a PIP>0.5 are shown. (Bottom right) Tissue scores vector for the component shown as a barplot.

Figure 7. Multi-omics data integration.

Graphical representation of a linked decomposition for several genomic assays. A matrix decomposition is applied to each data type. The matrix decompositions identify a different loadings matrix for each data type and a shared individual scores matrix.