Mapping eQTL networks with mixed graphical Markov models

Expression quantitative trait loci (eQTL) mapping constitutes a challenging problem due to, among other reasons, the high-dimensional multivariate nature of gene-expression traits. Next to the expression heterogeneity produced by confounding factors and other sources of unwanted variation, indirect effects spread throughout genes as a result of genetic, molecular and environmental perturbations. From a multivariate perspective one would like to adjust for the effect of all of these factors to end up with a network of direct associations connecting the path from genotype to phenotype. In this paper we approach this challenge with mixed graphical Markov models, higher-order conditional independences and q-order correlation graphs. These models show that additive genetic effects propagate through the network as function of gene-gene correlations. Our estimation of the eQTL network underlying a well-studied yeast data set leads to a sparse structure with more direct genetic and regulatory associations that enable a straightforward comparison of the genetic control of gene expression across chromosomes. Interestingly, it also reveals that eQTLs explain most of the expression variability of network hub genes.Comment: 48 pages, 8 figures, 2 supplementary figures; fixed problems with embedded fonts; figure 7 sideways for improving display; minor fixes; major revision of the paper after journal review; fixed missing .bbl file; 36 pages, 6 figures, 2 table

Detecting the Presence and Absence of Causal Relationships between Expression of Yeast Genes with Very Few Samples

Inference of biological networks from high-throughput data is a central problem in bioinformatics. Particularly powerful for network reconstruction is data collected by recent studies that contain both genetic variation information and gene expression profiles from genetically distinct strains of an organism. Various statistical approaches have been applied to these data to tease out the underlying biological networks that govern how individual genetic variation mediates gene expression and how genes regulate and interact with each other. Extracting meaningful causal relationships from these networks remains a challenging but important problem. In this article, we use causal inference techniques to infer the presence or absence of causal relationships between yeast gene expressions in the framework of graphical causal models. We evaluate our method using a well studied dataset consisting of both genetic variations and gene expressions collected over randomly segregated yeast strains. Our predictions of causal regulators, genes that control the expression of a large number of target genes, are consistent with previously known experimental evidence. In addition, our method can detect the absence of causal relationships and can distinguish between direct and indirect effects of variation on a gene expression level