Mapping eQTL Networks with Mixed Graphical Markov Models

Abstract

Expression quantitative trait loci (eQTL) mapping constitutes a challenging problem due to, among other reasons, the highdimensional 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 article we approach this challenge with mixed graphical Markov models, higherorder 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.

Networks Underpinning Symbiosis Revealed Through Cross-Species eQTL Mapping

“…Networks were inferred using results from both cross-species and within-species eQTL analyses ( Figure 3 and Figure S3 in File S2 ). DNA polymorphisms and expression profiles were connected by implementing a mixed graphical Markov model approach designed for eQTL data ( Tur et al 2014 ). This technique disentangles direct vs. indirect connections between genes and polymorphic sites.…”

“…From the eQTL results, plant and nematode genes associated with at least one genotype marker (with P -value <0.0001) were included in the network analysis. A mixed graphical Markov model as implemented in the Bioconductor package “qpgraph” ( Tur et al 2014 ) was used to infer the gene–gene interactions and marker to gene causal relationships. For details, see File S1 .…”

The Networked Partial Correlation and Its Application to the Analysis of Genetic Interactions

“…We downloaded and processed the resulting raw data as described in Tur et al . () leading to a normalized gene expression data matrix formed by p =6216 genes and n =112 samples.…”

Network-Guided Biomarker Discovery

“…While most network-guided biomarker discovery studies make use of generic gene-gene interaction networks such as STRING or BioGRID, many other possibilities are starting to open up. They include diseasespecific networks such as ACSN, but we can also imagine using for example eQTL networks based on previous studies [89], or three-dimensional chromatin interaction networks [90]. Methods that integrate these multiple types of networks may be needed; that the regularized regression or penalized relevance methods we discussed can all accomodate weighted networks (either directly or through simple modifications) will facilitate these developments.…”