A Bayesian framework for inference of the genotype-phenotype map for segregating populations

Abstract

Complex genetic interactions lie at the foundation of many diseases. Understanding the nature of these interactions is critical to developing rational intervention strategies. In mammalian systems hypothesis testing in vivo is expensive, time consuming, and often restricted to a few physiological endpoints. Thus, computational methods that generate causal hypotheses can help to prioritize targets for experimental intervention. We propose a Bayesian statistical method to infer networks of causal relationships among genotypes and phenotypes using expression quantitative trait loci (eQTL) data from genetically randomized populations. Causal relationships between network variables are described with hierarchical regression models. Prior distributions on the network structure enforce graph sparsity and have the potential to encode prior biological knowledge about the network. An efficient Monte Carlo method is used to search across the model space and sample highly probable networks. The result is an ensemble of networks that provide a measure of confidence in the estimated network topology. These networks can be used to make predictions of system-wide response to perturbations. We applied our method to kidney gene expression data from an MRL/MpJ × SM/J intercross population and predicted a previously uncharacterized feedback loop in the local renin-angiotensin system.

Figure 1.—

Example of a local family, where continuous child node y = X_m has discrete and continuous parents π_G(y) = {Q₁, Q₂, … , Q_s, X₁, X₂, … , X_t}.

Figure 2.—

The simulated network was generated as the compilation of local models.

Figure 3.—

The RAS pathway as depicted in KEGG was overrepresented in the chromosome 4 trans-band for the MRL/MpJ × SM/J intercross. Members of this pathway with significant QTL are indicated. These enzymes and QTL were selected as network variables.

Figure 4.—

Posterior probabilities estimated by BMA for each network node. Each point is an entry in the consensus matrix, which represents the probability of a connection associated with the given node. Connections with probabilities >0.5 serve as nodes in the final weighted network.

Figure 5.—

A graphical representation of the final RAS network based on BMA. Edges were drawn if their probability exceeded 0.5.

Figure 6.—

An illustration of the parameterization of local models for the purpose of making forward prediction. The parameterization is given by the least-squares estimates of the regression coefficients for the local models; they provide insight into the relationships between network variables. We selected a highly probable region of the graph, which suggests a feedback mechanism in the canonical pathway.