Using Stochastic Causal Trees to Augment Bayesian Networks for Modeling eQTL Datasets

Kyle C Chipman 0 Ambuj K Singh 0 1 0 Biomolecular Science and Engineering Program , UC Santa Barbara, Santa Barbara, CA , USA 1 Department of Computer Science , UC Santa Barbara, Santa Barbara, CA , USA Background: The combination of genotypic and genome-wide expression data arising from segregating populations offers an unprecedented opportunity to model and dissect complex phenotypes. The immense potential offered by these data derives from the fact that genotypic variation is the sole source of perturbation and can therefore be used to reconcile changes in gene expression programs with the parental genotypes. To date, several methodologies have been developed for modeling eQTL data. These methods generally leverage genotypic data to resolve causal relationships among gene pairs implicated as associates in the expression data. In particular, leading studies have augmented Bayesian networks with genotypic data, providing a powerful framework for learning and modeling causal relationships. While these initial efforts have provided promising results, one major drawback associated with these methods is that they are generally limited to resolving causal orderings for transcripts most proximal to the genomic loci. In this manuscript, we present a probabilistic method capable of learning the causal relationships between transcripts at all levels in the network. We use the information provided by our method as a prior for Bayesian network structure learning, resulting in enhanced performance for gene network reconstruction. Results: Using established protocols to synthesize eQTL networks and corresponding data, we show that our method achieves improved performance over existing leading methods. For the goal of gene network reconstruction, our method achieves improvements in recall ranging from 20% to 90% across a broad range of precision levels and for datasets of varying sample sizes. Additionally, we show that the learned networks can be utilized for expression quantitative trait loci mapping, resulting in upwards of 10-fold increases in recall over traditional univariate mapping. Conclusions: Using the information from our method as a prior for Bayesian network structure learning yields large improvements in accuracy for the tasks of gene network reconstruction and expression quantitative trait loci mapping. In particular, our method is effective for establishing causal relationships between transcripts located both proximally and distally from genomic loci. - Background In order to model and dissect the complexity underlying physiological processes, including diseases, developmental programs, and responses to pharmacological treatments, systematic approaches based on genome-wide data are imperative. Expression profiling technologies, such as microarray [1,2] and RNA-Seq platforms [3], provide quantification of mRNA levels on a genomewide scale, prompting computational methods aimed at learning a more holistic perspective of cellular processes. Parallel advancements in the area of genotypic profiling, including high-throughput sequencing and SNP detection, offer information complementary to that of expression data. These concurrent developments pave the way for genetical genomic studies, which provide the joint space of expression and genotypic data corresponding to offspring that arise from a segregating population [4]. To date, eQTL datasets have been published for several organisms [5-10], providing ample opportunity to develop novel computational methodologies. The tandem existence of expression and genotypic data is especially powerful in that it allows one to reconcile changes in expression programs in the context of the specific genetic combinations represented by the offspring. Since natural genetic variation is the sole source of perturbation, it is logical to view genomic loci as epicenters of phenotypic variation in eQTL-derived causal networks. Consequently, modeling eQTL datasets enables one to hypothesize on how genotypic variation results in phenotypic changes. Already several studies have provided methodologies aimed at exploiting the genotypic component of eQTL data to improve causal modeling in gene networks [9,11-16]. Bing et al. introduced methodology to build directed networks starting from a set of candidate cisgenes for each locus [14], establishing directed edges from candidate cis-genes to distally-located genes. This approach yields local regulatory models for individual loci, and the authors also present an innovative approach based on partial correlations to identify models where two regulators play complementary roles in controlling a common set of genes. The methodology of Bing et al. was later applied to an eQTL dataset representing Arabidopsis by Keurentjes et al., who also incorporated information regarding DNA sequence to improve the estimation of cis-genes [9]. While this application was successful in providing hypotheses regarding local regulatory models, it does not resolve causal orderings amongst distally located transcripts. Furthermore, modeling local regulatory programs with respect to individual loci leaves room for improvement in the sense that each of the respective models are disjoint. A worthwhile goal is to produce more holistic and systematic methodologies capable of modeling the complex interdependencies between multiple loci and transcripts. Indeed, it has been estimated that the genetic basis of many transcripts is extensively complex, with upwards of 50% of transcripts being linked to five or more loci [17]. The need for a comprehensive and systematic approach was addressed by Schadt and colleagues, who developed a novel method to augment Bayesian networks with probabilistic measures to direct causal orderings of gene pairs with respect to genomic loci [11-13,18]. Their method, which is based on a conditional bivariate normal model, determines if two transcripts linked to a common locus are best modeled as causal or independent [12]. Ultimately, the information generated by their method is incorporated as a prior for Bayesian network structure learning [19]. This approach has yielded promising results when applied to yeast [13] and mouse [12], providing hypotheses regarding the architecture of eQTL networks. Furthermore, the authors published a study on synthetic networks to quantify the performance gains associated with their method [18] as compared to standard Bayesian network structure learning. While their method proved efficacious at resolving causal orientations between correlated transcripts in the context of a global network, the scope is generally limited to the upper echelons of the causal hierarchy, an attribute that stems from their reliance on using genomic loci as causal anchors. Ideally, one could commence at the genomic loci, learn the causal orderings of the most proximal transcripts, then advance down the causal hierarchy propagating the structural information gleaned from the upper levels of th (...truncated)