A Graphical Modelling Approach to the Dissection of Highly Correlated Transcription Factor Binding Site Profiles

Inferring the combinatorial regulatory code of transcription factors (TFs) from genome-wide TF binding profiles is challenging. A major reason is that TF binding profiles significantly overlap and are therefore highly correlated. Clustered occurrence of multiple TFs at genomic sites may arise from chromatin accessibility and local cooperation between TFs, or binding sites may simply appear clustered if the profiles are generated from diverse cell populations. Overlaps in TF binding profiles may also result from measurements taken at closely related time intervals. It is thus of great interest to distinguish TFs that directly regulate gene expression from those that are indirectly associated with gene expression. Graphical models, in particular Bayesian networks, provide a powerful mathematical framework to infer different types of dependencies. However, existing methods do not perform well when the features (here: TF binding profiles) are highly correlated, when their association with the biological outcome is weak, and when the sample size is small. Here, we develop a novel computational method, the Neighbourhood Consistent PC (NCPC) algorithms, which deal with these scenarios much more effectively than existing methods do. We further present a novel graphical representation, the Direct Dependence Graph (DDGraph), to better display the complex interactions among variables. NCPC and DDGraph can also be applied to other problems involving highly correlated biological features. Both methods are implemented in the R package ddgraph, available as part of Bioconductor (http://bioconductor.org/packages/2.11/bioc/html/ddgraph.html). Applied to real data, our method identified TFs that specify different classes of cis-regulatory modules (CRMs) in Drosophila mesoderm differentiation. Our analysis also found depletion of the early transcription factor Twist binding at the CRMs regulating expression in visceral and somatic muscle cells at later stages, which suggests a CRM-specific repression mechanism that so far has not been characterised for this class of mesodermal CRMs. Author Summary: Transcription factors (TFs) are proteins that bind to DNA and regulate gene expression. Recent technological advances make it possible to map TF binding patterns across the whole genome. Multiple single-gene studies showed that combinatorial binding of multiple transcription factors determines the gene transcriptional output. A common naive assumption is that correlated binding profiles may indicate combinatorial binding. However, it has been found that many TFs bind to distinct hotspots whose role is currently unclear. It is thus of great interest to find transcription factor combinations whose correlated binding is causally most immediate to gene expression. Building upon theories of statistical dependence and causality, we develop novel graphical modelbased algorithms that handle highly correlated transcription factor binding profiles more efficiently and reliably than existing algorithms do. These algorithms can also be applied to other biological areas involving highly correlated variables, such as the analysis of high-throughput gene knock-down experiments.