Causal analysis of biological networks

Causal analysis algorithms are based on a ‘master’ network which is derived from the Ingenuity Knowledge Base, and given by a directed multigraph with nodes representing mammalian genes, chemicals, protein families, complexes, microRNA species and biological processes, and edges reflecting observed cause–effect relationships. For the following let be the set of all genes, and the set of all biological processes. For each edge we define functions and that map to its unique source and target nodes, respectively. The graph has no self-edges, i.e. Each edge in is associated with a set of underlying findings obtained from the literature, where each finding is associated with a ‘sign’ that represents the regulation direction of the causal effect. If effect is activating (inhibiting), and for the direction of the effect is unknown or ambiguous. Depending on the underlying findings, edges are classified into the distinct types, ‘T’, ‘A’ and ‘P’, represented by three disjoint subsets of E: E_t, E_a and E_p. T-edges are related to transcription and expression events including protein–DNA binding (i.e. regulation of the abundance of the target node), while A-edges represent the functional activation or inhibition of the target node (e.g. through phosphorylation in a signaling cascade). P-edges are associated with the regulation of biological processes (e.g. apoptosis). The master network G is a multigraph since two given source and target nodes can be connected by a T-edge, and an A-edge at the same time.
The various finding categories and their respective association with edge types and signs are given in a table in the Supplementary Material. Findings about changes of molecular modification states (e.g. phosphorylation) are included in the A-edge type if an activating or inhibiting effect can be inferred. All T-edges are connected to genes as their target nodes, and all P-edges connect to biological processes, Depending on the signs of the underlying findings, each edge is in turn associated with a unique direction of the causal effect that is either activating, inhibiting or unknown, and represented by the sign In addition, we also associate edges with weights reflecting our confidence in the assigned direction of the effect. Details are given in the Supplementary Material.