Signaling hypergraphs

Abstract

Signaling pathways function as the information-passing mechanisms of cells. A number of databases with extensive manual curation represent the current knowledge base for signaling pathways. These databases motivate the development of computational approaches for prediction and analysis. Such methods require an accurate and computable representation of signaling pathways. Pathways are often described as sets of proteins or as pairwise interactions between proteins. However, many signaling mechanisms cannot be described using these representations. In this opinion, we highlight a representation of signaling pathways that is underutilized: the hypergraph. We demonstrate the usefulness of hypergraphs in this context and discuss challenges and opportunities for the scientific community.

Keywords: graphs; hypergraphs; signaling pathways.

Figure 1. Signaling Pathway Representations

There are three main ways of representing signaling pathways. A signaling pathway may be simply represented as a set of proteins, with no additional information. Graphs encode pairwise interactions between proteins; these interactions may be undirected (green) or directed (blue). Hypergraphs, the focus of this article, encode multi-way interactions and reactions (see Box 1 for examples).

Figure 2

Events following Wnt signaling that lead to release of β-catenin. Black edges denote connections to other signaling pathways and biological processes. The inset shows a possible graph representation of these events. Green: undirected edge; blue: directed edge; purple: hyperedge; dashed purple: regulated component of hyperedge; gray circle: hypernode; red outline: active form.

Figure 3. Example nested organization of BioPAX pathway elements

This shows the nested hierarchy of the BioPAX file formats. Hypernodes may be complexes, proteins or small molecules. Reaction elements in BioPAX are equivalent to directed hyperedges, and controlled reactions to regulated hyperedges.

Figure I. Representations of three types of events in signaling pathways

In each panel, the biological representation (middle) can be converted into a graph (left) or a hyper- graph (right). Green: undirected edge; blue: directed edge; gray circle: hypernode; purple: hyperedge; red outline: active form; dashed purple: regulatory component of hyperedge.