Modeling Cell Signaling Networks with Prize-Collecting Subhypernetworks

Cell signaling pathways are important tools used by biologists to model how signals are transduced through cells. Though signaling pathways can be (and often are) modeled using graphs, we instead use a generalization known as directed hypergraphs. We find directed hypergraphs to be a useful alternative to standard graphs, because hypergraphs give us a way to represent complex biological reactions that may have more than one reactant or product. Prior work analyzing cell signaling as hypergraphs sought structures called hyperpaths. We develop the notion of a hy-pershrub, a multi-source, multi-target generalization of a hyperpath. We create a formulation that finds specific, prize-dense hypershrubs that may be representative of biological phenomena that went previously unnoticed in standard graph representations of the same signaling pathways. To build our graphs, we introduce a weighting scheme that uses differential expression data to assign weights to nodes, representative of proteins and protein complexes, based on confidence that a given node is differentially regulated between conditions. This method is agnostic about whether or not a node is up-regulated or down-regulated between conditions, allowing us to find pathways that may involve both positive and negative regulation. We apply this formulation to the human Hedgehog signaling pathway, using data from Basal Cell carcinoma (BCC), to analyze the effectiveness of our algorithm on real data.