Clustering Coefficients in Protein Interaction Hypernetworks

Modeling protein interaction data with graphs (networks) is insufficient for some common types of experimentally generated interaction data. For example, in affinity purification experiments, one protein is pulled out of the cell along with other proteins that are bound to it. This data is not intrinsically binary, so we lose information when we model it with a graph, which can only associate pairs of proteins. Hypergraphs, an extension of graphs which allows relationships among sets of arbitrary size, have been proposed to model this type of data. However, there is no consensus for appropriate measures for these "protein interaction hypernetworks" that are meaningful in both their interpretation and in their correspondence to a biological question (e.g., predicting the function of uncharacterized proteins, identifying new biological modules). The clustering coefficient is a measure commonly used in binary networks for biological insights. While multiple analogs of the clustering coefficient have been proposed for hypernetworks, the usefulness of these for generating biological hypotheses has not been established. We present several new definitions for a hypergraph clustering coefficient that pertain specifically to the biology of interacting proteins. We evaluate the biological meaning of these and previously proposed definitions in protein interaction hypernetworks and test their correlation with protein complexes. We conclude that hypergraph analysis offers important advantages over graph measures for non-binary data, and we discuss the clustering coefficient measures that perform best. Our work suggests a paradigm shift is needed to best gain insights from affinity purification assays and other non-binary data.