Application of Graph Coloring to Biological Networks

Abstract

We explore the application of graph coloring to biological networks, specifically protein-protein interaction (PPI) networks. First, we find that given similar conditions (i.e. number of nodes, number of links, degree distribution and clustering), fewer colors are needed to color disassortative (high degree nodes tend to connect to low degree nodes and vice versa) than assortative networks. Fewer colors create fewer independent sets which in turn imply higher concurrency potential for a network. Since PPI networks tend to be disassortative, we suggest that in addition to functional specificity and stability proposed previously by Maslov and Sneppen (Science 296, 2002), the disassortative nature of PPI networks may promote the ability of cells to perform multiple, crucial and functionally diverse tasks concurrently. Second, since graph coloring is closely related to the presence of cliques in a graph, the significance of node coloring information to the problem of identifying protein complexes, i.e. dense subgraphs in a PPI network, is investigated. We find that for PPI networks where 1% to 11% of nodes participate in at least one identified protein complex, such as H. sapien (DIP20070219, DIP20081014 and HPRD070609), DSATUR (a well-known complete graph coloring algorithm) node coloring information can improve the quality (homogeneity and separation) of initial candidate complexes. This finding may help to improve existing protein complex detection methods, and/or suggest new methods.