Viewing the Meso-Scale Structures in Protein-Protein Interaction Networks Using 2-Clubs

Many current analyses on protein-protein interaction (PPI) networks concentrate on developing the algorithms for identifying the functional modules within the PPI networks. However, understanding the internal structure in the functional modules is needed to define their roles within the entire network. We propose the use of a two-club meso-scale structure that possesses refined inner topological structural properties, useful for deciphering the aforementioned obscure structural supporting evidences. In this paper, we: 1) illustrate the feasibility and advantages of modeling functional modules as two-clubs in PPI networks by taking statistics on the diameter distribution of benchmark functional modules within several golden standard sets; 2) categorize the two-clubs into six subcategories through the use of well-defined internal graph-theoretic characterizations; and 3) analyze these six subcategories based on factors, such as their structure, and various metrics, such as topological centralities, the numbers of involved transcription factors and essential genes, and the numbers of matched protein complexes or GO terms. Our structure-driven analysis allows us to predict the roles of identified functional modules from their network structure alone. Our subcategories of coteries and social circles serve as a classification scheme for determining which functional modules are central, regional, and satellite and which are coordinating. Experimental results show that in order to precisely control and examine the PPI networks for further research, a clear understanding of how the internal topology of modules affects their function is essential.