k-Partite cliques of protein interactions: A novel subgraph topology for functional coherence analysis on PPI networks

Abstract

Many studies are aimed at identifying dense clusters/subgraphs from protein-protein interaction (PPI) networks for protein function prediction. However, the prediction performance based on the dense clusters is actually worse than a simple guilt-by-association method using neighbor counting ideas. This indicates that the local topological structures and properties of PPI networks are still open to new theoretical investigation and empirical exploration. We introduce a novel topological structure called k-partite cliques of protein interactions-a functionally coherent but not-necessarily dense subgraph topology in PPI networks-to study PPI networks. A k-partite protein clique is a maximal k-partite clique comprising two or more nonoverlapping protein subsets between any two of which full interactions are exhibited. In the detection of PPI's maximal k-partite cliques, we propose to transform PPI networks into induced K-partite graphs where edges exist only between the partites. Then, we present a maximal k-partite clique mining (MaCMik) algorithm to enumerate maximal k-partite cliques from K-partite graphs. Our MaCMik algorithm is then applied to a yeast PPI network. We observed interesting and unusually high functional coherence in k-partite protein cliques-the majority of the proteins in k-partite protein cliques, especially those in the same partites, share the same functions, although k-partite protein cliques are not restricted to be dense compared with dense subgraph patterns or (quasi-)cliques. The idea of k-partite protein cliques provides a novel approach of characterizing PPI networks, and so it will help function prediction for unknown proteins.

Discovering Maximal Motif Cliques in Large Heterogeneous Information Networks

“…Maximal clique enumeration (MCE), which finds maximal cliques (or maximal subgraphs whose nodes are adjacent to each other) from unlabelled graphs, has been extensively studied [1], [9], [17], [39]. Researchers have also examined bi-cliques (for bi-partite graphs) [42] and k-partite cliques (for k-partite graphs) [25]. In fact, these cliques are special cases of the m-clique (Section III).…”

“…• When G is a k-partite graph (k ≥ 2), the maximal k-partite clique problem [25] asks for all maximal k-partite cliques of G (i.e., maximal complete k-partite subgraphs of G). Particularly, when k = 2, it is the maximal bi-clique problem [42].…”

On Finding and Enumerating Maximal and Maximum k-Partite Cliques in k-Partite Graphs

“…For arbitrary k , however, much less seems to have been done. The only known direct method [4] is highly inefficient. It enumerates maximal bicliques for each pair of partite sets.…”

“…A k -partite clique is maximum if no larger k -partite clique exists; it is maximal if no vertex can be added to it to form a larger k -partite clique. The quest for maximum and maximal k -partite cliques arises in numerous applications, as examples, in textile engineering [1], in categorical data clustering for data mining [2], in the analysis of heterogeneous functional genomics data [3], and in the identification of coherence in protein–protein interaction networks [4].…”