BinTree Seeking: A Novel Approach to Mine Both Bi-Sparse and Cohesive Modules in Protein Interaction Networks

Abstract

Modern science of networks has brought significant advances to our understanding of complex systems biology. As a representative model of systems biology, Protein Interaction Networks (PINs) are characterized by a remarkable modular structures, reflecting functional associations between their components. Many methods were proposed to capture cohesive modules so that there is a higher density of edges within modules than those across them. Recent studies reveal that cohesively interacting modules of proteins is not a universal organizing principle in PINs, which has opened up new avenues for revisiting functional modules in PINs. In this paper, functional clusters in PINs are found to be able to form unorthodox structures defined as bi-sparse module. In contrast to the traditional cohesive module, the nodes in the bi-sparse module are sparsely connected internally and densely connected with other bi-sparse or cohesive modules. We present a novel protocol called the BinTree Seeking (BTS) for mining both bi-sparse and cohesive modules in PINs based on Edge Density of Module (EDM) and matrix theory. BTS detects modules by depicting links and nodes rather than nodes alone and its derivation procedure is totally performed on adjacency matrix of networks. The number of modules in a PIN can be automatically determined in the proposed BTS approach. BTS is tested on three real PINs and the results demonstrate that functional modules in PINs are not dominantly cohesive but can be sparse. BTS software and the supporting information are available at: www.csbio.sjtu.edu.cn/bioinf/BTS/.

Revealing the Hidden Relationship by Sparse Modules in Complex Networks with a Large-Scale Analysis

“…It is also worth mentioning that although there are a large number of overlapped nodes between the small modules from Newman-fast method and the sparse modules from BTS, their node component organizations are quite different. The reason for the differences is that the small modules are subjective to the cohesive definitions in the Newman-fast method, while in the BTS, sparse modules are totally diverse from the cohesive definition [24].…”

“…It is also worth pointing out that these bridge modules were also found in the biological networks as reported in refs. [23], [24]. Another common organization is different sparse modules interacting with each other as shown in Figure 5B.1, where Figure 5B.2 illustrates a real example from the Geom network.…”

“…Unlike previous approaches that mainly extract functional units by identifying cohesive modules, we have recently developed an algorithm called BinTree Seeking (BTS) that can also find sparse modules in PPI networks [24]. Members in a sparse module are defined as sparsely connected internally and densely connected with other sparse or cohesive modules at the same time [24].…”

“…Members in a sparse module are defined as sparsely connected internally and densely connected with other sparse or cohesive modules at the same time [24]. By using an adjacency matrix to represent a network, BTS detects modules by depicting edges and nodes simultaneously rather than nodes alone and its derivation procedure is based on matrix primary transpositions.…”

“…This finding indicated that we need to extend our traditional concept about the functional unit in a complex network by paying more attention to the sparse modules. By overcoming the resolution limit and over-split phenomena of the alternative approach [24], [25], we proposed a BinTree Seeking (BTS) method based on the Edge Density of Module (EDM) and binary tree theory to mine both sparse and cohesive functional modules in biological networks [24]. Experimental results on three real PPI networks demonstrate that functional modules in PPI networks are not dominantly cohesive but can be sparse.…”