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/.

Highlights

  • Most biological characteristics arise from complex interactions between the cell’s numerous constituents, such as proteins, DNA, RNA, and small molecules [1,2,3,4,5]

  • The results by applying Binary Tree (BinTree) Seeking (BTS) on synthetic network Detection of blocks is a classic issue in complex network studies and many methods were proposed in the literature [28,29,30]

  • Our experiments show that E-values in the Pinkert method can be changed dramatically when the number of classes is set to other values

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Summary

Introduction

Most biological characteristics arise from complex interactions between the cell’s numerous constituents, such as proteins, DNA, RNA, and small molecules [1,2,3,4,5]. Modules are of interest because they often correspond to functional subunits [5], such as protein complexes [6,7] or social spheres [8]. Revealing these modular constituents in networks will undoubtedly bring richer biological information in gaining insights into dynamic of molecular systems on a new landscape. As a representative example in complex biological systems, PIN is widely used to predict protein functions [9,10,11] because its dynamic and modular structures are considered to be capable of providing more significant and direct evidences in formation of protein functions. Considering the importance of the module information buried in a PIN, a number of mathematical and computer algorithms have been proposed to tackle module and protein complex detections in protein interaction networks [6,13,14,15,16,17,18]

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