Quantifying randomness in protein–protein interaction networks of different species: A random matrix approach

Abstract

We analyze protein-protein interaction networks for six different species under the framework of random matrix theory. Nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal Gaussian orthogonal statistics of random matrix theory. We demonstrate that spectral rigidity, which quantifies long range correlations in eigenvalues, for all protein-protein interaction networks follow random matrix prediction up to certain ranges indicating randomness in interactions. After this range, deviation from the universality evinces underlying structural features in network.the universality class of Gaussian orthogonal ensemble (GOE) [1,2,3,4]. Systematic investigations performed on model networks establish correlation between their structural properties and spectral properties inspected by RMT. This paper validates the access of a mathematical tool, RMT, to study protein-protein interaction (PPI) networks of different species, as model systems, under RMT framework. By interaction we mean that a protein may change conformation of another protein leading to a change in its affinity for different groups or may lead to addition or removal of a group in the molecule. The interaction is highly specific i.e. it can discriminate among thousands of different molecules in its environment and selectively interact with one or two [5].A network representation of PPI in addition to providing a better understanding of protein function, serves us with a powerful model of various functional pathways elucidating mechanics at cellular level [6,7,8]. Recently it has been realized that analysis of a network representation of such interactions, in comparison to pairwise analysis, provides a much better understanding of the processes occurring in biological systems [9,10,11,12,13].These studies indicate a strong correlation between the interaction networks and expression properties of the proteins having similar expression dynamics i.e. they tend to form clusters of either static or dynamic proteins [14,15]. Furthermore, analysis of PPI networks have contributed in various disease related biological studies, for instance study of human interaction data and Alzheimer's disease proteins has enriched our knowledge about its protein targets [16]. Some of the PPI network studies reveal that pathogens tend to interact with hub proteins and proteins that are central to many paths in the network [17].Analysis performed here involves construction of networks in such a way that any pair of proteins can achieve only two states i.e. either they are connected or not connected. We demonstrate that nearest neighbor spacing distribution (NNSD) of PPI networks of different species exhibit a similar statistical behavior of RMT, bringing them all under the same universality class. Furthermore, long range correlations in spectra display a wide range of behaviors. RMT and Networks -What is the connection?The random matrix approach regarded the Hamiltonian of a heavy nucleus (which is ...

Assortative and disassortative mixing investigated using the spectra of graphs

“…These networks have already been shown to follow universal RMT predictions of GOE statistics [53]. We concentrate here on the occurrence of high degeneracy at the zero eigen value.…”

Spectral properties of complex networks

“…It was found that spectra of such networks were governed by characteristic features of the underlying networks. The spectral density of an array of real-world networks exhibit triangular structure, owing to their underlying scale-free topology [28,47,48].…”

“…As discussed, for scale-free networks generated using preferential attachment mechanism, it fails to provide a quantitative measure of actual degeneracy observed in real world networks [41], indicating the contribution from other factors. Scale-free behaviour or sparseness of real world networks have been argued out to be other reasons responsible for degeneracy at the zero eigenvalues [40,41,47].…”

Spontaneous back-pain alters randomness in functional connections in large scale brain networks: A random matrix perspective

“…In such a scenario, one settles for a model that captures the statistical properties of the energy spectrum. RMT finds extensive applications in the statistical studies of various complex systems such as quantum chaotic systems, complex nuclei, atoms, molecules, disordered mesoscopic systems [16][17][18][19][20][21][22][23][24], atmosphere [25], financial applications [26], complex networks [27], societal networks [28], network forming systems [29,30], amorphous clusters [31][32][33][34], biological networks [35], protein networks [36,37], and cancer networks [38] etc. In recent years, RMT has also been applied towards brain network studies in studying universal behavior of brain functional connectivity and has been effective in detecting the differences in resting state and visual stimulation state [39,40].…”