Google matrix analysis of bi-functional SIGNOR network of protein-protein interactions

Abstract

Motivation: Directed protein networks with only a few thousand of nodes are rather complex and do not allow to extract easily the effective influence of one protein to another taking into account all indirect pathways via the global network. Furthermore, the different types of activation and inhibition actions between proteins provide a considerable challenge in the frame work of network analysis. At the same time these protein interactions are of crucial importance and at the heart of cellular functioning. Results: We develop the Google matrix analysis of the protein-protein network from the open public database SIGNOR. The developed approach takes into account the bi-functional activation or inhibition nature of interactions between each pair of proteins describing it in the frame work of Ising-spin matrix transitions. We also apply a recently developed linear response theory for the Google matrix which highlights a pathway of proteins whose PageRank probabilities are most sensitive with respect to two proteins selected for the analysis. This group of proteins is analyzed by the reduced Google matrix algorithm which allows to determine the effective interactions between them due to direct and indirect pathways in the global network. We show that the dominating activation or inhibition function of each protein can be characterized by its magnetization. The results of this Google matrix analysis are presented for three examples of selected pairs of proteins. The developed methods work rapidly and efficiently even for networks with several million of nodes and can be applied to various biological networks. Availability: The Google matrix data and executive code of described algorithms are available at

What is the central bank of Wikipedia?

“…The exact formulas for all three components of G R are given in [19,20]. The numerical computation methods of all three components of G R and numerical REGOMAX code developed in [19] are given in [26].…”

Linear response theory for Google matrix

“…• 2 ements in rows (instead of columns) to determine follower networks are available at [16]. This type of friend/follower effective network schemes constructed from the reduced Google matrix (or one of its components) were already presented in [11] in the context of Wikipedia networks of politicians.…”

“…The paper is constructed as follows: in Section 2 we provide the analytical description of the LIRGOMAX algorithm complemented by a brief description of the Google matrix construction and the REGOMAX algorithm, in Section 3 we present certain results for two examples of the Wikipedia network, the discussion of results is given in Section 4. Additional data are also available at [16].…”