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

TL;DR

This paper introduces a Google matrix-based method to analyze complex protein-protein interaction networks, accounting for activation and inhibition effects, and identifies key pathways influencing cellular functions.

Contribution

The study develops a novel Google matrix approach incorporating bi-functional interactions and applies linear response theory to biological networks, enhancing understanding of indirect protein influences.

Findings

Effective influence pathways identified between proteins.

Activation or inhibition characterized by magnetization.

Method applicable to large-scale biological networks.

Abstract

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. 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.