# Fibrosis Protein-Protein Interactions from Google Matrix Analysis of MetaCore Network
## 4 Conclusions  
Identifying fibrosis-associated proteins is a critical issue in treating heart failure. However, deciphering fibrosis proteins experimentally is extremely time-consuming and labor-intensive. Thus, alternative methods should be developed to discover fibrosis proteins. In the current study, we explored fibroblast transcriptome profiling data [5] to develop a model for predicting cardiac fibrosis protein-protein interactions using the Google matrix analysis. Thus, we implemented the REGOMAX algorithm to the MetaCore PPI network to dissect the key proteins driving cardiac fibroblast activation leading to fibrosis.  
In this work, we presented the Google matrix analysis of PPI of cardiac fibrosis. The group of 54 proteins actively participating in the fibrosis process is determined on the basis of INSERM experimental results presented in [5], which identify 44 proteins. In addition, we discover 10 external proteins with strongest sensitivity action on the fibrosis related 44-group. The sensitivity action is computed in the context of the REGOMAX approach applied to the MetaCore PPI network [8]. Our results allow us to identify the most important interactions between 54 proteins related to fibrotic cascade. The strongest integrated sensitivity actions of fibrosis proteins are summarized in Table 3, predicting the strongest influence of the myocardial fibrosis process. The strongest interactions between fibrosis proteins are also identified from the REGOMAX analysis and are summarized in Table 2.  
The current research not only significantly improves the prediction performance of fibrosis proteins, but also discovers several potential fibrosis-associated proteins for future experimental investigations. It is anticipated that the current research could provide new insights into fibrosis-related disease mechanisms and diagnosis. Confirmatory testing of these predictions is planned with the experimental investigations of fibrosis to be performed at INSERM.  
We argue that the developed Google matrix analysis for PPI has a generic and universal nature, being based on the strict mathematical features of Markov chains and directed networks [15; 16; 17; 18]. Thus, this approach can be applied not only to the MetaCore network but also to other PPI network databases, such as TRANSPATH [13] and REACTOM [14]. The mathematical foundations of the Google matrix analysis have proved to be useful and efficient for different types of directed networks, including the World Wide Web [15; 16], Wikipedia networks, and the world trade networks [17; 20; 23; 25; 26]. Thus, we expect that the analysis of the existing PPI network databases [8; 13; 14] with the Google matrix algorithms described here will find broad applications for analysis of various complex biosystems and diseases.  
All authors equally contributed to all stages of this work. All authors have read and agreed to the published version of the manuscript.  
This research was supported in part through the grant NANOX \(N^{o}\) ANR-17-EURE-0009, (project MTDINA) in the frame of the Programme des Investissements d'Avenir, France; it was granted access to the HPC resources of CALMIP (Toulouse) under the allocation 2021-P0110; it was also supported by INSERM funding.  
The authors declare no conflict of interest.