# Fibroblast-Specific Protein Interactions for Myocardial Fibrosis from MetaCore Network
## 2 Data Sets and INFI Model Description
### Without Formulas: Methods, Characteristics and Expected Network Results  
As in [16] here we present qualitative explanations without formulas of the mathematical methods and characteristics described in the next Subsections. Our aim here is to give a global view on our approach for a common reader. We use the MetaCore directed network [12] which represents an action of a protein A on a protein B in a form of a directed link (edge) for \(N=40\),079 proteins forming the network nodes (proteins). These links are obtained on the basis of careful and detailed analysis of scientific literature about thousands of experiments of various research groups that allowed to collect information about PPI and thus generated a network database with \(N=40\),079 nodes and \(N_{\ell}=292\),191 links. Certain medical applications of the MetaCore network can be found in [13; 14]. The universal mathematical methods to analyze such networks are generic and based on the concept of Markov chains and Google matrix [17; 18; 19]. The validity of these methods has been confirmed for various directed networks from various fields of science. Therefore, since the Google matrix analysis is based on a generic mathematical foundation, we expect that this analysis will also work efficiently for PPI networks. The Google matrix of the global MetaCore PPI network \(G\) is constructed with specific rules briefly described in the next Section 2.3 and in detail in [17; 18; 19]. The matrix \(G\) is obtained from a matrix of Markov chain transition elements \(S_{ij}\) that give weights of transitions between nodes. The important property of \(G\) is that its application (multiplication) to an arbitrary initial vector \(v\) preserves the probability and the normalization of this vector (sum of all vector elements) remains constant (taken to be unity). As a result of multiple multiplications by \(G\) any initial vector converges to the steady-state distribution given by the PageRank vector \(P\). The components of this vector represent the probabilities of each node (protein) in this limit. The nodes with the highest probabilities are the most influential nodes of the network (all nodes are monotonically ordered by decreasing values of the PageRank components which provides the \"PageRank index\" \(K\) such \(K(j)=1,2,\ldots\) for nodes \(j\) with largest values \(P(j)\)). These nodes have typically many ingoing links and it is likely that some of these ingoing links come from other nodes that also have large PageRank values. For the inverse network, in which all link directions are inverted, the corresponding PageRank is called CheiRank vector \(P^{*}\)[19]. The highest probabilities \(P^{*}(j)\) are for nodes \(j\) with the CheiRank index \(K^{*}(j)=1,2,\ldots\) being the most communicative nodes. They typically have many outgoing links. In the INFI model Ising spins with polarization \(\pm 1\) (red or blue) or \(0\) (white) are placed at each node of network. They describe fibrosis activated protein state (red or \(\sigma_{j}=+1\)) which can activate other proteins, healthy protein state (blue or \(\sigma_{j}=-1\)) which can prepare other proteins and neutral state proteins (white or \(\sigma_{j}=0\)) that cannot affect other proteins but can be activated or repaired by red or blue proteins. The initial spin configuration has certain fixed red proteins with index \(K_{g}=1,\ldots,10\) (see Table 1) and fixed blue proteins with index \(K_{g}=25,\ldots,30\) (or 34 or 38) whose colors always remain unchanged, all other proteins are white (or \(\sigma_{j}=0\)). These white proteins, and also red or blue non-fixed proteins, can change their color depending on the majority color of nodes directly linked to it (taking into account the weights of ingoing and outgoing links of the matrix \(S_{ij}\) taken without dangling nodes). This choice is similar to social relations when a member of society takes his opinion to be imposed by opinions of other members related with him.