## 3 Results
### PPI Network Constructionand Functional Enrichment Analysis  
To better understand the biological relationship of \(\beta\)-catenin, Ezrin, SATB1 and SMAD3, the PPI network consisting of seed proteins and their interaction partners was constructed using the STRING online database and Cytoscape software (Figure 7A). There were 54 nodes and 538 edges in the PPI network (PPI enrichment \(p\) value < 1.0 \(\times\) 10\({}^{-16}\); local clustering coefficient 0.69). Further details on the network parameters were obtained by the Cytoscape plugin Network Analyzer, and these are presented in Supplementary data (Table S3). The 10 hub genes were then determined based on the degree score of the nodes in the network using the Cytoscape plugin cytoHubba (Figure 7A; colored nodes). Next, the top two cluster subnetworks were identified from the PPI network with the help of the MCODE plugin (cluster 1: 25 nodes, 236 edges, cluster score: 19.67 (Figure 7B); cluster 2:10 nodes, 18 edges, cluster score: 4.0 (Figure 7C)). Furthermore, the Reactome Pathway, KEGG Pathway, GO and KEGG Brite enrichment analyses were performed to predict signaling pathways, gene ontological features and functional hierarchies of _CTNNB1_, _EZR_, _SATB1_, _SMAD3_ and their 50 interaction partners. The Reactome Pathway hierarchy panel is illustrated in Figure 8A. This analysis showed that the queried genes and their neighbors were mainly involved in signaling by WNT/\(\beta\)-catenin, diseases of signal transduction by growth factor receptors and second messengers, transcription and signal transduction (Figure 8B). KEGG pathway analysis demonstrated that the imputed genes were highly associated with adherens junction, endometrial cancer, WNT signaling pathway, Hippo signaling pathway and pathways in cancer (Figure 9A). KEGG BRITE functional hierarchies revealed that there was a preponderance of genes representing transcription factors, chromosome and associated proteins, enzymes and cytoskeleton proteins (Figure 9B). In GO analysis, the most enriched ontology terms were canonical WNT signaling pathway (Figure 9C), cell-cell adherens junction (Figure 9D) and \(\beta\)-catenin binding (Figure 9E). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**HR**} & \multicolumn{2}{c}{**95\% CI**} & \multirow{2}{*}{\(p\)**Value**} \\ \cline{3-3} \cline{5-5}  & & **Lower** & & **Upper** \\ \hline Others & & & Ref. & \\ \hline SATB1 lowSMAD3 highEZRhighCTNNB1 high & 3.28 & 2.02 & 5.33 & **\textless{}0.0001** \\ \hline SATB1 highSMAD3 lowEZRlowCTNNB1 low & 0.57 & 0.14 & 2.35 & 0.44 \\ \hline age & 1.02 & 1.00 & 1.05 & **0.01** \\ \hline grade & 1.57 & 0.83 & 2.98 & 0.17 \\ \hline pN & 2.24 & 1.27 & 3.95 & **0.01** \\ \hline pT & 1.28 & 0.61 & 2.66 & 0.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: _Cont._Figure 7: Protein–protein interaction network for \(\beta\)-catenin, Ezrin, SATB1, SMAD3 and their 50 neighbors. PPI network properties, such as node degree and clustering coefficient, are visualized by shape size and label font size, respectively. Top 10 hub genes in the network identified by the CytoHubba Cytoscape plugin are highlighted in a red to yellow gradient. The deeper color, the higher degree of enrichment. Other nodes in the network are highlighted in blue **(A)**. The MCODE clustering algorithm was used to identify the clusters in the PPI network. The top two clusters identified by MCODE are displayed (**B,C**). Figure 8: Reactome Pathway functional enrichment analysis for CTNNB1, _EZR_, _SATB1_, _SMAD3_ and their 50 interaction partners. (**A**) Reactome Pathway hierarchy panel; (**B**) Top 30 Reactome pathways. The \(p\) value was calculated and sorted with \(-\)log10 (\(p\) value). Figure 9: KEGG Pathway, KEGG Brite and GO functional enrichment analysis for _CTNNB1_, _EZR_, _SATB1_, _SMAD3_ and their 50 interaction partners.