br Pathway analysis of the ESA miRNAs and their performance
3.2. Pathway analysis of the ESA miRNAs and their performance on classification
The top-ranked miRNAs and mRNAs by the estimated essential score alterations (ESA) were kept for the following analysis. Differential Jasplakinolide analysis was carried out by using the edgeR package  in R for both mRNAs and miRNAs as the benchmark method (more details in Materials and Methods). Totally 167 DE miRNAs and 3596 DE mRNAs were detected. Then the same number of ESA miRNAs and ESA mRNAs were extracted for the comparison analysis.
50 miRNAs (30%) are shared by DE miRNAs set and ESA miRNAs set. The remaining 117 ESA miRNAs (over 70%) do not exhibit significant alteration at their expression levels. Interestingly, these 117 ESA miRNAs are also discriminative for prostate cancer/normal samples, with 80.77% total accuracy (in Table 1). Furthermore, the pathway enrichment anal-ysis was performed by DIANA miRPath  on the ESA miRNAs set and DE miRNAs set, respectively. As shown in Fig. 3c and d both are signif-icantly enriched on cancer or cancer-related pathways. The ESA miRNAs are enriched on Proteoglycans in cancer, ErbB signaling pathway, Path-ways in cancer, Cell adhesion molecules (CAMs) and Adherens junction, while the DE miRNAs on Proteoglycans in cancer, ECM-receptor
The performance of the Gradient Boosting Classifier machine learning (10-fold cross validation).
Genes ACC AUC Precision Recall
The ACC, AUC represents the accuracy and the area under curve, respectively.
interaction, TGF-beta signaling pathway, Pathways in cancer and Focal adhesion.
Similarly, only 747 mRNAs (~21%) are detected as both DE and ESA mRNAs. The remaining ~79% ESA mRNAs show the discriminative power of 93.27% total accuracy (in Table 1). The additional KEGG pathway enrichment analysis indicated they are dramatically correlated with cancer (Fig. 4d). All these results suggest ESA mRNAs detected by our method are cancer-related. Although the majority of these mRNAs would be ignored by the traditional differential expression method, they indeed alter be-tween tumor and control conditions.
3.3. FFLs analysis in sub-network of the top ESA nodes
Transcription factor (TF) and microRNA (miRNA) can mutually regulate each other and jointly regulate their shared target genes (mRNAs) to form feed-forward loops (FFLs) [34,35]. We then applied the FFLs to further investigate the ESA mRNAs/miRNAs for their co-regulatory mechanism. The top-ranked 167 ESA miRNAs and 3596 ESA mRNAs were focused on FFL construction. FFLs could be classified into three types according to the regulatory relationship between TF and miRNA. miRNA-FFL (miR-FFL), TF-FFL and composite FFL, indicating miRNA regulated TF, TF regulated miRNA and TF, miRNA mutually regulated each other, respectively. 42 cancer-related FFLs were finally identified, including 33 TF-FFLs, 9 miR-FFLs. The detail information of all FFLs was summarized in Table 2. A sub-network (in Fig. 5) was formed by these FFLs consisting of 13 mRNAs, 22 miRNAs, 13 TFs and 94 edges.
Four DE mRNAs, BIRC5, RAD51, ACTB and NLE1, are involved in the thirteen mRNAs in the sub-network. Three of which are reported related to prostate cancer. Kucukzeybek et al.  found the BIRC5 gene has pivotal roles in the regulation of apoptosis and cell cycle progression in the DU-I45 prostate carcinoma cells. Nowacka-Zawisza et al.  sug-gested the RAD51 gene may contribute to prostate cancer susceptibility.
Fig. 4. The Venn diagram of ESA/DE miRNAs and mRNAs, and the ESA miRNAs/mRNAs set of non-DE enrichment analysis bar chart. (a, b) The Venn diagram of DE and ESA miRNAs/mRNAs. (c, d) The bar chart of ESA miRNAs/mRNAs set of non-DE enrichment analysis.
Summary of feed-forward loops based on the selected ESA miRNAs, mRNAs and TFs.
Number of nodes
Number of links
mRNAs miRs TFs