Data sources

In order to evaluate the performance of the approach, we prepared two kinds of data, ncRNA-target interaction matrix (LncRNADisease database (2015)) and target-disease interaction matrix (DisGeNET database) which are the same database sources used in Chen et al. (2013) [15], to form the tripartite network, as well as the sequence expression of those targets and ncRNAs (extracted from Uniprot and LncRNADisease databases, respectively). Since there are ncRNA sequence expressions and targets that are still unknown, we could only collect 76 ncRNAs, 109 targets, and 514 diseases (see Table 1). In Fig. 1, the degree distribution of the resulting network is shown. The results indicate that the entire network may follow a power law distribution. Moreover, we collected experimentally confirmed interactions between ncRNAs and miRNAs from the database shown in [16] and from Alaimo [13] Supplementary Information files and reconstructed another dataset composed on 151 ncNRAs, 179 targets and 134 diseases (see Helwak dataset in Table 1).

Type of Data	Chen et al	Helwak et al.
Diseases	514	134
Targets	109	179
ncRNAs	76	151
Disease-target interactions	580	1572
Target-ncRNA interactions	111	610
Average degree	1.977	9.405

Computational approach

In our approach, disease-target and target-ncRNA interaction matrices are required to construct the tripartite network (See Fig. 2). Sequence expressions of both targets and ncRNAs are also needed to generate string-kernel features for the prediction method. The overall algorithm of our method is shown in Fig. 3.

Let D = {d₁, d₂, …, d _m } be a set of diseases, let T = {t₁, t₂, …, t _n } be a set of targets which refer to genes or microRNA, and let R = {r_1,r₂, …, r _p } be a set of non-coding RNAs. Let \( {SR}^l=\left\{{sr}_1^l,{sr}_2^l,\kern1.5em ,{sr}_p^l\right\} \) and let \( {ST}^l=\left\{{st}_1^l,{st}_2^l,\dots, {st}_n^l\right\} \) be sets of the sequence expressions of the targets and ncRNAs respectively.

L-gram-string kernel feature extraction and standardization

In our approach, the features of sequence expressions were extracted via the l-gram-string kernel method [17], in which each string is transformed into a vector consisting of the number of occurrences of each substring of length l. In bioinformatics, string kernel is considered a function that measures the similarity of a pair of sequence expressions (strings) with finite length, for the purpose of generating real-value feature vectors. In our case, the method was evaluated experimentally using length l = 1, 2, 3 and 4.

Thus, let \( {SST}^l=\left\{{sst}_1^l,{sst}_2^l,\dots, {sst}_n^l\right\} \) and \( {SSR}^l=\left\{{ssr}_1^l,{ssr}_2^l,\dots, {ssr}_p^l\right\} \) be sets of the normalized real-value feature vectors computed from the sequence expressions of the targets and ncRNAs respectively.

RBF kernel similarity among ncRNAs and targets

To effectively compute the similarity among each pair of ncRNA-ncRNA and target-target, the RBF kernel similarity technique was employed. In statistical learning, RBF kernel can be viewed as a common kernel function to measure the similarity [19].

Let k_rna (i, j) and k_target (i, j) be the RBF kernel similarity function of pair ncRNA-ncRNA and target-target respectively.

where \( {\gamma}_1=\frac{1}{2{\sigma}_1^2},{\sigma}_1\ \mathrm{is}\ \mathrm{the}\ \mathrm{parameter}\ 0<{\sigma}_1<1. \)

where \( {\gamma}_2=\frac{1}{2{\sigma}_2^2},{\sigma}_2\ \mathrm{is}\ \mathrm{the}\ \mathrm{parameter}\ 0<{\sigma}_2<1. \)

Constructing the tripartite network disease-target-ncRNA

G (D, T, R, E), where E denotes a set of edges, is a tripartite network (Fig. 2) representing the disease-target interactions and target-ncRNA interactions. \( {A}^{DT}={\left\{{a}_{ij}^{DT}\right\}}_{m\times n} \) denotes the adjacency matrix of the disease-target network, and \( {A}^{TR}={\left\{{a}_{ij}^{TR}\right\}}_{n\times p} \) represents the adjacency matrix of target-ncRNA network.

Targets represent a group of biomolecules functionalized by non-coding RNAs. Targets can be genes, proteins, microRNAs, etc., whose activities include expression regulation, binding, and complex formation. In our method, targets function as a bridge allowing us to extract further biological information, for enhancing the accuracy of disease-ncRNA association inference.

Our method integrates the resource-allocation algorithm in the network with pairwise similarity information derived from sequence expressions to produce scores showing the level of certainty of the interaction. Essentially, the resource-allocation algorithm carries prior understanding of the bipartite network, which can be employed to predict the interactions.

Multi-layer resource-allocation technique with sequence (MRAS) information

Since the tripartite network consists of two bipartite networks, two-layer resource-allocation techniques were applied. For the first-layer (disease-target bipartite network), the resource will be transferred from the nodes in T (targets) to the nodes in D (diseases) integrating with pairwise similarity information between each pair of the diseases, then move back to the nodes in T. For the second-layer (target-ncRNA bipartite network), the resource integrated with pairwise similarity information between each pair of the ncRNAs, is allocated from the nodes in R (ncRNAs) to the nodes in T, and then combined with the resource from the previous layer. Finally, the weights computed within the two layers were merged into one, called combined weight (W _C ), indicating the likelihood that in case a disease associates with a target t _i , it then possibly interacts with ncRNA r _j . Prediction scores (P) can then be computed from the combined weight W _C , and the higher the score, the greater the certainty that the ncRNA will associate with a particular disease.

Finally, the prediction score matrix can be computed based on the following formula: P = {p _ij }_m × p = A ^DT  ⋅ W _C

Based on the above procedures, the prediction score matrix was produced via the integration of biological similarities of sequence expressions and the resource-allocation technique in the tripartite network. The score matrix thus predicted associations between ncRNAs and diseases. The higher the score, the higher the certainty of ncRNA-disease connectivity.

Algorithm prediction performance and evaluation

As mentioned, the performance of our method was measured by applying a 5-fold-cross-validation procedure as well as other computational operations. The evaluation algorithm is described as follows:

1. 1)

   First, we consider all pairs of ncRNA and disease (N pairs) exiting in the tripartite network. These pairs are expected to be predicted by the algorithm in the score matrix P.

    
2. 2)

   Fix a pair of values for σ₁ and σ₂ .

    
3. 3)

   Consider k-fold cross validation with k = 5. Therefore, all N pairs are divided into 5 groups.

    
4. 4)

   Each group of N/5 elements becomes a test data one time. The rest four groups are training data

    
5. 5)

   From each test data group, we scan those pairs that are connected through targets and disconnect them (see Fig. 4b)

    
6. 6)

   Run the algorithm and make predictions only for the pairs in the test group P _test.

    
7. 7)

   Construct a ROC curve for the test group based on N/5 scores for P _test .

    
8. 8)

   Repeat 3~ 7 for different folds. We average all five ROC curves.

    
9. 9)

   Repeat 3~ 8 for randomization of test and training groups five more times and obtained an averaged ROC curve.

    
10. 10)

    Repeat 2~ 9 for each σ₁ [0.1,0.2,...,0.9] x σ₂ [0.1,0.2,..,0.9] and pick up the best AUROC among all results.

     

Evaluation results

In our approach, the RBF kernel technique was selected to conduct the similarity measure. In order to prove that RBF kernel can interpret the similarity of biological significance more appropriately, we conducted comparison experiments on the dataset listed in Table 1 with three representative kernel functions: linear kernel, polynomial (degree = 2) kernel and RBF kernel. Table 3 clearly illustrates the prediction performance of our approach underlying each kernel function. The results demonstrate that RBF kernel successfully outperforms the other two kernel techniques, showing the highest average AUC values (see Fig. 5b).

Dataset	AUC
	Linear Kernel	Polynomial Kernel (d = 2)	RBF Kernel
Chen et al. (2013)	0.51561	0.54175	0.57135

Performance results for the following three kernel functions: linear kernel, polynomial (degree = 2) kernel and RBF kernel. The length of l-gram is set to l = 3 in this experiment

The l-gram-string kernel technique was applied to extract biological features from the sequence data of ncRNAs and targets in the proposed method. In order to investigate which length of l can interpret and extract better information from the sequence data, we validated the performances underlying different lengths of l. We also compared the results of the proposed method under two assumptions. By using the cut link method described in algorithm performance evaluation section and without cut link. Table 4 shows the comparison for both methods and for l-gram-string kernel (when l = 1, 2, 3 and 4) in terms of AUC values using the dataset described in Table 1. The results show that link cut notably decreases the prediction of the algorithm as expected from 0.75 to 0.57 (see Fig. 6a and b). However, even though we perform this strict procedure, the algorithm is able to predict correctly interactions with an AUC above 0.5. The results also show that performance slightly improved at l = 3. Thus, l = 3 is the optimal parameter for the method (see Table 4 and Fig. 6b). Note that for Helwak dataset the optimal length is l = 1.

		l = 1	l = 2	l = 3	l = 4
Chen et al.(2013)	AUC	0.7507	0.7506	0.7513	0.7433
	Cut link AUC	0.5706	0.5644	0.5713	0.5476
Helwak et al.(2013)	AUC	0.8543	0.7855	0.7338	0.7080
	Cut link AUC	0.7744	0.7098	0.6430	0.6441

The performance of the l-gram-string kernel for l = 1, 2, 3 and 4 was examined using the AUC metric. The computation was done using the RBF kernel. Table also shows the prediction performance when the links between a disease and their associated ncRNAs are deleted (Cut link UAC). Italic numbers indicate the best performance

Case studies

Lung cancer

Lung Cancer (LC) is one of the most deadly diseases affecting both men and women worldwide. There are three types of lung cancer: non-small cell lung cancer, small cell lung cancer, and lung carcinoid tumor. In 2015 lung and bronchus cancer accounted for 13.3% of all cancer cases in the US. The proposed method predicted that seven ncRNAs, H19, HOTAIR, MALAT1, PVT1, WRAP53, XIST, CDKN2B-AS1 are associated with LC. Kondo et al. reported that the alteration and deregulation of H19 impacts lung cancer cell growth [20]. HOX transcript antisense RNA (HOTAIR) prevents gene expression via collection of chromatin modifiers. Loewen et al. demonstrated that HOTAIR plays an important role in the intervention of lung cancer [21]. lncRNA metastasis associated lung adenocarcinoma transcript 1 (MALAT1) can impair in vitro cell motility of lung cancer cells and simultaneously influence a number of genes (Tano et al. & Tseng et al. [22, 23]). Yang et al. reported that an increased expression of the lncRNA PVT1 promotes tumorigenesis in non-small cell lung cancer [24]. Tantai et al. suggested a combined identification of long non-coding RNA XIST and HIF1A-AS1 in serum as an effective screening for non-small cell lung cancer [25]. Park et al., observed evidences for lung cancer with two variants located in cancer pleiotropic regions, namely TERT and risk of lung adenocarcinoma and CDKN2BAS1 with risk of lung squamous cell carcinoma [26].

Liver cancer

Liver cancer is the third most deadly cancer worldwide [27]. Very few patients receive curative treatments, while the majority do not recover since they are diagnosed at later stages. Our method predicted that ncRNAs H19, PCNA-AS1 and WRAP51 are correlated with liver cancer. H19 ncRNA expression was shown to result in high H19 protein expression in liver cancer whenever there is a loss of imprinting [28]. Iizuka et al. investigated further the epigenetic abnormalities in the insulin-like growth factor 2 (IGF2) and H19 genes observed in hepatocellular carcinoma (HCC) [29]. Yuan et al. reported that antisense long non-coding RNA PCNA-AS1 promotes tumor growth in hepatocellular carcinoma [30]. Several studies have also linked WRAP51 with HCC [31].

Breast cancer

Breast cancer is a ductal carcinoma beginning in the cells of lobules, ducts and other tissues of the breast. In the United States, breast cancer is the second most common cancer, just after skin cancer. Both women and men can suffer from this severe disease. Our method predicted that four ncRNAs, H19, PVT1, SRA1 and WRAP53 may be associated with this disease. Berteaux et al. found out that H19 transcript antisense RNA stabilize breast cancer cells and is overexpressed in breast tumors [32]. Others evidences were found across literature [33, 34]. Zhang et al. reported that the non-protein coding plasmacytoma variant translocation 1 (PVT1) has been implicated in human cancers [35, 36]. In addition, Hube et al. reported that alternative splicing of SRA1 could lead to the generation of coding and non-coding RNA isoforms in breast cancer cell lines [37]. Cao et al. recently reported about the association between the WRAP53 gene rs2287499 C > G polymorphism and cancer risk [38].

Urinary bladder Neoplasms

Urinary bladder neoplasms are the result of abnormal growth of bladder cells, and are considered as one of the common cancers. Men are at higher risk for this disease than women. The predictive results derived from our method inferred that ncRNAs H19 and WRAP53 might be associated with urinary bladder cancer. Luo et al. demonstrated that the abnormal expression of H19, particularly its up-regulation, contributed to cell proliferation in bladder neoplasms [39]. Wrap53 is a multi-functional gene which is capable of regulating p53 levels in both normal and cancer cell lines [40].

Prostatic Neoplasms

Prostatic neoplasm is caused by uncontrolled growth of cells located in the prostate causing tumors. Based upon our proposed method, prostate cancer was predicted to be associated with H19, MALAT1, CDKN2B-AS1, HOTAIR, PCAT1, SRA1, XIST. Zhu et al. demonstrated that H19 was significantly downregulated in the metastatic prostatic tumor cell line M12 [41]. Perez et al. showed that the antisense intronic transcript of MALAT1 is correlated with tumor differentiation in prostate cancer [42]. Fehringer reported the involvement of CDKBN2B-AS1in Cross-cancer genome-wide analysis of lung, ovary, breast, prostate and colorectal cancer using a cross-cancer genome-wide analysis [43]. Zhang et al. discovered that LncRNA HOTAIR enhances the Androgen-Receptor-Mediated Transcriptional Program and Drives Castration-Resistant Prostate Cancer [44]. Ren et al. suggested the Long noncoding RNA MALAT-1 as a potential therapeutic target for castration resistant prostate cancer [45]. Presner et al. results implied that rhe Long Non-Coding RNA PCAT-1 Promotes Prostate Cancer Cell Proliferation through cMyc [46]. The same research group used a transcriptome sequencing across a prostate cancer cohort to identify PCAT-1 as an unannotated lincRNA implicated in disease progression [47]. Several works also reported on the involvement of SRA1 [48] and XIST [49] in prostatic neoplasm.

Stomach Neoplams

Stomach neoplams that occurs as a consequence of abnormal grothw of stomach cells have also been associated to ncRNAs in several works. Our method predicted CDKN2B-AS1, HOTAIR and MALAT1 as main correlated molecules with stomach neoplasms. Zhang et al., reported that ANRIL (CDKN2B-AS1) which recruits and binds to PRC2 is usually observed upregulated in human gastric cancer (GC) tissues [50]. Lee et al. found that long non-coding RNA HOTAIR tends to promote not only carcinogenesis but also invasion of gastric adenocarcinoma [51]. Wang et al. also observed that MALAT1 promotes cell proliferation in gastric cancer by recruiting SF2/ASF [52].