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Abstract

MicroRNAs (miRNAs) are closely related to a variety of human diseases, not only regulating gene expression, but also having an important role in human life activities and being viable targets of small molecule drugs for disease treatment. Current computational techniques to predict the potential associations between small molecule and miRNA are not that accurate. Here, we proposed a new computational method based on a deep autoencoder and a scalable tree boosting model (DAESTB), to predict associations between small molecule and miRNA. First, we constructed a high-dimensional feature matrix by integrating small molecule–small molecule similarity, miRNA–miRNA similarity and known small molecule–miRNA associations. Second, we reduced feature dimensionality on the integrated matrix using a deep autoencoder to obtain the potential feature representation of each small molecule–miRNA pair. Finally, a scalable tree boosting model is used to predict small molecule and miRNA potential associations. The experiments on two datasets demonstrated the superiority of DAESTB over various state-of-the-art methods. DAESTB achieved the best AUC value. Furthermore, in three case studies, a large number of predicted associations by DAESTB are confirmed with the public accessed literature. We envision that DAESTB could serve as a useful biological model for predicting potential small molecule–miRNA associations.

microRNA, small molecule, association prediction, deep autoencoder, scalable tree boosting

Introduction

With the development of sequencing technology, a large number of medical data has been accumulated in the biomedical field, which has provided researchers with more facilities to utilize the data to study the relationship between diseases and drugs. The presence of microRNA (miRNA), a short noncoding RNA, has been extensively studied in the human genome. More and more miRNAs have been discovered by researchers. Through intensive research, miRNAs have been found to play an important role in a variety of human life activities, influencing the proliferation, differentiation, aging and death of cells in humans and even other species [1]. Moreover, abnormal miRNA expression is closely associated with human diseases, which has led to the expectation that miRNAs can be used as clinical and prognostic biomarkers [2, 3]. An increasing number of researchers have worked on miRNA-targeting drugs, eventually discovering and demonstrating the potential of small molecule drugs to target miRNAs [4]. However, the use of traditional biological experiments to identify small molecule drug-associated miRNAs still suffers from the problem of blindness and requires significant experimental time and cost. Therefore, there is an urgent requirement to develop computational models to predict the associations between small molecule and miRNA. The computational models help the researchers to greatly improve experimental efficiency by allowing specific experimental validation of those associations that are most likely.

In recent decades, researchers have made great effort to exploit computational methods to solve different biological problems, such as the prediction of miRNA–disease associations [5–8], circular RNA–disease associations [9], gene–drug interactions [10] and so on. Chen et al. [11] have also developed a database for clinically or experimentally supported noncoding RNAs and drug targets associations. To a certain extent, these studies have contributed to the development of small molecule and miRNA associations prediction methods. In recent years, more and more researchers have proposed different computational models for predicting potential small molecule–miRNA associations [12–14]. Lv et al. [15] constructed a complete network by combining small molecule similarity network, miRNA similarity network and known small molecule-miRNA associations network. They calculated the similarity of small molecules and miRNAs separately by a weighted combination strategy, and then used the RWR (Random Walk With Restart) algorithm to predict the potential associations between small molecule and miRNA. SMiR-NBI [16] proposed a heterogeneous network based on drugs, miRNAs and genes using the NBI algorithm to predict miRNA responses to anti-cancer drugs. Later, TLHNSMMA [17] proposed a small molecule–miRNA associations prediction computational method based on a three-layer heterogeneous network. The heterogeneous network of this method contained not only small molecule similarity, miRNA similarity and known small molecule–miRNA associations, but also incorporated disease similarity, and known miRNA–disease associations, thus constructing a three-layer heterogeneous network. Information was then propagated through the heterogeneous network by constructing an iterative update algorithm to identify potential small molecule–miRNA associations. GISMMA [18] proposed Graphlet interaction-based predictive inference for small molecule–miRNA associations. This model used Graphlet interactions consisting of 28 isoforms to describe the relationship between two small molecules or between two miRNAs. The association scores between small molecule and miRNA were calculated by counting the number of small molecule–miRNA interactions in the small molecule similarity network and miRNA similarity network. HSSMMA [19] calculated the correlation between small molecules and miRNAs by a metric based on the search path of node-type sequences connecting two objects, and confirmed the association experimentally. RFSMMA [20] used a filter-based approach to extract reliable features of small molecules and miRNAs from integrated small molecule similarity and miRNA similarity, respectively. Machine learning techniques of random forest were then used to infer small molecule–miRNA associations. SNMFSMMA [21] proposed a new small molecule–miRNA associations prediction model, symmetric non-negative matrix decomposition, to predict the potential association of SM–miRNA pairs. BNNRSMMA [22] first defined a novel matrix to represent small molecule–miRNA heterogeneous networks using miRNA–miRNA similarity, small molecule–small molecule similarity and known small molecule–miRNA associations. This matrix was then completed by minimizing its nuclear parametric number, and alternating directional multiplication was used to minimize the nuclear parametric number and obtain the prediction scores. Among them, they introduced a regularization term to tolerate the noise in the integrated similarity. Wang et al. [23] proposed a nuclear ridge regression-based approach to predict the small molecule–miRNA associations. Feature subsets of small molecules and miRNAs were first constructed separately, and homogeneous base learners were trained according to the different feature subsets, and finally the average score obtained by these base learners was used as the SM–miRNA associations score. Wang et al. [24] proposed a new dual network collaborative matrix decomposition (DCMF) method to predict potential SM–miRNA associations. They firstly preprocessed the missing values of the SM–miRNA associations matrix using the WKNKN method, and then constructed a matrix decomposition model of the dual network to obtain the feature matrices containing the potential features of small molecules and miRNAs, respectively. Finally, the predicted SM–miRNA associations score matrix was gained by calculating the inner product of the two feature matrices. Most of the above methods are based on machine learning and matrix decomposition approaches. These models have all achieved encouraging results and have played an important role in the development of computational methods for small molecule–miRNA associations recognition. However, they have certain problems or limitations: the experimentally validated small molecule–miRNA associations are very limited, and there are many negative associations. Performed on such noisy and sparse small molecule–miRNA associations networks, the predictors tend to detect many false negative associations. This also motivated us to develop a new deep learning model to further reveal potential associations between small molecule–miRNA.

In this work, we proposed a scalable tree boosting (STB) model based on a deep autoencoder, named deep autoencoder and a scalable tree boosting model (DAESTB), to predict small molecule–miRNA associations. First, we constructed a high-dimensional feature matrix of small molecule–miRNA combined association pairs using small molecule similarity, miRNA similarity and known small molecule–miRNA associations to maximize the use of information from miRNAs and small molecules. Then, we utilized a three-layer deep autoencoder to perform dimensionality reduction on the constructed high-dimensional matrix to extract potential feature representation. This not only improved the learning efficiency of the model, but also eliminated noise. Finally, we used an STB method to predict potential associations between small molecule–miRNA. In the experiments, we performed 5-fold and 10-fold CV on the dataset 1 and the dataset 2, respectively, and compared them with other classifiers. The DAESTB model was shown to be more accurate than other classifiers in predicting the associations. In addition, we also compared them with other several methods, respectively, and the AUC accuracy of the DAESTB method was relatively higher. Finally, case studies were also deployed to demonstrate the ability of DAESTB in identifying candidate miRNAs which are potentially relevant to small molecules. The DAESTB calculation method has the following advantages: (i) the extraction of potential features of small molecule–miRNA association pairs by deep autoencoder can remove the noise in the data, thus effectively improving the prediction efficiency; (ii) STB is a scalable tree boosting method, and the parameters used in this paper are with all default values, so there is no need to adjust the parameters for the model to achieve good results. (iii) Comparing with relevant models and other machine learning classifiers, DAESTB achieves the best results in terms of area under receiver operating characteristic (ROC) curves, which indicates that the predictive performance of the DAESTB method is more accurate.

Materials

Known small molecule–miRNA associations

We obtained known small molecule–miRNA associations from SM2miR (version 1) [25], in which the total number of known associations was 664. A total number of 831 small molecules were then extracted and integrated from SM2miR, DrugBank [26] and PubChem [27], and 541 miRNAs were collected from SM2miR, HMDD [28], miR2Disease [29] and PhenomiR [30]. On the dataset 1, there are 831 small molecules, 541 miRNAs and 664 known small molecule–miRNA associations. Among them, only 39 small molecules and 286 miRNAs are associated, while added 792 completely new small molecules and 255 new miRNAs without any known association. Then, we removed the small molecules and miRNAs that had no association on the dataset 1, while retaining the 39 small molecules, 286 miRNAs and 664 known small molecule–miRNA associations that formed the dataset 2. We constructed an adjacency matrix |$A\in \mathbb{R}^{nm\times ns}$| to represent the associations between small molecule and miRNA, where the |$i$|-th row indicates that the miRNA is |$m(i)$| and the |$j$|-th column indicates the small molecule |$s(j)$|⁠. If there is an association between |$m(i)$| and |$s(j)$|⁠, |$A(i,j)$| is 1; otherwise, |$A(i, j)$| is 0. The association matrix |$A$| is defined as
(1)
where |$i\in \left \{1,2,...,nm\right \} $| represents miRNA |$m(i)$|⁠, |$j\in \left \{1,2,3,...,ns\right \} $| represents small molecule |$s(j)$|⁠, |$nm$| and |$ns$| represent the number of miRNAs and small molecules, respectively. In addition, the distribution map of miRNAs corresponding to small molecules are shown in the supplementary material (Figures S1–S2).

Integrated small molecule–small molecule similarity

The integrated small molecule similarity was derived by integrating four similarity calculation methods [15], which include the phenotypic similarity between diseases associated with small molecules [31], functional identity based on small molecule target gene set [32], similarity based on small molecule chemical structure [33] and similarity based on small molecule side effects [32].

Among them, disease-based phenotypic similarity was calculated using Jaccard score, which indicated that the more the diseases shared by small molecules, the greater the similarity between small molecules; functional congruence based on target gene set was calculated by extracting target genes of small molecules from DrugBank [34] and TTD [35] databases and based on GSFS [32] score, and if the target genes of two small molecules genes had functional identity, then they were more similar; chemical structure-based similarity was calculated by SIMCOMP [33], a graph-based approach that searched for the largest common subgraph isomorphism by finding the largest cluster in the association graph, thus responding to the global score of similarity; side-effect similarity based on small molecules was calculated using a Jaccard score in which the top 13 most relevant side-effects for each small molecule were extracted from the SIDER [36], and the more side-effects the two small molecules contained, the more similar they were. The final similarity was calculated with the following formula:
(2)
where |$S_{s m}^{d}$|⁠, |$S_{s m}^{f}$|⁠, |$S_{s m}^{c}$| and |$S_{s m}^{s}$| represent four types of similarity, i.e. similarity based on denotational phenotype, similarity based on functional consistency, similarity based on chemical structure and similarity based on side effects; |$\alpha _{i} (i\in \left \{1,2,3,4\right \} )$| is the weight parameter to measure the contributions of each similarity, and they are all set to 1 in order to reduce the bias of each similarity metric.

Integrated miRNA–miRNA similarity

We obtained miRNA similarity by integrating the identification of phenotypic similarity between miRNA-related diseases [31] and functional identity based on the set of target genes [32].

Similarly, disease-related miRNAs were extracted from three databases, HMDD [36], miR2Disease [25] and PhenomiR [30], and the Jaccard score was used to define the similarity between miRNAs. If two miRNAs are associated with more diseases in common, the more similar they were. And the target gene-based functional identity was calculated as the similarity between two miRNAs by calculating the functional identity between any two miRNA target gene sets, which was calculated by GCFS [32] score; the higher the GCFS score between target gene sets, the stronger the similarity between miRNAs. Eventually, we obtained the integrated miRNA similarity as the following formula:
(3)
where |$S_{m m}^{d}$| denotes the phenotype-based indicated similarity and |$S_{m m}^{f}$| denotes the functional consistency-based similarity; similarly, |$\beta _{j}(j\in \left \{1,2\right \} )$| is the weight of each similarity measure, and they are set to 1 in order to reduce the bias of each similarity metric.

Methods

The proposed DAESTB model includes the following three steps, which is illustrated in Figure 1. In the first step, we preprocessed the data of three matrices, namely, small molecule–small molecule similarity, miRNA–miRNA similarity and known small molecule–miRNA associations, and constructed them into a high-dimensional small molecule–miRNA association pairs feature matrix |$F_{MS}$|⁠. In detail, small molecule–miRNA association pairs consist of all small molecule and miRNA paired with each other. In the second step, the constructed high-dimensional feature matrix |$F_{MS}$| was processed using the deep autoencoder by reducing feature dimensionality, thus obtaining the corresponding low 128-dimensional feature representation matrix |$F_{M S}^{\prime }$|⁠. In the third step, the generated low-dimensional features were used to train an STB model to predict the potential associations between small molecule and miRNA.

The flowchart of DAESTB. Step 1, a high-dimensional feature matrix of small molecule–miRNA association pairs is constructed; Step 2, feature dimension of small molecule–miRNA association pairs is educed by deep autoencoder to obtain potential features of association pairs; Step 3, XGBoost is used to predict potential associations between small molecule and miRNA.
Figure 1

The flowchart of DAESTB. Step 1, a high-dimensional feature matrix of small molecule–miRNA association pairs is constructed; Step 2, feature dimension of small molecule–miRNA association pairs is educed by deep autoencoder to obtain potential features of association pairs; Step 3, XGBoost is used to predict potential associations between small molecule and miRNA.

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Construction of feature representation matrix

In this section, we mainly constructed a new high-dimensional feature matrix of small molecule–miRNA association pairs by integrating three different dimensional matrices, i.e. small molecule–small molecule similarity matrix |$SMS$|⁠, miRNA–miRNA similarity matrix |$MMS$| and known small molecules and miRNA associations matrix |$Y$|⁠. The high-dimensional matrix had |$(ns\times nm)$| rows and |$(ns+nm)$| columns; each row represented a small molecule–miRNA association pair, and each column represented the feature presentation in the small molecule–miRNA association pair. Considering from the perspective of small molecules, we could find that in each small molecule–miRNA association pair, there existed other small molecules similar to the corresponding small molecules in the association pair, and they could form an association pairs feature matrix |$F_{SM}\in R^{(ns\times nm)*ns}$| associated with small molecules.

Similarly, considering from the perspective of miRNAs, for each small molecule–miRNA association pair, there existed other miRNAs similar to the corresponding miRNA in the association pair, which could form an miRNA-related association pairs feature matrix |$F_{miRNA}\in R^{(ns\times nm)*nm}$|⁠.

We connected these two association pairs feature matrices according to the corresponding association pair in each row, and finally we could get a more comprehensive small molecule–miRNA association pairs feature matrix |$F_{MS}\in R^{(ns\times nm)*(ns+nm)}$|⁠, as shown in Figure 1. The number of small molecule is |$ns$|⁠, the number of miRNA is |$nm$| and a total of |$(ns\times nm)$| pairs existed for small molecule–miRNA combinations, regardless of whether small molecule was associated with miRNA or not.

Using deep autoencoder to extract low-dimensional feature

In the previous section, we obtained a high-dimensional feature representation of small molecule–miRNA association pairs, |$(nm+ns)$|-dimensional. High-dimensional features are particularly time-consuming in computation and also affect the accuracy of prediction. Therefore, we used a deep autoencoder with three hidden layers to reduce the feature dimension of the constructed high-dimensional small molecule–miRNA association pairs feature matrix and extract the most essential features of each association pair.

Specifically, the deep autoencoder was trained to extract a low-dimensional representation of features from small molecule–miRNA association pairs. The autoencoder learned the function as shown in equation (4) by
(4)
where the input vector is |$X$|⁠, |$w_{1}$| denotes the weights and |$b_{1}$| denotes the bias. The model training process in the deep autoencoder is divided into encoding and decoding. During encoding, the autoencoder used the mapping function |$\psi (\cdot )$| to compress the input |$X$| (high-dimensional feature representation of small molecule–miRNA association pairs) into a low-dimensional representation vector according to equation (5):
(5)
where
(6)
and |$\psi (\cdot )$| denotes the encoding function and |$h=g_{\theta _{1}}(X)$| is the low-dimensional representation obtained by encoding. In the decoding process, the obtained low-dimensional representation |$h$| was decoded into features |$\hat{X}$| which were similar to the input feature representation:
(7)
where |$w_{2}$| denotes the weight and |$b_{2}$| denotes the bias; |$\phi (\cdot )$| is the decoding function, and |$\hat{X}$| is the recovered feature representation. During the iterative process, the reconstruction error loss function was defined as
(8)
where |$k\in K$| denotes the number of training samples. According to the literature [37], we set the compressed feature dimension of the autoencoder to 128. During the training process, we used mean square error (MSE) as the loss function and Adam as the optimization algorithm to reduce the loss. For the dataset 1, the high-dimensional feature matrix of the combined small molecule and miRNA association pairs is (831+541) dimensions, i.e. 1372 dimensions, while for the dataset 2, the high-dimensional feature matrix is (39+286) dimensions, i.e. 325 dimensions. In order to achieve the effect of dimensionality reduction, the number of neurons in the hidden layer must be set smaller than the number of neurons in the input layer, while the number of neurons in the output layer needs to be set equal to the number of neurons in the input layer. Here, we chose 512, 256 and 128, respectively, for the number of neurons in these three layers on the dataset 1, thus achieving the reduction of the high dimensionality to 128 dimensions, while on the dataset 2, the number of neurons in these three layers was chosen to be 250, 200 and 128, respectively. Ultimately, we obtained the low-dimensional feature matrix |${F_{MS}}^{\prime }$| of small molecule–miRNA association pairs.

Predicting potential associations by STB

We used an STB [38] method (XGBoost) to predict potential associations of small molecule and miRNA. We called the STB method simply STB. STB is similar to Boosting, which iterates through a gradient of multiple weak classifiers and then obtains accurate classification. However, the weak classifiers are not independent of each other, and the next classifier is obtained by optimizing the results of the previous classifier. STB is a new tree-learning algorithm for processing sparse data, which has been well used in miRNA–disease associations prediction [39]. In our study, there are only a few known associations between small molecule and miRNA, and the association matrix they construct is very sparse, which allows us to make better use of this method for predicting potential associations. The low-dimensional feature matrix |${F_{MS}}^{\prime }$| is fed into the STB model of the obtained small molecule–miRNA association pairs and train multiple weak classifiers to obtain the best gradient regression tree, as shown in the following equation (9):
(9)
where |$\hat{z}_{i}^{(j)}$| denotes the classification result of the |$j$|th classifier, |$j\in (1,2,3,...,t)$| and |$t$| is the number of weak classifiers in the model; |$f_{k}\epsilon \mathcal{F} $| denotes the space of regression trees (i.e. CART). By minimizing the following objective function:
(10)
where |$\mathcal{L} (\Theta )=\sum _{i=1}^{n} l\left (z_{i}, \hat{z}_{i}^{(t)}\right )$| is the loss function used to calculate the error of the training set, and |$\Omega (\Theta )=\sum _{i=1}^{t} \Omega \left (z_{i}\right )$| is the regularization term used to penalize the complexity of the model to avoid overfitting. By minimizing the objective function through iterative training, new small molecule–miRNA features can be fitted effectively, and the potential associations between small molecule and miRNA can be predicted finally.
(A) DAESTB performs 5-fold CV on the dataset 1; (B) DAESTB performs 10-fold CV on the dataset 1; (C) DAESTB performs 5-fold CV on the dataset 2; (D) DAESTB performs 10-fold CV on the dataset 2.
Figure 2

(A) DAESTB performs 5-fold CV on the dataset 1; (B) DAESTB performs 10-fold CV on the dataset 1; (C) DAESTB performs 5-fold CV on the dataset 2; (D) DAESTB performs 10-fold CV on the dataset 2.

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Results

Performance evaluation

In this work, 5-fold cross-validation (5-fold CV) and 10-fold cross-validation (10-fold CV) were utilized on the dataset 1 and the dataset 2, respectively, to evaluate the predictive performance of our method. All predicted small molecule–miRNA pairs were ranked according to the obtained scores. Based on the rankings, we used the receiver operating characteristic (ROC) curves to illustrate the performance of our model in the two cross-validations. Our AUC values were 0.9863 and 0.9856 for the dataset 1 by 5-fold and 10-fold CV, respectively, and 0.8653 and 0.8812 for the dataset 2, as shown in Figure 2. We further evaluated several commonly measured metrics, namely accuracy (ACC), precision (PRE), sensitivity, F1-score (F1), Mathews correlation coefficient (MCC) and the area under the precision recall curve (AUPRC), calculated by the following equations:
(11)
(12)
(13)
(14)
(15)
(16)

Comparison on different potential characteristic dimensions

In the DAESTB method, we used the deep autoencoder to perform dimensionality reduction on the constructed high-dimensional small molecule–miRNA combination association pairs, so as to obtain the potential features of the association pairs. To illustrate the dimensionality of the features after the deep autoencoder dimensionality reduction, we set the dimensions to 8, 16, 32, 64, 128 and 256 on the dataset 1, respectively, and compared them by 5-fold CV to find out the dimensionality that achieved the best results of the model. From Figure 3, it can be shown that the best performance during the model training is the best when the dimensionality reached 128. In detail, we used AUC as the most important evaluation metric. Therefore, we set the number of the potential feature dimension of the combined small molecule–miRNA association pairs as 128.

(A) AUC and AUPR values achieved by DAESTB, with varying the latent dimension of the last layer in the deep autoencoder model from 8 to 256; (B) DAESTB was compared with other dimensions on the dataset 1 by 5-fold CV for other evaluation performance metrics.
Figure 3

(A) AUC and AUPR values achieved by DAESTB, with varying the latent dimension of the last layer in the deep autoencoder model from 8 to 256; (B) DAESTB was compared with other dimensions on the dataset 1 by 5-fold CV for other evaluation performance metrics.

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Parameter setting

Layers of deep autoencoder

A high-dimensional feature matrix of small molecule–miRNA combinatorial association pairs was trained by a three-layer deep autoencoder, and eventually low-dimensional latent features are extracted. The number of layers |$l$| of the deep autoencoder was determined from |$\{2,3,4\}$| on the dataset 1 by 5-fold CV. As can be seen in Figure 4(A), the value of 0.9863 for the AUC is the highest when |$l=3$|⁠.

(A) Comparison of the number of layers in deep autoencoder; (B) Loss curve of DAESTB on the dataset 1 when extracting potential features using deep autoencoder; (C) Loss curve of DAESTB on the dataset 2 when extracting potential features using deep autoencoder; (D) The performance comparison of DAESTB with different learning rate in terms of AUC. (E) Comparison of DAESTB with six other methods of dimensionality reduction; (F) The performance comparison of DAESTB with other classifiers in terms of AUC, with 5-fold CV and 10-fold CV experiments on the dataset 1. DAESTB achieved the highest AUC value; (G) The performance comparison of DAESTB with other classifiers in terms of AUC, with 5-fold CV and 10-fold CV experiments on the dataset 2.
Figure 4

(A) Comparison of the number of layers in deep autoencoder; (B) Loss curve of DAESTB on the dataset 1 when extracting potential features using deep autoencoder; (C) Loss curve of DAESTB on the dataset 2 when extracting potential features using deep autoencoder; (D) The performance comparison of DAESTB with different learning rate in terms of AUC. (E) Comparison of DAESTB with six other methods of dimensionality reduction; (F) The performance comparison of DAESTB with other classifiers in terms of AUC, with 5-fold CV and 10-fold CV experiments on the dataset 1. DAESTB achieved the highest AUC value; (G) The performance comparison of DAESTB with other classifiers in terms of AUC, with 5-fold CV and 10-fold CV experiments on the dataset 2.

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Deep autoencoder loss in extracting low-dimension features

In this process, we presented the deep autoencoder training results in Figure 4(B) and 4(C). As the epoch number increases, the value of the loss function of DAESTB first decreased rapidly, then decreased gently, and eventually reached a steady state. Hence, we set epoch to 20 and batch size to 128 on the dataset 1 by 5-fold CV.

Adjustment of learning rates

In this section, we adjusted the parameters of DAESTB. In the XGBoost predictive method, the learning rate |$\gamma $| was determined from |${\{ 0.1, 0.3, 0.5, 0.7}\}$| and the rest of the parameters were defaulted on the dataset 1 by 5-fold CV. The purpose of adjusting the parameter |$\gamma $| is to make the prediction of XGBoost more accurate. The training results are shown in Figure 4(D). DAESTB model has the highest prediction accuracy when |$\gamma $| is 0.3, and its corresponding AUC value is 0.9863. Assuming that all parameters are set with default values, the AUC value is still 0.9863.

Comparison with other dimensionality reduction methods

To evaluate the performance of DAESTB, we compared it with six other dimensionality reduction methods, including Principal Component Analysis (PCA) [40], t-Distributed Stochastic Neighbor Embedding (TSNE) [41], Uniform Manifold Approximation and Projection (UMAP) [42], Factor Analysis (FA) [43], Independent Component Correlation Algorithm (ICA) [44] and FastICA [45]. To be fair, all the dimensionality reduction methods were experimented on the dataset 1 using 5-fold CV, and the final AUC values of the models were calculated. After experimental validation, we can see from Figure 4(E) that the AUC values for DAESTB, PCA, TSNE, UMAP, FA, FastICA and ICA on the dataset 1 are 0.9863, 0.9855, 0.9584, 0.9825, 0.9847, 0.9837 and 0.9854, respectively. The results show that DAESTB has the highest AUC value, which indicates that the deep autoencoder in DAESTB is better than other dimensionality reduction methods.

Comparison with other classifiers

To further evaluate the performance of DAESTB, we compared it with seven other classifiers, including logistic regression (LR) [46], Naive Bayes (Bayes) [47], decision tree (DT) [48], AdaBoost [49], random forest (RF) [50], gradient boosting (GB) [51], support vector machine (SVM) [52], LightGBM (LGBM) [53] and CatBoost (CB) [54]. To be considered fair, the same data were used for all classifiers and the final ROC curves were drawn using 5-fold and 10-fold CV for these eight classifiers on the dataset 1 and the dataset 2, respectively. In addition, other performance evaluation metrics for these eight classifiers are shown in the supplementary material (Tables S1–S2).

After experimental validation, we can see from Figure 4(F) and 4(G) that the AUC value of the DAESTB method is the highest on the dataset 1 and the dataset 2, which also indicates that the DAESTB classifier has better performance than other classifiers. The reasons are assumed as follows: (1) Although logistic regression is faster to train, it cannot solve the nonlinearity problem and the accuracy is not very high. (2) In theory, the Naive Bayes model has less error compared with other classifiers, but this is based on an assumption that attributes of the Naive Bayes model are independent of each other. However, in our data, the attributes are not independent of each other, so the classification is not as effective. (3) The common decision tree approach tends to produce an overly complex model, which can have a poor generalization performance to the data and can lead to overfitting. Some features are difficult to be learnt by the decision tree, thus causing bias. (4) Random forest is more resistant to overfitting, but when there is noise in the sample data, it will affect the prediction results. (5) SVMs consume space mainly by storing training samples and kernel matrices. Since SVMs solve support vectors with the help of quadratic programming, the training time is relatively long. In addition, its performance depends mainly on the selection of the kernel function. (6) AdaBoost, Gradient Boosting and STB all belong to special integrated learning methods. In AdaBoost model training, the execution depends on the selection of weak classifiers and is sample sensitive. In Gradient Boosting training, there is a serial relationship between the base learners, making it difficult to train data in parallel. While traditional Gradient Boosting uses CART trees as base learners, STB further supports linear classifiers with a regular term added to the cost function for controlling the complexity of the model. (7) LightGBM, simply LGBM, is a bias-based algorithm which is more sensitive to noise. After adjusting the parameters, the learning rate was set to 0.01 and number of weak classifiers was set to 100, which resulted in the best AUC value. (8) CatBoost, shortly referred to as CB, requires a lot of memory and time for the processing of category-based features, and the setting of different random numbers has an impact on the model prediction results. After adjusting the parameters, we finally chose the best AUC value when the iterations were 1000 and the learning rate was 0.5. Finally, in this experiment, the parameters used by STB were default values, and there was no need to adjust the parameters for the model to achieve good results, which is one of the major advantages.

Comparison with other methods

To further evaluate the ability of the DAESTB model to predict potential small molecule–miRNA associations, we selected four other methods, namely, EKRRSMMA [23], GISMMA [18], BNNRSMMA [22], RWR [15], and compared them with our method by 5-fold CV on the dataset 1 and the dataset 2, respectively. For the four comparison methods, we used the same parameter settings as those set in the original paper, which are shown in the supplementary material (Table S3). Figure 5 demonstrates the experimental results of DAESTB with the other four competitive methods. On the dataset 1, the AUC values of DAESTB, EKRRSMMA, GISMMA, BNNRSMMA and RWR were 0.9863, 0.9718, 0.9452, 0.9674, and 0.8509, respectively, with the AUC of DAESTB being 0.0117 higher than that of the second best model (EKRRSMMA); on the dataset 2, the AUC values were 0.8653, 0.8217, 0.8360, 0.8595 and 0.6173, respectively, where the AUC of our method was 0.0042 higher than the second best model (BNNRSMMA). By comparing these two datasets, it is ultimately evident that DAESTB wins the best performance in predicting potential associations of small molecule–miRNA. In addition, we assessed the performance of the DAESTB method against the other four methods EKRRSMMA, GISMMA and BNNSMMA with 10 times 5-fold CV and 50 AUC values were collected for all methods. The AUC values of DAESTB were then statistically tested against those of EKRRSMMA, GISMMA and BNNSMMA using paired t-test, and the significant differences between DAESTB and other methods were marked. As shown in Figure 6, we can conclude that DAESTB does work more effectively than the other methods.

(A) The ROC curve of DAESTB on the dataset 1 compared with other methods; (B) The ROC curve of DAESTB on the dataset 2 compared with other methods.
Figure 5

(A) The ROC curve of DAESTB on the dataset 1 compared with other methods; (B) The ROC curve of DAESTB on the dataset 2 compared with other methods.

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DAESTB significantly outperformed other methods in terms of AUC. (paired t-test, **** stands for P-value¡0.0001).
Figure 6

DAESTB significantly outperformed other methods in terms of AUC. (paired t-test, **** stands for P-value¡0.0001).

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Case Studies

To evaluate the performance of DAESTB in predicting potential associations new small molecule and miRNA, we further implemented case studies for three common small molecules named 17beta-estradiol, 5-aza-2’-deoxycytidine, doxorubicin. It is worth noting that we predict unknown associations using all known small molecule–miRNA associations on the dataset 1. After employing the DAESTB model, we were able to obtain the score in the row corresponding to each small molecule in association matrix. Then, we ranked the association candidates based on the predicted association scores. Finally, we selected the top 50 corresponding rows of the studied small molecules and validated the associations between small molecule and miRNA through the experimental literature in the PubMed database.

The first small molecule is 17|$\beta $|-estradiol, also known as E2, which is a human estrogen with important effects in human reproduction [55]. After the DAESTB experiment, we obtained a ranking of all miRNAs associated with 17|$\beta $|-estradiol. 11 of the top 20 miRNAs were validated, while 24 of the top 50 miRNAs were validated (Table 1). For example, knockdown of XIST resulted in inhibition of cell proliferation and upregulation of miR-29c after treatment with a combination of 17|$\beta $|-estradiol and progesterone using a 3D sphere culture system [56]. Small RNA-Seq analysis of 17|$\beta $|-estradiol-treated muscles versus controls identified 36 differentially expressed miRNAs, with some important myogenic miRNAs, such as miR-145, being down-regulated [57]. In [58], to explore whether miR-155 is involved in E2 regulation of estrogen-responsive gene expression, miR-155 expression in human breast cancer cells was assessed by real-time PCR. Treatment of MCF-7 cells with E2 increased miR-155 expression promoted proliferation and reduced apoptosis. In assessing the expression levels of miR-34a and miR-15b in a transgenic model of HPV16K14E7 (K14E7) in mice after chronic estrogen (E2) treatment and their involvement in cervical cancer, although miR-34a expression was elevated by the HPVE7 oncogene, this expression was downregulated in the presence of both the E7 oncoprotein and chronic E2 in cervical cancer [59].

Table 1
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Based on the dataset 1, the top 50 miRNAs associated with the small molecule 17|$\beta $|-estradiol were predicted by DAESTB. The table shows the top 1–25 ranked miRNAs associated with 17|$\beta $|-estradiol on the left and the bottom 26–50 ranked miRNAs on the right. As a result, 11(20) of the top 24(50) were confirmed by the recent experimental literatures in PubMed

miRNAEvidencemiRNAEvidence
hsa-mir-29cPMID: 33070965hsa-mir-181b-1unconfirmed
hsa-mir-30aPMID: 29331043hsa-mir-99aunconfirmed
hsa-mir-106bPMID: 28422740hsa-mir-34aPMID: 33937961
hsa-mir-195PMID: 26345235hsa-mir-93PMID: 23492819
hsa-mir-141unconfirmedhsa-mir-30dPMID: 28066696
hsa-mir-125b-1unconfirmedhsa-mir-196a-1unconfirmed
hsa-mir-16-1unconfirmedhsa-mir-101-1unconfirmed
hsa-mir-16-2unconfirmedhsa-mir-302aunconfirmed
hsa-mir-30ePMID: 19223510hsa-mir-301bunconfirmed
hsa-mir-199a-1unconfirmedhsa-mir-331unconfirmed
hsa-mir-20aPMID: 21914226hsa-mir-516b-2unconfirmed
hsa-mir-145PMID: 28011237hsa-mir-34cPMID: 24245576
hsa-mir-29b-1PMID: 28466779hsa-mir-29aPMID: 22393047
hsa-mir-182PMID: 34201250hsa-mir-127PMID: 34201250
hsa-mir-221PMID: 30574741hsa-mir-106aunconfirmed
hsa-mir-210PMID: 25503465hsa-mir-329-2unconfirmed
hsa-mir-199a-2unconfirmedhsa-mir-137unconfirmed
hsa-mir-191PMID: 29247596hsa-mir-155PMID: 23568502
hsa-mir-22PMID: 24715036hsa-mir-516a-2unconfirmed
hsa-mir-129-2unconfirmedhsa-mir-125aunconfirmed
hsa-mir-26bPMID: 30690256hsa-mir-150unconfirmed
hsa-mir-373unconfirmedhsa-mir-100PMID: 26908882
hsa-mir-24-1unconfirmedhsa-mir-214PMID: 27884727
hsa-mir-494PMID: 29867756hsa-mir-199bunconfirmed
hsa-mir-222PMID: 27659519hsa-mir-29b-2unconfirmed
miRNAEvidencemiRNAEvidence
hsa-mir-29cPMID: 33070965hsa-mir-181b-1unconfirmed
hsa-mir-30aPMID: 29331043hsa-mir-99aunconfirmed
hsa-mir-106bPMID: 28422740hsa-mir-34aPMID: 33937961
hsa-mir-195PMID: 26345235hsa-mir-93PMID: 23492819
hsa-mir-141unconfirmedhsa-mir-30dPMID: 28066696
hsa-mir-125b-1unconfirmedhsa-mir-196a-1unconfirmed
hsa-mir-16-1unconfirmedhsa-mir-101-1unconfirmed
hsa-mir-16-2unconfirmedhsa-mir-302aunconfirmed
hsa-mir-30ePMID: 19223510hsa-mir-301bunconfirmed
hsa-mir-199a-1unconfirmedhsa-mir-331unconfirmed
hsa-mir-20aPMID: 21914226hsa-mir-516b-2unconfirmed
hsa-mir-145PMID: 28011237hsa-mir-34cPMID: 24245576
hsa-mir-29b-1PMID: 28466779hsa-mir-29aPMID: 22393047
hsa-mir-182PMID: 34201250hsa-mir-127PMID: 34201250
hsa-mir-221PMID: 30574741hsa-mir-106aunconfirmed
hsa-mir-210PMID: 25503465hsa-mir-329-2unconfirmed
hsa-mir-199a-2unconfirmedhsa-mir-137unconfirmed
hsa-mir-191PMID: 29247596hsa-mir-155PMID: 23568502
hsa-mir-22PMID: 24715036hsa-mir-516a-2unconfirmed
hsa-mir-129-2unconfirmedhsa-mir-125aunconfirmed
hsa-mir-26bPMID: 30690256hsa-mir-150unconfirmed
hsa-mir-373unconfirmedhsa-mir-100PMID: 26908882
hsa-mir-24-1unconfirmedhsa-mir-214PMID: 27884727
hsa-mir-494PMID: 29867756hsa-mir-199bunconfirmed
hsa-mir-222PMID: 27659519hsa-mir-29b-2unconfirmed
Table 1
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Based on the dataset 1, the top 50 miRNAs associated with the small molecule 17|$\beta $|-estradiol were predicted by DAESTB. The table shows the top 1–25 ranked miRNAs associated with 17|$\beta $|-estradiol on the left and the bottom 26–50 ranked miRNAs on the right. As a result, 11(20) of the top 24(50) were confirmed by the recent experimental literatures in PubMed

miRNAEvidencemiRNAEvidence
hsa-mir-29cPMID: 33070965hsa-mir-181b-1unconfirmed
hsa-mir-30aPMID: 29331043hsa-mir-99aunconfirmed
hsa-mir-106bPMID: 28422740hsa-mir-34aPMID: 33937961
hsa-mir-195PMID: 26345235hsa-mir-93PMID: 23492819
hsa-mir-141unconfirmedhsa-mir-30dPMID: 28066696
hsa-mir-125b-1unconfirmedhsa-mir-196a-1unconfirmed
hsa-mir-16-1unconfirmedhsa-mir-101-1unconfirmed
hsa-mir-16-2unconfirmedhsa-mir-302aunconfirmed
hsa-mir-30ePMID: 19223510hsa-mir-301bunconfirmed
hsa-mir-199a-1unconfirmedhsa-mir-331unconfirmed
hsa-mir-20aPMID: 21914226hsa-mir-516b-2unconfirmed
hsa-mir-145PMID: 28011237hsa-mir-34cPMID: 24245576
hsa-mir-29b-1PMID: 28466779hsa-mir-29aPMID: 22393047
hsa-mir-182PMID: 34201250hsa-mir-127PMID: 34201250
hsa-mir-221PMID: 30574741hsa-mir-106aunconfirmed
hsa-mir-210PMID: 25503465hsa-mir-329-2unconfirmed
hsa-mir-199a-2unconfirmedhsa-mir-137unconfirmed
hsa-mir-191PMID: 29247596hsa-mir-155PMID: 23568502
hsa-mir-22PMID: 24715036hsa-mir-516a-2unconfirmed
hsa-mir-129-2unconfirmedhsa-mir-125aunconfirmed
hsa-mir-26bPMID: 30690256hsa-mir-150unconfirmed
hsa-mir-373unconfirmedhsa-mir-100PMID: 26908882
hsa-mir-24-1unconfirmedhsa-mir-214PMID: 27884727
hsa-mir-494PMID: 29867756hsa-mir-199bunconfirmed
hsa-mir-222PMID: 27659519hsa-mir-29b-2unconfirmed
miRNAEvidencemiRNAEvidence
hsa-mir-29cPMID: 33070965hsa-mir-181b-1unconfirmed
hsa-mir-30aPMID: 29331043hsa-mir-99aunconfirmed
hsa-mir-106bPMID: 28422740hsa-mir-34aPMID: 33937961
hsa-mir-195PMID: 26345235hsa-mir-93PMID: 23492819
hsa-mir-141unconfirmedhsa-mir-30dPMID: 28066696
hsa-mir-125b-1unconfirmedhsa-mir-196a-1unconfirmed
hsa-mir-16-1unconfirmedhsa-mir-101-1unconfirmed
hsa-mir-16-2unconfirmedhsa-mir-302aunconfirmed
hsa-mir-30ePMID: 19223510hsa-mir-301bunconfirmed
hsa-mir-199a-1unconfirmedhsa-mir-331unconfirmed
hsa-mir-20aPMID: 21914226hsa-mir-516b-2unconfirmed
hsa-mir-145PMID: 28011237hsa-mir-34cPMID: 24245576
hsa-mir-29b-1PMID: 28466779hsa-mir-29aPMID: 22393047
hsa-mir-182PMID: 34201250hsa-mir-127PMID: 34201250
hsa-mir-221PMID: 30574741hsa-mir-106aunconfirmed
hsa-mir-210PMID: 25503465hsa-mir-329-2unconfirmed
hsa-mir-199a-2unconfirmedhsa-mir-137unconfirmed
hsa-mir-191PMID: 29247596hsa-mir-155PMID: 23568502
hsa-mir-22PMID: 24715036hsa-mir-516a-2unconfirmed
hsa-mir-129-2unconfirmedhsa-mir-125aunconfirmed
hsa-mir-26bPMID: 30690256hsa-mir-150unconfirmed
hsa-mir-373unconfirmedhsa-mir-100PMID: 26908882
hsa-mir-24-1unconfirmedhsa-mir-214PMID: 27884727
hsa-mir-494PMID: 29867756hsa-mir-199bunconfirmed
hsa-mir-222PMID: 27659519hsa-mir-29b-2unconfirmed

The second small molecule is 5-aza-2’-deoxycytidine (5-Aza-CdR), which is a nitrogenous nucleoside analog used in cell culture that re-expresses certain genes [60]. After the DAESTB experiment, we obtained all the rankings of miRNAs associated with 5-Aza-CdR. 11 of the top 20 miRNAs were validated, while 24 of the top 50 miRNAs were validated (Table 2). For example, human adult DPSCs were isolated from normal third molars using 5-Aza-2’-deoxycytidine, and miR-143 expression was significantly decreased during induced myogenic DPSCs [61]. Following 5-aza-2’-deoxycytidine treatment of gastric cancer cells, miR-10b methylation was significantly reduced and the expression of miR-10b and HOXD4 1 kb downstream of miR-10b was greatly restored [62]. 5-Aza-CdR induced cell death and increased miR-146a expression in LNCaP and PC3 cells, where miR-146a expression was much higher in LNCaP cells than in PC3 cells, and MiR-146a inhibitors were shown to inhibit apoptosis in 5-Aza-CdR-treated cells [63]. In WL-2 cells, miR-9-3 was fully methylated and 5-aza-2’-deoxycytidine treatment caused miR-9-3 promoter demethylation and pri-miR-9-3 re-expression [64].

Table 2
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Based on the dataset 1, the top 50 miRNAs associated with the small molecule 5-Aza-CdR were predicted by DAESTB. The table shows the top 1–25 ranked miRNAs associated with 5-Aza-CdR on the left and the bottom 26–50 ranked miRNAs on the right. As a result, 11(20) of the top 24(50) were confirmed by the recent experimental literatures in PubMed.

miRNAEvidencemiRNAEvidence
hsa-mir-18aPMID: 23888958hsa-mir-30c-2unconfirmed
hsa-mir-222PMID: 26975503hsa-mir-30c-1unconfirmed
hsa-mir-19b-1unconfirmedhsa-mir-30aPMID: 26934121
hsa-mir-106aPMID: 31115533hsa-mir-148aPMID: 21610744
hsa-mir-92a-1unconfirmedhsa-let-7a-3unconfirmed
hsa-mir-143PMID: 26351742hsa-mir-146bunconfirmed
hsa-mir-342unconfirmedhsa-mir-203aunconfirmed
hsa-mir-10bPMID: 21562367hsa-mir-9-2PMID: 25855800
hsa-mir-19b-2unconfirmedhsa-mir-23aPMID: 25213664
hsa-mir-221PMID: 23770133hsa-mir-99bunconfirmed
hsa-mir-186PMID: 30793488hsa-mir-100unconfirmed
hsa-mir-181cPMID: 20080834hsa-mir-96unconfirmed
hsa-mir-223PMID: 27704586hsa-mir-199a-2unconfirmed
hsa-mir-150unconfirmedhsa-mir-30eunconfirmed
hsa-mir-29cPMID: 26975503hsa-mir-142PMID: 24236112
hsa-mir-199a-1unconfirmedhsa-mir-423unconfirmed
hsa-mir-26bPMID: 20806079hsa-mir-144unconfirmed
hsa-mir-101-1unconfirmedhsa-mir-204PMID: 29850805
hsa-let-7dPMID: 26802971hsa-mir-206unconfirmed
hsa-mir-146aPMID: 24885368hsa-mir-181b-2unconfirmed
hsa-mir-199bunconfirmedhsa-mir-132PMID: 22310291
hsa-mir-197unconfirmedhsa-mir-15bPMID: 26934121
hsa-mir-181b-1unconfirmedhsa-mir-9-3PMID: 25855800
hsa-mir-128-2unconfirmedhsa-mir-30dunconfirmed
hsa-mir-224PMID: 23770133hsa-mir-133bPMID: 26622593
miRNAEvidencemiRNAEvidence
hsa-mir-18aPMID: 23888958hsa-mir-30c-2unconfirmed
hsa-mir-222PMID: 26975503hsa-mir-30c-1unconfirmed
hsa-mir-19b-1unconfirmedhsa-mir-30aPMID: 26934121
hsa-mir-106aPMID: 31115533hsa-mir-148aPMID: 21610744
hsa-mir-92a-1unconfirmedhsa-let-7a-3unconfirmed
hsa-mir-143PMID: 26351742hsa-mir-146bunconfirmed
hsa-mir-342unconfirmedhsa-mir-203aunconfirmed
hsa-mir-10bPMID: 21562367hsa-mir-9-2PMID: 25855800
hsa-mir-19b-2unconfirmedhsa-mir-23aPMID: 25213664
hsa-mir-221PMID: 23770133hsa-mir-99bunconfirmed
hsa-mir-186PMID: 30793488hsa-mir-100unconfirmed
hsa-mir-181cPMID: 20080834hsa-mir-96unconfirmed
hsa-mir-223PMID: 27704586hsa-mir-199a-2unconfirmed
hsa-mir-150unconfirmedhsa-mir-30eunconfirmed
hsa-mir-29cPMID: 26975503hsa-mir-142PMID: 24236112
hsa-mir-199a-1unconfirmedhsa-mir-423unconfirmed
hsa-mir-26bPMID: 20806079hsa-mir-144unconfirmed
hsa-mir-101-1unconfirmedhsa-mir-204PMID: 29850805
hsa-let-7dPMID: 26802971hsa-mir-206unconfirmed
hsa-mir-146aPMID: 24885368hsa-mir-181b-2unconfirmed
hsa-mir-199bunconfirmedhsa-mir-132PMID: 22310291
hsa-mir-197unconfirmedhsa-mir-15bPMID: 26934121
hsa-mir-181b-1unconfirmedhsa-mir-9-3PMID: 25855800
hsa-mir-128-2unconfirmedhsa-mir-30dunconfirmed
hsa-mir-224PMID: 23770133hsa-mir-133bPMID: 26622593
Table 2
Open in new tab

Based on the dataset 1, the top 50 miRNAs associated with the small molecule 5-Aza-CdR were predicted by DAESTB. The table shows the top 1–25 ranked miRNAs associated with 5-Aza-CdR on the left and the bottom 26–50 ranked miRNAs on the right. As a result, 11(20) of the top 24(50) were confirmed by the recent experimental literatures in PubMed.

miRNAEvidencemiRNAEvidence
hsa-mir-18aPMID: 23888958hsa-mir-30c-2unconfirmed
hsa-mir-222PMID: 26975503hsa-mir-30c-1unconfirmed
hsa-mir-19b-1unconfirmedhsa-mir-30aPMID: 26934121
hsa-mir-106aPMID: 31115533hsa-mir-148aPMID: 21610744
hsa-mir-92a-1unconfirmedhsa-let-7a-3unconfirmed
hsa-mir-143PMID: 26351742hsa-mir-146bunconfirmed
hsa-mir-342unconfirmedhsa-mir-203aunconfirmed
hsa-mir-10bPMID: 21562367hsa-mir-9-2PMID: 25855800
hsa-mir-19b-2unconfirmedhsa-mir-23aPMID: 25213664
hsa-mir-221PMID: 23770133hsa-mir-99bunconfirmed
hsa-mir-186PMID: 30793488hsa-mir-100unconfirmed
hsa-mir-181cPMID: 20080834hsa-mir-96unconfirmed
hsa-mir-223PMID: 27704586hsa-mir-199a-2unconfirmed
hsa-mir-150unconfirmedhsa-mir-30eunconfirmed
hsa-mir-29cPMID: 26975503hsa-mir-142PMID: 24236112
hsa-mir-199a-1unconfirmedhsa-mir-423unconfirmed
hsa-mir-26bPMID: 20806079hsa-mir-144unconfirmed
hsa-mir-101-1unconfirmedhsa-mir-204PMID: 29850805
hsa-let-7dPMID: 26802971hsa-mir-206unconfirmed
hsa-mir-146aPMID: 24885368hsa-mir-181b-2unconfirmed
hsa-mir-199bunconfirmedhsa-mir-132PMID: 22310291
hsa-mir-197unconfirmedhsa-mir-15bPMID: 26934121
hsa-mir-181b-1unconfirmedhsa-mir-9-3PMID: 25855800
hsa-mir-128-2unconfirmedhsa-mir-30dunconfirmed
hsa-mir-224PMID: 23770133hsa-mir-133bPMID: 26622593
miRNAEvidencemiRNAEvidence
hsa-mir-18aPMID: 23888958hsa-mir-30c-2unconfirmed
hsa-mir-222PMID: 26975503hsa-mir-30c-1unconfirmed
hsa-mir-19b-1unconfirmedhsa-mir-30aPMID: 26934121
hsa-mir-106aPMID: 31115533hsa-mir-148aPMID: 21610744
hsa-mir-92a-1unconfirmedhsa-let-7a-3unconfirmed
hsa-mir-143PMID: 26351742hsa-mir-146bunconfirmed
hsa-mir-342unconfirmedhsa-mir-203aunconfirmed
hsa-mir-10bPMID: 21562367hsa-mir-9-2PMID: 25855800
hsa-mir-19b-2unconfirmedhsa-mir-23aPMID: 25213664
hsa-mir-221PMID: 23770133hsa-mir-99bunconfirmed
hsa-mir-186PMID: 30793488hsa-mir-100unconfirmed
hsa-mir-181cPMID: 20080834hsa-mir-96unconfirmed
hsa-mir-223PMID: 27704586hsa-mir-199a-2unconfirmed
hsa-mir-150unconfirmedhsa-mir-30eunconfirmed
hsa-mir-29cPMID: 26975503hsa-mir-142PMID: 24236112
hsa-mir-199a-1unconfirmedhsa-mir-423unconfirmed
hsa-mir-26bPMID: 20806079hsa-mir-144unconfirmed
hsa-mir-101-1unconfirmedhsa-mir-204PMID: 29850805
hsa-let-7dPMID: 26802971hsa-mir-206unconfirmed
hsa-mir-146aPMID: 24885368hsa-mir-181b-2unconfirmed
hsa-mir-199bunconfirmedhsa-mir-132PMID: 22310291
hsa-mir-197unconfirmedhsa-mir-15bPMID: 26934121
hsa-mir-181b-1unconfirmedhsa-mir-9-3PMID: 25855800
hsa-mir-128-2unconfirmedhsa-mir-30dunconfirmed
hsa-mir-224PMID: 23770133hsa-mir-133bPMID: 26622593

The third small molecule is doxorubicin (DOX), which is a clinical first-line anti-cancer drug and is widely used by researchers [65]. After the DAESTB experiment, we obtained a ranking of all miRNAs associated with doxorubicin. 12 out of the top 20 miRNAs were validated, while 31 out of the top 50 miRNAs were validated in Table 3. For example, results from the study showed that miR-221 expression was upregulated after treatment of SCC4 and SCC9 cells with doxorubicin [66]. Using SUDHL9 (ABC-type) and OCI-Ly1 (GCB-type) cells, the effect of doxorubicin on reducing cell viability was enhanced by miR-197 transfection [67]. MiR-107 was identified as a target of circ-LTBP1, and by downregulating miR-107 abolished the circ-LTBP1-mediated response to doxorubicin-stimulated cells [68]. MiR-146a partially reversed doxorubicin-induced cardiotoxicity by targeting the TAF9b/P53 pathway to attenuate apoptosis and modulate autophagy levels [69].

Table 3
Open in new tab

Based on the dataset 1, the top 50 miRNAs associated with the small molecule doxorubicin were predicted by DAESTB. The table shows the top 1–25 ranked miRNAs associated with doxorubicin on the left and the bottom 26–50 ranked miRNAs on the right. As a result, 12(20) of the top 31(50) were confirmed by the recent experimental literatures in PubMed.

miRNAEvidencemiRNAEvidence
hsa-let-7a-2unconfirmedhsa-mir-223PMID: 31695022
hsa-mir-221PMID: 28677788hsa-mir-324unconfirmed
hsa-let-7a-3unconfirmedhsa-mir-26bPMID: 33767588
hsa-mir-125b-2PMID: 19890372hsa-mir-381PMID: 30266665
hsa-let-7a-1unconfirmedhsa-mir-150PMID: 31897096
hsa-mir-125b-1PMID: 25451164hsa-mir-30bPMID: 35134991
hsa-mir-197PMID: 29890998hsa-mir-122PMID: 27138141
hsa-mir-107PMID: 35076816hsa-mir-199bPMID: 27033315
hsa-mir-373unconfirmedhsa-mir-132PMID: 32505695
hsa-mir-146aPMID: 31511497hsa-mir-101-1unconfirmed
hsa-mir-423unconfirmedhsa-mir-486unconfirmed
hsa-mir-155PMID: 26893712hsa-mir-205PMID: 35451580
hsa-mir-191PMID: 20169152hsa-mir-342unconfirmed
hsa-let-7f-1unconfirmedhsa-mir-100PMID: 27990096
hsa-mir-23aPMID: 30831132hsa-mir-146bunconfirmed
hsa-mir-195PMID: 31300525hsa-mir-208aPMID: 27990619
hsa-let-7dPMID: 28665983hsa-mir-99aunconfirmed
hsa-mir-542PMID: 30245930hsa-mir-142PMID: 32302291
hsa-mir-16-2unconfirmedhsa-mir-194-1unconfirmed
hsa-mir-106bPMID: 18212054hsa-mir-15bPMID: 28145098
hsa-let-7bPMID: 25789066hsa-mir-32unconfirmed
hsa-mir-29cunconfirmedhsa-mir-18bunconfirmed
hsa-let-7cPMID: 33051247hsa-mir-199a-2unconfirmed
hsa-mir-125aPMID: 27880721hsa-mir-204PMID: 33274007
hsa-mir-483unconfirmedhsa-mir-34aPMID: 31235998
miRNAEvidencemiRNAEvidence
hsa-let-7a-2unconfirmedhsa-mir-223PMID: 31695022
hsa-mir-221PMID: 28677788hsa-mir-324unconfirmed
hsa-let-7a-3unconfirmedhsa-mir-26bPMID: 33767588
hsa-mir-125b-2PMID: 19890372hsa-mir-381PMID: 30266665
hsa-let-7a-1unconfirmedhsa-mir-150PMID: 31897096
hsa-mir-125b-1PMID: 25451164hsa-mir-30bPMID: 35134991
hsa-mir-197PMID: 29890998hsa-mir-122PMID: 27138141
hsa-mir-107PMID: 35076816hsa-mir-199bPMID: 27033315
hsa-mir-373unconfirmedhsa-mir-132PMID: 32505695
hsa-mir-146aPMID: 31511497hsa-mir-101-1unconfirmed
hsa-mir-423unconfirmedhsa-mir-486unconfirmed
hsa-mir-155PMID: 26893712hsa-mir-205PMID: 35451580
hsa-mir-191PMID: 20169152hsa-mir-342unconfirmed
hsa-let-7f-1unconfirmedhsa-mir-100PMID: 27990096
hsa-mir-23aPMID: 30831132hsa-mir-146bunconfirmed
hsa-mir-195PMID: 31300525hsa-mir-208aPMID: 27990619
hsa-let-7dPMID: 28665983hsa-mir-99aunconfirmed
hsa-mir-542PMID: 30245930hsa-mir-142PMID: 32302291
hsa-mir-16-2unconfirmedhsa-mir-194-1unconfirmed
hsa-mir-106bPMID: 18212054hsa-mir-15bPMID: 28145098
hsa-let-7bPMID: 25789066hsa-mir-32unconfirmed
hsa-mir-29cunconfirmedhsa-mir-18bunconfirmed
hsa-let-7cPMID: 33051247hsa-mir-199a-2unconfirmed
hsa-mir-125aPMID: 27880721hsa-mir-204PMID: 33274007
hsa-mir-483unconfirmedhsa-mir-34aPMID: 31235998
Table 3
Open in new tab

Based on the dataset 1, the top 50 miRNAs associated with the small molecule doxorubicin were predicted by DAESTB. The table shows the top 1–25 ranked miRNAs associated with doxorubicin on the left and the bottom 26–50 ranked miRNAs on the right. As a result, 12(20) of the top 31(50) were confirmed by the recent experimental literatures in PubMed.

miRNAEvidencemiRNAEvidence
hsa-let-7a-2unconfirmedhsa-mir-223PMID: 31695022
hsa-mir-221PMID: 28677788hsa-mir-324unconfirmed
hsa-let-7a-3unconfirmedhsa-mir-26bPMID: 33767588
hsa-mir-125b-2PMID: 19890372hsa-mir-381PMID: 30266665
hsa-let-7a-1unconfirmedhsa-mir-150PMID: 31897096
hsa-mir-125b-1PMID: 25451164hsa-mir-30bPMID: 35134991
hsa-mir-197PMID: 29890998hsa-mir-122PMID: 27138141
hsa-mir-107PMID: 35076816hsa-mir-199bPMID: 27033315
hsa-mir-373unconfirmedhsa-mir-132PMID: 32505695
hsa-mir-146aPMID: 31511497hsa-mir-101-1unconfirmed
hsa-mir-423unconfirmedhsa-mir-486unconfirmed
hsa-mir-155PMID: 26893712hsa-mir-205PMID: 35451580
hsa-mir-191PMID: 20169152hsa-mir-342unconfirmed
hsa-let-7f-1unconfirmedhsa-mir-100PMID: 27990096
hsa-mir-23aPMID: 30831132hsa-mir-146bunconfirmed
hsa-mir-195PMID: 31300525hsa-mir-208aPMID: 27990619
hsa-let-7dPMID: 28665983hsa-mir-99aunconfirmed
hsa-mir-542PMID: 30245930hsa-mir-142PMID: 32302291
hsa-mir-16-2unconfirmedhsa-mir-194-1unconfirmed
hsa-mir-106bPMID: 18212054hsa-mir-15bPMID: 28145098
hsa-let-7bPMID: 25789066hsa-mir-32unconfirmed
hsa-mir-29cunconfirmedhsa-mir-18bunconfirmed
hsa-let-7cPMID: 33051247hsa-mir-199a-2unconfirmed
hsa-mir-125aPMID: 27880721hsa-mir-204PMID: 33274007
hsa-mir-483unconfirmedhsa-mir-34aPMID: 31235998
miRNAEvidencemiRNAEvidence
hsa-let-7a-2unconfirmedhsa-mir-223PMID: 31695022
hsa-mir-221PMID: 28677788hsa-mir-324unconfirmed
hsa-let-7a-3unconfirmedhsa-mir-26bPMID: 33767588
hsa-mir-125b-2PMID: 19890372hsa-mir-381PMID: 30266665
hsa-let-7a-1unconfirmedhsa-mir-150PMID: 31897096
hsa-mir-125b-1PMID: 25451164hsa-mir-30bPMID: 35134991
hsa-mir-197PMID: 29890998hsa-mir-122PMID: 27138141
hsa-mir-107PMID: 35076816hsa-mir-199bPMID: 27033315
hsa-mir-373unconfirmedhsa-mir-132PMID: 32505695
hsa-mir-146aPMID: 31511497hsa-mir-101-1unconfirmed
hsa-mir-423unconfirmedhsa-mir-486unconfirmed
hsa-mir-155PMID: 26893712hsa-mir-205PMID: 35451580
hsa-mir-191PMID: 20169152hsa-mir-342unconfirmed
hsa-let-7f-1unconfirmedhsa-mir-100PMID: 27990096
hsa-mir-23aPMID: 30831132hsa-mir-146bunconfirmed
hsa-mir-195PMID: 31300525hsa-mir-208aPMID: 27990619
hsa-let-7dPMID: 28665983hsa-mir-99aunconfirmed
hsa-mir-542PMID: 30245930hsa-mir-142PMID: 32302291
hsa-mir-16-2unconfirmedhsa-mir-194-1unconfirmed
hsa-mir-106bPMID: 18212054hsa-mir-15bPMID: 28145098
hsa-let-7bPMID: 25789066hsa-mir-32unconfirmed
hsa-mir-29cunconfirmedhsa-mir-18bunconfirmed
hsa-let-7cPMID: 33051247hsa-mir-199a-2unconfirmed
hsa-mir-125aPMID: 27880721hsa-mir-204PMID: 33274007
hsa-mir-483unconfirmedhsa-mir-34aPMID: 31235998

Moreover, for the case study, we adopt an alternative approach to further demonstrate the predictive ability of DAESTB on isolated small molecule. We removed the known and verified small molecule–miRNA associations related to predictive small molecule. Namely, we set the row corresponding to the two small molecules 5-FU and DOX to 0 in turn in the known small molecule–miRNA associations matrix. It means that we only used similarity information and known small molecule–miRNA associations of the other small molecule to predict miRNA candidates. The predictive results are presented in supplementary material (Tables S4–S5). Some of the predictive miRNA candidates have been validated in SM2miR database and recent experimental literatures in Pubmeb. We also derived AUC curves for these small molecules as well as other assessment indicators as shown in supplementary material(Figure S3 and Table S6).

Discussion

The research has shown that miRNAs have an indispensable influence in biological and human diseases, as well as small molecule drugs that are crucial in the treatment of diseases. With the recent research, we can see that exploring the relationships between small molecule and miRNA will provide a guiding effect in disease diagnosis and treatment. In this work, we proposed an STB method based on deep autoencoder to predict the potential associations between small molecule–miRNA. First, we integrated small molecule–small molecule similarity, miRNA–miRNA similarity and known small molecule–miRNA associations to construct a high-dimensional feature representation matrix of combination pairs of small molecule–miRNA associations, and used the small molecule–miRNA associations as the corresponding labels of this high-dimensional matrix, with the aim at making the features of small molecule–miRNA properties more abundant. Second, the constructed high-dimensional feature attribute matrix was dimensionally reduced by a three-layer deep autoencoder to extract the potential feature representation between each combined small molecule–miRNA association pair, which aims to improve the efficiency of model learning as well as to remove noise. Finally, we used an STB method to predict potential associations between small molecule–miRNA. We used 5-fold CV and 10-fold CV for experimental comparison and validation on the dataset 1 and the dataset 2, respectively. Compared with other methods, the AUC values of DAESTB reached 0.9835 and 0.8637 on the dataset 1 and the dataset 2, respectively, which were higher than those of other methods. The experimental results demonstrated that the proposed method DAESTB could better predict the potential associations between small molecule–miRNA.

Although DAESTB achieves good performance in predicting small molecule–miRNA associations, it still has some limitations. Firstly, few small molecule–miRNA associations are collected in existing databases, and data on the side effects of small molecules and diseases from the current databases are incomplete; predictions based on these incomplete annotations will miss or overlook some small molecule–miRNA associations. In future research, the increase in more newly identified small molecule-related side effects and diseases information being collected will advances the development of computational approaches to predict small molecule–miRNA associations. Secondly, there is still room for improvement for data collection, if the miRNA sequence similarity and affiliation information of small molecules could be considered to construct more complete data, the prediction results would be more accurately. Thirdly, if the associations between small molecule and miRNA can be used to further predict the associations between miRNA and disease, to achieve an effective integration of small molecule drugs to miRNAs and then to diseases, it will be possible to further improve the precision of drug-targeted therapy.

Key Points

  • As miRNAs targeting small molecules are closely associated with the progression of various human diseases, it is critical to develop effective computational predictors to predict the relevance of small molecules to miRNAs.

  • We propose a new prediction method, DAESTB, which improves prediction efficiency by removing noise through deep autoencoder dimensionality reduction and identifies potential associations from new small molecule–miRNA associations networks using a scalable tree boosting methods.

  • The performance on widely used datasets shows that DAESTB outperforms other advanced prediction methods. In addition, several case studies have shown that DAESTB is also able to accurately identify novel small molecule–miRNA associations.

Data availability

The data and source code can be freely downloaded from: https://github.com/biohnuster/DAESTB.

Acknowledgments

We would like to thank the anonymous reviewers for their valuable comments and improvement suggestions that further lead us to improve this paper.

Funding

National Natural Science Foundation of China (Grant No. 61902125, 62002111, 62202162); Scientific Research Project of Hunan Education Department (Grant No. 19C1788, 21B0453).

Author Biographies

Li Peng is an associate professor at Hunan University of Science and Technology and Hunan Key Laboratory for Service computing and Novel Software. Her research interests are focused on machine learning, deep learning and bioinformatics.

Yuan Tu is a postgraduate student at Hunan University of Science and Technology. Her research interests include bioinformatics and machine learning.

Li Huang is a PhD student at Tsinghua University. His research interests include bioinformatics, complex networks and machine learning.

Yang Li is a PhD student at Xiangtan University. Her research interests include data mining and bioinformatics.

Xiangzheng Fu is a postdoctoral scholar at Hunan University. His research interest is classification of proteins in bioinformatics.

Xiang Chen is an assistant professor at Hunan University of Science and Technology. His research is in the areas of complex networks and bioinformatics.

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