Deep learning of multimodal networks with topological regularization for drug repositioning

Abstract

Motivation

Computational techniques for drug-disease prediction are essential in enhancing drug discovery and repositioning. While many methods utilize multimodal networks from various biological databases, few integrate comprehensive multi-omics data, including transcriptomes, proteomes, and metabolomes. We introduce STRGNN, a novel graph deep learning approach that predicts drug-disease relationships using extensive multimodal networks comprising proteins, RNAs, metabolites, and compounds. We have constructed a detailed dataset incorporating multi-omics data and developed a learning algorithm with topological regularization. This algorithm selectively leverages informative modalities while filtering out redundancies.

Results

STRGNN demonstrates superior accuracy compared to existing methods and has identified several novel drug effects, corroborating existing literature. STRGNN emerges as a powerful tool for drug prediction and discovery. The source code for STRGNN, along with the dataset for performance evaluation, is available at https://github.com/yuto-ohnuki/STRGNN.git.

Introduction

De-novo drug discovery, involving multiple rigorous stages to verify drug efficacy and safety, generally takes about 15 years and costs over one billion dollars. The high cost and lengthy development process pose significant challenges [1]. However, with the availability of diverse, high-throughput data in biological databases, in-silico drug discovery methods, which exhaustively search for drug candidate compounds using high-performance computing, have been actively developed. Drug repositioning, which seeks new applications for existing drugs, is gaining increasing attention.

In-silico methods for drug repositioning can be broadly classified into network propagation-based, recommendation-based, classical machine learning-based, and deep learning-based methods [2]. Network propagation methods represent biological entity interactions as networks, exploring new interactions through approaches like random walks. Node2Vec [3], a popular biased random walk method, is frequently applied in drug repositioning prediction [4]. Luo et al. [5] proposed RWHNDR, a random walk-based algorithm for heterogeneous networks in computational drug repositioning. Cheng et al. [6] quantified the network proximity between disease genes and drug targets in the human protein–protein interactome.

Recommendation-based methods interpret the interaction prediction problem as a recommendation task, primarily utilizing matrix decomposition and completion techniques. Luo et al. [7] proposed a drug-disease prediction algorithm DRRS using matrix interpolation for heterogeneous networks for drug repositioning. Xuan et al. [8] introduced DisDrugPred, a non-negative matrix factorization (NMF) method for predicting drug-disease associations using multiple similarity measures. Zhang et al. [9] developed the DRIMC method, a Bayesian-derived matrix imputation approach. These methods are advantageous as they do not require negative sampling, allowing for the flexible integration of extensive prior information. However, their application to large-scale data is limited due to the complexity of matrix operations [10].

Machine learning-based methods, assuming that similar drugs target similar diseases, treat interaction prediction as a binary classification problem [11]. Notable contributions include Nagamine and Sakakibara’s statistical prediction method [12] using support vector machines for protein-chemical interactions, Gottlieb et al.’s PREDICT [13], a similarity-based method employing logistic regression, and Zhou et al.’s NEDD [14], a metapath-based learning approach using a random forest classifier. To expand on the machine learning-based methods for drug repurposing, it's crucial to consider how each method leverages specific data types and analytical frameworks to improve predictive accuracy. While statistical prediction and similarity-based methods primarily focus on existing relationships and known properties, metapath-based approaches integrate multiple data sources, enabling a more holistic view of potential drug-disease interactions. These methods each have their strengths; for example, support vector machines are robust to overfitting, logistic regression offers interpretability, and random forest classifiers excel in handling heterogeneous data. However, deep learning (DL) approaches often surpass these methods in capturing complex nonlinear relationships through layered data representations.

Deep learning methods have gained prominence in bioinformatics for their ability to acquire data representations at multiple abstraction levels. For instance, Watanabe et al. [15] proposed a method integrating molecular and interactome data for protein-compound interaction prediction. Notably, graph neural network (GNN) methods [16] have been actively developed, allowing for node vector representations that reflect network topology. This includes the Graph Attention Network [17], which integrates an attention mechanism, and the Relational GCN [18], applicable to heterogeneous networks. Zeng et al.’s deepDR [19] and Wan et al.’s NeoDTI [20] are examples of network-based deep learning methods integrating various drug-related information. Yu et al. [10] proposed LAGCN, a GNN method with a layer attention mechanism for accurate drug-disease association prediction. Wan et al. [21] constructed a heterogeneous network containing protein–protein interactions and proposed a bipartite graph convolutional model called BiFusion. Cai et al. [22] introduced DRHGCN, which extracts features from domain information in heterogeneous networks for drug repositioning.

Systems biology research, viewing human diseases as perturbations in biological networks, emphasizes the importance of multi-omics data analysis for understanding complex biological systems [23] and investigating disease mechanisms [24,25,26]. Computational methods like Iwata et al.’s approach [27] using gene expression profile data from LINCS [28] and Wang et al.’s DeepDRK [29], which integrates multi-omics data for predicting cancer cell drug responses, demonstrate the value of extracting and integrating modality-specific information [30]. However, existing golden datasets for drug-disease association prediction, such as Fdataset [13], Cdataset [31], and Ldataset [10], focus solely on drugs and diseases. Moreover, few studies have constructed datasets encompassing comprehensive omics data, including RNA and metabolites. Biological networks are inherently noisy and complex [2], necessitating a regularization mechanism to mitigate noise effects and obtain robust feature representations that efficiently integrate heterogeneous data sources [32]. Peng et al.’s RNMFLP [33] and methods like BNNR [34], which incorporates bounded nuclear norm regularization, represent attempts to address these challenges. However, they do not fully address the nuances of heterogeneous networks, and methods like EnMUGR [32], which perform denoising as preprocessing, may not effectively select modalities during training.

To address these challenges, our study introduces STRGNN (Sequentially Topological Regularization Graph Neural Network), a deep learning model that effectively predicts drug-disease associations using large-scale multimodal networks rich in omics data. It is important to note the distinction between multimodal and heterogeneous networks. While both integrate various data types, multimodal networks focus on different modalities or sources, and heterogeneous networks on different node and edge types. Our approach specifically utilizes multimodal networks, acknowledging the broader context of “heterogeneous networks” in the literature. Initially, we methodically gather and integrate interaction information from biological databases, forming a multimodal network comprising 6 biomolecular entity types (drugs, diseases, proteins, mRNAs, miRNAs, metabolites) and 20 interaction or association types, including multifunctional interactions. Subsequently, we introduce a novel mechanism in GNN learning, called topological regularization which effectively selects informative modalities and eliminates redundant data from the multimodal network. This approach has led to superior prediction accuracy compared to other leading interaction prediction methods in drug repositioning, and has enabled the discovery of multiple new drug effects that align with empirical findings in the literature.

To provide a comprehensive review and discussion of machine learning-based methods for drug repurposing, we have compiled a comparative table of key approaches. Table 1 summarizes the characteristics of representative drug-disease association prediction methods, including their categories, used modalities, main features. This comparison highlights the unique aspects of our proposed STRGNN method, which integrates a diverse range of modalities and employs topological regularization GNN for effective processing of large-scale multimodal data.

Table 1 Comparison of drug-disease association prediction methods

Materials and methods

Dataset

In this study, in order to construct multimodal networks comprehensively including multi-omics information, a total of 6 types of biomolecular entities and 20 types of interactions or associations were collected from 9 databases (DrugBank [35], STRING [36], HuRI [37], CTD [38], HMDB [39], CREED [40], Harmonizome [41], RNAInter [42], HMDD [43]). As a result, compared to the golden data set Cdatasets, we succeeded in including approximately 4.8 times more drugs, 4.6 times more diseases, and 4.9 times more drug-disease associations. The number of entities of each biomolecular type and the number of interactions of each type are listed in Supplemental Table S1.

“Disease” entities were collected from KEGG [44]. “Drug-disease” associations were obtained from CTD, specifically focusing on pairs that have direct evidence of being used as a therapeutic drug in clinical practice. “Disease-protein” associations were also obtained from CTD. In CTD, manually curated association is available, and proteins with direct evidence such as markers or therapeutic targets were collected. “Disease-mRNA” associations were obtained from CREEDS and Harmonizome. In CREEDS, gene expression signatures based on Gene Expression Omnibus (GEO) [45] are available. Harmonizome standardized data formats and unified identifiers in gene expression profile information obtained from numerous databases. From these databases, information on fold changes in gene expression during disease was collected, and a network was constructed based on that information. “Disease-miRNA” associations were obtained from HMDD. Dysregulation of miRNAs is associated with numerous diseases such as cancer and neurodegenerative diseases [46]. “Disease-metabolite” interactions were obtained from HMDB. HMDB is the most comprehensive metabolomics database, annotating all known human metabolites. A weighted “disease-disease” network was constructed by calculating a similarity score based on the ICD-11 disease classification. Diseases are classified hierarchically in the form of a directed acyclic graph (DAG) structure using descriptors such as MeSH and ICD-11, and a method for evaluating semantic similarity between diseases based on this classification has been proposed [47]. Since diseases with similar molecular characteristics are expected to have similar drug targets, it is important to consider disease similarity. The semantic value $DV(A)$ of disease A is defined by the following formula.

$$DV\left(A\right)=\sum_{t\in {T}_{A}}{D}_{A}(t)$$

where ${T}_{A}$ represents the set of ancestor nodes of disease A, and the contribution ${D}_{A}(t)$ of disease t to disease A is defined by

$$ D_{A} \left( t \right) = \left\{ {\begin{array}{*{20}c} {1,} & {t = A} \\ {max\left\{ {\Delta *D_{A} \left( {t^{\prime } } \right)|t^{\prime } \in children\, of\, t} \right\},} & {t \ne A} \\ \end{array} } \right. $$

where $\Delta$ is the semantic contribution damping coefficient and is generally chosen to be $\Delta =0.5$. The semantic similarity score $S\left(A,B\right)$ between disease A and disease B is defined by the following formula

$$S\left(A,B\right)=\frac{\sum_{t\in {T}_{A}\cap {T}_{B}}({D}_{A}\left(t\right)+{D}_{B}(t))}{DV\left(A\right)+DV(B)}.$$

“Drug” entities were collected from DrugBank. DrugBank is a database that provides comprehensive information on FDA-approved drugs and experimental drugs in the approval process. “Drug-protein” interactions, “drug-mRNA” interactions, “drug-drug” interactions were retrieved from DrugBank. “Drug-metabolite” interactions were obtained from HMDB. Drugs are structurally modified into metabolites by various metabolic enzymes [48]. Therefore, metabolomics dealing with metabolites is regarded as an important tool for drug discovery [49]. In this study, in order to avoid duplication with compounds used as drug nodes, the metabolites were incorporated into the network independently. It is important to note that while our focus is on predicting drug-disease interactions, these interactions are not included in the input networks to avoid any bias. Our methodology aims to deduce these interactions based on the intricate patterns observed among other entities and their interactions.

“Proteins” play a vital role in a plethora of biological processes. Therefore, exploring the functional mechanisms of proteins lead to a comprehensive understanding of disease processes and drug mechanisms [50]. In particular, protein–protein interactions are not only known to play important roles in biological systems and disease states, but have also been shown to be important modalities in predicting drug repositioning [21]. “Protein–protein” interactions were obtained from STRING and Human Reference Protein Interactome (HuRI). STRING are accompanied with confidence scores based on experimental data and pathway databases. A confidence score of 900 or higher is considered the cutoff for the highest level of confidence [51], and protein–protein interaction networks were constructed accordingly. In addition, HuRI obtained direct interaction information experimentally verified by the Yeast Two-Hybrid System, and has achieved the most systematic and comprehensive screening of human protein interactions.

Transcriptome data are useful for systematic understanding of the functional mechanisms of drugs and diseases because they can capture the dynamic characteristics of cells [52]. Various types of RNA are involved in gene regulation, so we selected two of them, “mRNA” (coding-RNA) and “miRNA” (non-coding RNA), as entities to be included in the multimodal network. miRNA has the function of regulating gene expression by binding complementary to mRNA. Thus, interactions between RNAs are known to play important roles in various cellular processes [53]. While we included miRNA as a representative non-coding RNA entity due to its well-established role in drug interactions and its extensive documentation in databases, we acknowledge the importance of other non-coding RNAs such as lncRNA, piRNA, siRNA, and shRNA. The decision to focus on miRNA was based on data availability and its established relevance in drug-target interactions. RNA-related interactions were obtained from RNAInter. RNAInter integrates literature and multiple data sources to provide empirically-based reliability scores. “Drug-miRNA”, “protein-mRNA” and “protein-miRNA” interactions were introduced from RNAInter as a weighted network using this reliability score. Interactions between RNAs were also obtained as weighted networks based on reliability scores obtained from RNAInter.

Model workflow

This section describes in details our method, STRGNN, for predicting drug-disease associations. The STRGNN consists of three main steps: (i) Attribute Encoder, which encodes structural information of biomolecules; (ii) Network Encoder, which encodes network information; (iii) Decoder, which predicts drug-disease associations. The framework of STRGNN is illustrated in Fig. 1.

Fig. 1

Schematic diagram of STRGNN workflow. A STRGNN performs drug-disease link prediction using two encoders, Attribute Encoder and Network Encoder, and a Decoder. B Network Encoder sequentially applies Topological Regularization to each interacting network

The feature matrix obtained by the Attribute Encoder is used as the initial node feature in the Network Encoder. This low-dimensional distributed representation serves as the input to the Graph Neural Network layers, which then learn the node embeddings based on the multimodal network structure.

It is important to note that STRGNN does not require Attribute Decoders or Network Decoders, as the purpose of our method is to learn informative node representations for drug-disease association prediction. The final node embeddings obtained from the Network Encoder are directly utilized by the Decoder to compute the association scores.

In this study, we represent multimodal networks as graphs. A graph is defined as $G=(V,E)$ ($V,E$ are nodes and edges respectively). Each modal network is represented by a graph of its own type. The node $v$ of biomolecule type $o$ belongs to the set ${V}_{o}$ and the edge of interaction type $r$ belongs to the set ${E}_{r}$, where the set of biomolecular types $O=$ {drug, disease, protein, mrna, mirna, metabolite} and the set of interaction types $R=$ {drug-drug, drug-disease, drug-protein, drug-mrna, drug-mirna, drug-metabolite, disease-disease, disease-protein, disease-mrna, disease-mirna, disease-metabolite, protein–protein, protein-mrna, protein-mirna, mrna-mrna, mrna-mirna, mirna-mirna}. The multimodal network combines all those networks composed of biomolecular types and interaction types. Then the drug-disease association prediction is defined as the task of predicting the link probability of a pair (${v}_{i}$, ${u}_{j}$) of a drug node ${v}_{i}\in {V}_{drug}$ and a disease node ${u}_{j}\in {V}_{disease}$ on the multimodal network.

Attribute Encoder encodes drugs (compounds) and proteins (amino acid sequences). The feature matrix ${H}^{0}$ obtained by the Attribute Encoder is used as the initial value of the node feature in the Network Encoder. Molecular structures of chemical compounds and amino acid sequences of proteins are important information representing their structural characteristics and functions, and are useful for interaction prediction related to proteins and drugs [54].

Drugs were converted from SMILES representations obtained from DrugBank to 2048-dimensional Extended Connectivity Fingerprint (ECFP) [55] using RDKit. Then, by applying a fully-connected feedforward neural network (FNN), we obtained a low-dimensional distributed representation of the drug node ${H}_{drug}^{0}\in {\mathbb{R}}^{{N}_{drug}\times d}$, where ${N}_{drug}$ denotes the number of drug nodes, and d denotes the number of dimensions of the low-dimensional distributed representation.

Amino acid sequences of proteins were obtained from UniProt [56]. After converting the amino acid sequences into one-hot vectors, a one-dimensional convolutional neural network (CNN) was applied according to the method of ref. [15]. Then, by applying an FNN, we obtained a low-dimensional distributed representation ${H}_{protein}^{0}\in {\mathbb{R}}^{{N}_{protein}\times d}$ for the protein node, where ${N}_{protein}$ denotes the number of protein nodes, and d denotes the number of dimensions of the low-dimensional distributed representation.

These methods have been shown to be effective in many previous studies. ECFP-based drug representation is widely used in various tasks such as drug discovery and interaction prediction due to its high expressiveness and computational efficiency [57]. The application of CNN to protein amino acid sequences has demonstrated high performance in protein function prediction by effectively capturing local features of the sequences [58].

For diseases, RNA, and metabolites, initial values were sampled from a normal distribution with mean $\mu =0$ and standard deviation $\sigma =\frac{1}{\sqrt{d}}$, and their low-dimensional distributed representations (${H}_{disease}^{0}, {H}_{rna}^{0}, {H}_{metabolite}^{0}$ for disease, RNA and metabolite, respectively) were obtained.

Network Encoder acquires the distributed representation of each node (entity) based on the adjacency relations between nodes included in the multimodal network. Graph Neural Network (GNN) acquires node distribution representation based on adjacency relation for graph structure data according to the following update formula.

$${H}^{l+1}=f({D}^{-\frac{1}{2}}A{D}^{-\frac{1}{2}}{H}^{l}{W}^{l})$$

where $A$ is the adjacency matrix of the input graph, ${H}^{l}$ is the node feature (node distribution representation) matrix in the l-th layer, $D=diag(\sum_{j}{A}_{ij})$ is the degree matrix, ${W}^{l}$ represents the weight parameters of GNN, and $f(\cdot )$ is the activation function.

In STRGNN that learns each modality network sequentially, it is inevitable to deal with the problem caused by learning with deep layers, that is, over-smoothing. In this study, we employed DropEdge [59], which is a regularization method that probabilistically removes edges in the input graph, and NodeNorm [60], which conducts node-wise scaling for the feature of each node (see Supplemental in detail).

The large-scale networks may contain redundant and unnecessary information and noise, which causes overfitting of learned models. The “topological regularization” proposed in this study introduces a path that skips a modality learning by adding an FNN in parallel with the GNN that learns the modality network. We call this path “skip connection” and defined with the following formula.

$${H}^{l+1}=f\left({D}^{-\frac{1}{2}}{A}^{l}{D}^{-\frac{1}{2}}{H}^{l}{W}_{gnn}^{l}+{H}^{l}{W}_{fnn}^{l}\right)$$

where ${H}^{l}$ is the node feature matrix in the l-th layer, and ${W}_{gnn}^{l}, {W}_{fnn}^{l}$ represent the weight parameters of GNN and FNN, respectively. By successively applying this model learning consisting of two paths to the network of each modality, the node distributed representation is learned in a sequential manner. In addition, in order to enhance the effect of skipping the learning of unnecessary modalities, the involvement of the redundant weight parameter $W$ is removed by introducing ${L}_{1}$ regularization. Combined the skip connection with ${L}_{1}$ regularization, the mechanism of topological regularization was implemented.

The Inner Product Decoder [61] was used as a decoder to predict the association between drugs and diseases.

$$\widehat{A}=sigmoid({H}_{drug}{H}_{disease}^{T})$$

where $\widehat{A}\in {\mathbb{R}}^{{N}_{drug}\times {N}_{disease}}$ is the prediction probability matrix, ${H}_{drug}$ and ${H}_{disease}$ are the node feature matrices in the final layer for drugs and diseases, respectively, and the prediction score for the pair (${v}_{i}$, ${u}_{j}$) of drug ${v}_{i}$ and disease ${u}_{j}$ is obtained as a $\widehat{a}$ _i,j $\in \widehat{A}$.

The cross-entropy loss and the regularization term were adopted as the loss function. Regularization is important not only for suppressing overfitting, but also for suppressing bias between modalities in multimodal learning that integrates different modalities [62]. As stated above, in order to assist the effect of topological regularization, which skips the learning of unnecessary modalities, the contribution of the redundant weight parameter $W$ is eliminated by introducing ${L}_{1}$ regularization.

$$loss=\sum_{i=0}^{N}\left\{-{y}_{i}\text{log}\left({p}_{i}\right)-\left(1-{y}_{i}\right)\text{log}\left(1-{p}_{i}\right)\right\}+\lambda {\Vert w\Vert }_{1}$$

where ${p}_{i}$∈{0,1} is the i-th prediction, ${y}_{i}$ is the ground truth, $w$ represents the learning weight, and $\lambda$ is the coefficient of the regularization strength.

It is important to note that L1 regularization is applied to the weights of all layers in STRGNN. The motivation behind using L1 regularization is to induce sparsity in the weights, which allows for the selective inclusion or exclusion of interactions at each layer. By encouraging sparsity, L1 regularization helps the model to identify and focus on the most informative interactions while discarding the less relevant ones.

For performance evaluation, we used the following metrics: Area Under the Receiver Operating Characteristic curve (AUROC), Accuracy (ACC), and Area Under the Precision-Recall Curve (AUPRC). In particular, AUPRC is frequently used as an evaluation metric for imbalanced datasets. The model was evaluated using a nested cross-validation approach, where the drug-disease network was initially split into a test set and a training-validation set, following the approach described in the “Setting for drug repositioning prediction” section.

The training-validation set was then used for hyperparameter tuning using fivefold cross-validation. In each fold, the data was further split into training and validation sets, and the model was trained on the training set while the hyperparameters were tuned based on the performance on the validation set. The best-performing hyperparameters from this inner loop were then used to train the final model on the entire training-validation set.

Finally, the model’s performance was assessed on the held-out test set, which was not used during the hyperparameter tuning process. This approach ensures an unbiased evaluation of the model's performance on unseen data.

There are several hyperparameters in STRGNN, including kernel size, channel size, dropout probability, drop edge probability, embedding dimensionality, regularization strength, and learning rate. These hyperparameters were extensively searched using the validation sets in the inner loop of the nested cross-validation procedure. The best-performing configuration is provided in the supplementary material.

Setting for drug repositioning prediction

In this study, we evaluated a model for drug repositioning. Specifically, we constructed a data set to test the potential reuse of drugs that have been confirmed to be effective for specific diseases to other diseases. Figure 2 illustrates the method for constructing the test data. First, we selected drugs whose degree deg($v$) of the drug node $v\in {V}_{drug}$ in the drug-disease network satisfies deg($v$)$\ge 2$, that is, the number of edges connected to the node $v$ is more than or equal to 2. This enabled us to select drugs with multiple target diseases for test dataset. Second, we compared these target diseases with disease classifications at the shallowest hierarchies of the ICD-11. During this process, we ensured that there was no overlap between the ICD-11 classification of diseases in the training dataset and the ICD-11 classification of diseases in the test dataset. As a result, drug-disease pairs suitable for the purpose of drug repositioning were extracted as test data, and prediction performance was evaluated based on these datasets.

Fig. 2

Test data construction considering drug repositioning. (Left) Hierarchical classification based on disease characteristics and etiology in ICD-11. (Right) A pair of drug nodes with multiple target diseases and disease nodes with different ICD-11 is used as test data. For instance, the figure illustrates a drug targeting two diseases in category:02 and one in category:08. In this scenario, the pair consisting of the drug and the disease from category:08 is selected as test data

Negative examples cannot be obtained with the database CDT that collects positive examples for drug-disease associations. Therefore, negative sampling using unknown or unlabeled drug-disease pairs as negative examples is necessary. Specifically, for a drug-disease edge for (${v}_{i},{u}_{j}$) that is a positive example, we select random drug ${v}_{k1}\in {V}_{drug}$ and disease ${u}_{k2}\in {V}_{disease}$ exclusively for positive examples. Then, the pairs (${v}_{i},{u}_{k2}$) and (${v}_{k1},{u}_{j}$) obtained by replacing the nodes are taken as negative examples.

Results

Performance evaluation of STRGNN on different modality datasets

In order to verify that STRGNN can effectively learn the abundant modality information of multimodal networks, we compared the prediction accuracy when given different modalities. In the small-modality dataset, only drugs and diseases were handled as entities, and their association networks were provided as input. Specifically, the dataset involved drug-drug and disease-disease networks. For the middle-modality dataset, proteins were added as entities alongside drugs and diseases, with multiple interaction networks between them as input. This dataset incorporated drug-drug, drug-protein, protein–protein, disease-protein, and disease-disease networks. In the large-modality dataset, all modalities including RNA and metabolites were considered, utilizing their multimodal networks for model training. Table 2 shows the prediction performance for each modality dataset. Prediction performance improved with the introduction of more networks from different modalities. This result implies that it is important to utilize interaction networks based on multiple omics data in predicting drug-disease associations.

Table 2 STRGNN performance on different modality datasets

The performance improvement with the large modality dataset was not as significant as expected. This suggests that the additional modalities may not contribute substantially to prediction accuracy, possibly due to redundancy or irrelevance of the added information.

Effect of topological regularization

In order to verify the effect of the topological regularization proposed in this study, we compared the models with and without the FNN path that skips the learning of each modality, as well as with and without ${L}_{1}$ regularization. The result is shown in Table 3. The result shows that introducing both skip connection and ${L}_{1}$ regularization, that is topological regularization, achieves higher prediction performance. The novelty of STRGNN lies in the topological regularization, which integrates Graph Neural Networks (GNNs) and Feedforward Neural Networks (FNNs) through skip connections and combines them with ${L}_{1}$ regularization. This unique combination allows STRGNN to effectively exclude redundant modalities while learning from the most informative interactions in the multimodal network, as demonstrated by the improved performance when skip connections and ${L}_{1}$ regularization are used together. The low prediction performance without topological regularization implies the importance of selectively learning necessary modalities and discarding redundant ones from multimodal networks. In other words, a mechanism to eliminate potential noise is essential in interaction prediction based on biological data. In addition, by introducing ${L}_{1}$ regularization, the effect of modality selection is enhanced by competing for weight parameters that can be learned by GNN and skip connection in the STRGNN method.

Table 3 Effectiveness of topological regularization

Comparison with other state-of-the-art methods

Performance of STRGNN drug-disease association prediction was compared with existing state-of-the-art methods; NMF [63] as recommendation-based method, Node2Vec [3] as network propagation method, deepDR [19], Relational-GCN [18], NeoDTI [20], LAGCN [10], and DRHGCN [22] as most recent and representative deep learning methods.

To ensure a fair comparison, all methods were retrained using the Large-Dataset. For existing methods that do not support multimodal data, we utilized the maximum number of modalities available within each method. The retrained models were then tested using the same test set as the one used in our study, which was held out during the training process. This approach guarantees an unbiased evaluation of the models' performance on unseen data and ensures a direct comparison with STRGNN. The hyperparameters for the existing methods were kept the same as those proposed in their respective original papers to allow for a direct comparison without introducing additional tuning bias.

The result, shown in Table 4, indicates that STRGNN exhibits strong performance and the best on all indexes compared to other state-of-the-art methods. The bold values in the table highlight these best-performing results, emphasizing STRGNN's superiority. LAGCN and DRHGCN, which are state-of-the-art drug repositioning prediction methods, only utilize the network structure composed of drugs and diseases, and cannot be applied to multimodal networks with abundant interaction information. Considering the importance of introducing multiple modalities, this drawback can be a serious bottleneck in drug-disease association prediction. On the other hand, the remarkably high performance of STRGNN and NeoDTI, which can incorporate multimodal interaction information, suggests the necessity of integrating multimodal networks.

Table 4 Performance comparison with state-of-the-art methods

In this experiment, STRGNN outperformed NeoDTI, potentially due to NeoDTI’s inability to effectively extract features while considering the influence of noise and the importance of modalities contained in the network. Therefore, this result demonstrates the effectiveness of topological regularization to utilize diverse multimodal networks.

Performance evaluations were conducted with the modalities used by each method by default (shown in Supplementary Table S2).

Discussions

Effect of topological regularization

In order to verify the effect of topological regularization, which selectively learns important modalities, the heat map visualization of the strength of selected network modality is displayed in Fig. 3. The color of the heatmap represents the strength of the weights obtained by STRGNN for each interaction network, calculated separately for the Graph Neural Network (GNN) and the Feed-forward Neural Network (FNN) using the following formula:

$$\text{Weight Strength }=\sqrt{\sum_{i=1}^{{N}_{weight}}{{w}_{i}}^{2}}$$

where ${N}_{weight}$ is the number of weight parameters and ${w}_{i}$ is the value of the i-th weight parameter.

Fig. 3

Heatmap to display strength of weights obtained by STRGNN. The vertical axis repre-sents the GNN path and the FNN path. The horizontal axis represents each interaction network. Each modality is indicated by the following symbols; d: drug, z: disease, p: protein, m: mRNA, mi: miRNA, b: metabolite

This result indicates that two learners, GNN for network learning and FNN for skip connection are competing to acquire weight parameters in learning each interaction network. For example, in the learning of disease-disease modality network and drug-protein modality network, GNN obtained larger weights, which is consistent with previous results that drug-target information and similarities in disease classification are important factors in drug discovery [64]. On the other hand, it is worth noting that the FNN for skip connection acquired larger weights in drug-drug networks, although drug-drug networks are frequently employed in other graph-based deep learning methods. Considering that the drug-drug network contains a larger amount of interaction information compared to other networks, as shown in Supplemental Table S1, it might contain much redundant interaction information that becomes noise in drug-disease association prediction. RNA-related networks, especially miRNA-miRNA interaction, also gained large weights. This result indicates the necessity of introducing RNA-related interactions that have not been addressed in previous studies in drug-disease association prediction.

Case studies for discovering new drug efficacy

A novel drug-disease association prediction was performed by applying the fully trained STRGNN to predict all drug-disease pairs for which no association was confirmed. Table 5 shows novel drug-disease associations predicted by STRGNN and the literature supporting the validity of the prediction. Among the predicted pairs, we focused on the drug Quercetin (DrugBank Accession Number: DB04216) and its target disease, Amyotrophic lateral sclerosis (ALS). Quercetin is a natural flavonoid and is known to have anti-inflammatory and anti-oxidant effects [65]. ALS pathogenesis involves misfolding and monomerization of the homodimeric protein SOD1. Molecular biological experiments have confirmed that Quercetin interacts with SOD1 and inhibits self-assembly [66, 67]. This promising prediction of interactions between Quercetin and ALS, which are expected to be used as therapeutic drugs, is a valid prediction result from the viewpoint of mechanism of action.

Table 5 Discovery of novel drug-disease association

It is also worth noting that Anthralin (DrugBank Accession Number: DB11157) and its target disease, Inflammatory bowel disease had high predictive scores. Anthralin is classified as a drug for a skin disease by ICD-11 and is used as a treatment for psoriasis. Inflammatory bowel disease, on the other hand, is classified as disease of the digestive system in the ICD-11. This new efficacy prediction across different ICD-11 classifications is a useful case for drug repositioning. Anthralin is experimentally verified to inhibit cytokines such as TNF-α and IFN-γ [68]. Since TNF-α is related to the onset of Inflammatory bowel disease [69], it is expected that this new drug efficacy prediction considering the biological network could be correct.

Drug-disease association prediction for new drug

Existing methods for drug-disease association prediction based on graph deep learning have the problem that prediction cannot be applied to biological entities that are not included in multimodal networks. This implies that it is not possible to predict the association for novel compounds which are not registered in the database. On the other hand, in this study, we constructed an algorithm that can easily extend the association prediction of STRGNN to compounds outside the network. That is, the algorithm is to apply a loss function based on the similarity between the compound feature vector obtained from the Attribute Encoder and the Network Encoder. More specifically, by applying the cosine embedding loss, we projected a new compound onto the feature vector space based on the multimodal network using only the ECFP value of the new compound. In a preliminary experiment, we selected a limited number of drug nodes (614 nodes) as novel compounds and removed all edges connected to these drug nodes in the training dataset, and performed the association prediction (semi-inductive prediction) only between these drugs and diseases. It turned out that STRGNN exhibited high prediction performance (AUPRC: 0.833, AUROC:0.895, ACC:0.865) for novel drugs that did not exist in the multimodal network.

Conclusion

In this study, we developed STRGNN, a new framework for drug-disease association prediction from multimodal networks. STRGNN achieved higher prediction performance than other state-of-the-art methods by introducing Topological Regularization to selectively learn modalities from multimodal networks. In addition, STRGNN succeeded in predicting new efficacy of drugs with validity from the viewpoint of literature and mechanism of action. A future work is to perform association prediction considering more biological data sources. For example, by considering the RNA base sequence and the compound structure of metabolites, it is expected that a feature space reflecting more abundant information can be obtained.