In this section, inspired by the idea of KNN [K-Nearest-Neighbor (Cover and Hart, 1967)], we learn the substructures of the bipartite graph network to obtain the embedding representations of drug–microbe pairs.

First, we construct the drug–microbe bipartite graph network, G=(D,B,E), where D={d₁,d₂,…,d_m} represents m drugs, B={b₁,b₂,…,b_n} represents n microbes, and each edge (e_ij) in edge set E connects two nodes that belong to two different sets of vertexes (i.e., i in D, j in B). We regard the DMAs as bidirectional links. That is, e_dx→bp denotes the edge pointing from the drug d_x to the microbe b_p, and e_bp→dx denotes the edge pointing from the microbe b_p to the drug d_x. Correspondingly, the nearest-neighbor aggregator contains two blocks (Figure 2), the microbe-specific drug neighbor aggregator (MsDNA), and the drug-specific microbe neighbor aggregator (DsMNA). Due to their architectures being similar, we only illustrate the MsDNA block in this section.

Microbe-specific drug neighbor aggregator (Figure 2A) contains a virtual key dictionary; 𝒩={n₁,n₂,…,n_m} indicates all the drugs. In the dictionary, we imitate the idea of KNN to learn the substructures of the bipartite graph network, where virtual keys are sorted by their semantic nearest neighbors. In simple terms, n₁ denotes d_x itself, its nearest neighbor is the second key, and the farthest neighbor is the last key. The embedding representation of the edge, which is from drug d_x to microbe b_p, is formulated as follows:

where 𝒩^p⊆𝒩 is a set of instantiated keywords, and 𝒩^p denotes the neighbors of d_x in the Net_d. S_d(d_x,n_i) denotes the similarity of d_x and n_i, and v_i is the corresponding one-hot encoding vector of n_i (i.e., the one-hot encoding has a non-zero value only in the i_th element, and all other position elements are zero).

Similarly, DsMNA (Figure 2B) makes the single directional embedding representation from b_ptod_x as a(b_p,d_x). Then, the representation of drug–microbe pair could be encoded as

where e(d_x,b_p) is generated via the concatenation of bidirectional embedding, and ∥ is the concatenation operation. All the embedding representations of drug–microbe pairs could stack as a matrix E_k×g, where k is the number of all the drug–microbe pairs and g is the dimension of each embedding. The nearest-neighbor aggregator effectively learns the bipartite graph substructures, and E_k×g will be input into a feature attention block to select crucial features for achieving a better DMA prediction.

To improve the performance of the prediction, we build the feature attention block (Figure 3) for updating the embedding of drug–microbe pairs.

Recall the equation of output feature representation in GAT (Velickovic et al., 2018):

where σ is a nonlinear activation function, 𝒦ⁱ is the first-order neighbors of node i (including i), α_ij is the coefficients computed by the attention mechanism, and W is a weight matrix. To make equation (9) easier to understand. We compute the coefficients as:

where A~=A+I is the adjacency matrix of the undirected graph G with added self-connections (Kipf and Welling, 2017), ⊙ is the element-wise product operation, and M is the attention matrix. Then, the layer-wise propagation rules in GAT can be formulated as:

where σ is a nonlinear activation function, and W^(l) is the weight matrix of the l_th neural network layer.

Inspired by the conception of the layer-wise propagation rules in GAT, we calculate the augmented representation matrix F~k×g by

where E_k×g is the representation matrix of the drug–microbe pairs obtained from the nearest-neighbor aggregator, M_k×g is an attention matrix of E_k×g, and ⊙ is the element-wise product operation. We take the representation matrix E_k×g as a feature matrix F (F={f₁,f₂,…,f_g}), which is composed of g column vectors (f_i(i = 1,2,…,g)). The feature attention block mainly uses M_k×g to indicate the importance of features in the E_k×g. Each feature dimension f_i can be labeled as “selected” or “discarded” in a hard way, or be associated with a probability to be selected in a soft way; we employ DNNs to model the mapping by

the DNN contains an input layer for each element of the feature dimension f_i and an output layer with sigmoid as its activation function.

In total, we build k×g DNNs to obtain M_k×g. The final feature matrix F~k×g of the drug–microbe pairs is obtained after the element-wise product operation of M_k×g and E_k×g. F~k×g is further fed into a predictor to achieve better predictive performance.

To implement the link prediction in the drug–microbe bipartite graph network, an ordinary DNN is utilized as the binary predictor that contains an input layer for the embedding representation of drug–microbe pairs, a hidden layer with ReLU as its activation function, and the two-neuron output layer with Sigmoid as its activation function. The output layer generates a probability that indicates the association likelihood of the drug and the microbe. The probability is formulated as:

where φ is the sigmoid activation function, and ℱ(⋅) is the fully-connected layer.

The entire network of NNAN with the nearest-neighbor aggregator, feature attention weights, and DNN weights can be jointly optimized through the binary cross-entropy loss as follows:

where Y is the truth labels of drug–microbe pairs, 𝒟(⋅) is the DNN, θ denotes the weight parameters in the entire network, ℛ(⋅) is an L₂-norm, and λ is coefficient of the regularization item.

In our experiments, two databases are collected from MDAD (Sun et al., 2018) and Zimmermann et al. (2019a), respectively. The former work MDAD (Sun et al., 2018) investigated 5,505 clinically or experimentally DMAs between 1,388 drugs and 180 microbes. After removing redundant information, these association entries are grouped into Database 1, which contains 999 drugs, 133 microbes, and 1,708 DMAs.

The latter work (Zimmermann et al., 2019a) originally studied how 76 kinds of human gut bacteria metabolize 271 oral drugs, and found that 176 out of 217 drugs are significantly consumed by at least one bacteria strain. These associations are grouped into Database 2, which includes 176 drugs, 76 bacteria, and 4,194 associations (These two databases are shown in Table 1).

Since there are few existing approaches for predicting DMAs, we compare NNAN with three state-of-the-art methods, which were raised for bipartite link prediction.

To evaluate the performance of these methods, we regard the known DMA pairs as positive samples and unlabeled DMA pairs as negative samples (Peng et al., 2020; Li et al., 2022). We set up a 5-fold cross-validation scenario in which we randomly divide positive samples and negative samples into five groups, respectively. One group of positive samples and one group of negative samples are treated as test samples in turn for each round. The remaining groups are used for training purposes. Our model is trained by Gradient Descent Optimizer (Cauchy, 2009), with batch size 3,000 for 2,000 epochs, the initial learning rate is set to 0.9, and the regularization rate is set to 2e-4. We use AUROC (area under the receiver operating characteristic curve) and AUPRC (area under the precision-recall curve) as metrics to measure the DMA prediction performance. Moreover, we investigate the running time in terms of per epoch.

The comparison (Table 2) shows that NNAN obtains the best AUROC value (0.911) and the best AUPRC value (0.502) in Database 1. NNAN attains the next-highest AUROC value (0.902) and the best AUPRC value (0.840) in Database 2. To further present the performance of NNAN, we calculate the running time for one epoch of the baselines and NNAN, respectively. As presented, with the same computing equipment, NNAN takes the third-shortest running time in Database 1 and the shortest running time in Database 2. In general, we can see that NNAN are comparable in terms of AUROC, AUPRC, and computation time. It demonstrates that NNAN is superior to other methods on the databases we collected.

How does the NNAN interpret the hypothesis that “If a drug can associate with a microbe, the other drugs that associate with the microbe are usually the first l nearest neighbors to the drug.”

The model has two significant advantages to enhance interpretability. First, each column vector m_i of M_k×g indicates the global importance of each feature dimension f_i. Moreover, the element-wise product between E_k×g and M_k×g generates the importance map of embedding features.

We first use the MsDNA in the nearest-neighbor aggregator block to show how the representation of drug–microbe pairs can provide intuitive hints, on which embedding features lead to the association. For the queried drug d_x to the microbe b_p of associated, non-zero cells in the embedding representation of a(d_x,b_p) stand for its attention values derived from the drugs commonly linking b_p. Since the keys are sorted in descending order from the drug itself (n₁) to the farthest neighbor (n_m), the positions of non-zero cells are crucial to the final association.

Take Database 1 as an example. By calculating two average embedding vectors for approved DMAs and unlabeled drug–microbe pairs, we obtained a distribution along with the drug key dictionary from n₁ to n₆₆(Figure 4A). As illustrated, the significantly high values of embedding features occurring among the first l nearest neighbors reveal that a drug (d_x) associated with a specific microbe (b_p) can always find its top-l nearest neighbors among other drugs that associate with the same microbe. This observation demonstrates that a drug is possibly associated with the microbe if it has more non-zero value cells on the positions of the first l feature dimensions. This phenomenon could be caused by the fact that over 80% of approved drugs are of “follow-on” or “me-too” drugs. Due to high cost and high risk, the design of novel drugs, except for pioneer drugs, always starts from the structures of one or several existing drugs and then slightly modify them until meeting pharmacological needs (DiMasi and Faden, 2011). Analogously, the results of the DsMNA block along the microbe neighbor aggregator keys reveal that a microbe associated with a specific drug usually finds its near neighbors associated with the same drug.

Moreover, we illustrate how the feature attention matrix M_k×g can provide data-driven hints on which embedding features lead to the association. Since a high-value cell in M_k×g stands for a crucial feature dimension contributing to determine the association between a queried drug and a microbe, the importance m(i,:) of each feature f_i can be measured by the average of value entries in the i_th column of M_k×g (Figure 4B). The importance distribution along with the sorted drug neighbor keys illustrates that highly important features are usually located among the first l nearest neighbors. In addition, the predictive performance with top-l features concerning l is investigated (Figures 4C,D). The number of top features is tuned in the list {1, 6, 11, 16,…, 66}. As l is increasing to 16, the performance increases sharply in the top-l features. When l keeps increasing, the performance increases slowly, then even decreases at the greater value of l. Again, this illustration demonstrates that the selection of crucial features is significantly better than the set of all features.

In summary, both embedding feature matrix E_k×g, which is generated by the nearest-neighbor aggregator, and its feature attention matrix M_k×g provide mensurable clues to the association outcome.

To complement the verification of the interpretability of NNAN, we selected one microbe (i.e., Staphylococcus aureus, which is a common causative agent of food poisoning) and one drug (i.e., Hexyl gallate, which has strong antimalarial activity against Plasmodium falciparum) from Database 1, and there was an association between them (de Lima Pimenta et al., 2013). We calculated the similarities between drugs using Hexyl gallate as the reference molecule and sorted the drugs in order of their similarity to Hexyl gallate. Then, we picked the top 10 drugs and checked whether these drugs were associated with S. aureus in Database 1. Finally, we found out that 8 out of the top 10 ranked drugs for Hexyl gallate are associated with S. aureus (Table 3).

From Table 3, it is clear that a drug tends to associate with a microbe if it finds its top-l near neighbors associate with the same microbe. Moreover, the higher the ranks of its top-l near neighbors are, the more possible it is to associate with the microbe. This conclusion would be helpful to screen drug-like molecules.