Drug metabolite prediction method based on three-dimensional heterogeneous network

Abstract

The invention belongs to the technical field of metabolite prediction, and particularly relates to a drug metabolite prediction method based on a three-dimensional heterogeneous network. According to the method, the problem of key metabolic enzyme information loss in drug metabolite prediction is solved, and biochemical information of drug molecules, metabolic enzyme molecules, metabolite molecules and the like is incorporated into a model by calculating chemical structure similarity, similarity between protein sequences and the like; and the topology embedding representation of the nodes is obtained through a method based on matrix decomposition, the attribute embedding representation of the nodes is obtained through an improved GNN method for final prediction, a loss function is constructed in combination with multi-task collaborative loss and embedding consistency regularization, and the comprehensiveness and accuracy of the model are effectively improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of metabolite prediction, and particularly relates to a drug metabolite prediction method based on a three-dimensional heterogeneous network. BACKGROUND

[0002] Metabolism is a series of ordered chemical reactions that have important effects on maintaining human life, such as the growth, reproduction and response to the external environment of organisms. Drug metabolism refers to the process in which a drug is biotransformed into metabolites in the body, usually in the liver and other tissues. Drug metabolites refer to new compounds formed after a drug is metabolized in the body. These metabolites may have different pharmacological activities, toxicities or pharmacokinetic properties, and thus are of great significance to the evaluation of drug safety and effectiveness. Early drug metabolite research mainly relied on experimental animal models and in vitro experiments, such as liver microsomal enzyme in vitro reactions. However, animal models differ from human metabolism, and in vitro experiments cannot completely simulate the in vivo metabolic environment, so the prediction results may be biased. Moreover, experimental methods have huge time and labor costs. Drug metabolite prediction refers to predicting and inferring the metabolites produced in the in vivo metabolism of drugs through computer models, machine learning algorithms or other computational methods. Existing work has proposed to predict the relationship between drug molecules and metabolite molecules through the structure and properties of the molecules. However, drug metabolism is a complex process, and how to consider comprehensive information for effective prediction is a key problem.

[0003] Currently, there is a method that proposes to construct a heterogeneous network by integrating multiple data sources (including chemical structure information of metabolites and drugs, metabolite-gene, metabolite-disease, drug-gene and drug-disease relationships, gene ontology (GO) and disease ontology (DO) data, and known metabolite-drug associations), and to use random walk analysis on the network to predict new drug-metabolite associations.

[0004] There is also a method that predicts possible human metabolites of small molecules including drugs through a sequence translation problem. This method innovatively introduces a hint engineering to enrich domain knowledge and guide decision making, realizes high-accuracy metabolite prediction, and reduces false positive predictions.

[0005] The defects of the traditional method are that the traditional drug metabolite prediction method using machine learning often lacks comprehensiveness and systematicness, and it is difficult to comprehensively consider various influencing factors of drug molecule metabolism, such as molecular structure, biochemical properties, environmental factors and the like of the drug, thereby limiting the comprehensiveness and accuracy of the prediction model. The method of predicting drug metabolites by machine learning comprehensively considers the structure and function information of drug molecules and metabolite molecules, and uses the information to construct features to predict the relationship between them, but does not consider the effect of metabolic enzymes on the metabolic process, and lacks modeling of metabolic enzyme information. SUMMARY

[0006] In view of the above problems, the present application provides a method for predicting drug metabolites, which integrates drug information, metabolite information and metabolic enzyme information into the prediction of drug-metabolite relationships by constructing a three-dimensional heterogeneous network, so that the model has comprehensiveness and accuracy. By calculating the topological features and attribute features of the nodes in the three-dimensional heterogeneous network, the prediction of drug-metabolite relationships is finally realized.

[0007] The technical scheme adopted by the present application is:

[0008] A drug metabolite prediction method based on a three-dimensional heterogeneous network, comprising the following steps:

[0009] S1, obtaining information of drugs, metabolic enzymes and metabolites from a public database, including chemical structure of the drug, chemical structure of the metabolite, drug-metabolic enzyme relationship, drug-metabolite relationship, and metabolite-metabolic enzyme relationship;

[0010] S2, constructing similarity matrices of drug-drug, metabolic enzyme-metabolic enzyme and metabolite-metabolite, and relationship matrices of drug-metabolite, drug-metabolic enzyme and metabolic enzyme-metabolite according to the obtained information, respectively:

[0011] constructing the drug-drug similarity matrix by calculating the similarity based on the chemical structure and the metabolite-metabolite similarity matrix , constructing the metabolic enzyme-metabolic enzyme similarity matrix by calculating the similarity of the protein residue sequence ;

[0012] constructing the drug-metabolic enzyme relationship matrix DE, the drug-metabolite relationship matrix DM and the metabolic enzyme-metabolite relationship matrix EM according to the obtained drug-metabolic enzyme relationship, drug-metabolite relationship and metabolite-metabolic enzyme relationship;

[0013] if the drug c and the metabolic enzyme d have a known association, then ; otherwise 0, wherein This represents the c-th row and d-th column of matrix DE; the incidence matrices DM and EM are obtained in the same way.

[0014] S3. Construct a three-dimensional heterogeneous network G for drugs, metabolic enzymes, and metabolites based on the obtained similarity matrix and relation matrix:

[0015] ,

[0016] S4. Based on the constructed three-dimensional heterogeneous network G, the topological feature embeddings of drug and metabolite molecules are obtained using a matrix factorization-based method, and the attribute feature embeddings of drug and metabolite molecules are obtained using an improved GNN method, specifically:

[0017] The topological feature embeddings of drug and metabolite molecules are obtained using a matrix factorization-based method. The three-dimensional heterogeneous network G includes three different types of nodes: drug nodes, enzyme nodes, and metabolite nodes, corresponding to six different edge types: drug node-drug node, drug node-enzyme node, drug node-metabolite node, enzyme node-enzyme node, enzyme node-metabolite node, and metabolite node-metabolite node. Different attenuation factors are assigned to these six edge types. 1~ 6. Solve for the Katz matrix:

[0018] ,

[0019] In this matrix P, each element represents the higher-order proximity between the corresponding nodes, k represents the k-th order proximity, and t belongs to 1~6, representing the decay factor. Values ​​are assigned based on the different types of edges. This represents the product of β for each type and the edge of the corresponding type. The value of is obtained through a dynamic adaptive weighting mechanism, specifically, by defining learnable weight coefficients for six different edge types:

[0020] ,

[0021] The weight coefficients are randomly assigned during initialization and optimized through gradient backpropagation during training; the softmax function is used to convert the weight coefficients into normalized dynamic decay factors. Ensure that the sum of the weights of different edge types is 1:

[0022] ,

[0023] Matrix P is transformed into the following form using singular value decomposition:

[0024] ,

[0025] ,

[0026]

[0027] ,

[0028] ,

[0029] ,

[0030] where, are singular values of matrix P, and are columns of matrices U and V respectively, is a node topology feature matrix, , , represent the topology feature matrix of drugs, metabolic enzymes and metabolic products respectively, and the topology feature vector of the drug-metabolite pair composed of the last gth drug and the last qth metabolic product is spliced by the corresponding node topology features:

[0031] ;

[0032] The attribute feature embedding of drug and metabolic product molecules obtained by the improved GNN method includes: using molecular fingerprints as the initial attribute vectors of drug nodes and metabolic product nodes, generating sequence embedding vectors as the initial attribute vectors of metabolic enzyme nodes by encoding protein sequences, and mapping each initial attribute vector to the same dimension.

[0033] The improved GNN method refers to adding the capture of global features to the heterogeneous network G to realize message passing. The specific method is to add a supernode S connected with the remaining nodes in the graph G, and the initial features of the supernode S and the remaining nodes in the graph G are aggregated from the initial features of each node in the graph G:

[0034] ,

[0035] where, denotes the node set in G, denotes the number of nodes in G, denotes the ith node in G, corresponds to the initial feature of in the feature matrix;

[0036] The process of calculating the attribute features based on the improved GNN is as follows:

[0037] In the lth layer, for the target node ​, aggregate all its neighbors' messages:

[0038] ,

[0039] where, denotes the node the message vector after aggregation at the l-th layer, () is the aggregation function, denotes the neighbor set of

[0040] Meanwhile, in the l-th layer, for a supernode S, aggregate the messages from the rest of the nodes in the graph:

[0041] ,

[0042] When updating the features of S, combine the messages from S itself and from the rest of the nodes:

[0043] ,

[0044] where, () denotes the update function;

[0045] When updating the target node , aggregate the messages from itself, from its neighbors, and from the supernodes:

[0046] ,

[0047] After multi-layer message passing and updating, the final attribute feature matrix is obtained; the attribute feature vector of the drug-metabolite pair composed of the g-th drug and the q-th metabolite is obtained by concatenating the corresponding node attribute features:

[0048] ;

[0049] S5, predicting the drug-metabolite relationship to obtain possible drug metabolites, specifically:

[0050] After obtaining the topological feature vector and the attribute feature vector of the drug-metabolite pair, two different MLPs are used to predict the relationship score of the drug-metabolite pair:

[0051] ,

[0052] where, denotes the relationship score of the drug-metabolite pair, It is a parameter used to balance the contribution of the two features; for a specific drug, the k metabolites with the highest relationship scores with the drug are used as the final prediction results of its metabolites.

[0053] S6. Train the parameters required for obtaining topological feature embeddings and attribute feature embeddings from the three-dimensional heterogeneous network G in S4 and S5, as well as for predicting drug-metabolite relationships from features. The training process uses multi-task collaborative loss, and the total loss function is:

[0054] ,

[0055] in, To use the prediction of drug-metabolite relationships as the primary task and the prediction of drug-metabolizing enzyme and enzyme-metabolite relationships as auxiliary tasks, the loss function is... For balance coefficient, The embedding consistency regularization loss functions are as follows:

[0056] ,

[0057] ,

[0058] Where BCE represents the binary cross-entropy loss, Used to adjust the weight of auxiliary tasks. and These represent the predicted and actual values ​​of the drug-metabolite relationship, respectively. and These represent the predicted and actual values ​​of the drug-metabolizing enzyme relationship, respectively. and These represent the predicted and actual values ​​of the metabolite-metabolite enzyme relationship, respectively. express Divergence; after meeting the set training conditions, a well-trained relation prediction model is obtained, and the well-trained relation prediction model is used to predict the metabolites of the target drug.

[0059] Furthermore, when constructing network G in S3, the target drug is included in the network. However, since the relationship between the drug and metabolic enzymes and metabolites is unknown, the initial network G only contains drug-drug similarity matrices. The corresponding value for the drug can be calculated, and the corresponding value for the drug in the other matrices DM and DE should be 0. Then, training steps S4, S5, and S6 are performed. In step S6, when calculating the loss, only the known drug-metabolite, drug-metabolic enzyme, and enzyme-metabolite associations in the heterogeneous network are considered, and unknown associations are not considered. Then, the trained relationship prediction model is used to predict the metabolites of the target drug.

[0060] Further, the public database described in S1 is the human metabolome database (HMDB) and DrugBank.

[0061] Further, the method of constructing the drug-drug similarity matrix and the metabolite-metabolite similarity matrix by calculating the similarity based on the chemical structure in S2 . The method is:

[0062] For given two proteins a and b, define And The cosine similarity is used to represent the sequence similarity Sim between two proteins sec (a, b):

[0063] ,

[0064] The similarity matrix is constructed by calculating the similarity of the protein residue sequence of the metabolic enzyme

[0065] The beneficial effects of the present application are:

[0066] 1) The present application first designs a method for constructing a drug-metabolic enzyme-metabolite three-dimensional heterogeneous network from public databases DrugBank and HMDB, constructs a drug-drug similarity matrix and a metabolite-metabolite similarity matrix by calculating the similarity of the chemical structure, constructs a metabolic enzyme-metabolic enzyme similarity matrix by calculating the protein sequence similarity, and obtains the heterogeneous network by combining the known drug-metabolic enzyme, metabolic enzyme-metabolite, and drug-metabolite associations.

[0067] 2) In the three-dimensional heterogeneous network, the matrix decomposition-based method is used to extract the topological relationship between nodes to obtain the final topological embedding of the nodes, the improved GNN method is used to extract the attribute relationship between nodes to obtain the final attribute embedding of the nodes, the loss function is constructed by multi-task collaborative loss and embedding consistency regularization, and finally the relationship between drugs and metabolites is predicted by the final embedding of the drugs and metabolites. The k metabolites with the highest relationship score with a drug are used as the final prediction result of the metabolites of the drug. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 is a drug metabolite prediction flowchart based on a three-dimensional heterogeneous network;

[0069] Figure 2 is a schematic diagram of a drug-metabolic enzyme-metabolite three-dimensional heterogeneous network;

[0070] Figure 3 is a schematic diagram in which a supernode S is added to the three-dimensional heterogeneous network. DETAILED DESCRIPTION

[0071] For the purpose of the present application, the technical solutions and advantages are more clearly and explicitly described below, combined with the drawings, to further describe the specific embodiments of the present application.

[0072] The present application mainly includes the following steps: data acquisition, construction of three-dimensional heterogeneous network, embedding of drug and metabolite node topological features and attribute features, and drug metabolite prediction. The overall process is shown in Figure 1 The specific steps are as follows:

[0073] 1. Acquisition of drug, metabolic enzyme, and metabolite information:

[0074] The human metabolome database (HMDB) and DrugBank provide comprehensive human-confirmed known metabolite and drug information. HMDB provides comprehensive reference information about the human metabolome, and the name, chemical formula, chemical structure, and other information of the corresponding metabolite can be found in HMDB according to the unique HMDB ID. According to the database, if the concentration of the metabolite changes after the intake of the drug, it is considered that the metabolite has a relationship with the drug. Similarly, known drug-metabolic enzyme relationships and known metabolite-metabolic enzyme relationships can be obtained from the database. DrugBank is the most comprehensive network resource about drugs, and in DrugBank, the name, chemical formula, chemical structure, and other biochemical information of the corresponding drug can be found according to the unique DrugBank ID.

[0075] 2. Construction of three-dimensional heterogeneous network:

[0076] Drug similarity matrix and metabolite similarity matrix based on chemical structure: the present application calculates the metabolite similarity based on molecular chemical structure through molecular fingerprint and Kubota similarity coefficient. Molecular fingerprint is a simplification of the chemical information contained in any chemical entity through binary carrier, which can represent the structural information of metabolites and drugs. The fingerprints of metabolites and drugs are obtained from the software PaDEL Descriptor with default parameters. PaDEL Descriptor generates molecular descriptors by calculating the physicochemical properties of molecular structure. It can calculate various properties of molecules, such as octanol-water partition coefficient, solubility, polar surface area, molecular volume, bond length, bond angle, number of heteroatoms, etc. Given two molecules i and j, and respectively represent the molecular fingerprints of molecules i and j. The structural similarity Sim str (i, j) of molecules i and j is defined as follows:

[0077]

[0078] Drug similarity matrix can be constructed by calculating the similarity based on chemical structure Metabolite similarity matrix .

[0079] Metabolic enzyme similarity matrix based on protein residue sequence: The present application calculates the metabolic enzyme similarity based on the primary structure of the protein by the protein residue sequence and the cosine similarity of the metabolic enzyme. Protein residue sequence is the basic unit sequence that constitutes protein, with specific chemical properties and functions, and its arrangement order determines the structure and function of protein. Evolutionary Scale Modeling (ESM) is a model that uses deep learning technology to predict protein structure and function. Its core idea is to regard protein sequence as a language, and each amino acid as a character, and then use an autoregressive neural network (such as Transformer) to learn the statistical rules of this language. By inputting the protein sequence into ESM, its embedding representation can be obtained. Given two proteins a and b, and respectively represent the embedding representation of their sequences, and cosine similarity is used in this paper to represent the sequence similarity Sim sec (a, b):

[0080]

[0081] Metabolic enzyme similarity matrix can be constructed by calculating the metabolic enzyme similarity based on protein residue sequence .

[0082] After obtaining the drug similarity, metabolic enzyme similarity and metabolite similarity matrices, for each matrix, the top five nodes with the largest similarity are retained for each node, and the similarity of the remaining nodes is set to 0 to reduce the computational cost. Finally, combined with the known drug-metabolic enzyme association matrix DE, drug-metabolite association matrix DM and metabolic enzyme-metabolite association matrix EM, we can obtain the drug-metabolic enzyme-metabolite three-dimensional heterogeneous network G as shown in Figure 2

[0083]

[0084] where if drug c and metabolic enzyme d have known association, ; otherwise 0. denotes the transpose of DE, and DM and EM are the same.

[0085] 3. Obtain the topological feature embedding of drug and metabolite nodes based on matrix decomposition:

[0086] ​In the three-dimensional heterogeneous network G, the present application adopts a matrix decomposition-based method to obtain the topological feature embedding of the drug node and the metabolite node. Specifically as follows:

[0087] First, the high-order proximity of the nodes is calculated. In the present application, the Katz index is used to measure the high-order proximity. The Katz index is the weighted sum of all paths between nodes in the network, which can effectively reflect the topological properties of the heterogeneous network. The Katz index is calculated by the following formula:

[0088]

[0089] wherein is a decay factor that determines the decay rate of the path weight with the increase of the path length. Each element of the matrix P represents the high-order proximity between the corresponding nodes, and k represents the kth-order proximity, = .

[0090] In formula (4), the decay factor β between all edges is set to the same value when calculating the Katz index. In consideration of the specific circumstances of the present application, there are three different nodes and six different edges in the three-dimensional heterogeneous network. Therefore, the present application introduces different decay factors for the edges between different types of nodes. Specifically, the present application sets different decay factors for the six different edges of drug node-drug node, drug node-metabolic enzyme node, drug node-metabolite node, metabolic enzyme node-metabolic enzyme node, metabolic enzyme node-metabolite node, and metabolite node-metabolite node. 1~ 6. The Katz matrix is calculated by the following formula:

[0091]

[0092] wherein t belongs to 1~6, indicating the decay factor is valued according to the different types of edges, is obtained by the following dynamic adaptive weight mechanism, indicates that each type of β is multiplied by the corresponding type of edge.

[0093] Learnable weight coefficients are defined for the six types of edges in the three-dimensional heterogeneous network:

[0094]

[0095] These coefficients are randomly assigned (for example, sampled from a uniform distribution or a normal distribution) at the initialization of the model, and are optimized through gradient backpropagation during the training process. The weight coefficients are converted into normalized dynamic decay factors by the softmax function, ensuring that the total weight of different edge types is 1:

[0096]

[0097] Subsequently, the matrix P can be converted into the following form by singular value decomposition:

[0098]

[0099] wherein, ,

[0100] The node topology feature matrix :

[0101]

[0102]

[0103]

[0104] wherein, } are singular values of the matrix P, } and } are columns of the matrices U and V respectively, is the node topology feature matrix, , , represent the topology feature matrices of drugs, metabolic enzymes and metabolic products respectively. Finally, the topology feature vector of the drug-metabolite pair composed of the gth drug and the qth metabolic product is spliced by the corresponding node topology features:

[0105] 4. Obtain the attribute feature embedding of the drug and metabolic product nodes based on the improved GNN method:

[0106] In the three-dimensional heterogeneous network G, the drug, metabolic enzyme and metabolic product nodes not only contain topological relationships, but also have rich attribute information (such as drug molecular structure, metabolic product chemical properties, metabolic enzyme protein sequence, etc.). In order to effectively fuse node attributes and network structure, the present application proposes an improved graph neural network (Graph Neural Network, GNN) framework, which realizes comprehensive aggregation of node attributes by increasing global feature capture. The specific steps are as follows:

[0107] First, obtain the initial attribute feature matrix of the nodes. The molecular fingerprint generated based on PaDELDescriptor is used as the initial attribute vector of the drug node and the metabolic product node. The protein sequence is encoded by the evolutionary scale model (ESM) to generate a sequence embedding vector as the initial attribute vector of the metabolic enzyme node. Map each initial attribute vector to the same dimension.

[0108] Then in Figure G, the message passing and updating is performed by the improved GNN. The traditional CNN captures local features from adjacent nodes in the message passing and updating stage, and the present application adds the capture of global features to the heterogeneous network G to achieve more comprehensive message passing. The specific method is to add a supernode S to the graph G and connect it with the remaining nodes in the graph, as shown in Figure 3 The initial features of S are aggregated from the initial features of each node in G:

[0109]

[0110] where denotes the set of nodes in G, denotes the number of nodes in it, denotes the i-th node in it, corresponds to the initial feature of in the feature matrix.

[0111] In the l-th layer, for the target node , aggregate the messages of all its neighbors:

[0112]

[0113] where denotes the message vector of node after aggregation in the l-th layer. () is an aggregation function such as mean, maximum, summation, attention weighting, etc. denotes the neighbor set of .

[0114] At the same time, in the l-th layer, for the supernode S, aggregate the messages of the remaining nodes in the graph:

[0115]

[0116] In updating the features of S, combine the messages from S itself and from the remaining nodes:

[0117]

[0118] where () denotes an update function such as GRU, MLP, etc.

[0119] Then in updating the target node , aggregate the messages from itself, from its neighbors and from the supernode S:

[0120]

[0121] ​The final attribute feature matrix of the drug-metabolite pair is obtained by multi-layer message passing and updating The attribute feature vector of the drug-metabolite pair composed of the gth drug and the qth metabolite is spliced by the corresponding node attribute features:

[0122]

[0123] 5. Final drug-metabolite prediction based on MLP:

[0124] After obtaining the topological feature vector and the attribute feature vector of the drug-metabolite pair, the present application finally uses two different MLPs to predict its score:

[0125]

[0126] wherein represents the relationship score of each drug-metabolite pair, is a parameter for balancing the contribution size of the two features.

[0127] For a specific drug metabolite prediction, first, the drug is included in the three-dimensional heterogeneous network proposed by the present application, then the relationship score of the drug and all metabolites in the heterogeneous network is predicted by using the model proposed by the present application, and the k metabolites with the highest relationship score with the drug are used as the final prediction result of the metabolites of the drug.

[0128] 6. Multi-task collaborative loss:

[0129] The present application uses multi-task collaborative loss for training, introduces drug-metabolizing enzyme and metabolizing enzyme-metabolite correlation prediction as auxiliary tasks to enhance the utilization of metabolizing enzyme information by the model:

[0130]

[0131] wherein is used to adjust the weight of the auxiliary task, and BCE represents the binary cross-entropy loss. and respectively represent the predicted value and the true value of the drug-metabolite relationship, and similarly and respectively represent the predicted value and the true value of the drug-metabolizing enzyme relationship, and respectively represent the predicted value and the true value of the metabolite-metabolizing enzyme relationship.

[0132] In addition, the present application introduces embedding consistency regularization, which forces the topological embedding to be consistent with the attribute embedding Distribution consistency in semantic space:

[0133]

[0134] Wherein KL represents KL divergence, and the final total loss function integrates the above two items:

[0135]

[0136] The application solves the problem of missing key metabolic enzyme information in drug metabolite prediction, and biochemical information such as drug molecules, metabolic enzyme molecules, metabolite molecules and the like is included in the model by calculating the similarity between chemical structures and the similarity between protein sequences, and the topological embedding representation of the node is obtained by the method based on matrix decomposition, the attribute embedding representation of the node is obtained by improving the GNN method, and is used for final prediction, and the loss function is constructed by combining multi-task cooperative loss and embedding consistency regularization, which effectively improves the comprehensiveness and accuracy of the model.

Claims

1. A method for predicting drug metabolites based on three-dimensional heterogeneous networks, characterized in that, Includes the following steps: S1. Obtain information on drugs, metabolic enzymes, and metabolites from public databases, including the chemical structure of drugs, the chemical structure of metabolites, drug-metabolite relationships, drug-metabolite relationships, and metabolite-metabolite relationships. S2. Based on the obtained information, construct similarity matrices for drug-drug, metabolic enzyme-metabolic enzyme, and metabolite-metabolic product, as well as relationship matrices for drug-metabolic product, drug-metabolic enzyme, and metabolic enzyme-metabolic product, respectively: A drug-drug similarity matrix is ​​constructed by calculating chemical structure similarity. Similarity matrix between metabolites A metabolic enzyme-to-metabolic enzyme similarity matrix was constructed by calculating the similarity of metabolic enzymes based on protein residue sequences. ; Based on the obtained drug-metabolizing enzyme relationship, drug-metabolite relationship, and metabolite-metabolizing enzyme relationship, construct the drug-metabolizing enzyme relationship matrix DE, the drug-metabolite relationship matrix DM, and the metabolite-metabolite relationship matrix EM; If drug c has a known association with metabolic enzyme d, then ,otherwise 0, where This represents the c-th row and d-th column of matrix DE; the incidence matrices DM and EM are obtained in the same way. S3. Construct a three-dimensional heterogeneous network G for drugs, metabolic enzymes, and metabolites based on the obtained similarity matrix and relation matrix: ， S4. Based on the constructed three-dimensional heterogeneous network G, the topological feature embeddings of drug and metabolite molecules are obtained using a matrix factorization-based method, and the attribute feature embeddings of drug and metabolite molecules are obtained using an improved GNN method, specifically: The topological feature embeddings of drug and metabolite molecules are obtained using a matrix factorization-based method. The three-dimensional heterogeneous network G includes three different types of nodes: drug nodes, enzyme nodes, and metabolite nodes, corresponding to six different edge types: drug node-drug node, drug node-enzyme node, drug node-metabolite node, enzyme node-enzyme node, enzyme node-metabolite node, and metabolite node-metabolite node. Different attenuation factors are assigned to these six edge types. 1~ 6. Solve for the Katz matrix: ， In this matrix P, each element represents the higher-order proximity between the corresponding nodes, k represents the k-th order proximity, and t belongs to 1~6, representing the decay factor. Values ​​are assigned based on the different types of edges. This represents the product of β for each type and the edge of the corresponding type. The value of is obtained through a dynamic adaptive weighting mechanism, specifically, by defining learnable weight coefficients for six different edge types: ， The weight coefficients are randomly assigned during initialization and optimized through gradient backpropagation during training; the softmax function is used to convert the weight coefficients into normalized dynamic decay factors. Ensure that the sum of the weights of different edge types is 1: ， Matrix P is transformed into the following form using singular value decomposition: ， ， ， ， ， ， in,{ } are the singular values ​​of matrix P, { }and{ } are the columns of matrices U and V, respectively. It is the node topology feature matrix. , , The topological feature matrices represent the drug, metabolic enzyme, and metabolite, respectively. Finally, the topological feature vector of the drug-metabolite pair, consisting of the g-th drug and the q-th metabolite, is formed by concatenating the corresponding node topological features. ； The improved GNN method is used to obtain the attribute feature embedding of drug and metabolite molecules. This includes using molecular fingerprints as the initial attribute vectors of drug nodes and metabolite nodes, encoding protein sequences to generate sequence embedding vectors as the initial attribute vectors of metabolic enzyme nodes, and mapping each initial attribute vector to the same dimension. The improved GNN method refers to adding global feature capture to a heterogeneous network G to achieve message passing. Specifically, this involves adding a supernode S to the graph G and connecting it to the other nodes in the graph, using initial features... It is derived from the aggregation of the initial features of each node in G: ， in, Represents the set of nodes in G. This represents the number of nodes in G. This represents the i-th node in G. In the corresponding feature matrix Initial characteristics; The process of calculating attribute features based on the improved GNN is as follows: In the l-th layer, for the target node It aggregates messages from all its neighbors: ， in, Represents a node The message vector aggregated at layer l, () is an aggregate function. express The set of neighbors; Meanwhile, in layer l, for supernode S, the messages of the other nodes in the aggregate graph are: ， When updating the characteristics of S, combine the messages from S itself and from the other nodes: ， in, () represents the update function; At the target node During the update, messages from itself, from its neighbors, and from the supernode are aggregated simultaneously: ， The final attribute feature matrix is ​​obtained after multi-layer message passing and updating. Finally, the attribute feature vector of the drug-metabolite pair consisting of the g-th drug and the q-th metabolite is formed by concatenating the corresponding node attribute features: ； S5. Predicting drug-metabolite relationships to obtain possible drug metabolites, specifically: Obtain the topological feature vector of the drug-metabolite pair and attribute feature vector Subsequently, two different MLPs were used to predict the relationship scores of drug-metabolite pairs: ， in, The score represents the relationship between drug-metabolite pairs. It is a parameter used to balance the contribution of the two features; for a given drug, the k metabolites with the highest relationship scores with the drug are used as the final prediction results of its metabolites. S6. Train the parameters required for obtaining topological feature embeddings and attribute feature embeddings from the three-dimensional heterogeneous network G in S4 and S5, as well as for predicting drug-metabolite relationships from features. The training process uses multi-task collaborative loss, and the total loss function is: ， in, To use the prediction of drug-metabolite relationships as the primary task and the prediction of drug-metabolizing enzyme and enzyme-metabolite relationships as auxiliary tasks, the loss function is... For balance coefficient, The embedding consistency regularization loss functions are as follows: ， ， Where BCE represents the binary cross-entropy loss, Used to adjust the weight of auxiliary tasks. and These represent the predicted and actual values ​​of the drug-metabolite relationship, respectively. and These represent the predicted and actual values ​​of the drug-metabolizing enzyme relationship, respectively. and These represent the predicted and actual values ​​of the metabolite-metabolite enzyme relationship, respectively. express Divergence; after meeting the set training conditions, a well-trained relation prediction model is obtained, and the well-trained relation prediction model is used to predict the metabolites of the target drug.

2. The method for predicting drug metabolites based on three-dimensional heterogeneous networks according to claim 1, characterized in that, While constructing the three-dimensional heterogeneous network G in S3, the target drug to be predicted is incorporated into this network G. Since the relationship between the target drug and metabolic enzymes and metabolites is unknown, the initial network G only contains drug-drug similarity matrices. The corresponding value of the target drug in the matrix is ​​0, and the corresponding value of the target drug in the other matrices DM and DE is 0. Then, the training steps S4, S5 and S6 are performed. In S6, when calculating the loss, only the known drug-metabolite, drug-metabolic enzyme and metabolite-metabolite associations in the heterogeneous network are considered. Unknown associations are not considered. Then, the trained relationship prediction model is used to predict the metabolites of the target drug.

3. The method for predicting drug metabolites based on three-dimensional heterogeneous networks according to claim 1, characterized in that, The publicly available databases mentioned in S1 are the Human Metabolomics Database (HMDB) and DrugBank.

4. The method for predicting drug metabolites based on three-dimensional heterogeneous networks according to claim 1, characterized in that, In S2, a drug-drug similarity matrix is ​​constructed by calculating chemical structure similarity. Similarity matrix between metabolites The method is: Given two proteins a and b, define and Let Sim be the embedding representation of their sequences, and let cosine similarity be used to represent the sequence similarity between the two proteins. sec (a, b): ， A similarity matrix is ​​constructed by calculating the similarity of metabolic enzymes based on protein residue sequences.

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