Cooperative drug prediction method based on hypergraph

Abstract

The application discloses a kind of based on hypergraph collaborative drug prediction method, belong to drug collaborative combination prediction technical field.The method first constructs hypergraph according to the relationship between drug combination and cell line;Second, learn drug characteristics using hypergraph node encoder;Then learn cell line characteristics using hypergraph hyperedge encoder;Then the two features learned are input into hypergraph decoder to reconstruct hypergraph to calculate loss to learn optimal features;Finally, the learned features are calculated Hadamard product to carry out link prediction.The application can improve the accuracy of collaborative drug combination prediction without using any drug and cell line characteristics, and help to open a new vision for the field of drug collaborative combination prediction technology.

Description

TECHNICAL FIELD

[0001] The application discloses a supergraph-based collaborative drug prediction method and belongs to the technical field of drug collaborative combination prediction. BACKGROUND

[0002] Single drug therapy indeed plays an important role in the treatment of many diseases. However, single drug therapy is often subject to the double constraints of drug resistance and limited efficacy when facing complex diseases, and it is difficult to meet the clinical needs. Therefore, combination drug therapy has gradually become an important strategy, through the synergistic effect of multiple drugs, not only can improve the efficacy, but also can reduce the side effects and drug resistance risk caused by single drug to a certain extent. However, how to identify drug combinations with synergistic effect is still a great challenge. Although comprehensive clinical experiments can verify the effectiveness of drug combinations, the high cost, time-consuming process and large experimental scale make it difficult to realize in actual operation. Therefore, it is urgent to develop efficient and accurate drug combination prediction methods to assist scientists and clinicians to make faster and more scientific decisions in drug development and treatment plan optimization.

[0003] With the development of machine learning and deep learning, algorithms for predicting synergistic drug combinations have emerged and shown certain potential. Current methods usually rely on specific feature selection processes, for example, drug features can be represented by SMILES (Simplified molecular input line entry specification) to generate molecular graphs or fingerprint features, or based on the physical and chemical properties of drugs to extract descriptors; cell line features are mainly based on gene expression data. Subsequently, these features are input into the model to predict the synergistic effect of drug combinations. For example, DeepSynergy uses drug fingerprints generated by jCompoundMapper, physical and chemical properties calculated by ChemoPy and binary toxic features as drug inputs, uses gene expression profiles to represent cell line features, and simulates the synergistic effect between drugs through a conical layer. MatchMaker uses drug chemical descriptors calculated by ChemoPy and gene expression features, and learns the representation of drugs in specific cell lines through two parallel sub-networks.

[0004] However, such methods still have shortcomings in application. First, they are too dependent on feature selection, and the performance of the model is highly dependent on the quality and completeness of the selected features. Once a drug or cell line feature is missing, it is difficult for the model to predict synergistic drug combinations, resulting in limited generalization. Second, these methods mainly focus on the relationship between features and ignore the intrinsic correlation between cell lines and drug pairs. However, this correlation is essentially a kind of graph structure information, which can more comprehensively reflect the complex interactions between cell lines and drug pairs. If this correlation relationship can be constructed as a graph structure and combined with existing methods, it is expected to significantly enhance the model's ability to capture synergy, thereby further improving the accuracy and robustness of the prediction. Summary of the Invention

[0005] The purpose of the present invention is to provide a hypergraph-based synergistic drug prediction method, which aims to solve the technical problem that it is difficult to effectively identify drug combinations with synergistic effects when multiple drugs act synergistically.

[0006] To achieve the above objectives, the technical solution of the present invention is: a hypergraph-based synergistic drug prediction method, which specifically comprises the following steps:

[0007] Step 1: Based on the relationship between drug combinations and cell lines, a hypergraph is constructed with drug pairs as nodes and cell lines as hyperedges.

[0008] Step 2: Use the hypergraph node encoder to extract drug features;

[0009] Step 3: Use the hypergraph hyperedge encoder to extract cell line features;

[0010] Step 4: Input drug features and cell line features into the hypergraph decoder, reconstruct the hypergraph and calculate the loss function to learn the optimal drug features and cell line features;

[0011] Step 5: Perform link prediction based on the learned optimal drug features and cell line features.

[0012] The Step 1 is specifically as follows:

[0013] Step 1.1: Read the synergistic drug dataset and obtain the triples of (drug 1, drug 2, cell line) and the corresponding synergistic and non-synergistic labels. The synergistic and non-synergistic labels are the results of the drug combination analysis model based on the preset threshold. The synergistic class is considered to be greater than the preset threshold, and the non-synergistic class is considered to be less than or equal to the preset threshold.

[0014] Step 1.2: Treat the triplet (drug 1, drug 2, cell line) as a binary pair (drug pair, cell line) and construct the association matrix H∈R of the hypergraph G N×C, where N is the number of drug pairs, C is the number of cell lines, and the columns are regarded as hyperedges and the rows as nodes;

[0015] Step 1.3: Randomly select a preset proportion of positive samples and the same number of negative samples in the hypergraph, use the combination of positive and negative samples as the training set and clear them to zero in the hypergraph.

[0016] The Step 2 is specifically as follows:

[0017] Step 2.1: Map the incidence matrix H of the hypergraph to the latent space Calculated by the following formula:

[0018]

[0019] Among them, W v and b v are the learned weights and biases;

[0020] Step 2.2: Get the mean μ through the linear module v and variance σ v , calculated by the following formula:

[0021]

[0022] in, and are two learnable weights, and It is a deviation;

[0023] Step 2.3: Reparameterize to get the final drug pair representation Z v , calculated by the following formula:

[0024] Z v =μ v +σ v ⊙∈

[0025] in, represents the generation of random values ​​from a standard normal distribution, and ⊙ represents the element-wise product.

[0026] The Step 3 is specifically as follows:

[0027] Step 3.1: Map the incidence matrix H of the hypergraph to the latent space Calculated by the following formula:

[0028]

[0029] Where T represents the matrix transpose operation, W E and b E are the learned weights and biases;

[0030] Step3.2: Obtain the mean value μ by linear module E and variance σ E , which are calculated by the following formula:

[0031]

[0032] wherein, and are two learnable weights, and are biases;

[0033] Step3.3: Re-parameterization to obtain the final cell line representation Z E , which is calculated by the following formula:

[0034] Z E = μ E + σ E ⊙ ∈

[0035] wherein, ⊙ represents element-wise multiplication.

[0036] The Step4 is specifically:

[0037] Step4.1: Using the extracted drug features and cell line features, reconstruct the hypergraph G re , which is calculated by the following formula:

[0038] G re = Sigmoid(Z v (Z E ) T )

[0039] wherein, Sigmoid is an activation function, and T represents a matrix transposition operation;

[0040] Step4.2: Calculate the binary cross-entropy loss of the reconstructed graph and the original hypergraph , which is calculated by the following formula:

[0041]

[0042] wherein, BCE represents a binary cross-entropy function, and the specific form is:

[0043]

[0044] wherein, x i represents the predicted value of the i-th sample after the reconstruction of the hypergraph; y i represents the true value of the i-th sample of the hypergraph;

[0045] Step4.3: Calculate the KL divergence loss of drugs and cell lines, which is calculated by the following formula:

[0046]

[0047] wherein, represents the KL divergence of drugs, represents the KL divergence of cell lines, and represents the variance and mean of the i-th drug, and represents the variance and mean of the i-th cell line, represents the expected value.

[0048] Step4.3: Add the binary cross-entropy loss and the KL divergence loss to obtain the total loss, which is calculated by the following formula:

[0049]

[0050] wherein, is the total loss.

[0051] The Step5 is specifically:

[0052] Step5.1: Based on the final representation of drugs and cell lines obtained by training and wherein d is the embedding dimension, for each pair of links (a, b), the link feature is calculated using Hadamard product which is calculated by the following formula:

[0053] f a,b = e a ⊙ e b

[0054] wherein e a represents the embedding vector of drug a, e b represents the embedding vector of cell line b.

[0055] Step5.2: Use the link feature to train the classifier based on the gradient boosting tree model, aiming to minimize the loss function of the binary classification task which is calculated by the following formula:

[0056]

[0057] wherein M is the number of training samples, y i is the true value of the i-th sample, is the prediction probability of the i-th sample by the model.

[0058] The beneficial effects of the present application are: firstly, the present application constructs a hypergraph according to the relationship between the drug combination and the cell line; secondly, the drug features are learned using a hypergraph node encoder; then the cell line features are learned using a hypergraph hyperedge encoder; then the two learned features are input into a hypergraph decoder to reconstruct the hypergraph to calculate the loss to learn the optimal features; finally, the learned features are calculated Hadamard product for link prediction. Compared with the traditional method, the method proposed by the present application can improve the accuracy of collaborative drug combination prediction without using any drug and cell line features, which helps to open a new vision for the field of drug combination prediction technology. BRIEF DESCRIPTION OF DRAWINGS

[0059] Figure 1 is the overall framework diagram of the present application;

[0060] Figure 2 is a flowchart of link prediction of the present application. DETAILED DESCRIPTION

[0061] The present application will be further described below in combination with the drawings and specific embodiments.

[0062] Example 1: as shown, a collaborative drug prediction method based on hypergraph, the method steps are as follows: Figure 1

[0063] Step1: according to the relationship between drug combination and cell line, taking drug pair as node and cell line as hyperedge, a hypergraph is constructed.

[0064] as shown in Figure 1 (a), specifically:

[0065] Step1.1: read in the collaborative drug data set in CSV format to obtain the triplets of (drug 1, drug 2, cell line) and the corresponding collaborative and non-collaborative labels. The collaborative and non-collaborative labels are the results of the Loewe additivity model divided by 30 as the threshold, greater than 30 is considered as collaborative, and less than or equal to 30 is considered as non-collaborative.

[0066] Step1.2: (drug 1, drug 2, cell line) triplets are regarded as (drug pair, cell line) binary groups, and are constructed as the association matrix H∈R N×C of hypergraph G. Where N is the number of drug pairs, C is the number of cell lines, and the column is taken as the hyperedge and the row is taken as the node.

[0067] Step1.3: randomly select 20% of the positive samples in the hypergraph and the same number of negative samples, combine the positive and negative samples as the training set and clear the hypergraph.

[0068] Step2: use the hypergraph node encoder to extract drug features.​

[0069] like Figure 1 (b), specifically:

[0070] Step 2.1: Map the incidence matrix H of the hypergraph to the latent space Calculated by the following formula:

[0071]

[0072] Among them, W v and b v are the learned weights and biases;

[0073] Step 2.2: Get the mean μ through the linear module v and variance σ v , calculated by the following formula:

[0074]

[0075] in, and are two learnable weights, and It is a deviation;

[0076] Step 2.3: Reparameterize to get the final drug pair representation Z v , calculated by the following formula:

[0077] Z v =μ v +σ v ⊙∈

[0078] in, represents the generation of random values ​​from a standard normal distribution, and ⊙ represents the element-wise product.

[0079] Step 3: Use the hypergraph hyperedge encoder to extract cell line features.

[0080] like Figure 1 (c), specifically:

[0081] Step 3.1: Map the incidence matrix H of the hypergraph to the latent space Calculated by the following formula:

[0082]

[0083] Where T represents the matrix transpose operation, W E and b E are the learned weights and biases;

[0084] Step 3.2: Get the mean μ through the linear module Eand variance σ E is calculated by the following formula:

[0085]

[0086] wherein, and are two learnable weights, and are biases;

[0087] Step 3.3: Re-parameterization to obtain the final cell line representation Z E is calculated by the following formula:

[0088] Z E = μ E + σ E ⊙ ∈

[0089] wherein, ⊙ represents element-wise multiplication.

[0090] Step 4: Input drug features and cell line features into the hypergraph decoder, reconstruct the hypergraph and calculate the loss function to learn the optimal drug features and cell line features.

[0091] As shown in Figure 1 (d), specifically:

[0092] Step 4.1: Using the extracted drug features and cell line features, reconstruct the hypergraph G re is calculated by the following formula:

[0093] G re = Sigmoid(Z v (Z E ) T )

[0094] wherein, Sigmoid is an activation function, and T represents a matrix transpose operation;

[0095] Step 4.2: Calculate the binary cross-entropy loss between the reconstructed graph and the original hypergraph is calculated by the following formula:

[0096]

[0097] wherein, BCE represents the binary cross-entropy function, and the specific form is:

[0098]

[0099] wherein, x i represents the predicted value of the i-th sample after reconstructing the hypergraph; y i represents the true value of the i-th sample of the hypergraph;

[0100] Step4.3: Calculate the KL divergence loss of drugs and cell lines, which is calculated by the following formula:

[0101]

[0102] where, denotes the KL divergence of drugs, denotes the KL divergence of cell lines, and denotes the variance and mean of the i-th drug, and denotes the variance and mean of the i-th cell line, denotes the expected value.

[0103] Step4.3: Add the binary cross-entropy loss and the KL divergence loss to get the total loss, which is calculated by the following formula:

[0104]

[0105] where, is the total loss.

[0106] Step5: According to the learned optimal drug features and cell line features, link prediction is performed.

[0107] As shown in Figure 2 , specifically:

[0108] Step5.1: Based on the final representation of drugs and cell lines obtained by training and where d is the embedding dimension, taking the value of 100, for each pair of links (a, b), the link feature is calculated using the Hadamard product which is calculated by the following formula:

[0109] f a,b = e a ⊙e b

[0110] where e a denotes the embedding vector of drug a, e b denotes the embedding vector of cell line b.

[0111] Step5.2: Use the link feature to train the classifier based on the gradient boosting tree model, the goal is to minimize the loss function of the binary classification task which is calculated by the following formula:

[0112]

[0113] where M is the number of training samples, y i is the true value of the i-th sample, is the predicted probability of the i-th sample by the model.

[0114] To test the effectiveness of the present application, it was applied to the O'Neil dataset. In this embodiment, 37 drugs and 31 cell lines were collected from the O'Neil dataset, with 546 samples in each cell line, a total of 16,926 samples, including 1,622 positive samples and 15,304 negative samples.

[0115] To evaluate the performance of the model, the model was compared with two classic machine learning methods: decision tree and random forest.

[0116] In the O'Neil dataset, all data were randomly divided into training set and test set, using 80% of the data for training and the remaining 20% of the data for testing. Then, the model hyperparameters were optimized using five-fold cross-validation on the training set. The final result was the average result of five-fold cross-validation.

[0117] The gradient boosting tree model was selected as the base learner used in the experiment, and the early stopping strategy was used. To comprehensively evaluate the performance of the model proposed in the present application and all comparison methods, a variety of classification performance indicators were selected, including the area under the receiver operating characteristic curve (AUC), AUPR (area under the precision-recall curve), and precision. These indicators can reflect the prediction ability and generalization performance of the model from different angles. The specific calculation methods are as follows:

[0118]

[0119] where, represents the true positive rate, represents the false positive rate. P represents the precision, and R represents the recall. TP and FP represent the number of true positive cases and the number of false positive cases, respectively.

[0120] The results in Table 1 show that the present application achieved the best classification results in all cases of the three evaluation indicators. The bolded part in Table 1 is the optimal result.

[0121] Table 1 Comparison of experimental results

[0122]

[0123]

[0124] In summary, after comparing with other prediction methods, the effectiveness of the supergraph-based collaborative drug prediction method was proved.

[0125] The specific embodiments of the present application are described above with reference to the accompanying drawings, but the present application is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present application.

Claims

1. A hypergraph-based synergistic drug prediction method, characterized in that: The steps include: Step 1: Based on the relationship between drug combinations and cell lines, a hypergraph is constructed with drug pairs as nodes and cell lines as hyperedges. Step 2: Use the hypergraph node encoder to extract drug features; Step 3: Use the hypergraph hyperedge encoder to extract cell line features; Step 4: Input drug features and cell line features into the hypergraph decoder, reconstruct the hypergraph and calculate the loss function to learn the optimal drug features and cell line features; Step 5: Perform link prediction based on the learned optimal drug features and cell line features; The Step 4 is specifically as follows: Step 4.1: Use the extracted drug features and cell line features to reconstruct the hypergraph , calculated by the following formula: ； in, is the activation function, T represents the matrix transpose operation; Step 4.2: Calculate the binary cross entropy loss between the reconstructed graph and the original hypergraph , calculated by the following formula: ； Among them, BCE represents the binary cross entropy function, which is in the form of: ； in, represents the predicted value of the i-th sample after reconstructing the hypergraph; represents the true value of the i-th sample in the hypergraph; Step 4.3: Calculate the KL divergence loss of drugs and cell lines using the following formula: ； ； in, represents the KL divergence of the drug, represents the KL divergence of the cell line, and represents the variance and mean of the i-th drug, and represents the variance and mean of the ith cell line, Indicates expected value; Step 4.3: Binary Cross Entropy Loss Add the KL divergence loss to get the total loss, which is calculated as follows: ； in, For the total loss.

2. The hypergraph-based synergistic drug prediction method according to claim 1, characterized in that: The Step 1 is specifically as follows: Step 1.1: Read the synergistic drug dataset and obtain the triples of (drug 1, drug 2, cell line) and the corresponding synergistic and non-synergistic labels. The synergistic and non-synergistic labels are the results of the drug combination analysis model based on the preset threshold. Values ​​greater than the preset threshold are considered synergistic, and values ​​less than or equal to the preset threshold are considered non-synergistic. Step 1.2: Treat the (drug 1, drug 2, cell line) triple as a (drug pair, cell line) binary and construct the association matrix of the hypergraph G , where N is the number of drug pairs, C is the number of cell lines, and the columns are regarded as hyperedges and the rows as nodes; Step 1.3: Randomly select a preset proportion of positive samples and the same number of negative samples in the hypergraph, use the combination of positive and negative samples as the training set and clear them to zero in the hypergraph.

3. The hypergraph-based collaborative drug prediction method according to claim 1, characterized in that: The Step 2 is specifically as follows: Step 2.1: Map the incidence matrix H of the hypergraph to the latent space , calculated by the following formula: ； in, and are the learned weights and biases; Step 2.2: Get the mean through the linear module and variance , calculated by the following formula: ； ； in, and are two learnable weights, and It is a deviation; Step 2.3: Reparameterize to get the final drug pair representation , calculated by the following formula: ； in, , which means generating random values ​​from a standard normal distribution, Represents element-wise product.

4. The hypergraph-based synergistic drug prediction method according to claim 1, characterized in that: The Step 3 is specifically as follows: Step 3.1: Map the incidence matrix H of the hypergraph to the latent space , calculated by the following formula: ； Where T represents the matrix transpose operation, and are the learned weights and biases; Step 3.2: Get the mean through the linear module and variance , calculated by the following formula: ； ； in, and are two learnable weights, and It is a deviation; Step 3.3: Reparameterize to obtain the final cell line representation , calculated by the following formula: ； in, , Represents element-wise product.

5. The hypergraph-based collaborative drug prediction method according to claim 1, characterized in that: The Step 5 is specifically as follows: Step 5.1: Final representation of drugs and cell lines based on training and , where d is the embedding dimension, for each pair of links (a, b), the link feature is calculated using the Hadamard product , calculated by the following formula: ； in, represents the embedding vector of drug a, represents the embedding vector of cell line b; Step 5.2: Use the link features to train the classifier based on the gradient boosting tree model, with the goal of minimizing the loss function of the binary classification task , calculated by the following formula: ； Where M is the number of training samples, is the true value of the i-th sample, is the predicted probability of the model for the i-th sample.

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