A drug reaction prediction method based on a multi-source heterogeneous network

Abstract

The present application relates to a kind of drug reaction prediction methods based on multi-source heterogeneous network, comprising: extracting the structural features of drug, constructs drug structure similarity matrix, introduces drug physical and chemical property information and constructs drug physical and chemical property similarity matrix, drug structure similarity, physical and chemical property similarity matrix and synergistic drug matrix are fused to obtain drug similarity fusion matrix, constructs three cell line similarity matrix and adopts nuclear fusion strategy and is fused to obtain cell line similarity fusion matrix;Based on drug similarity fusion matrix, cell line similarity fusion matrix and drug-cell line association matrix, construct heterogeneous network, and extract drug embedding features and cell line embedding features from it, reconstruct drug-cell line association matrix, realize prediction.The present application introduces drug physical and chemical property information and drug synergistic information, enriches the features of drug, solves the problem of highly sparse chemical descriptor and molecular fingerprint feature vector.

Description

Technical Field

[0001] This invention relates to the field of drug analysis technology, and in particular to a method for predicting drug response based on multi-source heterogeneous networks. Background Technology

[0002] Cancer is a complex and heterogeneous disease, and different cancer patients may respond differently to cancer treatment due to their different genomic characteristics. Therefore, identifying drug responses in different cell lines can guide drug designers to design personalized treatments for patients, which is also the goal of precision medicine research in cancer. With the continuous development of pharmacogenomics, a wealth of genomic data has been generated, including somatic mutation data, copy number aberration data, methylation data, and hundreds of drug sensitivity and resistance data for different cancer cell lines. This data provides rich information for building computational models, which can utilize multi-omics data to predict the effects of drugs on different cancer cell lines. To date, several computational models for predicting anticancer drug responses have been proposed, which can be divided into two main categories from a methodological perspective. The first is a network-driven approach, which analyzes information extracted from drug similarity and cancer cell line similarity. The core idea of ​​this type of approach is to construct a similarity-based model and assign the sensitivity distribution of known drugs to new anticancer drugs under conditions of structural similarity. However, network-driven methods often exhibit poor scalability and low computational efficiency. Machine learning-based methods are another computational analysis approach for directly exploring large-scale drug and cancer cell line atlases. The typical steps of this approach are: ① Extracting initial cell line features from data such as gene expression, somatic mutations, copy number variations, or methylation data; ② Extracting initial drug structural features from chemical descriptors, molecular fingerprints, or SMILES; ③ Constructing a drug-cell line heterogeneous network; ④ Extracting cell line and drug features from the drug-cell line heterogeneous network using matrix factorization, convolutional neural networks, or graph convolutional neural networks; ⑤ Predicting drug-cell line associations based on cell line and drug features.

[0003] Existing methods for drug feature extraction only consider chemical descriptors, molecular fingerprints, or SMLES. While chemical descriptors and molecular fingerprints are used in drug discovery and drug similarity search, the feature vectors of chemical descriptors and molecular fingerprints corresponding to drugs are usually highly sparse. This can lead to overfitting risks and reduce model interpretability, and the computational cost of highly sparse feature vectors is also very high. While directly inputting SMILES into a convolutional neural network to obtain drug representations solves the problem of highly sparse feature vectors, even slight differences in SMILES can correspond to completely different molecules, making drug features obtained directly from SMILES very fragile. Furthermore, existing methods typically extract structural features of drugs using molecular fingerprints. While molecular fingerprints can help us quickly describe and represent the structure of drug molecules, they cannot completely describe the structural features of the entire drug molecule. This results in the loss of some structural features, preventing the model from capturing global features of the molecule.

[0004] Current research indicates that similar drugs exhibit similar inhibitory effects on similar cell lines, a significant breakthrough in drug research that reveals the close relationship between drugs and cells. However, when studying the characteristics of drugs and cell lines, most existing methods extract drug and cell line features separately, without considering the interplay between these features. The interaction between drugs and cell lines is complex and diverse, with inhibitory effects influenced by various factors such as the drug's chemical structure, cell line gene expression, and metabolic pathways. Simply extracting features independently without considering these factors can lead to information loss, misleading conclusions, and an inability to fully understand the drug's mechanism of action or accurately predict its effects. Since data such as gene expression, somatic mutations, copy number variations, or methylation are often used when considering cell line characteristics, feature fusion is often necessary after extracting features from multiple data sources. However, existing methods typically use averaging to fuse features, which not only leads to information ambiguity but also fails to account for the correlations between different features. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a drug response prediction method based on multi-source heterogeneous networks, thus solving the deficiencies of existing methods.

[0006] The objective of this invention is achieved through the following technical solution: a drug response prediction method based on multi-source heterogeneous networks, the prediction method comprising:

[0007] Step 1: Extract the structural features of the drug using a multi-layer stacked graph convolutional network combined with a multi-head attention mechanism, construct a drug structure similarity matrix, introduce drug physicochemical property information to construct a drug physicochemical property similarity matrix, and use an iterative fusion strategy to fuse the drug structure similarity, physicochemical property similarity matrix and the synergistic drug matrix to obtain a drug similarity fusion matrix. Based on the gene expression, copy number variation and somatic mutation data of the cell line, construct three cell line similarity matrices respectively, and use a kernel fusion strategy to fuse them to obtain a cell line similarity fusion matrix.

[0008] Step 2: Construct a heterogeneous network based on the drug similarity fusion matrix, cell line similarity fusion matrix, and drug-cell line association matrix, and extract drug embedding features and cell line embedding features from it;

[0009] Step 3: Calculate the Pearson correlation coefficient between drug embedding features and cell line embedding features, reconstruct the drug-cell line association matrix, and fill in the missing values ​​of the input drug-cell line association matrix with the reconstructed drug-cell line association matrix to achieve prediction of unknown drug response.

[0010] The method of extracting structural features of drugs using multi-layered stacked graph convolutional networks combined with multi-head attention mechanisms includes the following:

[0011] The SMILES of the drug molecule are used to generate a two-dimensional undirected graph G = (V, E) corresponding to the drug molecule, where V is the set of nodes, E is the set of edges, and N = |V| represents the total number of nodes.

[0012] Given an adjacency matrix A with G. struct The network, through This represents the hierarchical propagation rules of GCN, where, It is the embedding matrix of the l-th layer nodes, F is the feature dimension, and D is the embedding matrix of the l-th layer nodes. struct =diag(∑ j (A struct ) ij ) is A struct The degree matrix, Let be the trainable weight matrix of the l-th layer, and σ(·) be the non-linear activation function;

[0013] An L-layer GCN is deployed on a two-dimensional undirected graph G of drug molecules to learn low-dimensional representations of multiple drug atom nodes. These low-dimensional representations are then fused using a multi-head attention mechanism, generating an attention weight matrix for each of the K attention heads in each GCN layer. The attention weight matrix is ​​given by the formula We obtained, among which, This represents the weight value corresponding to the i-th row and j-th column of the weight matrix for the k-th attention head in layer l. This represents the feature vector of the i-th node obtained from the (l-1)-th layer of the GCN, where T represents the transpose operation. Let A be the weight matrix, LeakyReLU(·) and softmax(·) represent the LeakyReLU activation function and the softmax function, respectively, and mask((A struct ) ij ) is a mask matrix used to preserve the final node features obtained by fusing multi-head attention in graph G;

[0014] Update formula based on node features Node features are obtained by fusing attention weights. Let be the weight matrix corresponding to the k-th attention head in the l-th layer. The Aggregate() function aggregates the features of the nodes according to the attention weights.

[0015] By concatenating the node features processed by all attention heads in layer l, we obtain the final node features of layer l. in, Let l be the node feature matrix of the l-th layer. Let L be the multi-head fusion parameter matrix of the L-th layer, and concat(·) be the concatenation function. By iterating sequentially, the output of the L-th layer is finally obtained. That is, the structural characteristics of the drug.

[0016] The step one, which involves constructing a drug structure similarity matrix based on drug structural features, includes the following:

[0017] The drug structure feature matrix is ​​converted into feature vectors using a degree-weighted fusion method. in, For drug d i F-dimensional eigenvectors, Representative drug d i The structural feature matrix, Representative drug d i The i-th row vector of the structural feature matrix is ​​the feature vector of the i-th node in the graph, d(i) is the degree of the i-th node in the two-dimensional undirected graph, and N is the total number of nodes in the two-dimensional undirected graph.

[0018] For drug d i and drug d j In other words, by calculating its corresponding eigenvector and The cosine similarity is used to obtain the drug d. i and drug d j The structural similarity between them is used to construct a drug structure similarity matrix. Among them, (S) struct ) ij Represents the similarity matrix S structThe value of the element in the i-th row and j-th column of the vector is given by cos(·), where cos(·) represents the cosine function, · represents the vector dot product, * represents the multiplication operation, and |||| represents the Euclidean norm of the vector.

[0019] The process involves introducing drug physicochemical property information to construct a drug physicochemical property similarity matrix. An iterative fusion strategy is then used to fuse the drug structure similarity, physicochemical property similarity matrix, and synergistic drug matrix to obtain a drug similarity fusion matrix, which includes the following:

[0020] Experimental water solubility data, hydration free energy data, lipophilicity data, and drug target affinity data of drug molecules were collected from the Deepchem dataset. All data values ​​were normalized to [0, 1] to obtain the molecular attribute vector of the i-th drug. Furthermore, by calculating the cosine similarity between the molecular attribute vectors of different drugs, the physicochemical property similarity between different drugs is obtained, thereby constructing a drug physicochemical property similarity matrix. Among them, (S) attr ) ij Represents the similarity matrix S attr The value of the element in the i-th row and j-th column; and They represent drug d respectively i and drug d j Molecular property vectors;

[0021] Introducing drug synergistic information, using matrix S syner It means that (S) syner ) ij Indicator drug d i and drug d j Does a synergistic effect exist between them? If so, then (S syner ) ij =1, otherwise (S syner ) ij =0;

[0022] Through similarity matrix fusion method To fuse the drug structure similarity matrix S struct , Drug physicochemical property similarity matrix S attr Drug synergy matrix S syner Where k = struct, attr, syner, v takes the values ​​of struct, attr, or syner, and k takes the other two values ​​besides v. 0<λ k <1 is a parameter for measuring different similarity matrices, and t is the number of iterations;

[0023] Define a diagonal matrix D k,fusion D k,fusionThe i-th element on the diagonal is S k Let the sum of the elements in the i-th row be... To reduce the impact of high-weight nodes on the overall system, Convert to

[0024] Since 0 < λ k <1, while S' k ∈[-1,1], therefore And thus obtain This represents the similarity matrix after convergence;

[0025] Finally, the drug similarity fusion matrix was obtained. A v A is a diagonal matrix. v The i-th diagonal element is The i-th diagonal element.

[0026] The gene expression, copy number variation, and somatic mutation data based on cell lines were used to construct three cell line similarity matrices, which were then fused using a nuclear fusion strategy to obtain a cell line similarity fusion matrix, which includes the following:

[0027] Through formula Calculate the Gaussian regularized representations of gene expression, copy number variation, and somatic mutation, respectively, using expr. i μ represents a column vector representing the expression values ​​of genes, copy number variations, or somatic mutations of the i-th cell line across all cell lines. i and σ i represents the mean and standard deviation of the expression abundance of the gene, copy number variation or somatic mutation of the i-th cell line in all cell lines, respectively;

[0028] Through formula Calculate the similarity of gene expression in cell lines, the similarity of copy number variation, and the similarity of somatic mutations, respectively. ij This represents the numerical similarity between the i-th cell line and the j-th cell line in gene expression, copy number variation, or somatic mutation. Let represent the gene expression, copy number variation, or somatic mutation vector of the i-th cell line, and ε be the scale hyperparameter. Based on the calculated cell line gene expression similarity, copy number variation similarity, and somatic mutation similarity values, the cell line gene expression similarity matrix, copy number variation similarity matrix, and somatic mutation similarity matrix are obtained, respectively.

[0029] Using cell line gene expression similarity matrices, copy number aberration similarity matrices, and somatic mutation similarity matrices, respectively, through formulas... and Calculate the global kernel matrix and the local kernel matrix. The global kernel matrix G measures the distribution of omics similarity across the entire network, while the local kernel matrix L measures the similarity information transmitted within a certain distance. E ij This is the similarity between cell line i and cell line j based on specific omics data, where d(i) represents the degree of the i-th node, C is the total number of cell lines, N(i) represents the set of neighboring nodes of the i-th node, Jaccard(·) represents the Jaccard function, and N i It is a proximity parameter, representing the top N cells most similar to the i-th cell line. i A collection of cell lines;

[0030] The global nuclear matrix GG, copy number variation, and somatic mutation are calculated based on the formula for calculating the global nuclear matrix G. The local nuclear matrix GL, copy number variation, and somatic mutation are calculated based on the formula for calculating the local nuclear matrix L.

[0031] Let GG0 = GG, CG0 = CG, MG0 = MG. The global kernel matrix is ​​iteratively updated starting from t = 1. Finally, the cell line similarity fusion matrix is ​​constructed as follows:

[0032] The construction of heterogeneous networks based on drug similarity fusion matrix, cell line similarity fusion matrix, and drug-cell line association matrix includes the following:

[0033] Introduce a matrix To store cell line similarity and drug similarity information, SD is the drug similarity fusion matrix, and SC is the cell line similarity fusion matrix;

[0034] Data from the GDSC database were binarized using the logarithmic IC50 value to form the drug-cell line association matrix (DC). response ij Threshold represents the logarithmic IC50 value of the i-th drug in the j-th cell. j This represents the sensitivity threshold of the i-th drug;

[0035] Add drug-cell line association matrix DC to matrix R S This process involves updating the network to form a heterogeneous network consisting of a drug similarity network, a cell line similarity network, and a drug-cell line association network.

[0036] The extracted drug embedding features and cell line embedding features include the following:

[0037] Drug and cell line characteristics were initially extracted using two GCNs, and their stratified propagation was... , This represents the input to the l-th layer of the GCN network used to extract drug features. This represents the output of layer l, which is also the input of layer l+1. This represents the input to the l-th layer of the GCN network used to extract cell line features. This represents the output of the l-th layer, which is also the input of the (l+1)-th layer. σ(·) is the non-linear activation function, and D... S-DC For R S-DC The degree matrix, and It is a trainable weight matrix;

[0038] The initial feature matrices obtained from the two GCN processes are obtained. and Among them, X drug The initial feature matrix of the drug, vector For the initial characteristics corresponding to the i-th drug, X cell The initial feature matrix of the cell line, vector For the initial features corresponding to the i-th cell line, M and C are the total number of drugs and the total number of cell lines, respectively, and P is the initial feature dimension of the drugs and the initial feature dimension of the cell lines.

[0039] Drug embedding and cell line embedding are learned using two GATs. The inputs to the two GATs are respectively and The attention coefficients between the i-th drug and the j-th drug, and between the i-th cell line and the j-th cell line are respectively and W drug and W cell It is a parameter matrix, proj drug (·) is the projection function: R M×M →R, proj cell (·) is the projection function: R C×C →R;

[0040] Attention coefficient and Normalization yields and N(d i ) is drug d i The set of neighboring nodes, N(c i ) is cell line c i The set of neighboring nodes;

[0041] Therefore, the output characteristics of the i-th drug and the j-th cell line are obtained as follows: and and For the fusion weight matrix;

[0042] Finally, the drug embedding features and cell line embedding features are respectively and

[0043] The calculation of the Pearson correlation coefficient between drug embedding features and cell line embedding features, and the reconstruction of the drug-cell line association matrix, includes the following:

[0044] pass Calculate vectors The mean, through Calculate vectors The mean of the features, where P is the dimension of the feature vector. and These represent the k-th elements of the i-th drug embedding feature vector and the j-th cell line embedding feature vector, respectively;

[0045] pass Calculate vectors The standard deviation, through Calculate vectors Standard deviation;

[0046] pass Calculate vectors and The covariance between them is finally determined by... Calculate the Pearson correlation coefficient. and These are the P-dimensional feature vectors of the i-th drug and the j-th cell line, respectively;

[0047] pass and To activate the output, x∈[-1,1]. The scaling parameter is x, which is a function variable. max(x) and min(x) represent the maximum and minimum values ​​of variable x in the interval [-1, 1], respectively. The drug-cell line association matrix is ​​then reconstructed as follows:

[0048] During iterative training, a binary cross-entropy loss function is used. Minimize the reconstructed drug-cell line association matrix The error between the original drug-cell line association matrix DC and the original drug-cell line association matrix DC, where M and C represent the total number of drugs and cell lines, respectively, and ln(·) represents the logarithmic error. e (·) is a function.

[0049] This invention offers the following advantages: a drug response prediction method based on multi-source heterogeneous networks introduces drug physicochemical properties and synergistic information, enriching drug characteristics and solving the problem of highly sparse chemical descriptors and molecular fingerprint feature vectors. It describes drug similarity from multiple perspectives, including chemical properties, chemical structure, and synergistic effects. A multi-layered stacked graph convolutional network combined with a multi-head attention mechanism is used to extract drug structural features, overcoming the limitation that molecular fingerprints cannot fully describe the structural features of the entire drug molecule, leading to the loss of some structural features. This captures the global structural features of the drug. A matrix iterative fusion strategy is employed to construct a drug similarity fusion matrix, and a global kernel matrix and a local kernel matrix are used to construct a cell line similarity fusion matrix, fully considering the correlation between different features. The drug-cell line association matrix is ​​reconstructed by calculating the Pearson correlation coefficient between drug embedding features and cell line embedding features, improving the model's stability. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application provided below with reference to the accompanying drawings is not intended to limit the scope of protection of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The present invention will be further described below with reference to the accompanying drawings.

[0052] This invention relates to a drug response prediction method based on multi-source heterogeneous networks. Firstly, it overcomes the high sparsity of drug chemical descriptors and molecular fingerprint feature vectors by introducing drug physicochemical properties and synergistic information. Secondly, it utilizes multi-layered stacked graph convolutional networks combined with multi-head attention mechanisms to extract drug structural features, overcoming the limitation that molecular fingerprints cannot fully describe the structural features of the entire drug molecule, leading to the loss of some structural features. Thirdly, when fusing drug similarity matrices, an iterative matrix fusion algorithm is used, ensuring that each similarity matrix not only retains its own information but also acquires additional information from other similarity matrices. When fusing cell line similarity matrices, a global kernel matrix and a local kernel matrix are introduced to extract information from global node feature similarity, node... This paper considers the global and local similarity between nodes from multiple perspectives, including node connection density, nearest neighbor local node feature similarity, and node nearest neighbor similarity, overcoming the shortcomings of information ambiguity caused by averaging and fusion, and the failure to consider the correlation between different features. Then, a heterogeneous network is constructed based on the drug similarity fusion matrix, cell line similarity fusion matrix, and drug-cell line association matrix. Using a two-layer graph neural network of GCN and GAT, with the drug-cell line association matrix as the feature transmission medium, drug features and cell line features are extracted from the original heterogeneous network, overcoming the problem of not considering the relationship between drug properties, cell line properties, and drug-cell line association. Finally, based on drug embedding features and cell line embedding features, the drug-cell line association matrix is ​​reconstructed by calculating the Pearson correlation coefficient, which improves the stability of the model.

[0053] like Figure 1 As shown, it specifically includes the following:

[0054] 1. Steps for constructing a similarity matrix:

[0055] Step 1: Convert drug molecules into two-dimensional diagrams based on drug SMILES;

[0056] Based on the SMILES of drug molecules, a two-dimensional undirected graph G = (V, E) corresponding to the drug molecules is generated using the RDKit tool, where V is the set of nodes, E is the set of edges, and N = |V| represents the total number of nodes. The adjacency matrix A of graph G is... struct The elements in the array are represented as follows:

[0057]

[0058] Among them, (A) struct ) ij For the adjacency matrix A struct The element corresponding to the i-th row and j-th column in the data, v i Let represent the i-th node in graph G.

[0059] Step 2: Extract drug structural features using a multi-layer graph convolutional network based on an attention mechanism;

[0060] Generic Networks (GCNs) are multi-layered neural network architectures used to learn low-dimensional representations of nodes from graph-structured data. Each layer of a GCN aggregates information about neighbors through direct links in the graph, reconstructing the embeddings as input to the next layer. Specifically, given a corresponding adjacency matrix A... struct In a network like this, the layered propagation rules of GCN can be formulated as follows:

[0061]

[0062] in, Here, D is the embedding matrix of the nodes in the l-th layer, N is the total number of nodes in graph G, and F is the feature dimension; struct =diag(∑ j (A struct ) ij ) is A struct The degree matrix; Let be the trainable weight matrix of the l-th layer; σ(·) is the non-linear activation function.

[0063] To fully learn the structural features of drugs, this invention considers deploying an L-layer GCN on a two-dimensional undirected graph G of the drug molecule to learn low-dimensional representations of multiple drug atom nodes, and then fusing these low-dimensional representations through a multi-head attention mechanism. For each GCN layer with K attention heads, each attention head generates an attention weight matrix. It can be calculated using the following formula:

[0064]

[0065] in, This represents the weight value corresponding to the i-th row and j-th column of the weight matrix for the k-th attention head in the l-th layer; This represents the feature vector of the i-th node obtained from the (l-1)-th layer of the GCN; T represents the transpose operation. Here is the weight matrix; LeakyReLU(·) and softmax(·) represent the LeakyReLU activation function and the softmax function, respectively; mask((A struct ) ij ) is a mask matrix used to preserve the final node features obtained by fusing multi-head attention in graph G.

[0066] The node features are obtained by fusing the attention weights. For the k-th attention head, the node feature update formula is as follows:

[0067]

[0068] in, Let be the weight matrix corresponding to the k-th attention head in the l-th layer; the Aggregate() function aggregates the features of the nodes according to the attention weights; This is the weight matrix.

[0069] By concatenating the node features processed by all attention heads in layer l, the final node features of layer l are obtained as follows:

[0070]

[0071] in, Let L be the node feature matrix of the l-th layer; Let be the multi-head fusion parameter matrix of the l-th layer; concat(·) is the concatenation function. Iterate sequentially until the output of the L-th layer is obtained. That is, the structural characteristics of the drug.

[0072] Step 3: Construct a drug structure similarity matrix based on drug structural features;

[0073] In a two-dimensional undirected graph, the degree of a node reflects its connectivity with other nodes. A higher degree indicates that the node has more edges connecting it to other nodes, meaning it is more central and crucial in the network. Therefore, this invention uses a degree-weighted fusion method to convert the drug structure feature matrix into a feature vector, as shown below:

[0074]

[0075] in, For drug d i F-dimensional eigenvectors; Representative drug d i The structural feature matrix; Representative drug d i The i-th row vector of the structural feature matrix is ​​the feature vector of the i-th node in the graph; d(i) is the degree of the i-th node in the two-dimensional undirected graph (i.e., the sum of the in-degree and out-degree); N is the total number of nodes in the two-dimensional undirected graph.

[0076] For drug d i and drug d j In other words, by calculating its corresponding eigenvector and The cosine similarity is used to obtain the drug d. i and drug d j The structural similarity between them is used to construct the drug structure similarity matrix S. struct As shown below:

[0077]

[0078] Among them, (S)struct ) ij Represents the similarity matrix S struct The value of the element in the i-th row and j-th column of the vector; cos(·) represents the cosine function; · represents the vector dot product operation; * represents the multiplication operation; || represents the Euclidean norm of the vector.

[0079] Step 4: Construct a drug physicochemical property similarity matrix based on molecular attributes;

[0080] To incorporate the physicochemical properties of molecules, experimental water solubility data, hydration free energy in water data, lipophilicity data, and drug target affinity data of drug molecules were collected from the Deepchem dataset. All data values ​​were normalized to [0,1], resulting in the molecular attribute vector for the i-th drug. Furthermore, by calculating the cosine similarity between the molecular attribute vectors of different drugs, the physicochemical property similarity between different drugs is obtained, and a drug physicochemical property similarity matrix S is constructed accordingly. attr As shown below:

[0081]

[0082] Among them, (S) attr ) ij Represents the similarity matrix S attr The value of the element in the i-th row and j-th column; and They represent drug d respectively i and drug d j Molecular property vectors.

[0083] Step 5: Construct the drug similarity fusion matrix;

[0084] Introducing drug synergistic information, using matrix S syner It means that (S) syner ) ij Indicator drug d i and drug d j Does a synergistic effect exist between them? If so, then (S syner ) ij =1, otherwise (S syner ) ij =0. Next, we need to fuse the three drug similarity matrices, namely the drug structure similarity matrix S. struct , Drug physicochemical property similarity matrix S attr Drug synergy matrix S syner In simple terms, we aim to ensure that when fusing similarity matrices, each similarity matrix not only retains its own information but also acquires additional information from other similarity matrices. Therefore, this invention proposes a novel similarity matrix fusion method, as shown in the following equation:

[0085]

[0086] k = struct, attr, syner

[0087] Where v can take the values ​​of "struct, attr, or syner", while k can take the other two values ​​besides v; λ k (0<λ k <1) is a parameter that measures the relative importance of different similarity matrices; t is the number of iterations. This invention addresses the hyperparameter λ. k Sensitivity tests were conducted, and it was found that when λ k The model exhibits optimal performance when the similarity is 0.25; therefore, this invention treats each similarity matrix equally. Define a diagonal matrix D. k,fusion D k,fusion The i-th element on the diagonal is S k Let the sum of the elements in the i-th row be... The purpose of this is to reduce the global impact of nodes with higher weights. The above formula can be generalized as:

[0088]

[0089] Since 0 < λ k <1, while S' k ∈[-1,1], therefore it can be deduced that:

[0090]

[0091]

[0092] Therefore, we can conclude that:

[0093]

[0094] in, This represents the converged similarity matrix. The drug similarity fusion matrix SD is further obtained as follows:

[0095]

[0096] Among them, A v A is a diagonal matrix. v The i-th diagonal element is The i-th diagonal element. Since... The diagonal elements are not necessarily all 1, therefore using Normalize it.

[0097] Step Six: Construct a cell line similarity fusion matrix;

[0098] Cell line similarity can be measured in various ways, such as co-expression, co-variation, and co-mutation. Therefore, this invention utilizes gene expression, copy number variation, and somatic mutation to calculate cell similarity. First, the Gaussian regularized representations of gene expression, copy number variation, and somatic mutation are calculated using the following formulas:

[0099]

[0100] Among them, expr i μ represents a column vector representing the expression values ​​of genes, copy number variations, or somatic mutations of the i-th cell line across all cell lines. i and σ i Let represent the mean and standard deviation of the expression abundance (expression abundance refers to the level of expression of a specific gene or protein in a cell, tissue, or biological sample in biology, reflecting the degree of activity of a specific gene or protein in an organism) of the i-th cell line across all cell lines, respectively. Then, the following formulas are used to calculate the similarity of cell line gene expression, copy number variation, and somatic mutation, respectively:

[0101]

[0102] Among them, E ij This represents the numerical similarity between the i-th cell line and the j-th cell line in gene expression, copy number variation, or somatic mutation. Let represent the gene expression, copy number variation, or somatic mutation vector of the i-th cell line; ε is a scale hyperparameter. Based on the calculated cell line gene expression similarity, copy number variation similarity, and somatic mutation similarity values, the cell line gene expression similarity matrix, copy number variation similarity matrix, and somatic mutation similarity matrix are obtained, respectively.

[0103] To integrate the three omics data from cell lines, the cell line gene expression similarity matrix, copy number aberration similarity matrix, and somatic mutation similarity matrix were used. The global kernel matrix and local kernel matrix were calculated using the following two equations: the global kernel matrix G measures the distribution of omics similarity across the entire network, and the local kernel matrix L measures the similarity information transmitted over a certain distance, as shown below:

[0104]

[0105]

[0106] Among them, E ijd(i) represents the similarity between cell line i and cell line j based on specific omics data; d(i) represents the degree of the i-th node; C is the total number of cell lines; N(i) represents the set of neighboring nodes of the i-th node; Jaccard(·) represents the Jaccard function; N i It is a proximity parameter, representing the top N cells most similar to the i-th cell line. i A set of cell lines. The global kernel matrix considers the global similarity between nodes from two perspectives: global node feature similarity and node connection density, while the local kernel matrix considers the local similarity between nodes from two perspectives: nearest neighbor local node feature similarity and node nearest neighbor similarity.

[0107] Based on the formula for calculating the global kernel matrix G, the global kernel matrix GG for gene expression, the global kernel matrix CG for copy number variation, and the global kernel matrix MG for somatic mutation are calculated respectively. Based on the formula for calculating the local kernel matrix L, the local kernel matrix GL for gene expression, the local kernel matrix CL for copy number variation, and the local kernel matrix ML for somatic mutation are calculated respectively. Let GG0 = GG, CG0 = CG, MG0 = MG, and the global kernel matrix is ​​iteratively updated starting from t = 1 as follows:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114] Where T represents the transpose operation; · represents matrix-vector multiplication; t is the number of iterations; C is the total number of cell lines; (GG t-1 ) i Let represent the i-th row vector corresponding to matrix GG after t-1 iterations. Finally, construct the cell line similarity fusion matrix SC:

[0115]

[0116] 2. Features extraction steps for heterogeneous networks:

[0117] Step 1: Constructing a drug-cell line heterogeneous network;

[0118] Introduce a matrix R S ∈R (M+C)×(M+C) To store cell line similarity and drug similarity information:

[0119]

[0120] Wherein, SD is the drug similarity fusion matrix, and SC is the cell line similarity fusion matrix.

[0121] For data from the GDSC database, the drug-cell line association matrix DC is binarized based on the logarithmic IC50 value:

[0122]

[0123] Among them, response ij Threshold represents the logarithmic IC50 value of the i-th drug in the j-th cell. j This represents the sensitivity threshold of the i-th drug.

[0124] Add drug-cell line association matrix DC to matrix R S This process involves updating the network to form a heterogeneous network R consisting of a drug similarity network, a cell line similarity network, and a drug-cell line association network. S-DC :

[0125]

[0126] Step 2: Extract drug embedding features and cell line embedding features;

[0127] To fully extract heterogeneous network R S-DC Based on the structural information, this invention designs a deep learning module based on GCN and GAT to learn drug feature embeddings and cell line feature embeddings. Two GCNs are used for initial extraction of drug features and cell line features, respectively, and their hierarchical propagation formula is as follows:

[0128]

[0129]

[0130] in, This represents the input to the l-th layer of the GCN network used to extract drug features. This represents the output of the l-th layer, and also the input of the (l+1)-th layer; This represents the input to the l-th layer of the GCN network used to extract cell line features. This represents the output of layer l, which is also the input of layer l+1; σ(·) is the non-linear activation function; D S-DC For R S-DC The degree matrix; and It is a trainable weight matrix. This yields the initial feature matrices obtained from two GCN processing steps. and Among them, X drug The initial feature matrix of the drug, vector The initial characteristics corresponding to the i-th drug; X cell The initial feature matrix of the cell line, vector The initial features correspond to the i-th cell line; M and C represent the total number of drugs and the total number of cell lines, respectively; P represents the initial feature dimensions of the drugs and the initial feature dimensions of the cell lines. The initial input is:

[0131]

[0132]

[0133] After obtaining initial features through GCN processing, this invention learns drug embeddings and cell line embeddings using GAT. The purpose of designing this feature extraction network is based on the idea that similar drugs have similar inhibitory effects on similar cell lines. By leveraging the inhibitory relationship between drugs and cell lines, cell line features are transferred to the drug feature extraction process, and vice versa, thus achieving feature fusion. The inputs to the two GATs are... and The attention coefficients between the i-th drug and the j-th drug, and between the i-th cell line and the j-th cell line, are defined as follows:

[0134]

[0135]

[0136] Among them, W drug and W cell It is a parameter matrix; proj drug (·) is the projection function: R M×M →R, proj cell (·) is the projection function: R C×C →R. Furthermore, this invention addresses the attention coefficient. and Normalization was performed, as shown below:

[0137]

[0138]

[0139] Wherein, N(d) i ) is drug d i The set of neighboring nodes, N(c i ) is cell line c i The set of neighboring nodes; and They can be fully expanded as follows:

[0140]

[0141]

[0142] Among them, a drug and a cell This is the weight vector; and Here, represents the weight matrix; LeakyReLU(·) is the LeakyReLU activation function; || represents the connection operation. Based on this, the output features of the i-th drug and the j-th cell line are obtained as follows:

[0143]

[0144]

[0145] in, and This is the fusion weight matrix.

[0146] After the above operations, the drug embedding feature and the cell line embedding feature are respectively and

[0147] 3. Drug-Cell Line Association Reconstruction Steps: The Pearson correlation coefficient between the i-th drug embedding feature vector and the j-th cell line embedding feature vector can be calculated using the following steps. First, calculate the mean of each vector:

[0148]

[0149]

[0150] Where P is the dimension of the feature vector. and These represent the k-th elements of the i-th drug embedding feature vector and the j-th cell line embedding feature vector, respectively. Then, the standard deviation of each vector is calculated.

[0151]

[0152]

[0153] Next, calculate the vector. and Covariance between:

[0154]

[0155] Finally, the Pearson correlation coefficient can be calculated as follows:

[0156]

[0157] in, and These are the P-dimensional feature vectors of the i-th drug and the j-th cell line, respectively. and They are vectors and The average value. Since the correlation coefficient ranges from [-1, 1], this invention uses the following two equations to activate the output:

[0158]

[0159]

[0160] in, Here, is the scaling parameter, and x is the function variable; max(x) and min(x) represent the maximum and minimum values ​​of the variable x in the interval [-1, 1], respectively. Compared to directly using a linear transformation, suitable parameters... This allows f(x) to have a more suitable gradient in the interval [-1, 1], which promotes model convergence and accelerates parameter updates. Finally, the drug-cell line association matrix can be reconstructed as follows:

[0161]

[0162] During iterative training, it is necessary to minimize the reconstructed drug-cell line association matrix. To determine the error between the original drug-cell line association matrix (DC) and the original drug-cell line association matrix (DC), this invention employs a binary cross entropy loss function, namely:

[0163]

[0164] Where M and C represent the total number of drugs and cell lines, respectively; ln(·) represents log e (·) is a function.

[0165] After the model is trained, the known drug-cell line association matrix is ​​input into the model. After processing, the model will return a reconstructed drug-cell line association matrix. This reconstructed association matrix will fill in the missing values ​​of the input drug-cell line association matrix to achieve the prediction of unknown drug responses.

[0166] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and improvements, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A drug response prediction method based on multi-source heterogeneous networks, characterized in that: The prediction method includes: Step 1: Extract the structural features of the drug using a multi-layer stacked graph convolutional network combined with a multi-head attention mechanism, construct a drug structure similarity matrix, introduce drug physicochemical property information to construct a drug physicochemical property similarity matrix, and use an iterative fusion strategy to fuse the drug structure similarity, physicochemical property similarity matrix and the synergistic drug matrix to obtain a drug similarity fusion matrix. Based on the gene expression, copy number variation and somatic mutation data of the cell line, construct three cell line similarity matrices respectively, and use a kernel fusion strategy to fuse them to obtain a cell line similarity fusion matrix. This includes: collecting experimental water solubility data, water hydration free energy data, lipophilicity data, and drug target affinity data of drug molecules from the Deepchem dataset, normalizing all data values ​​to [0, 1], and obtaining the molecular attribute vector of the i-th drug. Furthermore, by calculating the cosine similarity between the molecular attribute vectors of different drugs, the physicochemical property similarity between different drugs is obtained, thereby constructing a drug physicochemical property similarity matrix. ,in, Represents the similarity matrix The value of the element in the i-th row and j-th column; and They represent drug d respectively i and drug d j Molecular property vectors; Introducing drug synergistic information, in matrix It means that, among them Indicator drug d i and drug d j Does a synergistic effect exist between them? If so, then... ,otherwise ; Step 2: Construct a heterogeneous network based on the drug similarity fusion matrix, cell line similarity fusion matrix, and drug-cell line association matrix, and extract drug embedding features and cell line embedding features from it; Step 3: Calculate the Pearson correlation coefficient between drug embedding features and cell line embedding features, reconstruct the drug-cell line association matrix, and fill in the missing values ​​of the input drug-cell line association matrix with the reconstructed drug-cell line association matrix to achieve prediction of unknown drug response.

2. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The method of extracting structural features of drugs using multi-layered stacked graph convolutional networks combined with multi-head attention mechanisms includes the following: The SMILES of the drug molecule are used to generate a two-dimensional undirected graph G = (V, E) corresponding to the drug molecule, where V is the set of nodes, E is the set of edges, and N = |V| represents the total number of nodes. Given an adjacency matrix G The network, through This represents the hierarchical propagation rules of GCN, where, It is the embedding matrix of the l-th layer nodes, and F is the feature dimension. for The degree matrix, Let L be the trainable weight matrix of the l-th layer. It is a non-linear activation function; An L-layer GCN is deployed on a two-dimensional undirected graph G of drug molecules to learn low-dimensional representations of multiple drug atom nodes. These low-dimensional representations are then fused using a multi-head attention mechanism, generating an attention weight matrix for each of the K attention heads in each GCN layer. The attention weight matrix is ​​given by the formula We obtained, among which, This represents the weight value corresponding to the i-th row and j-th column of the weight matrix for the k-th attention head in layer l. This represents the feature vector of the i-th node obtained from the (l-1)-th layer of the GCN, where T represents the transpose operation. This is the weight matrix. and Represents the LeakyReLU activation function and the softmax function. It is a mask matrix used to preserve the final node features obtained by fusing multi-head attention in graph G; Update formula based on node features Node features are obtained by fusing attention weights. Let be the weight matrix corresponding to the k-th attention head in the l-th layer. The function aggregates node features according to attention weights; By concatenating the node features processed by all attention heads in layer l, we obtain the final node features of layer l. ,in, Let l be the node feature matrix of the l-th layer. Let l be the multi-head fusion parameter matrix of the l-th layer. The concatenation function is iterated sequentially, and the output of the Lth layer is finally obtained. That is, the structural characteristics of a drug.

3. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The step one, which involves constructing a drug structure similarity matrix based on drug structural features, includes the following: The drug structure feature matrix is ​​converted into feature vectors using a degree-weighted fusion method. ,in, For drug d i F-dimensional eigenvectors, Representative drug d i The structural feature matrix, Representative drug d i The i-th row vector of the structural feature matrix is ​​the feature vector of the i-th node in the graph, d(i) is the degree of the i-th node in the two-dimensional undirected graph, and N is the total number of nodes in the two-dimensional undirected graph. For drug d i and drug d j In other words, by calculating its corresponding eigenvector and The cosine similarity is used to obtain the drug d. i and drug d j The structural similarity between them is used to construct a drug structure similarity matrix. ,in, Represents the similarity matrix The value of the element in the i-th row and j-th column. The symbol represents the cosine function, · represents the vector dot product, and * represents multiplication. The Euclidean norm represents a vector.

4. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The process of constructing a drug physicochemical property similarity matrix by introducing drug physicochemical property information and fusing the drug structure similarity, physicochemical property similarity matrix, and synergistic drug matrix using an iterative fusion strategy to obtain a drug similarity fusion matrix also includes the following: Through similarity matrix fusion method To fuse drug structure similarity matrices Drug physicochemical property similarity matrix Drug synergy matrix ,in, v can take the values ​​of struct, attr, or syner, while k can take the other two values ​​besides v. , , , The parameter t is used to measure the different similarity matrices; Define a diagonal matrix , The i-th element on the diagonal is Let the sum of the elements in the i-th row be... To reduce the impact of high-weight nodes on the overall system, Convert to ; because ,and ,therefore , And thus obtain , This represents the similarity matrix after convergence; Finally, the drug similarity fusion matrix was obtained. , It is a diagonal matrix. The i-th diagonal element is The i-th diagonal element.

5. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The gene expression, copy number variation, and somatic mutation data based on cell lines were used to construct three cell line similarity matrices, which were then fused using a nuclear fusion strategy to obtain a cell line similarity fusion matrix, which includes the following: Through formula Calculate the Gaussian regularized representations of gene expression, copy number variation, and somatic mutation, respectively. A column vector representing the expression values ​​of genes, copy number variations, or somatic mutations of the i-th cell line across all cell lines. and represents the mean and standard deviation of the expression abundance of the gene, copy number variation or somatic mutation of the i-th cell line in all cell lines, respectively; Through formula Cell line gene expression similarity, copy number variation similarity, and somatic mutation similarity were calculated separately. This represents the numerical similarity between the i-th cell line and the j-th cell line in gene expression, copy number variation, or somatic mutation. This represents the gene expression, copy number variation, or somatic mutation vector for the i-th cell line. These are scale hyperparameters. Based on the calculated cell line gene expression similarity, copy number variation similarity, and somatic mutation similarity values, the cell line gene expression similarity matrix, copy number variation similarity matrix, and somatic mutation similarity matrix are obtained, respectively. Using cell line gene expression similarity matrices, copy number aberration similarity matrices, and somatic mutation similarity matrices, respectively, through formulas... and The global kernel matrix and local kernel matrix are calculated. The global kernel matrix G measures the distribution of omics similarity across the entire network, while the local kernel matrix L measures the similarity information transmitted within a certain distance. d(i) represents the similarity between cell line i and cell line j based on specific omics data, where d(i) represents the degree of the i-th node, C is the total number of cell lines, and N(i) represents the set of neighboring nodes of the i-th node. This refers to the Jaccard function. It is a proximity parameter, representing the closest similarity to the i-th cell line. A collection of cell lines; The global nuclear matrix GG, copy number variation, and somatic mutation are calculated based on the formula for calculating the global nuclear matrix G. The local nuclear matrix GL, copy number variation, and somatic mutation are calculated based on the formula for calculating the local nuclear matrix L. Let GG0 = GG, CG0 = CG, MG0 = MG. The global kernel matrix is ​​iteratively updated starting from t = 1. Finally, the cell line similarity fusion matrix is ​​constructed as follows: .

6. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The construction of heterogeneous networks based on drug similarity fusion matrix, cell line similarity fusion matrix, and drug-cell line association matrix includes the following: Introduce a matrix To store cell line similarity and drug similarity information, SD is the drug similarity fusion matrix, and SC is the cell line similarity fusion matrix; Data from the GDSC database were binarized using the logarithmic IC50 value to form the drug-cell line association matrix (DC). , This represents the logarithmic IC50 value of the i-th drug in the j-th cell. This represents the sensitivity threshold of the i-th drug; Add drug-cell line association matrix DC to matrix This process involves updating the network to form a heterogeneous network consisting of a drug similarity network, a cell line similarity network, and a drug-cell line association network. .

7. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The extracted drug embedding features and cell line embedding features include the following: Drug and cell line characteristics were initially extracted using two GCNs, and their stratified propagation was... , , This represents the input to the l-th layer of the GCN network used to extract drug features. This represents the output of layer l, which is also the input of layer l+1. This represents the input to the l-th layer of the GCN network used to extract cell line features. This represents the output of layer l, which is also the input of layer l+1. It is a non-linear activation function. for The degree matrix, and It is a trainable weight matrix; The initial feature matrices obtained from the two GCN processes are obtained. and ,in, The initial feature matrix of the drug, vector The initial characteristics corresponding to the i-th drug, The initial feature matrix of the cell line, vector For the initial features corresponding to the i-th cell line, M and C are the total number of drugs and the total number of cell lines, respectively, and P is the initial feature dimension of the drugs and the initial feature dimension of the cell lines. Drug embedding and cell line embedding are learned using two GATs. The inputs to the two GATs are respectively and The attention coefficients between the i-th drug and the j-th drug, and between the i-th cell line and the j-th cell line are respectively and , and It is a parameter matrix. It is the projection function: , It is the projection function: ; Attention coefficient and Normalization yields and , It is drug d i The set of neighboring nodes, It is cell line c i The set of neighboring nodes; Therefore, the output characteristics of the i-th drug and the j-th cell line are obtained as follows: and , and For the fusion weight matrix; Finally, the drug embedding features and cell line embedding features are respectively and .

8. The drug response prediction method based on multi-source heterogeneous networks according to claim 1, characterized in that: The calculation of the Pearson correlation coefficient between drug embedding features and cell line embedding features, and the reconstruction of the drug-cell line association matrix, includes the following: pass Calculate vectors The mean, through Calculate vectors The mean of the features, where P is the dimension of the feature vector. and These represent the k-th elements of the i-th drug embedding feature vector and the j-th cell line embedding feature vector, respectively; pass Calculate vectors The standard deviation, through Calculate vectors Standard deviation; pass Calculate vectors and The covariance between them is finally determined by... Calculate the Pearson correlation coefficient. and These are the P-dimensional feature vectors of the i-th drug and the j-th cell line, respectively; pass and To activate the output, It is the scaling parameter, and x is the function variable. and Let x represent the maximum and minimum values ​​of variable x in the interval [-1, 1], and reconstruct the drug-cell line association matrix as follows: .

9. A drug response prediction method based on multi-source heterogeneous networks according to claim 8, characterized in that: During iterative training, a binary cross-entropy loss function is used. Minimize the reconstructed drug-cell line association matrix The error between the original drug-cell line association matrix DC and the original matrix, where M and C represent the total number of drugs and cell lines, respectively. for That is, a function.

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