Method for spatial domain identification and regulation analysis based on hierarchical graph representation learning

Abstract

This invention discloses a spatial domain identification and regulation analysis method based on hierarchical graph representation learning, belonging to the field of spatial multi-omics data analysis technology. The method first acquires spatial multi-omics data and constructs a gene-protein interaction graph within cells based on prior biological knowledge. After extracting initial node features using a graph convolutional network, a regulation matrix is ​​learned through a cross-graph matching module, and enhanced features are obtained through cross-graph convolution operations. Then, a weighted fusion using an attention mechanism is employed to generate a joint representation of intracellular multi-omics. Subsequently, a spatial and feature proximity graph between cells is constructed, and contextual information is aggregated using a graph attention network to obtain inter-cell multi-omics embedding representations. Finally, graph contrastive learning is used for training and unsupervised clustering to identify spatial domains, and the regulation matrix is ​​aggregated to extract the unique regulatory relationships of specific spatial domains. This invention achieves the correlation analysis between molecular regulation and tissue niche, realizing fine spatial structure division while maintaining biological interpretability.

Description

Technical Field

[0001] This invention relates to the technical field of spatial multi-omics data analysis and computational biology, and in particular to a spatial domain identification and regulation analysis method based on hierarchical graph representation learning. Background Technology

[0002] The spatial distribution of cells is closely linked to the biological functions of tissues, and decoding these microenvironments that form specific physiological structures is key to understanding disease mechanisms. The emergence of spatial multi-omics technologies has made it possible to simultaneously measure genomics and proteomics on the same tissue slice, providing a foundation for exploring complex cell interactions.

[0003] However, existing computational methods have significant drawbacks. These methods rely solely on data-driven clustering to partition spatial domains, overemphasizing the elimination of differences between data modalities while severely neglecting biological interpretability. This limitation results in current techniques rarely revealing the underlying multi-omics regulatory mechanisms driving tissue spatial heterogeneity. Furthermore, existing analyses are often constrained by the extreme sparsity of genomic data and the high noise levels in protein measurements. These unavoidable technical biases severely distort biological signals and undermine the reliability of downstream analyses. The current research challenge lies in how to achieve both high-precision tissue spatial structure partitioning from these flawed multimodal data and simultaneously infer the molecular regulatory logic behind specific spatial domains. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a spatial domain identification and regulation analysis method based on hierarchical graph representation learning. A hierarchical graph representation learning framework is introduced to bridge the gap between spatial domain discovery and the explanation of molecular regulatory mechanisms. This invention utilizes prior biological knowledge to construct molecular interaction networks from an intracellular perspective and learns spatial domain-specific molecular affinities through a cross-graph matching strategy, thereby extracting cross-omics regulatory features.

[0005] The objective of this invention is achieved through the following technical solution: a spatial domain identification and control analysis method based on hierarchical graph representation learning, comprising the following steps:

[0006] S1. Acquire spatial multi-omics data and construct a molecular interaction map within cells, wherein the molecular interaction map includes a gene interaction map and a protein interaction map;

[0007] S2. Use graph convolutional networks to extract features from molecular interaction graphs to obtain initial node features of multi-omics molecules within cells;

[0008] S3. Based on the initial node features, the regulatory matrix of intracellular multi-omics molecules and enhanced node features are obtained through the preset cross-graph matching module.

[0009] S4. Use attention mechanism to weightedly fuse the features of enhanced nodes to generate a multi-omics joint representation within the cell;

[0010] S5. Construct spatial proximity maps and feature proximity maps between cells, and aggregate information from the multi-omics joint representation through a graph attention network to obtain the multi-omics embedding representation between cells.

[0011] S6. Unsupervised clustering of multi-omics embedding representations is performed using graph contrastive learning strategies to identify the spatial domain of organizational structure.

[0012] S7. For each identified spatial domain, construct the aggregation regulation matrix corresponding to the cells within each spatial domain, and extract the regulatory relationship between genes and protein molecules in the spatial domain through permutation test as the result of multi-omics regulation analysis.

[0013] Furthermore, step S1 includes the following steps:

[0014] S11. Constructing a gene interaction graph: Mapping each gene to its associated biological process, and using the Jaccard index to calculate the interaction between two gene nodes. and Functional similarity between :

[0015] ;

[0016] In the formula, and Respectively represent and and A set of related biological terms; if Then at the gene node and Establish connecting edges between them, and conversely, if Then the gene node and No connecting edges are established between them; The preset similarity threshold;

[0017] S12. Construct a protein interaction graph: Extract the interactions between protein molecules from the STRING database. If the confidence score of the interaction is greater than a preset threshold, establish a connection edge between the corresponding protein nodes; otherwise, if the confidence score of the interaction is less than or equal to the preset threshold, do not establish a connection edge between the corresponding protein nodes.

[0018] Furthermore, step S2 includes:

[0019] Learning by applying graph convolutional networks The first molecule The initial node features of the layer, the first Intermediate results of the layer The calculation formula is as follows:

[0020] ;

[0021] In the formula, This represents a symmetric normalized adjacency matrix. This is the adjacency matrix of the molecular interaction graph. For the angle matrix, and These are the weight matrix and bias vector trained in the network, respectively. Represents a non-linear activation function; after all processing by the graph convolutional network, the gene interaction graph... The initial node features of each node are represented as follows: The protein interaction diagram The initial node features of each node are represented as follows: .

[0022] Furthermore, step S3 includes the following steps:

[0023] S31. Design a cross-graph matching module and utilize a control function. The regulatory matrix between the initial node features of the gene interaction graph and the protein interaction graph is evaluated, and the regulatory score is calculated. :

[0024] ;

[0025] In the formula, Represents a cross-omics regulatory matrix The element in represents the first element. The gene node and the first Regulatory fractions between protein nodes; and These represent the first gene interaction in the gene interaction diagram. The node and protein interaction graph of the nth node Initial node characteristics of each node, Represents a non-linear activation function;

[0026] S32. Using a control matrix composed of control scores For each gene interaction graph, the initial node features of the protein interaction graph with the highest regulatory score are found. Simultaneously, for each protein interaction graph, the initial node of the gene interaction graph with the highest regulatory score is found. Cross-graph convolutional feature updates are then performed on each node.

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] In the formula, and These represent the first gene interaction in the updated gene interaction graph. The node and protein interaction graph of the nth node The enhanced node characteristics of each node, Represents the cross-graph feature transformation function. Represents vector concatenation. This represents the update function that projects the object back to its original dimension. In the control matrix China's target The operation involves finding the maximum value of each gene node across all protein nodes. Representatives made The protein node index at which the maximum value is obtained; In the control matrix China's target The operation involves finding the maximum value of a protein node across all gene nodes. Representatives made The gene node index at which the maximum value is obtained.

[0032] Furthermore, step S4 includes the following steps:

[0033] S41. Obtain the interaction diagram of each molecule through linear projection. Graph-level embedding :

[0034] ;

[0035] In the formula, Representing the The enhanced node features of each omics, representing the matrix The Column features, For the total feature dimension, and These are learnable parameters;

[0036] S42, Calculate the first Attention importance score of each omics And attention weights after Softmax normalization :

[0037] ;

[0038] ;

[0039] In the formula, The generation Attention importance score for each omics; A row vector representing learnable parameters; This represents the dot product operation between vectors; Represents the hyperbolic tangent activation function; and These represent the learnable weight matrix and bias vector in the attention mechanism, respectively. Representing the Attention weights for each omics modality; Represented by the natural constant An exponential function with base 0; Represents all The symbol for summing omics modes; The total number of representative omics modes; The summation index variable is used to iterate through all omics modalities; Representing the Attention importance scores for each omics modality;

[0040] S43. Using attention weights, weighted combinations of embeddings at each graph level are performed to obtain a multi-omics joint representation within the cell:

[0041] ;

[0042] In the formula, This represents the combined intracellular multi-omics representation of the final fusion.

[0043] Furthermore, step S5 includes the following steps:

[0044] S51. Constructing a spatial proximity graph and feature neighborhood map The construction rules of the spatial proximity graph depend on the Euclidean distance between cells. If the Euclidean distance is less than or equal to a preset radius threshold, an edge is constructed; if the Euclidean distance is not less than the preset radius threshold, no edge is constructed. The feature proximity graph constructs edges based on the multimodal similarity captured by weighted nearest neighbor analysis.

[0045] S52. A two-layer attention network is used to encode the spatial proximity map and the feature proximity map. The first layer aggregates information along the feature proximity nodes, and the second layer aggregates information along the spatial proximity nodes. In each layer, the first... A cell and its neighboring cells Attention weights The update formulas are as follows:

[0046] ;

[0047] ;

[0048] In the formula, This represents a modified linear unit activation function with leakage; The weight parameters of the single-layer feedforward neural network used to calculate the attention score in the graph attention network are in the transpose of a vector. , and Representing cells respectively Neighboring cells and neighboring nodes Feature input representation; This represents the concatenation operation of vectors; This represents the updated cell obtained after aggregating neighbor information through a graph attention network. Multi-omics embedding representation.

[0049] Furthermore, step S6 includes the following steps:

[0050] S61, For each cell It aggregates the hidden embedding representations of its spatial neighbors and feature-similar neighbors to form positive samples. Simultaneously, the features of all nodes in the spatial proximity graph and feature proximity graph are shuffled, and negative samples are generated after processing by a graph attention network. ;

[0051] S62. Compare the learning loss function using the binary cross-entropy definition graph. :

[0052] ;

[0053] In the formula, Represents the total number of cells in a tissue section; Represents mathematical expectation operation; Represents the natural logarithm function; This is the discriminator function, used to evaluate the probability score of an input node pair being a positive sample pair;

[0054] S63. Perform self-supervised training of the network by minimizing the contrastive learning loss function;

[0055] S64. After the network is trained in a self-supervised manner, unsupervised clustering is performed on the multi-omics embedding representation to achieve the recognition of the spatial domain of the organizational structure.

[0056] Furthermore, step S7 includes the following steps:

[0057] S71. For each spatial domain, average the regulatory matrix of all cells assigned to that spatial domain to construct a aggregation regulatory matrix representing the consistent molecular pattern of that spatial domain.

[0058] S72. Prioritize candidate gene-protein regulatory pairs based on the absolute regulatory fractions in the aggregated regulatory matrix.

[0059] S73. Perform a permutation test on each candidate gene-protein regulatory pair after sorting to screen out gene-protein regulatory pairs specific to this spatial domain.

[0060] A spatial domain identification and control analysis system based on hierarchical graph representation learning, used to implement the aforementioned spatial domain identification and control analysis method based on hierarchical graph representation learning, includes:

[0061] A molecular interaction graph construction module is used to acquire spatial multi-omics data to construct intracellular molecular interaction graphs, including gene interaction graphs and protein interaction graphs.

[0062] The feature extraction module extracts features from the molecular interaction graph using a graph convolutional network to obtain the initial node features of multi-omics molecules within the cell.

[0063] The cross-graph matching module, based on initial node features, obtains the regulatory matrix of intracellular multi-omics molecules and enhanced node features through cross-graph convolution;

[0064] The weighted fusion module weights and fuses the features of enhanced nodes according to the attention mechanism to generate a multi-omics joint representation within the cell;

[0065] The proximity graph construction module builds spatial proximity graphs and feature proximity graphs between cells.

[0066] The information aggregation module aggregates contextual information of the multi-omics joint representation through a graph attention network to obtain multi-omics embedding representations between cells;

[0067] The spatial domain identification module uses a graph contrastive learning strategy to perform unsupervised clustering of multi-omics embedding representations, thereby identifying the spatial domain of the organizational structure.

[0068] The regulatory relationship analysis module constructs a clustered regulatory matrix for each identified spatial domain, corresponding to the cells within each spatial domain, and extracts the regulatory relationships between genes and protein molecules in the spatial domain through permutation tests.

[0069] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0070] 1. This invention designs a hierarchical graph representation learning framework that correlates microscopic molecular regulatory activities with the macroscopic ecological niche of tissues. This framework overcomes the pain point of existing methods that separate spatial domain identification from molecular regulatory analysis, and can more comprehensively analyze spatial domain heterogeneity.

[0071] 2. This invention designs a cross-graph matching module, which realizes bidirectional information flow between genomics and proteomics through cross-graph convolution operations, effectively alleviating the heterogeneity gap between multi-omics data and generating more discriminative cellular multi-omics joint representations.

[0072] 3. This invention enables spatial domain-specific regulatory analysis, giving the regulatory analysis a clear spatial contextual meaning, which is conducive to the discovery of key molecular mechanisms of action in the formation of specific tissue microenvironments.

[0073] In summary, this invention can adaptively extract multi-omics data by constructing a hierarchical graph learning framework that integrates microscopic molecular interactions and macroscopic spatial features. While achieving fine division of tissue spatial domains, it can also reveal the underlying cross-omics regulatory mechanisms that drive the formation of specific spatial domains, effectively balancing the accuracy and biological interpretability of spatial multi-omics analysis. Attached Figure Description

[0074] Figure 1 This is a flowchart of a spatial domain identification and control analysis method based on hierarchical graph representation learning.

[0075] Figure 2 A schematic diagram of intracellular modeling.

[0076] Figure 3 A schematic diagram illustrating intercellular modeling.

[0077] Figure 4 This is a schematic diagram of spatial domain identification and control analysis. Detailed Implementation

[0078] The present invention will be further described below with reference to specific embodiments.

[0079] Example 1

[0080] See Figure 1 As shown, the spatial domain identification and control analysis method based on hierarchical graph representation learning provided in this embodiment includes the following steps:

[0081] S1. Acquire spatial multi-omics data and construct intracellular molecular interaction maps, including gene interaction maps and protein interaction maps, comprising the following steps:

[0082] S11. Constructing a gene interaction graph: Mapping each gene to its associated biological process, and using the Jaccard index to calculate the interaction between two gene nodes. and Functional similarity between :

[0083] ;

[0084] In the formula, and Respectively represent and and A set of related biological terms; if Then at the gene node and Establish connecting edges between them, and conversely, if Then the gene node and No connecting edges are established between them; This is the preset similarity threshold.

[0085] S12. Construct a protein interaction graph: Extract the interactions between protein molecules from the STRING database. If the confidence score of the interaction is greater than a preset threshold, establish a connection edge between the corresponding protein nodes; otherwise, if the confidence score of the interaction is less than or equal to the preset threshold, do not establish a connection edge between the corresponding protein nodes.

[0086] S2. Feature extraction of the molecular interaction graph is performed using a graph convolutional network to obtain the initial node features of multi-omics molecules within the cell, including:

[0087] See Figure 2 As shown, the graph convolutional network is applied to learn the first... The first molecule The initial node features of the layer, the first Intermediate results of the layer The calculation formula is as follows:

[0088] ;

[0089] In the formula, This represents a symmetric normalized adjacency matrix. This is the adjacency matrix of the molecular interaction graph. For the angle matrix, and These are the weight matrix and bias vector trained in the network, respectively. Represents a non-linear activation function; after all processing by the graph convolutional network, the gene interaction graph... The initial node features of each node are represented as follows: The protein interaction diagram The initial node features of each node are represented as follows: .

[0090] S3. Based on the initial node features, the regulatory matrix of intracellular multi-omics molecules and enhanced node features are obtained through a preset cross-graph matching module, including the following steps:

[0091] S31, see also Figure 2 As shown, a cross-graph matching module is designed, utilizing a control function. The regulatory matrix between the initial node features of the gene interaction graph and the protein interaction graph is evaluated, and the regulatory score is calculated. :

[0092] ;

[0093] In the formula, Represents a cross-omics regulatory matrix The element in represents the first element. The gene node and the first Regulatory fractions between protein nodes; and These represent the first gene interaction in the gene interaction diagram. The node and protein interaction graph of the nth node Initial node characteristics of each node, This represents a non-linear activation function.

[0094] S32. Using a control matrix composed of control scores For each gene interaction graph, the initial node features of the protein interaction graph with the highest regulatory score are found. Simultaneously, for each protein interaction graph, the initial node of the gene interaction graph with the highest regulatory score is found. Cross-graph convolutional feature updates are then performed on each node.

[0095] ;

[0096] ;

[0097] ;

[0098] ;

[0099] In the formula, and These represent the first gene interaction in the updated gene interaction graph. The node and protein interaction graph of the nth node The enhanced node characteristics of each node, Represents the cross-graph feature transformation function. Represents vector concatenation. This represents the update function that projects the object back to its original dimension. In the control matrix China's target The operation involves finding the maximum value of each gene node across all protein nodes. Representatives made The protein node index at which the maximum value is obtained; In the control matrix China's target The operation involves finding the maximum value of a protein node across all gene nodes. Representatives made The gene node index at which the maximum value is obtained.

[0100] S4, see also Figure 2 As shown, the process of generating a multi-omics joint representation within a cell by weighted fusion of enhanced node features using an attention mechanism includes the following steps:

[0101] S41. Obtain the interaction diagram of each molecule through linear projection. Graph-level embedding :

[0102] ;

[0103] In the formula, Representing the The enhanced node features of each omics, representing the matrix The Column features, For the total feature dimension, and These are learnable parameters.

[0104] S42, Calculate the first Attention importance score of each omics And attention weights after Softmax normalization :

[0105] ;

[0106] ;

[0107] In the formula, The generation Attention importance score for each omics; A row vector representing learnable parameters; This represents the dot product operation between vectors; Represents the hyperbolic tangent activation function; and These represent the learnable weight matrix and bias vector in the attention mechanism, respectively. Representing the Attention weights for each omics modality; Represented by the natural constant An exponential function with base 0; Represents all The symbol for summing omics modes; The total number of representative omics modes; The summation index variable is used to iterate through all omics modalities; Representing the Attention importance score for each omics modality.

[0108] S43. Using attention weights, weighted combinations of embeddings at each graph level are performed to obtain a multi-omics joint representation within the cell:

[0109] ;

[0110] In the formula, This represents the combined intracellular multi-omics representation of the final fusion.

[0111] S5, see also Figure 3 As shown, constructing spatial proximity maps and feature proximity maps between cells, and aggregating information from the multi-omics joint representation through a graph attention network to obtain the multi-omics embedding representation between cells includes the following steps:

[0112] S51. Constructing a spatial proximity graph and feature neighborhood map The construction rules of the spatial proximity graph depend on the Euclidean distance between cells. If the Euclidean distance is less than or equal to a preset radius threshold, an edge is constructed; if the Euclidean distance is not less than the preset radius threshold, no edge is constructed. The feature proximity graph constructs edges based on the multimodal similarity captured by weighted nearest neighbor analysis.

[0113] S52. A two-layer attention network is used to encode the spatial proximity map and the feature proximity map. The first layer aggregates information along the feature proximity nodes, and the second layer aggregates information along the spatial proximity nodes. In each layer, the first... A cell and its neighboring cells Attention weights The update formulas are as follows:

[0114] ;

[0115] ;

[0116] In the formula, This represents a modified linear unit activation function with leakage; The weight parameters of the single-layer feedforward neural network used to calculate the attention score in the graph attention network are in the transpose of a vector. , and Representing cells respectively Neighboring cells and neighboring nodes Feature input representation; This represents the concatenation operation of vectors; This represents the updated cell obtained after aggregating neighbor information through a graph attention network. Multi-omics embedding representation.

[0117] S6, see also Figure 3 As shown, an unsupervised clustering strategy based on graph contrastive learning is used to identify the spatial domain of organizational structure by performing multi-omics embeddings. This includes the following steps:

[0118] S61, For each cell It aggregates the hidden embedding representations of its spatial neighbors and feature-similar neighbors to form positive samples. Simultaneously, the features of all nodes in the spatial proximity graph and feature proximity graph are shuffled, and negative samples are generated after processing by a graph attention network. .

[0119] S62. Compare the learning loss function using the binary cross-entropy definition graph. :

[0120] ;

[0121] In the formula, Represents the total number of cells in a tissue section; Represents mathematical expectation operation; Represents the natural logarithm function; This is the discriminator function, used to evaluate the probability score of an input node pair being a positive sample pair.

[0122] S63. Perform self-supervised training of the network by minimizing the contrastive learning loss function.

[0123] S64. After the network is trained in a self-supervised manner, unsupervised clustering is performed on the multi-omics embedding representation to achieve the recognition of the spatial domain of the organizational structure.

[0124] S7, see also Figure 4 As shown, for each identified spatial domain, a clustered regulatory matrix corresponding to the cells within each spatial domain is constructed. The regulatory relationships between genes and protein molecules within the spatial domain are extracted using a permutation test, serving as the result of the multi-omics regulatory analysis. This includes the following steps:

[0125] S71. For each spatial domain, average the regulatory matrix of all cells assigned to that spatial domain to construct a aggregation regulatory matrix representing the consistent molecular pattern of that spatial domain.

[0126] S72. Prioritize candidate gene-protein regulatory pairs based on the absolute regulatory fractions in the aggregated regulatory matrix.

[0127] S73. Perform a permutation test on each candidate gene-protein regulatory pair after sorting to screen out gene-protein regulatory pairs specific to this spatial domain.

[0128] This invention constructs a dual-context network from an intercellular perspective, integrating physical spatial proximity and multimodal feature similarity, and achieves consistent segmentation of tissue functional microenvironments through a graph contrastive learning strategy. This method, which unifies microscopic intracellular molecular regulation with the macroscopic tissue spatial environment, not only significantly improves the accuracy and noise resistance of spatial clustering, but also successfully identifies deep gene and protein interaction pathways overlooked by traditional methods. Simultaneously, it effectively elucidates the molecular regulatory mechanisms within complex tissue microenvironments, providing a novel computational method for spatial multi-omics data that combines accuracy and biological interpretability.

[0129] Example 2

[0130] The spatial domain identification and control analysis system based on hierarchical graph representation learning provided in this embodiment is used to implement the spatial domain identification and control analysis method based on hierarchical graph representation learning described in Embodiment 1, including:

[0131] 1) Molecular interaction graph construction module, used to acquire spatial multi-omics data to construct intracellular molecular interaction graphs, including gene interaction graphs and protein interaction graphs.

[0132] 1.1) Constructing a gene interaction graph: Mapping each gene to its associated biological process, and using the Jaccard index to calculate the interaction between two gene nodes. and Functional similarity between :

[0133] ;

[0134] In the formula, and Respectively represent and and A set of related biological terms; if Then at the gene node and Establish connecting edges between them, and conversely, if Then the gene node and No connecting edges are established between them; This is the preset similarity threshold.

[0135] 1.2) Constructing a protein interaction graph: Extract the interactions between protein molecules from the STRING database. If the confidence score of the interaction is greater than a preset threshold, then establish a connection edge between the corresponding protein nodes; otherwise, if the confidence score of the interaction is less than or equal to the preset threshold, then no connection edge is established between the corresponding protein nodes.

[0136] 2) Feature extraction module: Based on the graph convolutional network, feature extraction is performed on the molecular interaction graph to obtain the initial node features of multi-omics molecules in the cell.

[0137] Learning by applying graph convolutional networks The first molecule The initial node features of the layer, the first Intermediate results of the layer The calculation formula is as follows:

[0138] ;

[0139] In the formula, This represents a symmetric normalized adjacency matrix. This is the adjacency matrix of the molecular interaction graph. For the angle matrix, and These are the weight matrix and bias vector trained in the network, respectively. Represents a non-linear activation function; after all processing by the graph convolutional network, the gene interaction graph... The initial node features of each node are represented as follows: The protein interaction diagram The initial node features of each node are represented as follows: .

[0140] 3) Cross-graph matching module: Based on the initial node features, cross-graph convolution is used to obtain the regulatory matrix of intracellular multi-omics molecules and the enhanced node features.

[0141] 3.1) Using the control function The regulatory matrix between the initial node features of the gene interaction graph and the protein interaction graph is evaluated, and the regulatory score is calculated. :

[0142] ;

[0143] In the formula, Represents a cross-omics regulatory matrix The element in represents the first element. The gene node and the first Regulatory fractions between protein nodes; and These represent the first gene interaction in the gene interaction diagram. The node and protein interaction graph of the nth node Initial node characteristics of each node, This represents a non-linear activation function.

[0144] 3.2) Using a control matrix composed of control scores For each gene interaction graph, the initial node features of the protein interaction graph with the highest regulatory score are found. Simultaneously, for each protein interaction graph, the initial node of the gene interaction graph with the highest regulatory score is found. Cross-graph convolutional feature updates are then performed on each node.

[0145] ;

[0146] ;

[0147] ;

[0148] ;

[0149] In the formula, and These represent the first gene interaction in the updated gene interaction graph. The node and protein interaction graph of the nth node The enhanced node characteristics of each node, Represents the cross-graph feature transformation function. Represents vector concatenation. This represents the update function that projects the object back to its original dimension. In the control matrix China's target The operation involves finding the maximum value of each gene node across all protein nodes. Representatives made The protein node index at which the maximum value is obtained; In the control matrix China's target The operation involves finding the maximum value of a protein node across all gene nodes. Representatives made The gene node index at which the maximum value is obtained.

[0150] 4) Weighted fusion module: Based on the attention mechanism, the features of the enhanced nodes are weighted and fused to generate a multi-omics joint representation within the cell.

[0151] 4.1) Obtain the interaction diagram of each molecule through linear projection. Graph-level embedding :

[0152] ;

[0153] In the formula, Representing the The enhanced node features of each omics, representing the matrix The Column features, For the total feature dimension, and These are learnable parameters.

[0154] 4.2) Calculate the first Attention importance score of each omics And attention weights after Softmax normalization :

[0155] ;

[0156] ;

[0157] In the formula, The generation Attention importance score for each omics; A row vector representing learnable parameters; This represents the dot product operation between vectors; Represents the hyperbolic tangent activation function; and These represent the learnable weight matrix and bias vector in the attention mechanism, respectively. Representing the Attention weights for each omics modality; Represented by the natural constant An exponential function with base 0; Represents all The symbol for summing omics modes; The total number of representative omics modes; The summation index variable is used to iterate through all omics modalities; Representing the Attention importance score for each omics modality.

[0158] 4.3) Weighted combination of graph-level embeddings using attention weights to obtain a multi-omics joint representation within the cell:

[0159] ;

[0160] In the formula, This represents the combined intracellular multi-omics representation of the final fusion.

[0161] 5) Proximity graph construction module: Constructs spatial proximity graphs. and feature neighborhood map The construction rules of the spatial proximity graph depend on the Euclidean distance between cells. If the Euclidean distance is less than or equal to a preset radius threshold, an edge is constructed; if the Euclidean distance is not less than the preset radius threshold, no edge is constructed. The feature proximity graph constructs edges based on the multimodal similarity captured by weighted nearest neighbor analysis.

[0162] 6) Information aggregation module: The graph attention network is used to aggregate the contextual information of the multi-omics joint representation to obtain the multi-omics embedding representation between cells.

[0163] A two-layer attention network is used to encode the spatial proximity map and the feature proximity map. The first layer aggregates information along the feature proximity nodes, and the second layer aggregates information along the spatial proximity nodes. In each layer, the first... A cell and its neighboring cells Attention weights The update formulas are as follows:

[0164] ;

[0165] ;

[0166] In the formula, This represents a modified linear unit activation function with leakage; The weight parameters of the single-layer feedforward neural network used to calculate the attention score in the graph attention network are in the transpose of a vector. , and Representing cells respectively Neighboring cells and neighboring nodes Feature input representation; This represents the concatenation operation of vectors; This represents the updated cell obtained after aggregating neighbor information through a graph attention network. Multi-omics embedding representation.

[0167] 7) Spatial domain identification module: It uses graph contrastive learning strategy to perform unsupervised clustering of multi-omics embedding representations to identify the spatial domain of the organizational structure.

[0168] 7.1) For each cell It aggregates the hidden embedding representations of its spatial neighbors and feature-similar neighbors to form positive samples. Simultaneously, the features of all nodes in the spatial proximity graph and feature proximity graph are shuffled, and negative samples are generated after processing by a graph attention network. ;

[0169] 7.2) Compare the learning loss function using the binary cross-entropy definition graph. :

[0170] ;

[0171] In the formula, Represents the total number of cells in a tissue section; Represents mathematical expectation operation; Represents the natural logarithm function; This is the discriminator function, used to evaluate the probability score of an input node pair being a positive sample pair;

[0172] 7.3) Self-supervised training of the network is performed by minimizing the contrastive learning loss function;

[0173] 7.4) After the network is trained in a self-supervised manner, unsupervised clustering is performed on the multi-omics embedding representation to achieve the recognition of the spatial domain of the organizational structure.

[0174] 8) Regulatory relationship analysis module: For each identified spatial domain, construct the aggregated regulatory matrix corresponding to the cells within each spatial domain, and extract the regulatory relationship between genes and protein molecules in the spatial domain through permutation test.

[0175] 8.1) For each spatial domain, average the regulatory matrix of all cells assigned to that spatial domain to construct a aggregation regulatory matrix representing the consistent molecular pattern of that spatial domain;

[0176] 8.2) Prioritize candidate gene-protein regulatory pairs based on the absolute regulatory fractions in the aggregated regulatory matrix;

[0177] 8.3) Perform a permutation test on each candidate gene-protein regulatory pair after sorting to screen out gene-protein regulatory pairs specific to that spatial domain.

[0178] Example 3

[0179] This embodiment discloses a non-transitory computer-readable medium storing instructions that, when executed by a processor, perform the steps of the spatial domain identification and control analysis method based on hierarchical graph representation learning as described in Embodiment 1.

[0180] In this embodiment, the non-transitory computer-readable medium can be a disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), USB flash drive, portable hard drive, etc.

[0181] Example 4

[0182] This embodiment discloses a computing device, including a processor and a memory for storing processor-executable programs. When the processor executes the program stored in the memory, it implements the spatial domain recognition and control analysis method based on hierarchical graph representation learning described in Embodiment 1.

[0183] The computing device described in this embodiment may be a desktop computer, laptop computer, smartphone, PDA handheld terminal, tablet computer, programmable logic controller (PLC), or other terminal device with processor function.

[0184] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Therefore, any changes made in accordance with the shape and principle of the present invention should be covered within the protection scope of the present invention.

Claims

1. A spatial domain identification and control analysis method based on hierarchical graph representation learning, applied to spatial multi-omics data analysis, characterized in that... Includes the following steps: S1. Acquire spatial multi-omics data and construct a molecular interaction map within cells, wherein the molecular interaction map includes a gene interaction map and a protein interaction map; S2. Use graph convolutional networks to extract features from molecular interaction graphs to obtain initial node features of multi-omics molecules within cells; S3. Based on the initial node features, the regulatory matrix of intracellular multi-omics molecules and enhanced node features are obtained through the preset cross-graph matching module. S4. Use attention mechanism to weightedly fuse the features of enhanced nodes to generate a multi-omics joint representation within the cell; S5. Construct spatial proximity maps and feature proximity maps between cells, and aggregate information from the multi-omics joint representation through a graph attention network to obtain the multi-omics embedding representation between cells. S6. Unsupervised clustering of multi-omics embedding representations is performed using graph contrastive learning strategies to identify the spatial domain of organizational structure. S7. For each identified spatial domain, construct the aggregation regulation matrix corresponding to the cells within each spatial domain, and extract the regulatory relationship between genes and protein molecules in the spatial domain through permutation test as the result of multi-omics regulation analysis.

2. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 1, characterized in that, Step S1 includes the following steps: S11. Constructing a gene interaction graph: Mapping each gene to its associated biological process, and using the Jaccard index to calculate the interaction between two gene nodes. and Functional similarity between : ； In the formula, and Respectively represent and and A set of related biological terms; if Then at the gene node and Establish connecting edges between them, and conversely, if Then the gene node and No connecting edges are established between them; The preset similarity threshold; S12. Construct a protein interaction graph: Extract the interactions between protein molecules from the STRING database. If the confidence score of the interaction is greater than a preset threshold, establish a connection edge between the corresponding protein nodes; otherwise, if the confidence score of the interaction is less than or equal to the preset threshold, do not establish a connection edge between the corresponding protein nodes.

3. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 2, characterized in that, Step S2 includes: Learning by applying graph convolutional networks The first molecule The initial node features of the layer, the first Intermediate results of the layer The calculation formula is as follows: ； In the formula, This represents a symmetric normalized adjacency matrix. This is the adjacency matrix of the molecular interaction graph. For the angle matrix, and These are the weight matrix and bias vector trained in the network, respectively. Represents a non-linear activation function; after all processing by the graph convolutional network, the gene interaction graph... The initial node features of each node are represented as follows: The protein interaction diagram The initial node features of each node are represented as follows: .

4. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 3, characterized in that, Step S3 includes the following steps: S31. Design a cross-graph matching module and utilize a control function. The regulatory matrix between the initial node features of the gene interaction graph and the protein interaction graph is evaluated, and the regulatory score is calculated. : ； In the formula, Represents a cross-omics regulatory matrix The element in represents the first element. The gene node and the first Regulatory fractions between protein nodes; and These represent the first gene interaction in the gene interaction diagram. The node and protein interaction graph of the nth node Initial node characteristics of each node, Represents a non-linear activation function; S32. Using a control matrix composed of control scores For each gene interaction graph, the initial node features of the protein interaction graph with the highest regulatory score are found. Simultaneously, for each protein interaction graph, the initial node of the gene interaction graph with the highest regulatory score is found. Cross-graph convolutional feature updates are then performed on each node. ； ； ； ； In the formula, and These represent the first gene interaction in the updated gene interaction graph. The node and protein interaction graph of the nth node The enhanced node characteristics of each node, Represents the cross-graph feature transformation function. Represents vector concatenation. This represents the update function that projects the object back to its original dimension. In the control matrix China's target The operation involves finding the maximum value of each gene node across all protein nodes. Representatives made The protein node index at which the maximum value is obtained; In the control matrix China's target The operation involves finding the maximum value of a protein node across all gene nodes. Representatives made The gene node index at which the maximum value is obtained.

5. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 4, characterized in that, Step S4 includes the following steps: S41. Obtain the interaction diagram of each molecule through linear projection. Graph-level embedding : ； In the formula, Representing the The enhanced node features of each omics, representing the matrix The Column features, For the total feature dimension, and These are learnable parameters; S42, Calculate the first Attention importance score of each omics And attention weights after Softmax normalization : ； ； In the formula, The generation Attention importance score for each omics; A row vector representing learnable parameters; This represents the dot product operation between vectors; Represents the hyperbolic tangent activation function; and These represent the learnable weight matrix and bias vector in the attention mechanism, respectively. Representing the Attention weights for each omics modality; Represented by the natural constant An exponential function with base 0; Represents all The symbol for summing omics modes; The total number of representative omics modes; The summation index variable is used to iterate through all omics modalities; Representing the Attention importance scores for each omics modality; S43. Using attention weights, weighted combinations of embeddings at each graph level are performed to obtain a multi-omics joint representation within the cell: ； In the formula, This represents the combined intracellular multi-omics representation of the final fusion.

6. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 5, characterized in that, Step S5 includes the following steps: S51. Constructing a spatial proximity graph and feature neighborhood map The construction rules of the spatial proximity graph depend on the Euclidean distance between cells. If the Euclidean distance is less than or equal to a preset radius threshold, an edge is constructed; if the Euclidean distance is not less than the preset radius threshold, no edge is constructed. The feature proximity graph constructs edges based on the multimodal similarity captured by weighted nearest neighbor analysis. S52. A two-layer attention network is used to encode the spatial proximity map and the feature proximity map. The first layer aggregates information along the feature proximity nodes, and the second layer aggregates information along the spatial proximity nodes. In each layer, the first... A cell and its neighboring cells Attention weights The update formulas are as follows: ； ； In the formula, This represents a modified linear unit activation function with leakage; The weight parameters of the single-layer feedforward neural network used to calculate the attention score in the graph attention network are in the transpose of a vector. , and Representing cells respectively Neighboring cells and neighboring nodes Feature input representation; This represents the concatenation operation of vectors; This represents the updated cell obtained after aggregating neighbor information through a graph attention network. Multi-omics embedding representation.

7. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 6, characterized in that, Step S6 includes the following steps: S61, For each cell It aggregates the hidden embedding representations of its spatial neighbors and feature-similar neighbors to form positive samples. Simultaneously, the features of all nodes in the spatial proximity graph and feature proximity graph are shuffled, and negative samples are generated after processing by a graph attention network. ; S62. Compare the learning loss function using the binary cross-entropy definition graph. : ； In the formula, Represents the total number of cells in a tissue section; Represents mathematical expectation operation; Represents the natural logarithm function; This is the discriminator function, used to evaluate the probability score of an input node pair being a positive sample pair; S63. Perform self-supervised training of the network by minimizing the contrastive learning loss function; S64. After the network is trained in a self-supervised manner, unsupervised clustering is performed on the multi-omics embedding representation to achieve the recognition of the spatial domain of the organizational structure.

8. The spatial domain identification and control analysis method based on hierarchical graph representation learning according to claim 7, characterized in that, Step S7 includes the following steps: S71. For each spatial domain, average the regulatory matrix of all cells assigned to that spatial domain to construct a aggregation regulatory matrix representing the consistent molecular pattern of that spatial domain. S72. Prioritize candidate gene-protein regulatory pairs based on the absolute regulatory fractions in the aggregated regulatory matrix. S73. Perform a permutation test on each candidate gene-protein regulatory pair after sorting to screen out gene-protein regulatory pairs specific to this spatial domain.

9. A spatial domain recognition and control analysis system based on hierarchical graph representation learning, characterized in that, The spatial domain identification and control analysis method based on hierarchical graph representation learning as described in any one of claims 1-8 includes: A molecular interaction graph construction module is used to acquire spatial multi-omics data to construct intracellular molecular interaction graphs, including gene interaction graphs and protein interaction graphs. The feature extraction module extracts features from the molecular interaction graph using a graph convolutional network to obtain the initial node features of multi-omics molecules within the cell. The cross-graph matching module, based on initial node features, obtains the regulatory matrix of intracellular multi-omics molecules and enhanced node features through cross-graph convolution; The weighted fusion module weights and fuses the features of enhanced nodes according to the attention mechanism to generate a multi-omics joint representation within the cell; The proximity graph construction module builds spatial proximity graphs and feature proximity graphs between cells. The information aggregation module aggregates contextual information of the multi-omics joint representation through a graph attention network to obtain multi-omics embedding representations between cells; The spatial domain identification module uses a graph contrastive learning strategy to perform unsupervised clustering of multi-omics embedding representations, thereby identifying the spatial domain of the organizational structure. The regulatory relationship analysis module constructs a clustered regulatory matrix for each identified spatial domain, corresponding to the cells within each spatial domain, and extracts the regulatory relationships between genes and protein molecules in the spatial domain through permutation tests.

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