Unicellular organism network inference method based on multi-omics multilayer heterogeneous network

Abstract

The invention discloses a unicellular organism network inference method based on a multi-omics multilayer heterogeneous network. According to the method, unified integration of three kinds of single-cell multi-omics data of scRNA-seq, scATAC-seq and ST is achieved, the performance of single-cell biological network inference is improved, unified integration of three kinds of omics data of scRNA-seq, scATAC-seq and ST is achieved through an extensible framework, access of more omics types is supported, and the method is applied to the field of single-cell biological network inference. A multi-omics multilayer heterogeneous network structure is designed, different omics data are organized into mutually associated layers, and unified representation of the multi-omics data is realized through innovative design of cross-layer cell mapping and interlayer relationships. According to the method, common information among different omics is effectively fused, meanwhile, specific characteristics of various omics data are reserved, and a new perspective is provided for deep understanding of unicellular organism network inference.

Description

Technical Field

[0001] The present invention relates to the technical fields of bioinformatics and machine learning. Specifically, it relates to a method for inferring single-cell biological networks based on multi-omics multi-layer heterogeneous networks, which is mainly applied to fields such as single-cell sequencing data analysis, cell type identification and functional annotation, and cancer stage analysis. Background Art

[0002] In single-cell biological network inference, multi-omics data can provide more comprehensive and detailed biological system information. However, each type of omics usually only provides single-dimensional information on cell activities. Therefore, integrating different types of combined data has become an important task in single-cell biological network inference. Multi-omics methods include transcriptomics (scRNA-seq), epigenomics (such as scATAC-seq), spatial transcriptomics (ST), etc., which can analyze multiple biological layers simultaneously. By integrating data from different omics, a deeper understanding of the potential regulatory mechanisms controlling cell processes can be obtained, thus achieving more accurate analysis and prediction results.

[0003] Currently, existing methods for integrating multi-omics data mainly focus on integrating two types of omics data in multi-omics data. The method for integrating scTNA-seq and scATAC-seq has deficiencies in dealing with cell heterogeneity and data sparsity. The lack of spatial information makes it impossible to reveal gene regulation and expression distribution within the tissue spatial structure. Integrating scRNA-seq and ST data combines gene expression information with the spatial localization of cells to reveal the space of gene expression within the tissue, but lacks chromatin state information, making it difficult to have a good understanding of upstream regulatory mechanisms and chromatin accessibility. Integrating scATAC-seq and ST data can deepen the understanding of the spatial dimension of gene regulation, but it is difficult to fully understand the functional state and molecular characteristics of cells due to the lack of specific gene expression information.

[0004] With the rapid development of sequencing technology, more and more types of omics data can be obtained at a lower cost, which has led to the emergence of rich datasets containing more than two omics layers. Although deep learning algorithms, such as variational autoencoders and generative adversarial networks, have been applied to integrate and analyze single-cell multi-omics data, these methods still face many challenges in dealing with the heterogeneity and scale differences of multi-omics data. Especially in the data integration process, there are problems such as incomplete information integration and poor scalability. In addition, existing methods often have difficulty in simultaneously maintaining the unique characteristics of each omics data, showing limitations when dealing with complex biological systems. These challenges severely restrict the accuracy and reliability of multi-omics data analysis, and there is an urgent need to develop new methods to effectively integrate and analyze multi-omics data and improve the performance of single-cell biological network inference. Summary of the Invention

[0005] To solve the above problems existing in the prior art, the present invention proposes a single-cell biological network inference method based on multi-omics multi-layer heterogeneous networks, which can be effectively applied to the field of single-cell biological network inference, and has application scenarios such as cell function annotation, drug repositioning, and revealing complex biological processes. It is suitable for processing high-dimensional heterogeneous multi-omics data, realizing the unified integration of three omics data of scRNA-seq, scATAC-seq, and ST, integrating the common information between different omics, while retaining the specific characteristics of various omics data, improving the cell clustering effect, and enhancing the performance of single-cell biological network inference.

[0006] A single-cell biological network inference method based on multi-omics multi-layer heterogeneous networks provided by the present invention includes the following steps:

[0007] Step 1: Preprocess the data set to obtain the scRNA-seq normalized matrix E′ and the scATAC-seq normalized matrix P′. The specific steps are as follows:

[0008] Step a1: For scRNA-seq data, the gene expression matrix is represented as E = {e ij |i = 1, 2, …, I; j = 1, 2, …, J}, where i and j represent genes and cells respectively. To obtain the qualitative representation of each gene in all cells, a Hidden Markov Model (HMM) is used. In this model, the state of each gene i can be discretized into M i states, and the HMM defines and generates M i discrete states, representing the different regulatory signals or expression levels of gene i in all J cells. By applying the HMM, M i different states are generated for each gene, thereby capturing its discrete expression patterns in different cells. To handle the part with too low expression values, rows or columns with non-zero values less than 0.1% in the matrix will be deleted, and the gene expression matrix is logarithmically normalized to identify the top 2000 highly variable genes in each matrix. If the matrix contains fewer than 2000 genes, all available genes will be retained. The preprocessed matrix is E′.

[0009] [[ID=2,0]]Step a2: For scATAC-seq data, the chromatin accessibility matrix is represented as P = {p kj |k = 1, 2, …, K; j = 1, 2, …, J}, where k and j represent peaks and cells respectively. To integrate scRNA-seq data and scATAC-seq data, P is transformed into a gene-cell matrix P′. First, calculate the regulatory potential weight W ki from peak k to gene i:

[0010]

[0011] where d ki is the distance from the center of peak k to the transcription start site (TSS) of gene i, and d0 is the user-defined half-life distance, usually set to 10 kb. For a given gene i, if the distance d ki from peak k exceeds 150 kb, then when d0 is 10 kb, the weight W ki is less than 0.0005. In this method, to optimize the computational efficiency, if d ki exceeds 150 kb, then W ki is set to 0.

[0012] For peaks located in exon regions, the weights are adjusted to account for gene length bias. If peak k is located in the exon region of gene i, its weight will be normalized by the total exon length to correct the problem of higher peak detection probability in longer genes. Conversely, peaks located in the promoter or exon regions of nearby genes will be excluded from the calculation of the regulatory potential of that gene.

[0013] To accurately reflect the regulatory potential, the present invention adjusts the bias introduced by different gene region lengths by normalizing the weights of each peak. This normalization takes into account the differences in detection probabilities of different gene regions and provides a more accurate measure of regulatory activity. The final regulatory potential matrix P′ is calculated by combining these adjusted weights with the original peak matrix, thereby obtaining the regulatory score at the gene level.

[0014] Step 2: Apply the two matrices obtained in Step 1 to calculate the intercellular combined distance D W between scRNA-seq and scATAC-seq, and construct the weighted nearest neighbor matrix W NN , and the specific steps are as follows:

[0015] Step b1: Calculate the intercellular Euclidean distance D E of scRNA-seq data. For each cell j, the Euclidean distance between it and each other cell j′ is calculated as follows:

[0016]

[0017] Step b2: Calculate the intercellular Euclidean distance D P of scATAC-seq data. For each cell j, the Euclidean distance

[0018]

[0019] Step b3: Calculate the intercellular combined distance D between scRNA-seq and scATAC-seq W . The combined distance of cell j is calculated by taking the weighted sum of the individual distances:

[0020]

[0021] where α is a parameter that balances the contributions of the two data types, and in this invention, it is set to 0.5.

[0022] Step b4: Construct a new nearest neighbor matrix W through the combined distance D W . The entries in W NN represent the nearest neighbors based on the weighted combination of gene expression and regulatory potential distances. The integrated WNN matrix W NN is defined as: NN

[0023]

[0024] Step three: Integrate to obtain a comprehensive matrix X using the weighted nearest neighbor (WNN) method, as follows:

[0025] For each cell j, its comprehensive expression x j is obtained by averaging the expressions of its nearest neighbors (defined by ) from the two datasets:

[0026]

[0027] where N(j) represents the set of nearest neighbors of cell j in the WNN graph, e′ j′ is the gene expression of cell j′ from the RNA data, and p′ j′ is the gene expression of cell j′ from the ATAC data. The resulting comprehensive matrix X is a gene expression matrix that integrates scRNA-seq and scATAC-seq data;

[0028] Step four: Calculate the pairwise cosine similarity between cells based on the comprehensive matrix X obtained in step three to obtain the intercellular similarity matrix S, as follows:

[0029] Step d1: The comprehensive matrix X = {x ij |i = 1, 2, …, I; j = 1, 2, …, J}, where i represents the number of genes and j represents the number of cells. To understand the relationships between cells, this invention calculates the cosine similarity of their expression features. This involves calculating the pairwise cosine similarity between cells based on their gene expression vectors. The cosine similarity sim jj′ between cell j and cell j′ is defined as follows:​

[0030]

[0031] Step d2: Construct an inter - cellular similarity matrix S using these distances, where s jj′ represents the similarity between cell j and cell j'. To convert these similarities into binary values, the present invention adopts a threshold method, and the calculation process is as follows:

[0032]

[0033] Step 5: Construct a heterogeneous network G using the comprehensive matrix X and the inter - cellular similarity matrix S. In this network, there are two types of nodes: cells and genes, and the edges represent the similarity between cells and the expression relationship between cells and genes.

[0034] Use the inter - cellular relationships of cells in the inter - cellular similarity matrix S as the initial representation of cell nodes and use the expression levels of genes in all cells in the comprehensive matrix X as the initial representation of gene nodes These initial representations are used as the input to the encoder in the graph auto - encoder (GAE). The role of the initial representation is to provide the encoder with meaningful features directly derived from biological data, ensuring that the initial representation of each node can capture important information about its gene expression.

[0035] To obtain a meaningful low - dimensional representation from graph G, the present invention adopts GAE. GAE consists of two main components: an encoder and a decoder. The encoder maps the nodes in graph G to a low - dimensional space. For each node v (which can be a cell or a gene), the encoder generates a low - dimensional representation matrix H(v), and its formal definition is

[0036] GAE is trained by minimizing the reconstruction loss, which measures the ability of the decoder to reconstruct the original graph structure from the representations generated by the encoder. The loss function L is defined as follows:

[0037]

[0038] where Ed is the set of edges in the original graph, and (v s ,v t ) represents a pair of nodes.

[0039] After the training is completed, the encoder outputs the cell representation matrix H(c) and the gene representation matrix H(g) of the scRNA - seq and scATAC - seq heterogeneous network. In subsequent tasks, these low - dimensional representations can be used for various downstream tasks, such as clustering, visualization, or further biological analysis.

[0040] Step 6: Construct a spatial transcriptome network from the spatial transcriptome data in the dataset to obtain the spatial transcriptome cell representation matrix H(s).

[0041] Step f1: The present invention preprocesses the input ST data, filters out low-expression and low-variance genes, and normalizes the counts for each cell. The ST graph can be represented by two matrices: the cell location adjacency matrix and the node feature matrix.

[0042] Step f2: Calculate the distance d ij , and select an appropriate threshold d0 to construct the cell location adjacency matrix A = {a ij | i = 1, 2, …, N; j = 1, 2, …, N}, where N is the number of cells.

[0043]

[0044] The cell location adjacency matrix forms an undirected graph representing the spatial information between cells, where cells are nodes and spatially adjacent cells are connected by edges. The node feature matrix F = {f ij | i = 1, 2, …, I; j = 1, 2, …, N} is derived from the preprocessed gene count data and then normalized as follows:

[0045]

[0046] where i represents gene i and j represents gene j. Then, genes with a normalized expression variance lower than 1 are removed to exclude low-variance genes.

[0047] Step f3: The present invention introduces the Deep Graph Infomax method (DGI) (an unsupervised graph embedding method) to learn node representations from graph-structured data. Different from the GCN-based method that relies on random walks, DGI maximizes the mutual information between the global and local representations of the graph. The features extracted by DGI include both local and global parts. The combined adjacency matrix A and node feature matrix F are used as the input to DGI. The encoder maps these two matrices to the embedding space as follows:

[0048] ε(F, A) = H = {h1, h2, …, h N}

[0049] where H represents the high-order representation.

[0050] Step f4: The encoder consists of four graph convolutional layers for passing messages to adjacent nodes and uses the parametric rectified linear unit (PReLU) as the activation function. The graph convolutional layer is defined as follows:

[0051]

[0052] Among them, H (l) and H (l+1) are the input and output matrices, W (l) is the weight matrix, and D is the degree matrix.

[0053] The PReLU activation function is:

[0054]

[0055] Among them, θ is the learnable parameter, set to 0.25.

[0056] Step f5: The global representation is obtained from the local representation using the Readout function:

[0057] h s = Readout({h j})

[0058] Step f6: The present invention introduces a discriminator to maximize the mutual information between local and global features. The higher the score, the better the encapsulation of graph-level information. To train the discriminator, negative samples are generated by randomly destroying the adjacency matrix A The objective function to be maximized is:

[0059]

[0060] Among them, D is the discriminant function. After training, the cell representation matrix H(s) of the ST network is output.

[0061] Step seven: Using the cell representation matrix H(c) and gene representation matrix H(g) of the scRNA-seq and scATAC-seq heterogeneous network obtained in step five and the spatial transcriptome cell representation matrix H(s) obtained in step six, construct a multi-omics multi-layer heterogeneous network. The steps are as follows:

[0062] Construct a single-cell multi-omics two-layer heterogeneous network. One layer is the scRNA-seq and scATAC-seq heterogeneous network, which has two types of nodes: cells and genes. The cell-cell edges and cell-gene edges are represented by the cell representation matrix H(c) and gene representation matrix H(g) of the scRNA-seq and scATAC-seq heterogeneous networks respectively. The other layer represents the ST network, and the edges between cells are represented by the ST network cell representation matrix H(s). The two-layer heterogeneous networks are connected through matching inter-layer cell edges.

[0063] Step eight: Integrate the three omics data, obtain the node representations H′(c) and H′(g) of the single-cell multi-omics multi-layer heterogeneous network, and use the UMAP method to achieve cell clustering and infer the single-cell biological network. The steps are as follows:

[0064] Step h1: To facilitate the integration of these representation matrices, first use principal component analysis (PCA) to reduce the matrices H(c) and H(s) to the same dimension. Specifically, reduce them to 128 dimensions: the dimensions of H(c) and H(s) are K×128 and J×128 respectively.

[0065] Step h2: Next, use cosine similarity to calculate the similarity between cells in the reduced-dimensional matrices H(c) and H(s). For the k-th cell in H(c) and the j-th cell in H(s), the cosine similarity s kj is given by:

[0066]

[0067] Step h3: To make full use of the information from different omics layers, connect the cell nodes between the layers to learn the similarity embeddings from each other. In addition, the present invention uses the gene representation matrix to enrich the information learning process. For each cell node k in the matrix H(c) and each cell node j in the matrix H(s), define the update rule of its embedding according to their similarity and gene representation:

[0068]

[0069] where β and γ are the learning rates that control the cross-layer similarity and the contribution of gene representation respectively. In the experiment, the present invention conducted a comprehensive parameter experiment on the cross-layer similarity learning rate β, testing the values from 0.1 to 0.9. The results show that among all evaluation metrics, the performance is optimal when β = 0.4. For the gene representation contribution rate γ, the present invention implemented a data-driven dynamic adjustment strategy instead of using a fixed value.

[0070] This iterative update continues until convergence, ensuring that the cell representations in the two layers are fused with each other through their cross-layer connections and gene information, thereby refining the heterogeneous multi-omics network.

[0071] Step h4: Use the refined representation matrix for clustering and other downstream tasks. By integrating multi-omics data into a unified framework, the representation can capture the complex relationships and interactions between different types of data, thereby obtaining more accurate and robust cell clustering results. Specifically, this paper uses the K-means clustering algorithm, aiming to divide N cells into M clusters. The objective function of K-means clustering is defined as: where C m is the set of cells in the m-th cluster, h n is the representation of cell n, and μm is the centroid of the m-th cluster. The centroid μm is calculated as:

[0072] This iterative process continues until there are no significant changes in cluster assignments, and the final clustering results will reveal the underlying structure of the multi-omics data.

[0073] The present invention has the following features: (1) It innovatively realizes the unified integration of three types of omics data, namely scRNA-seq, scATAC-seq, and ST, and designs an extensible framework to support the access of more omics types. This method effectively integrates the common information between different omics while retaining the specific characteristics of each type of omics data. (2) It proposes a novel multi-layer graph structure design, organizing different omics data into interconnected layers. The first layer integrates scRNA-seq and scATAC-seq data, and the second layer represents ST data. Through the innovative design of cross-layer cell mapping and inter-layer relationships, a unified representation of multi-omics data is achieved. This architecture has good scalability and can integrate new omics layers without re-design. (3) It break-throughly expands the representation ability of traditional heterogeneous networks by introducing intra-layer cell-cell edges on the basis of cell-gene edges, enhancing the expression ability of the network. This design not only strengthens the intra-layer connectivity but also enriches cell representation, providing a new perspective for in-depth understanding of cell-cell interactions.

[0074] The present invention is applied to the field of single-cell biological network inference. By constructing a multi-omics multi-layer heterogeneous network, it realizes the unified integration of three types of omics data, namely scRNA-seq, scATAC-seq, and ST, which can improve the cell clustering effect and lay a foundation for subsequent analysis of regulatory mechanisms, cancer stage analysis, and revealing complex biological processes in single-cell biological network inference. Brief Description of the Drawings

[0075] The present invention will be further described below in conjunction with the drawings and embodiments.

[0076] Figure 1 It is a schematic structural diagram of the single-cell biological network inference method based on the multi-omics multi-layer heterogeneous network of the present invention. Detailed Embodiments

[0077] For a clearer understanding of the technical features, objectives, and effects of the present invention, the detailed embodiments of the present invention will now be described in detail with reference to the drawings. The implementation effects of the present invention are demonstrated on a matching multi-omics dataset in the field of single-cell sequencing data analysis.

[0078] Figure 1This is a schematic diagram of the single-cell biological network inference method based on multi-omics multi-layer heterogeneous networks, mainly including the scRNA-seq and scATAC-seq heterogeneous network construction module, the spatial transcriptome network construction module, and the biological network inference module for multi-layer heterogeneous networks. The scRNA-seq and scATAC-seq heterogeneous network construction module extracts the node representations and graph representations of the two omics data, and then inputs them into the graph autoencoder for feature extraction to obtain the embedded expression after dimensionality reduction. The spatial transcriptome network construction module further captures spatial information more deeply through deep graph information maximization based on cell spatial position information and gene counts in cells to obtain spatial cell representations. The biological network inference module for multi-layer heterogeneous networks integrates the outputs of the previous two modules into a comprehensive multi-layer structure while retaining the specific features of each data type, thereby obtaining more accurate clustering results.

[0079] (1) Parameter settings

[0080] To obtain relatively stable experimental results, all methods were repeated 10 times, and the average value was used to represent the final performance of the model on different datasets. The model learning rate was set to 0.001. In the scRNA-seq and scATAC-seq heterogeneous networks, the half-life distance d0 for peak-gene weight calculation was set to 10 kb, and the number of node samplings was 2000. In the multi-layer heterogeneous network, the cross-layer similarity learning rate β was set to 0.4, and the gene representation contribution rate γ adopted a data-driven dynamic adjustment strategy.

[0081] (2) Three sub-datasets

[0082] The samples used in the study were from the publicly available mouse breast cancer dataset (GSE212482). This dataset contains matched scRNA-seq, scATAC-seq, and ST data from the same breast tissue sections at different cancer progression stages. In the dataset, tissues were dissociated into single cells by optimized enzymatic and mechanical methods, which minimized selection bias while maintaining cell viability. In this paper, subsets C3, L2, and S2 were selected, covering three stages: non-breast cancer, pre-breast cancer, and late breast cancer. The detailed information of the dataset is shown in Table 1. The number of cells refers to the number of cells in the scRNA-seq and scATAC-seq data, and the number of spatial sites refers to the number of spatial distribution points in the ST data.

[0083]

[0084]

[0085] Table 1 Dataset information statistics

[0086] (3) Four clustering metrics

[0087] Three common unsupervised clustering evaluation metrics were selected for the experiment to evaluate the clustering effect: Silhouette Coefficient (SC), Davies-Bouldin Index (DBI), and Calinski-Harabasz Index (CH). These metrics comprehensively evaluate the clustering effectiveness from different perspectives, ensuring a robust and reliable evaluation of the clustering results.

[0088] SC measures the similarity of an object to other clusters compared to its own cluster. For each data point i, the SC value SC(i) is defined as:

[0089]

[0090] where a(i) is the average distance between i and all other points in the same cluster, and b(i) is the minimum average distance between i and points in other clusters (i.e., the nearest cluster). The overall SC is the average silhouette value of all points. The range of SC is from -1 to 1, and a higher value indicates a clearer clustering.

[0091] DBI is a metric used to quantify the average similarity ratio of each cluster to its most similar cluster. Its definition is as follows:

[0092]

[0093] where k is the number of clusters, s i is the average distance between each point in the i-th cluster and the centroid of the i-th cluster, and d ij is the distance between the centroids of the i-th and j-th clusters. A lower DBI indicates better clustering performance because it means the clusters are compact and well-separated.

[0094] CH, also known as the variance ratio criterion, is used to evaluate the ratio of the between-cluster dispersion to the sum of the within-cluster dispersions. Its definition is:

[0095]

[0096] where trace(B k ) is the distance between each cluster center and the overall mean of all data points, trace(W k ) is the distance between the data points within each cluster and the cluster center, and n is the total number of data points. A higher CH index indicates a more clearly defined clustering.

[0097] (4) 6 clustering algorithms

[0098] The example was tested on 3 common multi-view datasets, and the method was compared with a contrast multi-view deep fusion clustering algorithm based on double data augmentation and 18 common clustering algorithms. The specific introduction of each algorithm is as follows:

[0099] DeepMAPS: A deep learning-based multi-omics data integration method proposed by Stuart T et al. in the paper "Single-cell chromatin state analysis with Signac" in Nature Biotechnology 2023, 39(8): 936-944. This method integrates scRNA-seq and scATAC-seq data through a deep neural network to achieve cell type annotation.

[0100] Seurat: A classic single-cell data analysis toolkit proposed by Hao Y et al. in the paper "Integrated analysis of multimodal single-cell data" in Nature Biotechnology 2021, 39(8): 912-922. This method uses the weighted nearest neighbor (WNN) algorithm to integrate scRNA-seq and scATAC-seq data.

[0101] MOFA+: A factor analysis-based multi-omics data integration method proposed by Argelaguet R et al. in the paper "MOFA+: a statistical framework for comprehensive integration of multi-modal single-cell data" in Genome Biology 2020, 21(1): 1-17. This method learns latent factors through Bayesian inference to achieve joint analysis of scRNA-seq and scATAC-seq data.

[0102] STLearn: An analysis method specifically developed for spatial transcriptome data proposed by Pham D et al. in the paper "STLearn: integrating spatial location, tissue morphology and gene expression to find cell types, cell-cell interactions and spatial trajectories within undissociated tissues" in Nature Communications 2020, 11(1): 1-13. This method integrates scRNA-seq and scATAC-seq gene expression data for cell type identification.

[0103] CCST: A spatial transcriptome analysis method based on graph convolutional network, proposed by Hu J et al. in the paper "SpaGCN: Integrating gene expression, spatial location and histology to identify spatial domains and spatially variable genes by graph convolutional network" in Nature Methods 2021, 18(11): 1333-1341. This method learns cell representations through a spatially constrained graph convolutional network.

[0104] SEDR: A method for dimensionality reduction of spatial transcriptome data using deep autoencoders, proposed by Chen W et al. in the paper "SEDR: a deep learning framework for spatial transcriptomics data analysis through dimension reduction" in Bioinformatics 2022, 38(18): 4437-4444. This method learns low-dimensional representations of spatial transcriptome data through a deep learning model.

[0105] The comparison experiment results of the three datasets are shown in Table 2-4. Underlines indicate sub-optimal results, and bold indicates the optimal results.

[0106] Table 2 Comparative experiment of silhouette coefficient algorithms [[ID=_{10}]]

[0107]

[0108] Table 3 Comparative experiment of DBI algorithms

[0109]

[0110] Table 4 Comparative experiment of CH algorithms

[0111]

[0112] MOH always achieves higher clustering performance. For the SC metric, its performance on C3 and L2 is 5.70% and 18.24% higher than that of the sub-optimal model respectively, and it is only 1.3% lower than the best result on S2. This indicates that MOH forms more cohesive clusters and can better reflect the underlying biological structure. For the DBI metric, a lower value of this metric indicates tighter clusters, and MOH achieves a reduction of 26.83%, 15.45%, and 12.18% compared to the sub-optimal model on C3, S2, and L2 respectively. The CH metric measures the ratio of the sum of between-cluster dispersion and within-cluster dispersion, and MOH increases by 5.85% on C3, 0.36% on S2, and 18.20% on L2. These findings demonstrate the robustness and consistency of MOH in different datasets, showing its ability to excellently depict different clusters with strong within-cluster cohesion and large between-cluster separation.

[0113] MOH represents a significant advancement in multi-omics integration methods. Models such as Deepmaps, Seurat, and MOFA+ focus on scRNA-seq and scATAC-seq data, while models such as Stlearn, CCST, and SEDR focus on ST data, but MOH consistently outperforms these models in all metrics. For example, on the C3 dataset, MOH obtains the highest SC and CH scores and the lowest DBI score, indicating its excellent clustering performance. This shows that MOH has the outstanding ability to effectively integrate multi-omics data, surpassing the performance of models limited to fewer data types.

[0114] These results indicate that the present invention can effectively integrate multi-omics data, form more cohesive clusters, and better reflect the underlying biological structure. The present invention can more clearly depict the cluster boundaries, which is crucial for identifying subtle differences in cell populations and understanding potential biological processes.

[0115] The present invention constructs a single-cell multi-omics multi-layer heterogeneous network, realizing the unified integration of three omics data: scRNA-seq, scATAC-seq, and ST. One layer of the network integrates scRNA-seq and scATAC-seq data, and the other layer represents ST data. The two layers are unified into a framework through cross-layer mapping and the design of inter-layer edges. The introduction of cell-to-cell edges enhances the intra-layer connections, significantly improving the feature learning effect and the performance of single-cell biological network inference.

[0116] From the above embodiments, it can be seen the excellent performance of the present invention in single-cell multi-omics integration, which further demonstrates that the present invention makes good use of multi-omics characteristics, considers the rich data information in multi-omics data, effectively extracts the specific information and shared information of single-cell multi-omics, and effectively solves the technical difficulties in the actual application process in the field of single-cell biological inference.

[0117] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative rather than restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit of the present invention and the scope protected by the claims. All of these are within the protection scope of the present invention.

Claims

1. A method for inferring single-cell biological networks based on multi-omics multi-layer heterogeneous networks, characterized in that, It includes the following steps: Step 1: Preprocess the dataset to obtain the scRNA-seq normalized matrix and the scATAC-seq normalized matrix ; Step 2: Apply the two matrices obtained in Step 1 to calculate the Euclidean distance between cells in scRNA-seq and the Euclidean distance between cells in scATAC-seq ; the combined distance between scRNA-seq and scATAC-seq cells is calculated by taking the weighted sum of the distances: , where is a parameter, set to 0.5; the combined distance shows the nearest neighbor relationship between cells, and a weighted nearest neighbor matrix is constructed; Step 3: Integrate to obtain a comprehensive matrix using the weighted nearest neighbor (WNN) method , as follows: For each cell , its combined expression is obtained by averaging the expression of its nearest neighbors (defined by ) from two omics datasets: Among them, represents the set of nearest neighbors of cells in the WNN matrix, is the gene expression of cells in the scRNA-seq data, is the gene expression of cells in the scATAC-seq data, and the resulting integrated matrix is a gene expression matrix integrating scRNA-seq and scATAC-seq data; Step 4: According to the comprehensive matrix obtained in Step 3 , calculate the pairwise cosine similarity between cells to obtain the cell similarity matrix , which reflects the similarity relationship between the two omics cells; Step 5: Utilize the comprehensive matrix and the intercellular similarity matrix to construct a scRNA-seq and scATAC-seq fusion heterogeneous network , where there are two types of nodes, namely cells and genes. The edges connecting the nodes are different from the construction methods of other heterogeneous networks. In addition to the cell-gene edges commonly found in other heterogeneous networks, this method also uses the intercellular similarity matrix to construct cell-cell edges. Input X and S into the graph autoencoder (GAE), and train it by minimizing the reconstruction loss. After the training is completed, output the cell representation matrix and gene representation matrix of the scRNA-seq and scATAC-seq heterogeneous network; Step 6: Construct an ST network from the spatial transcriptome data in the dataset to obtain the spatial transcriptome cell representation matrix , and the process is as follows: Cell position adjacency matrix of ST data Constructed by calculating the distance between cells, cell expression matrix Derived from the count data of genes in cells after preprocessing, introducing the Deep Graph Infomax (DGI) method, combining the adjacency matrix and the node feature matrix Used as the input of DGI to learn the cell representation matrix from the graph structure data ; Step 7: Use the cell representation matrix of the scRNA-seq and scATAC-seq heterogeneous network obtained in Step 5 and the gene representation matrix as well as the spatial transcriptomics cell representation matrix obtained in Step 6 , to construct a multi-omics multi-layer heterogeneous network. The steps are as follows: Construct a two-layer heterogeneous network for single-cell multi-omics. One layer is the scRNA-seq and scATAC-seq heterogeneous network, which has two types of nodes: cells and genes. The cell-cell edges and cell-gene edges are represented by the cell representation matrix of the scRNA-seq and scATAC-seq heterogeneous network and the gene representation matrix respectively. The other layer represents the ST network, and the edges between cells are represented by the cell representation matrix of the ST network respectively. The two-layer heterogeneous networks are connected by matching the inter-layer cell edges; Step 8: Integrate three types of omics data to obtain the node representation of the single-cell multi-omics multi-layer heterogeneous network and , and use the UMAP method to achieve cell clustering and infer the single-cell biological network. The steps are as follows: Calculate the matrix after dimensionality reduction using cosine similarity and the cosine similarity between cells in , and define the update rule for its embedding according to their similarity and the gene representation matrix: Among them, and are the learning rates for controlling cross-layer similarity and gene representation contribution respectively, set to 0.4, Using a data-driven dynamic adjustment strategy, the representation matrix is continuously iteratively updated until convergence. The final node representation uses the UMAP method to achieve cell clustering and infer the single-cell biological network.

2. The single-cell biological network inference method based on multi-omics multi-layer heterogeneous networks according to claim 1, wherein In step 4, construct a scRNA-seq and scATAC-seq integrated heterogeneous network , whose network structure contains two types of nodes and two types of edges. The two types of nodes are cells and genes; the two types of edges are cell-gene and cell-cell. Introduce the relationship between cells as an edge into the heterogeneous network. By calculating the similarity relationship between cells, the association between cells is added as a new edge type to the heterogeneous network, so that the network can describe the information exchange and mutual regulation relationship between cells; The steps are as follows: Step d1: Calculate the association strength between cells using cosine similarity. The and the cosine similarity between cells is defined as follows: Step d2: Based on the calculated similarity, construct an intercellular similarity matrix , where represents the similarity between cell and cell . Convert these similarities into binary values. The present invention adopts a threshold method: A value of 1 indicates that there is an edge between cells, and a value of 0 indicates that there is no edge between cells.

3. The single-cell biological network inference method based on multi-omics multi-layer heterogeneous networks according to claim 1, wherein, Step 7 and Step 8 construct a single-cell multi-omics multi-layer heterogeneous network to achieve deep integration of three single-cell multi-omics data, namely scRNA-seq, scATAC-seq, and ST. The multi-layer heterogeneous network architecture of this method effectively captures the synergistic relationship between different omics data and improves the performance of downstream tasks through modeling of inter-layer cell relationships and interaction of cross-layer information. The specific implementation steps are as follows: Step h1: Use principal component analysis (PCA) to reduce the scRNA-seq and scATAC-seq cell representation matrices and the ST cell representation matrix to the same dimension; Step h2: Calculate the intercellular relationship between two layers, and calculate the similarity between cells in the matrix after dimensionality reduction using cosine similarity and in, for in the th cell and in the th cell, the cosine similarity is given by: Step h3: Utilize the information from different omics layers, introduce an interactive learning mechanism for the multi-layer network, achieve bidirectional information flow through inter-layer cell connections, and use the gene representation matrix to enrich the information learning process. For each cell node in matrix and each cell node in matrix , and each cell node in matrix , define the update rule of its embedding according to their similarity and gene representation: Among them, and are the learning rates for controlling cross-layer similarity and gene representation contribution respectively, which is set to 0.4, and a data-driven dynamic adjustment strategy is used; Step h4: Use the refined representation for clustering by the UMAP method to infer the single-cell biological network. Through the construction of a multi-omics multi-layer heterogeneous network, unified integration of three omics data, namely scRNA-seq, scATAC-seq, and ST, is achieved.

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