Weighted gene co-expression hyper-network module identification method and system based on hypergraph

Abstract

The invention provides a hypergraph-based weighted gene co-expression hypernetwork module identification method and system, and the method comprises the steps: obtaining a gene expression profile matrix, and integrating an effective gene set of each sample to construct a weighted hypergraph; calculating a Laplacian matrix of the weighted hypergraph, and obtaining a topological overlapping matrix based on the Laplacian matrix; and based on the topological overlapping matrix, performing module identification on the gene by adopting a hierarchical clustering method, and outputting a gene co-expression module. According to the method, the calculation efficiency is effectively improved by optimizing hypergraph construction and utilizing the hypergraph Laplacian matrix to carry out network analysis. Compared with a traditional WGCNA method, the WGCHNA shows higher calculation speed and processing capacity when processing a large-scale gene data set, so that the gene co-expression network can be analyzed more quickly, and the requirements of multiple samples and complex networks are met.

Description

Technical Field

[0001] The present invention belongs to the technical field of data mining, and in particular relates to a method and system for identifying weighted gene co-expression supernetwork modules based on a hypergraph. Background Art

[0002] With the rapid development of gene sequencing technology, biological research has entered the era of big data. High-throughput gene sequencing technology (such as RNA-Seq) can measure the expression levels of thousands of genes in a single experiment, generating massive amounts of gene expression data. These data provide a basis for studying the functions of genes, the relationships between genes, and their roles in complex biological processes. However, how to extract meaningful biological information from these complex and massive gene expression data has become one of the core challenges in the field of bioinformatics. In genomic research, researchers usually want to understand the co-expression relationship between genes, that is, which genes show similar expression patterns in a specific biological state or disease state. In order to analyze these co-expression relationships, weighted gene co-expression network analysis (WGCNA) came into being. This method can help researchers discover potential interactions between genes and reveal gene modules that are closely related to biological processes or disease states.

[0003] WGCNA is one of the most widely used methods for constructing gene co-expression networks. The algorithm constructs a weighted network by calculating the similarity between genes (usually based on the Pearson correlation coefficient), in which nodes represent genes and the weights of edges represent the co-expression strength between gene pairs. Subsequently, gene modules (i.e., highly co-expressed gene groups) are identified through a hierarchical clustering algorithm, and the biological significance of these modules is inferred through functional enrichment analysis. WGCNA is widely used in the study of various complex diseases (such as cancer and neurodegenerative diseases). Its advantage is that it can identify key gene modules, thereby providing potential targets for the diagnosis and treatment of diseases.

[0004] Scholars have improved the accuracy or applicability of network analysis by improving certain steps of WGCNA. For example: Improvements based on different distance metrics: Some researchers have proposed using different distance or similarity metrics to replace the Pearson correlation coefficient, such as using Hellinger correlation or distance correlation. These methods aim to improve the accuracy of similarity calculations, but they are still limited to the analysis of pairwise relationships; Multi-omics data integration: Some extended methods attempt to integrate multi-omics data (such as gene expression, proteomic data) into WGCNA analysis, and capture the associations between different levels of biological data by constructing a joint network. Although this method has expanded the scope of application of WGCNA, it still has shortcomings in capturing high-order multi-gene synergistic relationships; Modularity metrics and clustering algorithm optimization: Such as dynamic pruning algorithms and modular methods based on random block models, these methods have improved the clustering steps to improve the accuracy of module detection. However, their core still relies on the calculation of pairwise interactions of genes in the WGCNA framework.

[0005] Traditional weighted gene co-expression network analysis (WGCNA) methods have the following problems:

[0006] (1) It is difficult to capture the high-order interaction relationship of multiple genes: Since WGCNA relies on pairwise gene similarity to construct a network, it can only process the pairwise co-expression relationship between genes, but cannot effectively capture the complex high-order interaction patterns between multiple genes. Therefore, when multiple genes act synergistically on a biological process, WGCNA's analytical ability is limited, and it is difficult to fully reveal the synergistic relationship of these genes.

[0007] (2) Low computational efficiency: When processing large-scale genetic data (such as interactive datasets of tens of thousands of genes and multiple samples), WGCNA has a high computational complexity, especially when constructing networks and extracting co-expression modules, the algorithm efficiency is low. This results in a slow processing speed of WGCNA when facing large datasets, affecting the timeliness and efficiency of analysis.

[0008] (3) Limited accuracy of module identification: Since WGCNA is mainly based on pairwise similarities, it fails to fully utilize the information of multi-gene synergy, and its accuracy may be limited when extracting gene modules related to specific biological processes or diseases. This may lead to the neglect of important regulatory gene modules, reducing the effect of pathogenic gene screening. Summary of the invention

[0009] The purpose of the present invention is to provide a method and system for identifying weighted gene co-expression supernetwork modules based on a hypergraph to solve the above problems.

[0010] To achieve the above object, the present invention adopts the following technical solutions:

[0011] In a first aspect, the present invention provides a method for identifying a weighted gene co-expression supernetwork module based on a hypergraph, comprising:

[0012] Obtain the gene expression matrix and integrate the effective gene set of each sample to construct a weighted hypergraph;

[0013] Calculate the Laplacian matrix of the weighted hypergraph, and based on the Laplacian matrix, obtain the topological overlap matrix;

[0014] Based on the topological overlap matrix, the hierarchical clustering method was used to identify gene modules and output the gene co-expression modules.

[0015] Furthermore, the step of obtaining a gene expression matrix and integrating the effective gene set of each sample to construct a weighted hypergraph includes:

[0016] In the gene expression matrix, rows represent samples and columns represent genes. The effective gene sets of each sample are integrated to construct a weighted hypergraph H = (V, E, W), where V is the set of gene nodes, E is the set of sample hyperedges, and W is the weight matrix of sample hyperedges.

[0017] Furthermore, the construction process of the weight matrix W is as follows:

[0018] First, based on the gene expression matrix, the co-expression intensity between genes is determined by calculating the correlation between genes. For each pair of genes g i and g j , calculate their expression correlation in multiple samples corr(g i ,g j ), indicating the strength of their co-expression relationship;

[0019] After determining the correlation between gene pairs, for each hyperedge e, its weight W e It is defined by associating the co-expression strength of all gene pairs in the hyperedge; assuming that the hyperedge e connects the gene set {g1,g2,…,g k}, then its weight W e Defined as the average or weighted average of the pairwise correlations within the gene set:

[0020]

[0021] Where |E| represents the number of gene pairs in the hyperedge, corr(g i ,g j ) indicates gene g i and g j The correlation between them.

[0022] Furthermore, the calculating the Laplacian matrix of the weighted hypergraph includes:

[0023] The hypergraph Laplacian matrix is ​​a mathematical representation of the complex associations between node genes and hyperedge samples in the hypergraph. It can capture high-order relationships between multiple genes and samples. The Laplacian matrix of the hypergraph is defined as:

[0024]

[0025] Among them, D v is the hyper-degree diagonal matrix of gene nodes in the hypergraph, D e is the hyperdegree diagonal matrix of the sample hyperedge, W is the weight matrix of the hyperedge, and H is the incidence matrix of the hypergraph.

[0026] Normalize the Laplacian matrix:

[0027]

[0028] Where I is the identity matrix.

[0029] Furthermore, the topological overlap matrix is ​​obtained based on the Laplace matrix, including:

[0030] Based on the hypergraph Laplacian matrix, the topological overlap matrix TOM is calculated. TOM reflects the topological overlap between gene pairs and is used to measure the similarity of gene pairs. For genes i and j, the calculation formula of TOM is expressed as:

[0031]

[0032] Among them, Δ ij is the value between gene i and gene j in the hypergraph Laplacian matrix; d i and d j are the degrees of genes i and j, that is, the number of connections between them and other genes; the TOM matrix is ​​the similarity measure between each pair of genes.

[0033] Furthermore, the method of using a hierarchical clustering method to identify genes as modules based on a topological overlap matrix and outputting a gene co-expression module includes:

[0034] After obtaining the TOM matrix, the hierarchical clustering method is used to identify the modules of genes. Specifically, the dissimilarity of the topological overlap matrix dissTOM is first calculated, which is defined as:

[0035] dissTOM(i,j)=1-TOM(i,j)

[0036] Adopt the strategy of dynamic module merging, dynamically detect similar modules and merge them;

[0037] Finally, the gene co-expression module is output, which represents the gene groups that are co-expressed in different samples.

[0038] In a second aspect, the present invention provides a hypergraph-based weighted gene co-expression supernetwork module identification system, comprising:

[0039] The data acquisition module is used to obtain the gene expression matrix and integrate the effective gene set of each sample to construct a weighted hypergraph;

[0040] A topological overlap matrix acquisition module is used to calculate the Laplace matrix of the weighted hypergraph and obtain the topological overlap matrix based on the Laplace matrix;

[0041] The identification output module is used to identify the modules of genes based on the topological overlap matrix and the hierarchical clustering method, and output the gene co-expression modules.

[0042] Furthermore, the step of obtaining a gene expression matrix and integrating the effective gene set of each sample to construct a weighted hypergraph includes:

[0043] In the gene expression matrix, rows represent samples and columns represent genes. The effective gene set of each sample is integrated to construct a weighted hypergraph H = (V, E, W), where V is the set of gene nodes, E is the set of sample hyperedges, and W is the weight matrix of sample hyperedges.

[0044] The construction process of the weight matrix W is as follows:

[0045] First, based on the gene expression matrix, the co-expression intensity between genes is determined by calculating the correlation between genes. For each pair of genes g i and g j , calculate their expression correlation in multiple samples corr(g i ,g j ), indicating the strength of their co-expression relationship;

[0046] After determining the correlation between gene pairs, for each hyperedge e, its weight W e It is defined by associating the co-expression strength of all gene pairs in the hyperedge; assuming that the hyperedge e connects the gene set {g1,g2,…,g k}, then its weight W e Defined as the average or weighted average of the pairwise correlations within the gene set:

[0047]

[0048] Where |E| represents the number of gene pairs in the hyperedge, corr(g i ,g j ) indicates gene g i and g jThe correlation between them.

[0049] In a third aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the hypergraph-based weighted gene co-expression supernetwork module identification method when executing the computer program.

[0050] In a fourth aspect, the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the hypergraph-based weighted gene co-expression supernetwork module identification method are implemented.

[0051] Compared with the prior art, the present invention has the following technical effects:

[0052] The present invention introduces hypergraph theory and constructs a weighted hypergraph to represent the complex interaction patterns between multiple genes. The use of hypergraph enables the method to connect multiple genes at the same time and capture their synergistic relationships in multiple biological samples, thereby making up for the deficiency of WGCNA being limited to pairwise interactions. In this way, WGCHNA can more accurately reveal the biological mechanism of the joint action of multiple genes.

[0053] The present invention effectively improves the computational efficiency by optimizing the hypergraph construction and using the hypergraph Laplacian matrix for network analysis. Compared with the traditional WGCNA method, WGCHNA shows higher computing speed and processing power when processing large-scale gene data sets, so that the gene co-expression network can be analyzed more quickly to meet the needs of multiple samples and complex networks.

[0054] By integrating high-order interaction information of multiple genes, WGCHNA can more accurately identify co-expression modules related to biological processes or diseases. Experimental results show that WGCHNA has a higher accuracy in screening pathogenic genes and successfully identifies key gene modules related to specific diseases (such as Alzheimer's disease). This not only verifies known biological information, but also reveals new potential regulatory relationships, enhancing its application value in actual biomedical research. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 Weighted gene co-expression supernetwork analysis pipeline.

[0056] Figure 2 Soft threshold processing and scale-free verification, where A is the 5xFAD dataset. When the soft threshold is 9, the constructed hypernetwork meets the scale-free characteristics; B is the GSE48213 dataset, and the soft threshold is 6; C and D are the GSE75360 and GSE75670 datasets, respectively, and the soft threshold is 19.

[0057] Figure 3 Comparison of running time of WGCHNA and Python and R versions of WGCNA for different numbers of genes.

[0058] Figure 4 Visualization of the correlation between characteristic gene expression profile modules (A) (black) and (B) (dark grey) and sample traits in the 5xFAD mouse model.

[0059] Figure 5 Downstream analysis and visualization of co-expression modules. A. Module-trait correlation calculation B. GO function enrichment analysis of black modules C. Hub genes in detection modules D. Protein-protein interaction diagram.

[0060] Figure 6 Comparison of GO enrichment analysis of top-10 genes. A, WGCHNA; B, PyWGCNA.

[0061] Figure 7 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0062] The present invention is further described below in conjunction with the accompanying drawings:

[0063] Example 1, please refer to Figure 7 The present invention provides a method for identifying a weighted gene co-expression supernetwork module based on a hypergraph, comprising:

[0064] Obtain the gene expression matrix and integrate the effective gene set of each sample to construct a weighted hypergraph;

[0065] Calculate the Laplacian matrix of the weighted hypergraph, and based on the Laplacian matrix, obtain the topological overlap matrix;

[0066] Based on the topological overlap matrix, the hierarchical clustering method was used to identify gene modules and output the gene co-expression modules.

[0067] The present invention proposes a weighted gene co-expression hypernetwork analysis method based on hypergraph theory, which is used to identify disease-related gene co-expression modules. By introducing a high-order association model of hyperedges, it effectively overcomes the limitation that traditional WGCNA can only process simple binary relationships between gene pairs. This method can capture complex multi-gene interactions, thereby more accurately identifying disease-related gene modules. In terms of clustering performance, functional enrichment verification, etc., it is significantly superior to the existing technology, so that the accuracy and biological relevance of gene module screening are improved. This innovation not only improves the efficiency of data processing, but also enhances the ability to identify potential pathogenic genes in complex biological networks, and further expands the application potential of gene co-expression networks in disease mechanism research.

[0068] Embodiment 2, the present invention provides a method for identifying weighted gene co-expression supernetwork modules based on a hypergraph, specifically comprising:

[0069] In order to more accurately capture the complex high-order interactions between genes and improve the computational efficiency of large-scale data sets, we designed an algorithm flow of the weighted gene co-expression hypernetwork analysis (WGCHNA) system based on hypergraphs, such as Figure 1 The process covers data preprocessing, hypergraph construction, gene module identification and functional enrichment analysis, ultimately revealing the relationship between modules and the potential functions of key genes.

[0070] WGCHNA connects multiple genes together by constructing a weighted hypergraph to reflect the complex co-expression patterns among samples. Next, we will introduce the specific steps of the system algorithm in detail:

[0071] The construction process of weighted hypergraph and the definition of weights

[0072] The input of the algorithm is a gene expression matrix, where rows represent samples and columns represent genes. After preprocessing the gene expression profile, the algorithm integrates the effective gene set of each sample and constructs a weighted hypergraph H = (V, E, W). Among them, V is the set of gene nodes, E is the set of sample hyperedges, and W is the weight matrix of sample hyperedges.

[0073] Definition of the weight matrix W

[0074] The weight matrix W reflects the weight of each hyperedge, that is, the strength of co-expression between different genes. In a weighted hypergraph, the weight of a hyperedge is a quantitative measure of the strength of gene co-expression. Specifically, the construction process of the weight matrix W is as follows:

[0075] Gene expression correlation: First, based on the gene expression matrix, the co-expression strength between genes is determined by calculating the correlation between genes (such as the Pearson correlation coefficient). i and g j , their expression correlation in multiple samples can be calculated corr(g i ,g j ), indicating the strength of their co-expression relationship.

[0076] Definition of hyperedge weight: After determining the correlation between gene pairs, for each hyperedge e, its weight W e It can be defined by associating the co-expression strength of all gene pairs in the hyperedge. Assume that the hyperedge e connects the gene set {g1,g2,…,g k}, then its weight W eIt can be defined as the average or weighted average of the pairwise correlations within the gene set:

[0077]

[0078] Where |E| represents the number of gene pairs in the hyperedge, corr(g i ,g j ) indicates gene g i and g j In this way, each hyperedge of the hypergraph not only represents the co-expression relationship between gene sets, but also reflects the strength of this synergy through weight. The stronger the co-expression relationship between genes, the greater the weight of the hyperedge, thus playing a more significant role in the hypergraph.

[0079] Compute the hypergraph Laplacian matrix

[0080] After the hypergraph is constructed, the next step is to calculate the Laplacian matrix of the hypergraph for further topological analysis. The hypergraph Laplacian matrix is ​​a mathematical representation of the complex associations between nodes (genes) and hyperedges (samples) in the hypergraph, which can capture high-order relationships between multiple genes and samples. The Laplacian matrix of the hypergraph is defined as:

[0081]

[0082] Among them, D v is the hyper-degree diagonal matrix of gene nodes in the hypergraph, D e is the hyperdegree diagonal matrix of the sample hyperedge, W is the weight matrix of the hyperedge, and H is the incidence matrix of the hypergraph. The symbols that appear in the following text have the same meaning as here.

[0083] In order to further adapt to the scale of data and the stability of calculation, the Laplace matrix is ​​normalized:

[0084]

[0085] Where I is the identity matrix. Compared with the Laplacian matrix of a simple graph, this definition can better reflect the high-order structure in the weighted gene co-expression supernetwork.

[0086] Compute the topological overlap matrix

[0087] Next, based on the hypergraph Laplacian matrix, the topological overlap matrix (TOM) is calculated. TOM reflects the topological overlap between gene pairs and is used to measure the similarity of gene pairs. For genes i and j, the calculation formula of TOM is expressed as:

[0088]

[0089] Among them, Δ ij is the value between gene i and gene j in the hypergraph Laplacian matrix; d i and d j are the degrees of genes i and j, i.e., the number of connections between them and other genes. The TOM matrix is ​​a measure of similarity between each pair of genes, which helps to identify gene pairs that are co-expressed in multiple samples and is ultimately used for clustering analysis of modules.

[0090] Gene module clustering

[0091] After obtaining the TOM matrix, WGCHNA uses a hierarchical clustering method to identify gene modules. Specifically, the dissimilarity of the Topological Overlap Matrix (dissTOM) is first calculated, which is defined as:

[0092] dissTOM(i,j)=1-TOM(i,j)

[0093] In order to further improve the accuracy of module identification, the algorithm adopts a dynamic module merging strategy. By dynamically detecting similar modules and merging them, the modules are guaranteed to have higher stability and biological relevance.

[0094] Module output and subsequent analysis

[0095] Finally, WGCHNA outputs gene co-expression modules. These modules represent gene groups that are co-expressed in different samples and can reflect potential biological functions or regulatory mechanisms. The identified gene modules can be further used for functional enrichment analysis, disease correlation studies, or other subsequent biological analyses.

[0096] The gene data used by WGCHNA comes from the mouse Alzheimer's disease dataset (5xFAD) in MODEL-AD, and the breast cancer (GSE48213) and hypertension (GSE75360, GSE75670) datasets in the GEO database. Table 1 shows the detailed information of each dataset.

[0097] Table 1 Detailed information of the experimental dataset

[0098]

[0099] To evaluate the effectiveness of WGCHNA, we compared it with traditional WGCNA methods (PyWGCNA and RWGCNA). WGCNA was originally widely used in R language, but as Python's influence in the field of bioinformatics continues to grow, Python versions of WGCNA have gradually been developed and widely used. Both versions have their own advantages in functions and usage scenarios, and are suitable for different research needs.

[0100] 3. Data preprocessing and scale-free verification

[0101] Because the first step of WGCNA is to construct a gene co-expression network that conforms to scale-free characteristics by selecting an appropriate soft threshold. This step can effectively reflect the inherent characteristics of biological networks, that is, the imbalance of connections between a few hub genes and a large number of genes. When we extend the analysis to weighted hypergraphs, we also need to construct a weighted gene co-expression supernetwork that conforms to scale-free characteristics through soft thresholds. Scale-free hypernetworks can not only capture the complex high-order relationships between multiple genes, but also ensure that the topological structure of the network is consistent with the characteristics of actual biological systems.

[0102] Therefore, before the experiment begins, it is necessary to first perform missing value processing and soft threshold selection operations on each gene data set to construct a weighted gene co-expression supernetwork. The supernetwork constructed by the soft threshold we selected has been verified by the super-degree distribution law and all meet the scale-free characteristics. Figure 2 shown.

[0103] In the present invention, Silhouette Index,(SI), Calinski-Harabasz Index,(CHI) and Davies-Bouldin Index,(DBI) are used as internal clustering evaluation indicators to evaluate the clustering quality obtained using various methods. In addition, Adjusted Mutual Information,(AMI) and Adjusted Rand Index,(ARI) external clustering evaluation indicators are also used to evaluate the clustering quality of the data set.

[0104] In the clustering process, for the fairness of the experiment, we set the same parameters for WGCHNA, PyWGCNA, and R WGCNA: the minimum module size (minClusterSize) is set to 50, the module partition depth (deepSplit) is set to 2, and the modules with similarity exceeding 80% are merged. The experimental results are listed in Tables 2 and 3 respectively.

[0105] Table 2 Comparison of internal evaluation indicators obtained by WGCHNA with different modeling methods on all gene expression datasets

[0106]

[0107] Table 3 Comparison of external evaluation indicators obtained by WGCHNA with different modeling methods on all gene expression datasets

[0108]

[0109] From the experimental data in Tables 2 and 3, we can see that WGCHNA has the best clustering effect on multi-sample datasets, especially in capturing complex gene expression patterns. However, when the data size is relatively small or similar, the performance differences of each method are relatively limited.

[0110] In the experiment, the average running time of three algorithms (WGCHNA, PyWGCNA, and RWGCNA) was calculated for gene datasets of different magnitudes. The results are shown in the figure. Figure 3 The experiments cover gene datasets ranging from small to large, aiming to evaluate the performance of each algorithm when dealing with different numbers of genes.

[0111] The subsequent processing steps of WGCHNA follow the same method as WGCNA. The topological overlap matrix of the hypergraph Laplacian matrix is ​​calculated and dynamic tree cutting is performed to identify the co-expression modules of genes, such as Figure 4 Shown is a bar graph representation of the 5xFAD gene module identified by WGCHNA and sample traits.

[0112] Figure 4 In the figure, the first three rows show the traits of each sample, including sex, tissue, and age. The bar graph shows the module characteristic gene expression of each sample divided by genotype, and the module characteristic gene expression of a single sample is shown as a point.

[0113] Depend on Figure 4 It can be seen that the expression of two gene modules (black and dark gray) in 5xFAD under different experimental conditions. The color bar represents the genotype, gender, tissue type and age group of the sample. The gene expression of the black module showed obvious differences under different conditions, especially in specific age groups (such as 8 months and 12 months) and hippocampal tissue, where samples of the 5xFAD / WT genotype showed higher characteristic gene values. The gene expression of the dark gray module was relatively low, and did not change much under most conditions, with only some upward trends in the 8-month-old 5xFAD / HEMI group.

[0114] WGCHNA supports the same downstream analysis functions and visualization of co-expression modules as PyWGCNA. It can calculate module-trait correlations and summarize the expression of module characteristic genes in sample source data, detect hub genes in each module, and perform functional enrichment analysis in each module using databases such as GO, KEGG, and REACTOME. Figure 5 Shown are the downstream analysis results of the black module in the 5xFAD gene co-expression module identified by WGCHNA.

[0115] Figure 5 The trait correlation and functional annotation results of the black module genes in the WGCHNA analysis are shown. The heat map (A) shows the correlation between the characteristic genes of the module and different traits (such as age and gender). It is found that the module genes are significantly negatively correlated in the 12-month-old samples and positively correlated in the 18-month-old samples. The bubble chart (B) reveals the main biological processes involved in the module genes through GO functional annotation, including cytoplasmic translation, protein targeting membrane, and mitochondrial ATP synthesis. The co-expression network (C) shows the strong correlation between the module genes, and the STRING protein interaction network (D) further reveals the close cooperative relationship between these genes in molecular function.

[0116] Existing studies have shown that high-order network modeling methods have significant advantages in the analysis of complex biological networks, especially in the identification of key gene modules. For example, by introducing a hypergraph model, the complex synergy between multiple genes can be captured more effectively, especially when dealing with multi-sample disease data, the hypergraph model can screen out gene modules that are highly related to the disease. To verify this point of view, we took the mouse Alzheimer's disease dataset (5xFAD) as an example to compare the performance of the two methods WGCHNA and PyWGCNA. Table 4 shows the top 10 genes in the gene co-expression modules mined by the two methods. N / A means that the relevant genes could not be identified due to the limitations of the numerical calculation accuracy of the algorithm.

[0117] Table 4 Comparison of 5xFAD gene co-expression modules

[0118]

[0119] By comparison, it can be found that PyWGCNA and WGCHNA have significant differences in the key genes they identify. The top 10 genes identified by PyWGCNA include genes such as Cttn, Prkcg, and Rasgrf1 related to Alzheimer's disease, which have been reported in existing literature to be related to neurodegenerative diseases. However, PyWGCNA is greatly affected by noise in some gene tests (such as Cttn and Prkcg), which may lead to uncertainty in the functional information of some genes.

[0120] Relatively speaking, the gene modules identified by WGCHNA are more diverse and capture genes related to key biological processes such as mitochondrial function and translation regulation. For example, mt-Nd4l and Cox8b are genes encoded by mitochondrial DNA, which are known to be closely related to neuronal energy metabolism, and energy metabolism disorders are one of the main pathological mechanisms of Alzheimer's disease. This shows that WGCHNA can more effectively capture complex and highly relevant high-order gene synergies with disease mechanisms. Although WGCHNA has N / A in some gene identifications, it may be due to the accuracy limitations of the algorithm under specific computing conditions, but this does not significantly affect the biological functionality of the overall module. Overall, WGCHNA can identify more biologically relevant gene lists, especially in disease-related module mining.

[0121] To further verify the differences between the two methods, we performed GO functional enrichment analysis on the identified gene modules. Figure 6 The enrichment results of two methods are shown, A is the enrichment analysis of the WGCHNA method, and B is the enrichment analysis of the PyWGCNA method.

[0122] The advantages of WGCHNA can be illustrated from three aspects through GO functional enrichment analysis: first, the gene modules identified by WGCHNA have higher statistical significance, especially in pathways closely related to the core mechanisms of the disease, such as mitochondrial function and energy metabolism; second, the biological processes revealed by WGCHNA are more diverse, covering biological functions at multiple levels such as translation, protein targeting and gene expression regulation, while the enrichment results of PyWGCNA are relatively single and focus on a relatively limited number of biological processes; finally, WGCHNA captures complex gene synergies through high-order modeling, showing stronger analytical capabilities, and therefore has obvious advantages in identifying key gene modules related to the disease.

[0123] In yet another embodiment of the present invention, a hypergraph-based weighted gene co-expression supernetwork module identification system is provided, which can be used to implement the above-mentioned hypergraph-based weighted gene co-expression supernetwork module identification method. Specifically, the system includes:

[0124] The data acquisition module is used to obtain the gene expression matrix and integrate the effective gene set of each sample to construct a weighted hypergraph;

[0125] A topological overlap matrix acquisition module is used to calculate the Laplace matrix of the weighted hypergraph and obtain the topological overlap matrix based on the Laplace matrix;

[0126] The identification output module is used to identify the modules of genes based on the topological overlap matrix and the hierarchical clustering method, and output the gene co-expression modules.

[0127] The division of modules in the embodiments of the present invention is schematic and is only a logical function division. There may be other division methods in actual implementation. In addition, each functional module in each embodiment of the present invention may be integrated into one processor, or may exist physically separately, or two or more modules may be integrated into one module. The above-mentioned integrated modules may be implemented in the form of hardware or in the form of software functional modules.

[0128] In another embodiment of the present invention, a computer device is provided, the computer device comprising a processor and a memory, the memory being used to store a computer program, the computer program comprising program instructions, and the processor being used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or may be other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions in a computer storage medium to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the weighted gene co-expression super network module identification method based on the hypergraph.

[0129] In another embodiment of the present invention, the present invention also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device for storing programs and data. It is understandable that the computer-readable storage medium herein may include a built-in storage medium in a computer device, and of course may also include an extended storage medium supported by a computer device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by a processor are also stored in the storage space, and these instructions may be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium herein may be a high-speed RAM memory, or may be a non-volatile memory (non-volatile memory), such as at least one disk memory. The processor may load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the weighted gene co-expression super network module identification method based on a supergraph in the above-mentioned embodiment.

[0130] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0131] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0132] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0133] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A hypergraph-based weighted gene co-expression supernetwork module identification method, characterized in that: include: Obtain the gene expression matrix and integrate the effective gene set of each sample to construct a weighted hypergraph; Calculate the Laplacian matrix of the weighted hypergraph, and based on the Laplacian matrix, obtain the topological overlap matrix; Based on the topological overlap matrix, the hierarchical clustering method was used to identify gene modules and output the gene co-expression modules.

2. The method for identifying weighted gene co-expression supernetwork modules based on a hypergraph according to claim 1, characterized in that: The step of obtaining a gene expression matrix and integrating the effective gene set of each sample to construct a weighted hypergraph includes: In the gene expression matrix, rows represent samples and columns represent genes. The effective gene sets of each sample are integrated to construct a weighted hypergraph H = (V, E, W), where V is the set of gene nodes, E is the set of sample hyperedges, and W is the weight matrix of sample hyperedges.

3. The method for identifying weighted gene co-expression supernetwork modules based on a hypergraph according to claim 2, characterized in that: The construction process of the weight matrix W is as follows: First, based on the gene expression matrix, the co-expression intensity between genes is determined by calculating the correlation between genes. For each pair of genes g i and g j , calculate their expression correlation in multiple samples corr(g i ,g j ), indicating the strength of their co-expression relationship; After determining the correlation between gene pairs, for each hyperedge e, its weight W e It is defined by associating the co-expression strength of all gene pairs in the hyperedge; assuming that the hyperedge e connects the gene set {g1,g2,…,g k }, then its weight W e Defined as the average or weighted average of the pairwise correlations within the gene set: Where |E| represents the number of gene pairs in the hyperedge, corr(g i ,g j ) indicates gene g i and g j The correlation between them.

4. The method for identifying weighted gene co-expression supernetwork modules based on a hypergraph according to claim 1, characterized in that: The calculating of the Laplacian matrix of the weighted hypergraph comprises: The hypergraph Laplacian matrix is ​​a mathematical representation of the complex associations between node genes and hyperedge samples in the hypergraph. It can capture high-order relationships between multiple genes and samples. The Laplacian matrix of the hypergraph is defined as: Among them, D v is the hyper-degree diagonal matrix of gene nodes in the hypergraph, D e is the hyperdegree diagonal matrix of the sample hyperedge, W is the weight matrix of the hyperedge, and H is the incidence matrix of the hypergraph; Normalize the Laplacian matrix: Where I is the identity matrix.

5. The method for identifying weighted gene co-expression supernetwork modules based on a hypergraph according to claim 4, characterized in that: The topological overlap matrix is ​​obtained based on the Laplace matrix, including: Based on the hypergraph Laplacian matrix, the topological overlap matrix TOM is calculated. TOM reflects the topological overlap between gene pairs and is used to measure the similarity of gene pairs. For genes i and j, the calculation formula of TOM is expressed as: Among them, Δ ij is the value between gene i and gene j in the hypergraph Laplacian matrix; d i and d j are the degrees of genes i and j, that is, the number of connections between them and other genes; the TOM matrix is ​​the similarity measure between each pair of genes.

6. The method for identifying weighted gene co-expression supernetwork modules based on a hypergraph according to claim 1, characterized in that: The method uses a hierarchical clustering method based on a topological overlapping matrix to identify genes as modules and output a gene co-expression module, including: After obtaining the TOM matrix, the hierarchical clustering method is used to identify the modules of genes. Specifically, the dissimilarity of the topological overlap matrix dissTOM is first calculated, which is defined as: dissTOM(i,j)=1-TOM(i,j) Adopt the strategy of dynamic module merging, dynamically detect similar modules and merge them; Finally, the gene co-expression module is output, which represents the gene groups that are co-expressed in different samples.

7. A hypergraph-based weighted gene co-expression hypernetwork module identification system, characterized in that: include: The data acquisition module is used to obtain the gene expression matrix and integrate the effective gene set of each sample to construct a weighted hypergraph; A topological overlap matrix acquisition module is used to calculate the Laplace matrix of the weighted hypergraph and obtain the topological overlap matrix based on the Laplace matrix; The identification output module is used to identify the modules of genes based on the topological overlap matrix and the hierarchical clustering method, and output the gene co-expression modules.

8. The hypergraph-based weighted gene co-expression supernetwork module identification system according to claim 7, characterized in that: The step of obtaining a gene expression matrix and integrating the effective gene set of each sample to construct a weighted hypergraph includes: In the gene expression matrix, rows represent samples and columns represent genes. The effective gene set of each sample is integrated to construct a weighted hypergraph H = (V, E, W), where V is the set of gene nodes, E is the set of sample hyperedges, and W is the weight matrix of sample hyperedges. The construction process of the weight matrix W is as follows: First, based on the gene expression matrix, the co-expression intensity between genes is determined by calculating the correlation between genes. For each pair of genes g i and g j , calculate their expression correlation in multiple samples corr(g i ,g j ), indicating the strength of their co-expression relationship; After determining the correlation between gene pairs, for each hyperedge e, its weight W e It is defined by associating the co-expression strength of all gene pairs in the hyperedge; assuming that the hyperedge e connects the gene set {g1,g2,…,g k }, then its weight W e Defined as the average or weighted average of the pairwise correlations within the gene set: Where |E| represents the number of gene pairs in the hyperedge, corr(g i ,g j ) indicates gene g i and g j The correlation between them.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the hypergraph-based weighted gene co-expression supernetwork module identification method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method for identifying weighted gene co-expression supernetwork modules based on a hypergraph as described in any one of claims 1 to 7 are implemented.

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