A single sample gene regulatory network construction method based on mutual information

Abstract

The present application belongs to the field of system biology, and particularly relates to a single sample gene regulation network construction method based on mutual information. The method comprises the following steps: specifying a background group and a foreground group of a research object; calculating a single sample gene regulation network of the background group and the foreground group based on a mutual information method; and performing significance test on network edges by using random permutation test. Compared with the prior art, the present application can identify a biological gene regulation network based on a nonlinear relationship, and is more in line with actual biological characteristics. The present application can specifically construct a gene regulation network of each sample, and can perform diversified data analysis according to different selected background groups.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of systems biology, and specifically relates to a single-sample gene regulatory network construction method for bulk transcriptome and single-cell transcriptome data of a large sample size. BACKGROUND

[0002] Gene regulatory networks (GRN) play a crucial role in the study of biological systems and complex diseases. They elucidate how the genomic sequence precisely controls the spatial and temporal patterns of gene expression and specifies cell type-specific functions and interactions. Experimental methods have helped us obtain a large number of regulatory relationships between transcript factors (TF) and target genes. However, there are certain limitations in experimental techniques themselves, and people have not yet been able to reveal the complete picture.

[0003] Many computational methods have been developed to reconstruct GRN from RNA sequencing (RNA-seq) and single-cell RNA sequencing (scRNA-seq) data sets. These algorithms can be roughly divided into two categories: one is to infer the aggregated network of the whole sample or cell type; the other is to construct sample-specific or cell type-specific networks. With the development of single-cell technology, the latter has become increasingly important. The latest progress in single-cell technology has made it possible to study cell heterogeneity at high resolution, thus providing a deeper understanding of cell heterogeneity in different biological processes. Therefore, the application and development of sample-specific networks (SSN) have become increasingly important. Liu et al. developed a single-sample-based SSN based on Pearson correlation, which is a linear method. Dai et al. first proposed a cell-specific network at the single-cell level by studying the non-parametric joint distribution of gene expression, retaining the heterogeneity between two cells. Wang et al. improved the cell-specific network by considering the mixing effect of cell populations and developed an algorithm for local cell-specific networks. Li et al. developed the c-CSN method to address the overfitting effect of cell-specific networks to non-directly related genes. These studies show that single-sample networks have significant potential in depicting highly heterogeneous biological systems.

[0004] However, obtaining SSN alone can not be enough to reveal important changes in cell development and disease progression. Recently, differential networks emerged as a more effective means to identify these changes. However, current algorithms to construct SSN cannot generate differential networks, except for the "SSN" based on Pearson correlation developed by Liu et al., which is only applicable to linear systems. The complex regulatory relationships between various biological phenomena such as transcription factor regulation, receptor cascade, epigenetic modification, genome editing, RNA editing, cell signaling pathways, and RNA interference can all affect the changes in gene expression levels to varying degrees. Therefore, the regulatory relationships in most biological systems are not simply linearly correlated. SUMMARY

[0005] The present application aims to provide a single-sample gene regulatory network construction method based on mutual information theory to overcome the above-mentioned defects in the prior art.

[0006] The single-sample gene regulatory network construction method based on mutual information provided by the present application, referred to as diffMIN, has the following specific steps:

[0007] S1: First, pre-process the gene expression data to eliminate genes and samples with low gene expression levels; then, uniformly discretize the gene expression data;

[0008] S2: Before starting the calculation, designate a portion of the samples as background samples (assuming N1) and the remaining samples as foreground samples (assuming N2) according to biological significance; obtain the initial differential network by calculating the perturbation of the foreground samples on the background samples;

[0009] S3: Calculate the mutual information correlation network of the background samples and the perturbed samples, respectively; wherein, the mutual information correlation network between any two genes X = (x1, x2, x3,..., x n ) and gene Y = (y1, y2, y3,..., y n ) in the sample is calculated as follows:

[0010]

[0011] Where n represents the number of samples, p(x), p(y) represent the marginal probability of X, Y, respectively, and p(x, y) represents the joint probability of X, Y.

[0012] S4: Then, standardize the mutual information network to obtain the sample correlation network after standardization, and the standardization calculation formula is as follows:

[0013]

[0014] Wherein, respectively, represent the information entropy of variables X, Y. The mutual information network calculated from the background samples is represented as The mutual information network obtained by adding a foreground sample j (j = 1, 2,..., N2) to the background samples is represented as

[0015] S5: By calculating the difference between the perturbed network and the background network, the network changes caused by the perturbed samples are identified, and the calculation formula is as follows:

[0016]

[0017] Wherein, j represents the jth foreground sample to be calculated;

[0018] S6: For the calculation of the individual network of the background samples, an approximate method is adopted, but the difference is that each time a single sample i, i = 1, 2,..., N1, is removed from the background group, and the perturbation change of the overall network after removing the single sample is calculated; the calculation formula is as follows:

[0019]

[0020] Wherein, i represents the ith background sample to be calculated;

[0021] S7: The significance test of the edges of the network is performed by using the random permutation test method to obtain the significance value (referred to as P value) of the edges of the network; a random network is constructed by randomly rearranging the gene distribution, and the specific method is to maintain the order of the samples unchanged, and randomly rearrange the expression level of each gene, and construct a new random network under the condition of maintaining the gene distribution unchanged;

[0022] S8: According to the same method as described above, the difference network of the random network is calculated. And the random permutation test method is used to perform the permutation test on the edges of the calculated real network.

[0023] Based on the single-sample gene regulatory network construction method described above, the present application also includes a single-sample regulatory network construction system. The system specifically includes 8 modules, which are: a gene expression data preprocessing module, an initial difference network calculation module, a mutual information correlation network calculation module, a sample correlation network calculation module, a network perturbation change calculation module, an overall network perturbation change calculation module, a random network construction module, and a random network difference network calculation module. The 8 modules respectively perform the specific operations of the 8 steps of the single-sample regulatory network construction method described above.

[0024] The mutual information (MI) technology adopted by the present application has been proved to have advantages in measuring gene expression regulation in biological systems.

[0025] The diffMIN provided by the application is superior to the existing SSN algorithm in cell clustering and more effective than clustering based on gene expression only, as indicated by analysis of various single-cell data sets. The application successfully applies the diffMIN to transverse aortic constriction (TAC) single-cell data, constructs a differential network under pressure overload, and identifies the single modulation of the regulatory network in the heart failure process. The application also applies the diffMIN to breast cancer samples from The Cancer Genome Atlas (TCGA) and finds that the diffMIN can identify key genes that are strongly related to prognosis but have insignificant expression differences. Overall, the method has wide applicability and performs well in cell clustering, key gene identification, biological process research, and disease diagnosis.

[0026] Compared with the prior art, the technical features and performance advantages of the application mainly include:

[0027] (1) Strong flexibility, which can construct different single-sample gene regulatory networks according to different research purposes. The first step to identify a differential network is to select a background group, and then add samples one by one to identify the influence of individual samples on the background network. The selection of the background group significantly affects network construction and also provides flexibility for researchers studying biological phenomena. For example, if the researcher wants to investigate the regulatory network of cells in different developmental states, the initial developmental state can be used as the background group. Alternatively, if the researcher is interested in the differences in the regulatory network between other cell types and a specific cell type, the specific cell type can be used as the background group. In summary, selecting different background groups can meet different research needs.

[0028] (2) Using a nonlinear method to more truly measure the biological network. As a method for identifying nonlinear models, mutual information is more effective than linear model methods in evaluating complex biological networks. Gene activation, expression enhancement, positive and negative feedback, and cascading reactions often exhibit complex nonlinear correlations. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 A schematic diagram of the diffMIN network construction principle of the application.

[0030] Figure 2 Distribution of edges of a random network and a real network. A. Distribution of edges of a random network; B. Distribution of edges of a real network with perturbation.

[0031] Figure 3 Relationship between the number of tests of the random permutation test and the significance of the edges.

[0032] Figure 4The relationship between computation time and related parameters is shown in Figure 2. A represents the relationship between the number of selected background cells and computation time. B represents the relationship between the number of genes selected for computation and computation time. C represents the relationship between the number of random networks and computation time. D represents the relationship between the number of random permutation tests and computation time.

[0033] Figure 5 Figure 1 shows the application of the diffMIN method in studying the progression of cardiovascular disease. Figure A shows the visualization of the sample gene expression matrix after dimensionality reduction using t-Distributed Stochastic Neighbor Embedding (t-SNE). Figure B shows a heatmap of gene expression for the sample on the left and a heatmap of gene pairs (i.e., edges calculated by diffMIN) on the right. Figure C shows the gene regulatory network of the sample at different time points.

[0034] Figure 6 Results of survival analysis of the LAPTMB gene in the diffMIN network for groups with high and low node degrees. DETAILED DESCRIPTION

[0035] The present invention is further described below through embodiments in conjunction with the accompanying drawings.

[0036] Example 1:

[0037] The public dataset GSE95140 from the GEO database was used to calculate the single-sample gene regulatory network.

[0038] The method of the present invention was applied to single-cell RNA sequencing data (GSE95140) to reveal the gene regulatory network pattern of cardiomyocytes undergoing transverse aortic constriction (TAC). In this case, normal cardiomyocytes were selected as the background group to calculate diffMIN. The gene expression matrix (GEM) and degree matrix (DEM) calculated by diffMIN were used for UMAP dimensionality reduction. After dimensionality reduction using DEM, as shown in Figure 2, the gene expression matrix (GEM) and degree matrix (DEM) calculated by diffMIN were used for UMAP dimensionality reduction. Figure 5As shown, the samples exhibit clear temporal trajectories, whereas in the GEM images, the samples are completely disorganized, making it impossible to discern trajectory information. Heatmaps of gene expression and edge relationships were further plotted. Specific genes exhibited discontinuous patterns across disease states, but differential edges calculated using diffMIN revealed some clear trends with disease progression. The complexity of all cells was assessed by counting the number of significantly differential edges, demonstrating that disease states exhibit increasingly complex interconnections, with complexity decreasing with disease progression. This is consistent with a series of gene regulatory changes initiated by cardiomyocytes upon receiving pressure overload signals, designed to combat stress on the heart. While compensation is generally considered a beneficial response, under conditions of persistent pressure overload, it can transition to a decompensated state, leading to pathological structural remodeling and ultimately heart failure. Furthermore, key hub genes in distinct networks, Nppa, Ankrd1, and Acta1, were observed to play a key role in the progression of pressure overload. These results suggest the potential advantages of diffMIN for exploring disease progression, particularly in hypertension.

[0039] Example 2:

[0040] Cancer typing and prognosis analysis are crucial for studying cancer in the field of bioinformatics. In order to further explore the biological functions of cancer, the diffMIN method was applied to the TCGA-BRCA dataset. The data were preprocessed and sampled, and the degree matrix (DEM) and gene expression matrix (GEM) calculated by diffMIN were used as input clustering results. The study found that the network-based dimensionality reduction method can better distinguish between tumor samples and normal samples. Interestingly, it was observed that the gene expression of LAPTMB remained relatively consistent in most patients, but a higher degree appeared in some samples. The patients were further typed according to the degree of LAPTMB, and it was found that Figure 6 As shown, patients with higher LAPTMB degrees tend to have a worse prognosis, while those with lower degrees have a relatively better prognosis. The results suggest that network-based features can enhance gene expression signatures, potentially revealing additional biological information that may be overlooked by gene expression alone.

[0041] The preferred embodiments of the present invention are described in detail above.

Claims

1. A method for constructing a single-sample gene regulatory network based on mutual information, characterized in that: The specific steps are: S1: First, preprocess the gene expression data to remove genes and samples with low gene expression; then, uniformly discretize the gene expression data; S2: According to biological significance, a portion of samples is first designated as background samples, with N1 being the number, and the remaining samples are designated as foreground samples, with N2 being the number. The initial difference network is obtained by calculating the perturbation of the foreground samples on the background samples. S3: Calculate the mutual information correlation network of background samples and perturbation samples respectively; where any two genes in the sample X=(x1,x2,x3,...,x n ) and gene Y=(y1,y2,y3,...,y n ) The formula for calculating the mutual information correlation network between is as follows: Where n represents the number of samples, p(x) and p(y) represent the marginal probabilities of X and Y respectively, and p(x,y) represents the joint probability of X and Y; S4: Normalize the mutual information network to obtain the normalized sample correlation network. The normalization calculation formula is as follows: in, Represent the information entropy of variables X and Y respectively; the mutual information network calculated by background samples is expressed as The mutual information network obtained by adding a foreground sample j (j = 1, 2, ..., N2) to the background sample is expressed as S5: By calculating the difference between the perturbed network and the background network, the network changes caused by the perturbed sample are identified. The calculation formula is as follows: Among them, j represents the jth foreground sample to be calculated; S6: For the calculation of the individual network of the background sample, an approximate method is used, wherein each time a single sample i is removed from the background population, i = 1, 2, ..., N1, and the perturbation change of the overall network after removing the single sample is calculated; the calculation formula is as follows: Where i represents the i-th background sample to be calculated; S7: Perform a significance test on the edges of the network using a random permutation test to obtain the significance value of the edges of the network; construct a random network by randomly perturbing the gene distribution. Specifically, the method is to keep the order of the samples unchanged, randomly perturb the expression level of each gene, and construct a new random network while keeping the gene distribution unchanged; S8: Calculate the difference network of the random network in the same way as above; and use the random permutation test method to perform a permutation test on the edges of the calculated real network.

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