A method for evaluating cell population heterogeneity based on energy indicators

Abstract

The present invention provides a method for evaluating the heterogeneity of a cell population based on an energy index, which belongs to the field of biorecognition technology, and comprises the following steps: step S1, preprocessing single cell transcriptome data; step S2, feature selection of the preprocessed data, and definition of cell state; step S3, constructing a local gene network based on a Hopfield neural network; step S4, calculating the local gene network energy and cell energy, and normalizing the cell energy; step S5, introducing a Gaussian mixture model, identifying the potential state of the cell by analyzing the energy distribution difference of the cell, and clustering cells in the same differentiation potential state; step S6, evaluating the heterogeneity of the cell population. The present invention adopts the above-mentioned method for evaluating the heterogeneity of a cell population based on an energy index, which can more accurately reveal the complexity and differences within the cell population.

Description

Technical Field

[0001] The present invention relates to the field of biorecognition technology, and in particular to a method for evaluating cell population heterogeneity based on energy indicators. Background Art

[0002] Cell heterogeneity is defined as an inherent property of biological systems that contributes to genetic diversity. Identifying and characterizing heterogeneity within cell populations can effectively reveal the complexity and differences within seemingly homogeneous cell populations, which are not only reflected in gene expression, protein levels, and metabolic states, but also reflect the responsiveness and functional states of cells under different physiological and pathological conditions. Traditionally, the characterization of cell population heterogeneity has mainly relied on some well-understood dimensions, such as cell cycle stages or cell types. These dimensions are often used to divide cell populations into unique and biologically meaningful mixtures. However, in the absence of obvious or known biological explanations for cell-to-cell variation, cell states can be distinguished by selecting specific molecular differences, such as cell adhesion or immune molecules, which show great diversity due to differences in individual cells. However, characterizing cell states based solely on these molecular differences may be one-sided and insufficient to reveal the biological characteristics of the cell as a whole.

[0003] With the rapid development of single-cell sequencing technology, a large amount of single-cell data has been obtained, providing unprecedented opportunities for in-depth understanding of the heterogeneity of cell populations. However, how to fully explore the internal differences and functions of cell populations from these massive single-cell data remains a challenge. Therefore, there is an urgent need to develop new tools that can effectively identify and explain the heterogeneity of cell populations and identify homogeneous cells with the same potential state. Summary of the invention

[0004] The purpose of the present invention is to provide a method for evaluating the heterogeneity of a cell population based on energy indicators, which can more accurately reveal the complexity and differences within the cell population.

[0005] To achieve the above object, the present invention provides a method for evaluating cell population heterogeneity based on energy indicators, comprising the following steps:

[0006] Step S1, preprocessing single-cell transcriptome data;

[0007] Step S2, performing feature selection on the preprocessed data to define the cell state;

[0008] Step S3, constructing a local gene network based on the Hopfield neural network;

[0009] Step S4, calculating the gene local network energy and cell energy, and normalizing the cell energy;

[0010] Step S5, introducing a Gaussian mixture model, identifying the potential state of cells by analyzing the energy distribution difference of cells, and clustering cells in the same differentiation potential state;

[0011] Step S6: assessing the heterogeneity of the cell population.

[0012] Preferably, in step S1, for a single cell expression matrix comprising N cells and M1 genes The set of all genes in cell n is represented as follows:

[0013]

[0014] in, Represents the expression level of gene M1 in cell n.

[0015] Preferably, in step S1, the preprocessing includes logarithmic transformation processing and standardization processing.

[0016] Preferably, in step S2, feature selection is performed on the preprocessed data to define the cell state, and the specific operation is: screening the preprocessed data for highly variable genes through the FindVariableFeatures function, and retaining 1000 to 5000 highly variable genes;

[0017] Get the dataset contains N cells and M highly variable genes, and the state of cell n is represented by the vector To express;

[0018] in, Represents the state value of gene i in cell n, according to The sign of is determined as follows:

[0019]

[0020] in, Represents the normalized expression level of gene i in cell n.

[0021] Preferably, in step S3, the nodes in the gene local network represent genes, and the interactions between genes in the network are specified by their adjacency matrix W, where the matrix elements w ij Represents the relationship between genes i and j:

[0022]

[0023] in, represents the state value of gene j in cell n; p represents the number of stable states.

[0024] Preferably, in step S4, the calculation formula of Gene Local Network Energy (GLNE) is as follows:

[0025]

[0026] in, is the energy value of the local network centered on gene i in cell n; N(i) represents the neighborhood of node i in the network.

[0027] Preferably, in step S4, the cell energy is composed of the local network energy levels of all genes contained in the cell, and is defined as:

[0028]

[0029] Among them, E n is the energy value of cell n; M represents the number of highly variable genes.

[0030] Preferably, in step S4, the normalization process is:

[0031]

[0032] in, and Respectively represent the minimum and maximum energy values ​​of all cells; E' n is the normalized cellular energy.

[0033] Preferably, in step S5, a Gaussian mixture model is introduced to identify the potential state of cells by analyzing the energy distribution difference of cells, and cells in the same differentiation potential state are clustered. The specific operation is:

[0034] For a cell population S containing N cells, the normalized cell energy E' n∈N To quantify the differentiation potential status of each cell;

[0035] The cells are sorted according to their energy and the E' of all cells is calculated using a Gaussian mixture model. n∈N The values ​​are fitted;

[0036] Among them, the Gaussian mixture model is as follows:

[0037]

[0038] in, represents the kth Gaussian distribution with a given mean μ k and variance The probability density function under the condition λ k >0 is the mixing weight of the kth Gaussian distribution, satisfying

[0039] The number of components K of the Gaussian distribution is determined by the Bayesian Information Criterion BIC, which is defined as:

[0040]

[0041] Here, v is the number of estimated parameters.

[0042] Preferably, in step S6, the heterogeneity of the cell population is evaluated, and the specific operations are as follows:

[0043] Each cell in the cell population S is assigned to K specific potential states, and the probability of a cell being assigned to the kth potential state is defined as p k :

[0044]

[0045] Among them, N(C k ) and N(S) represent the kth potential state and the total number of cells contained in the cell population S, respectively;

[0046] The heterogeneity index is then used to measure the diversity of cells in each population in terms of their potential states. The heterogeneity index is calculated as follows:

[0047]

[0048] Among them, HI is the heterogeneity index.

[0049] Therefore, the present invention adopts the above-mentioned method for evaluating cell population heterogeneity based on energy index, and the beneficial technical effects are as follows:

[0050] (1) The present invention introduces a Gaussian mixture model (GMM) to identify the potential state of cells by analyzing the energy distribution differences of cells, and more accurately identify cell populations with consistent differentiation potential, overcoming the limitation of traditional methods that rely too much on transcriptome similarity, and providing a more flexible and accurate cell clustering method;

[0051] (2) The present invention proposes a heterogeneous index (HI), which can quantify and evaluate the diversity within different cell populations, helping researchers to distinguish and screen cell populations with different potential states and biological characteristics. If a population contains multiple potential states, the heterogeneity index score is high, indicating that its internal heterogeneity is large; on the contrary, if the potential states of cells in the population are relatively consistent, the heterogeneity index score is low;

[0052] (3) The present invention not only helps to deeply understand the biological characteristics of cells, but also can identify new or dynamically changing homogeneous cell populations in studies such as cell differentiation and reprogramming, providing more comprehensive and accurate tools for biological research and clinical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A flow chart of a method for evaluating cell population heterogeneity based on energy indicators according to the present invention;

[0054] Figure 2 It is the dimensionality reduction analysis of cells at different sampling points; among them, Figure 2 (A) shows the dimensionality reduction analysis results of the gene local network energy matrix of cells at different sampling points; Figure 2 (B) shows the dimensionality reduction analysis results of the expression matrix of cells at different sampling points;

[0055] Figure 3 is the energy calculation of cells at different sampling points; Figure 3 (A) in the figure is the normalized energy value of cells at different sampling points; Figure 3 (B) shows the energy density distribution of cells at different sampling points;

[0056] Figure 4 To assess the heterogeneity of different cell populations; Figure 4 (A) in the figure is the identification of the optimal number of clusters; Figure 4 (B) in the figure shows the energy distribution of three potential states; Figure 4 (C) is the evaluation of cell population heterogeneity derived from different sampling points and Seurat v.3 clustering results; Figure 4 (D) in the middle shows the GLNE level of the pluripotency gene Sox2 in three potential states; Figure 4 (E) in the middle shows the GLNE level of Zfp352 gene in three potential states; Figure 4 (F) in the figure shows the GLNE level of the pluripotency gene MT2-Mm in three potential states. DETAILED DESCRIPTION

[0057] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0058] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0059] Embodiment 1

[0060] like Figure 1As shown, it is a flow chart of a method for evaluating cell population heterogeneity based on energy indicators of the present invention, which specifically includes five parts: definition of cell state, construction of local gene network, calculation of local gene network energy, identification of cell differentiation potential state, and evaluation of heterogeneity of cell population.

[0061] Definition of cell states;

[0062] The data involved in this example are single-cell transcriptome data of Dux-induced 2-cell (2C)-like cells, and the specific gene expression matrix is ​​derived from GSE133233.

[0063] First, according to the data preprocessing method provided in the article (Fu X, Djekidel M, Zhang Y. Sci Adv. 2020 May 29; 6 (22): eaay5181) of the data source, cells with less than 800 transcripts and cells in which mitochondrial transcripts accounted for more than 10% of the total transcripts were excluded. At the same time, genes expressed in less than 3 cells were also removed. The filtered data included 19918 genes and 2298 cells, which were 2C-like cells collected immediately after Dux induction (H0, n = 1304) and cells collected after further culture for 24 hours (H24, n = 994).

[0064] The above data were screened using feature selection methods. The specific operations are as follows: the NormalizeData and ScaleData functions of the Seurat software package were used to logarithmically transform and standardize the data, and finally the FindVariableFeatures function with default parameters was used to identify highly variable genes (HVGs). The final data set obtained There are 2298 cells and 2000 HVGs in it. The state of cell n is represented by the vector To express. Represents the status value of gene i in cell n, based on its expression level after standardized processing in cell n The sign of is determined as follows:

[0065]

[0066] Construction of local gene networks;

[0067] This embodiment refers to the Hopfield Neural Network (HNN) when constructing the local gene network. The network is a single-layer fully connected feedback neural network consisting of nodes and weighted undirected edges. In the HNN model, the output of each node is calculated based on the interaction between the node and other nodes in the network. The interaction between the nodes forms a fully connected graph. Specifically, the interaction between the i-th and j-th nodes is calculated through the connection weight w ij To describe, all connection weights together form a weight matrix. An important feature of HNN is that its work is based on the principle of minimizing the energy function. When the network converges to a stable state, it corresponds to the minimum value of the energy function.

[0068] The nodes of the network represent genes, and the interactions between genes in the network are specified by their adjacency matrix W. The matrix elements w ij Represents the relationship between genes i and j:

[0069]

[0070] in, and represents the state of gene i and j in cell n respectively. p represents the number of stable states. Here, cells with clear phenotypic information are directly modeled as attractors (stable states) of HNN. Therefore, depending on whether nodes i and j are connected, w ij The value is 1 or 0. When the network reaches a stable fixed point, the connection w between genes i and j ij is symmetrical, that is, w ij =w ji .

[0071] Calculation of gene local network energy;

[0072] For any given gene i in cell n, a local network with gene i as the core can be constructed according to the above method. The network consists of gene i and its first-order neighbor genes. The local network is given a local network energy The specific calculation formula is as follows:

[0073]

[0074] in, represents the state value of gene j in cell n, and N(i) represents the neighborhood of node i in the network (i.e., other nodes excluding node i). After traversing each gene, a GLNE matrix is ​​obtained. The elements of the matrix It represents the energy value of the local network centered on gene i in cell n. This value reflects the activity of gene i in cell n, where a higher GLNE value represents a higher gene activity. It is particularly noteworthy that the GLNE matrix E has the same dimension as the input gene expression matrix A, so this matrix is ​​also used for dimensionality reduction analysis in subsequent studies.

[0075] exist Figure 2 In the dimensionality reduction analysis, GLNE matrix and gene expression matrix were used respectively. The dimensionality reduction results based on GLNE matrix showed that most cells in the H0 and H24 stages followed stage-specific energy characteristics, but there were still some cells that shared energy characteristics across stages ( Figure 2 Correspondingly, a small number of cells at the H24 stage share similar transcriptional signatures with cells at the H0 stage ( Figure 2 (B)). The results show that compared with traditional transcriptional features, gene local energy features can also reflect the state of the cell.

[0076] Energy value E of cell n n It consists of the local network energy levels of all genes it contains and is defined as:

[0077]

[0078] In order to facilitate subsequent comparative analysis, this embodiment normalizes the energy value of cell n, and the processed energy value E' n The definition is as follows:

[0079]

[0080] in, and Respectively represent the minimum and maximum energy values ​​of all cells. E' n The value range is between 0 and 1. This value is used as a quantitative indicator of cell plasticity, reflecting the overall activity of the gene interaction network within each cell. A higher energy value reflects that the gene interaction network within the cell has a higher activity, indicating that the cell has a higher plasticity. On the contrary, a lower energy value implies that the overall activity of the gene interaction network within these cells is lower, corresponding to its lower plasticity state.

[0081] According to the above steps, the energy of cells in the H0 and H24 stages was calculated respectively. The results showed that the energy level of cells in the H0 stage was significantly higher than that of cells in the H24 stage. This result is consistent with the fact that the H0 stage induced by Dux mainly contains high-potential 2C-like cells ( Figure 3In addition, some cells showed a low energy density distribution in the H0 stage, while some cells in the H24 stage showed a high energy density distribution ( Figure 3 (B) ), indicating that cells in these two stages are heterogeneous and need further exploration.

[0082] Identification of cell differentiation potential status;

[0083] Identifying the differentiation potential state of cells is crucial for understanding developmental processes and disease occurrence. The development of single-cell technology can not only analyze the heterogeneity within the cell population, but also reveal the dynamic changes of individual cells in the fate determination process. Different from the traditional method of clustering cells based on transcriptome similarity, this embodiment introduces a Gaussian mixture model (GMM) to identify the possible potential state of cells by analyzing the energy distribution differences of cells, and cluster cells with the same differentiation potential state into one category. First, for a cell population S containing N cells, the present invention uses the normalized energy value E' n∈N To quantify the differentiation potential of each cell. Next, the cells are sorted according to the energy value, and the E' n∈N The purpose of this step is to identify the different potential states that may exist in the cell population S and classify the cells according to their differentiation potential. The mathematical description of GMM is as follows:

[0084]

[0085] in, represents the kth Gaussian distribution with a given mean μ k and variance The probability density function under the condition. k >0 is the mixing weight of the kth Gaussian distribution, satisfying The number of components K of the Gaussian distribution is determined by the Bayesian Information Criterion BIC, which is defined as:

[0086]

[0087] Where v is the number of estimated parameters, this step was implemented using the R package mclust (version 6.0.1). Specifically, the optimal number K of cell potential states was determined by selecting the maximized BIC.

[0088] Generally, the potential states of cells can be divided into three categories: Low Potential State (LPS), High Potential State (HPS) and Intermediate Potential State (IPS). Based on the maximization of the BIC criterion, cells at the H0 and H24 stages can be divided into three different clusters according to their differentiation potential differences ( Figure 4 The cells in these three clusters have low energy, intermediate energy, and high energy levels, respectively, and thus correspond to LPS, IPS, and HPS ( Figure 4 (B) in the figure.

[0089] Assessment of heterogeneity of cell populations;

[0090] The heterogeneity assessment of a cell population aims to identify and describe the diversity and variation within the cell population. In the present invention, each cell in the cell population S is assigned to K specific potential states, and the probability of a cell being assigned to the kth potential state is defined as p k , the specific calculation formula is as follows:

[0091]

[0092] Among them, N(C k ) and N(S) represent the kth potential state and the total number of cells contained in the cell population S, respectively. The probability reflects the relative distribution of cells in each potential state.

[0093] Next, referring to the concept of Shannon entropy, a normalized HI is proposed to measure the level of heterogeneity of cells in each cell population in terms of potential state. In information theory, Shannon entropy is used to measure the uncertainty of information or the uncertainty of random variables. For a random variable, the higher its Shannon entropy, the higher the uncertainty of the variable. The specific calculation formula of HI is as follows:

[0094]

[0095] The value range of this index is between 0 and 1, where 1 represents that the analyzed cell population is highly heterogeneous, and 0 represents that the cells in the cell population are all in the same potential state, so the cell population has no heterogeneity. Based on this step, the heterogeneity index of the cell populations at the H0 and H24 stages was calculated respectively. The results showed that the cells at the H0 stage were mainly composed of HPS and IPS cells, showing high heterogeneity (heterogeneity index score of 0.93). In contrast, most cells at the H24 stage showed low differentiation potential, and the heterogeneity index of this stage was 0.41 ( Figure 4 (C) in the.

[0096] In the original study from which the data was derived, Seurat v.3 was used to divide the cells in these two stages into three subgroups based on the similarity of expression patterns, namely Exit_1, Exit_2 and Exit_3, corresponding to the three stages of exit from the 2C-like state. The results showed that Exit_1 contained a large number of HPS and IPS cells, as well as a small number of LPS cells, with a heterogeneity index of 0.93. Exit_2 and Exit_3 were mainly composed of a large number of LPS cells. In addition, along with the transition from the 2C-like state to the pluripotent state, the pluripotency gene Sox2 was highly active in LPS cells, corresponding to the lower differentiation potential of these cells ( Figure 4 (D)). Zfp352 is specifically activated in IPS cells ( Figure 4 In contrast, the pluripotency marker gene MT2_Mm is specifically active in HPS cells, suggesting that these cells may be typical 2C-like cells ( Figure 4 (F) in the figure.

[0097] Therefore, the present invention adopts the above-mentioned method for evaluating the heterogeneity of a cell population based on energy indicators, which can more accurately reveal the complexity and differences within the cell population.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for evaluating cell population heterogeneity based on energy indicators, characterized in that: The following steps are involved: Step S1, preprocessing single-cell transcriptome data; Step S2, performing feature selection on the preprocessed data to define the cell state; Step S3, constructing a local gene network based on the Hopfield neural network; Step S4, calculating the gene local network energy and cell energy, and normalizing the cell energy; Step S5, introducing a Gaussian mixture model, identifying the potential state of cells by analyzing the energy distribution difference of cells, and clustering cells in the same differentiation potential state; Step S6, evaluating the heterogeneity of the cell population; In step S5, a Gaussian mixture model is introduced to identify the potential state of cells by analyzing the energy distribution difference of cells, and cells in the same differentiation potential state are clustered. The specific operation is as follows: For a cell population S containing N cells, the normalized cell energy E′ is used n∈N To quantify the differentiation potential status of each cell; The cells are sorted according to the size of their energy, and the E′ of all cells is calculated using a Gaussian mixture model. n∈N The values ​​are fitted; Among them, the Gaussian mixture model is as follows: in, represents the kth Gaussian distribution with a given mean μ k and variance The probability density function under the condition λ k >0 is the mixing weight of the kth Gaussian distribution, satisfying The number of components K of the Gaussian distribution is determined by the Bayesian Information Criterion BIC, which is defined as: Where v is the number of estimated parameters; In step S6, the heterogeneity of the cell population is evaluated, and the specific operations are as follows: Each cell in the cell population S is assigned to K specific potential states, and the probability of a cell being assigned to the kth potential state is defined as p k : Among them, N(C k ) and N(S) represent the kth potential state and the total number of cells contained in the cell population S, respectively; The heterogeneity index is then used to measure the diversity of cells in each population in terms of their potential states. The heterogeneity index is calculated as follows: Among them, HI is the heterogeneity index.

2. A method for evaluating cell population heterogeneity based on energy indicators according to claim 1, characterized in that: In step S1, for a single cell expression matrix containing N cells and M1 genes The set of all genes in cell n is represented as follows: in, Represents the expression level of gene M1 in cell n.

3. A method for evaluating cell population heterogeneity based on energy indicators according to claim 2, characterized in that: In step S1, the preprocessing includes logarithmic conversion processing and standardization processing.

4. The method for evaluating cell population heterogeneity based on energy index according to claim 3, characterized in that: In step S2, feature selection is performed on the preprocessed data to define the cell state. The specific operations are as follows: The preprocessed data were screened for highly variable genes using the FindVariableFeatures function, and 1,000 to 5,000 highly variable genes were retained; Get the dataset contains N cells and M highly variable genes, and the state of cell n is represented by the vector To express; in, Represents the state value of gene i in cell n, according to The sign of is determined as follows: in, Represents the normalized expression level of gene i in cell n.

5. The method for evaluating cell population heterogeneity based on energy index according to claim 4, characterized in that: In step S3, the nodes in the gene local network represent genes, and the interactions between genes in the network are specified by their adjacency matrix W. The matrix elements w ij Represents the relationship between genes i and j: in, represents the state value of gene j in cell n; p represents the number of stable states.

6. The method for evaluating cell population heterogeneity based on energy index according to claim 5, characterized in that: In step S4, the calculation formula of the gene local network energy is as follows: in, is the energy value of the local network centered on gene i in cell n; N(i) represents the neighborhood of node i in the network.

7. The method for evaluating cell population heterogeneity based on energy index according to claim 6, characterized in that: In step S4, the cell energy consists of the local network energy levels of all genes contained in the cell and is defined as: Among them, E n is the energy value of cell n; M represents the number of highly variable genes.

8. The method for evaluating cell population heterogeneity based on energy index according to claim 7, characterized in that: In step S4, the normalization process is: in, and Respectively represent the minimum and maximum energy values ​​of all cells; E′ n is the normalized cellular energy.

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