A method for detecting the critical state of complex biological systems

Abstract

This invention discloses a method for detecting critical states in complex biological systems. First, gene expression is converted into a probability distribution, and a mutual information network is constructed at each stage. Then, local networks are extracted from the global network. Based on the weights between genes in each stage network, the weighted differential entropy of each local network is calculated to quantitatively characterize the system's fluctuations at each stage, thereby detecting critical states in complex biological systems. This invention utilizes differential entropy information from each stage to detect critical states, enabling the detection of critical states before critical transitions occur in complex biological systems and identifying signaling genes in the critical state. It is applicable to both batch expression data and single-cell expression data, fully utilizing network information and accurately reflecting the dynamics and complexity of system changes.

Description

Technical Field

[0001] This invention belongs to the field of biological systems technology, specifically the field of critical point detection in biological systems, and more specifically, a method for detecting the critical state of complex biological systems. Background Technology

[0002] The development of complex disease systems can be divided into three stages: normal state, critical state, and disease state. Human systems exhibit high resilience and robustness in both normal and disease states. In the critical state, the human system is unstable and reversible, exhibiting low resilience and weak robustness. If the system is disturbed at this point, it may enter a new stable state or revert to the previous stable state. Most diseases are discovered at this symptomatic stage, and although patients receive appropriate treatment, it is difficult for them to return to a normal state. The ability to detect the critical state of complex disease systems in their early stages and determine the critical point before serious complications occur enables more precise and personalized treatment.

[0003] In single-cell experiments, cell fate commitment represents a critical state transition, and characterizing and predicting this transition is crucial for patient-specific disease modeling and drug testing. Therefore, describing the dynamic properties of biological systems and accurately detecting critical states has significant biomedical implications.

[0004] Identifying critical points not only helps us better understand the crucial underlying mechanisms in disease development but also provides early warning signals of impending disease deterioration, enabling timely intervention and diagnosis. With the ever-increasing scale of available data, effectively handling high-dimensional and noisy data remains a significant challenge in studies detecting critical states of disease deterioration.

[0005] Significant progress has been made in the study of complex biological systems, utilizing methods such as dynamic network markers, differential networks, and network entropy to detect early warning signals. While much research can advance fields related to detecting critical transition early warning signals, most current algorithms are designed based on discrete variables, leaving considerable room for research in algorithm design based on single-cell data. Compared to traditional bulk omics information, single-cell analysis is significantly affected by high-dimensionality, noise, sparseness, and heterogeneity of samples. Describing the dynamic characteristics of biological systems and accurately detecting critical states from single-cell datasets remains challenging.

[0006] In the dynamic evolution of complex biological systems, critical transitions are often accompanied by catastrophic progress. Therefore, describing the dynamic characteristics of biological systems and accurately detecting critical states are crucial for revealing the underlying mechanisms of complex biological systems. Summary of the Invention

[0007] In view of this, in order to overcome the shortcomings of the prior art, the purpose of this invention is to provide a method for detecting the critical state of complex biological systems. When calculating the local network entropy value, network edge weights are introduced to make full use of network information. From the perspective of the mutual information weighted entropy of the global network, the dynamic development of the biological system is tracked and critical point signals are identified. This accurately reflects the dynamics and complexity of system changes and enables the accurate detection of the critical stage of qualitative change in complex biological systems.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is: a method for detecting the critical state of a complex biological system, the method comprising the following steps:

[0009] Step 1: Fit a Gaussian distribution for each gene at each stage; based on the given samples at each time point, convert gene expression into a probability distribution;

[0010] Step 2: Construct the mutual information network for each time point. The process is as follows: Use mutual information to measure the amount of information contained in one random variable by another, and construct the gene mutual information network for each time point based on the calculated mutual information between genes as edge weights.

[0011] Step 3: Extract the local network from the global network at each time point, and use the mutual information between genes as the edge weights of the local network;

[0012] Step 4: Calculate the differential entropy of neighborhood genes in each local network at time T;

[0013] Step 5: Calculate the mutual information weighted entropy of the global network to identify the critical point signal, defined as follows: Based on the edge weights of the local network and the differential entropy of the first-order neighborhood genes, calculate the weighted entropy score of each local network at time T. If the entropy value increases sharply in a certain stage, the stage is considered to be the critical point.

[0014] Furthermore, in step one, based on gene g i (i = 1, 2, ..., m) n samples {S1, S2, ..., Sm} at time point T n The expression values ​​in} are fitted with a Gaussian distribution, and the goodness-of-fit of the fitted Gaussian distribution is tested.

[0015] Furthermore, step two describes the degree of association between genes from an information perspective. When there is a certain degree of association between variables, the less randomness between variables, the greater the mutual information.

[0016] Furthermore, edge weights are used to quantitatively characterize the degree of association between genes, where gene g i With gene g j The network edge weights between them are determined by mutual information MI T (g i ,gj Indicators were determined.

[0017] Furthermore, in step three, local networks are extracted from the global network obtained in step two at each stage. Each local network contains a central gene and its first-order neighboring genes.

[0018] Furthermore, in step four, the uncertainty information in the probability distribution of continuous random variables is quantified. Gene expression is regarded as a continuous random variable, and the probability distribution is fitted. During the quantification stage, the dynamic changes in the association between genes in the network are observed. The higher the entropy value, the greater the uncertainty.

[0019] Furthermore, the critical point in step five is determined as follows:

[0020] When a complex dynamic system undergoes a critical transition, biosignal molecules exhibit significant collective behavior and strong fluctuations. The weighted entropy of a local network containing biosignal molecules in the critical state differs significantly from the weighted entropy in the pre-transition state. If the entropy value increases sharply at a certain stage, that stage can be considered the critical point.

[0021] The beneficial effects of this invention are:

[0022] 1. From the perspective of continuous variables, this method can describe the interaction between genes more accurately than discrete variables, and can capture small changes and trends when dealing with complex data structures and nonlinear relationships, thus exhibiting strong robustness.

[0023] 2. This method is applicable to both batch expression data and single-cell expression data, and makes full use of network information, accurately reflecting the dynamics and complexity of system changes, thus improving its effectiveness;

[0024] 3. Based on this method, critical states can be detected before critical transitions occur in complex biological systems, and signaling genes in critical states can be identified, leading to the discovery of key transcription factors related to embryonic differentiation and many potential dark genes that cannot be detected by traditional biomarkers. Although these dark genes are non-differential signaling genes, they have been shown to participate in the embryonic differentiation process through functional pathways;

[0025] 4. This method is model-free, which helps to identify and detect critical states in complex biological systems, providing a theoretical basis for timely clinical intervention and disease modeling. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart of the detection method of the present invention;

[0028] Figure 2 This is a graph showing the entropy values ​​at each stage of the differentiation of mouse embryonic fibroblasts into neurons, as presented in this invention.

[0029] Figure 3 This is a graph showing the changes in local entropy values ​​of signaling genes at different stages of the differentiation of mouse embryonic fibroblasts into neurons, as presented in this invention.

[0030] Figure 4 This is a graph showing the entropy index of colon adenocarcinoma data at different stages in this invention;

[0031] Figure 5 This is a graph showing the changes in local entropy values ​​of all genes at each stage in the colorectal adenocarcinoma data of this invention;

[0032] Figure 6 This is a survival analysis graph of colon adenocarcinoma data before and after the critical state in this invention;

[0033] Figure 7 This is a schematic diagram illustrating the dynamic changes and evolution of the signal gene regulatory network at different stages of the differentiation of mouse embryonic fibroblasts into neurons, as described in this invention.

[0034] Figure 8 This is a schematic diagram illustrating the dynamic changes and evolution of the colorectal adenocarcinoma data signaling gene regulatory network at different stages of the present invention.

[0035] Figure 9 This is a diagram of the numerical simulation node control network model of the present invention;

[0036] Figure 10 This is a bar chart showing the MIWE score of each parameter at each node in the numerical simulation of this invention;

[0037] Figure 11 The figure shows the prediction results of the numerical simulation under different noise conditions of this invention;

[0038] Figure 12 This is a graph showing the percentage of transcription factor regulatory signaling genes in the data on the differentiation of mouse embryonic fibroblasts into neurons according to the present invention.

[0039] Figure 13This is a chord diagram of important biological pathways involving transcription factors and their regulated signaling genes in the differentiation data of mouse embryonic fibroblasts into neurons in this invention;

[0040] Figure 14 This is a comparison of the differences in dark gene expression values ​​and MIWE scores at different stages of the differentiation data of mouse embryonic fibroblasts into neurons in this invention.

[0041] Figure 15 This is a bubble diagram of functional pathways enriched by data on the differentiation of mouse embryonic fibroblasts into neurons, as presented in this invention.

[0042] Figure 16 This is a diagram illustrating the potential embryonic developmental regulatory mechanism revealed by the dark gene, based on data on the differentiation of mouse embryonic fibroblasts into neurons in this invention.

[0043] Figure 17 A bubble diagram illustrating the main biological processes involved by the colon adenocarcinoma signaling gene in this invention;

[0044] Figure 18 This is a network diagram showing the association between colon adenocarcinoma signaling genes and biological processes in this invention;

[0045] Figure 19 This is a diagram of cancer-related pathways involving colon adenocarcinoma signaling genes in this invention; Figure 20 This is a diagram showing the association between colorectal adenocarcinoma signaling genes and pathways in this invention. Detailed Implementation

[0046] Specific embodiments are given below to further clarify, completely, and in detail the technical solution of the present invention. These embodiments are the preferred embodiments based on the technical solution of the present invention, but the scope of protection of the present invention is not limited to the following embodiments.

[0047] Example 1

[0048] A method for detecting the critical state of complex biological systems, such as Figure 1 As shown, it includes five main steps, the specific steps are as follows:

[0049] Step 1: Fit the Gaussian distribution of each gene at different time points;

[0050] Based on a given sample, gene expression is transformed into a probability distribution. According to gene g... i (i = 1, 2, ..., m) n samples {S1, S2, ..., Sm} at time point T n The expression values ​​in the sample are fitted with a Gaussian distribution, and the goodness-of-fit of the fitted Gaussian distribution is tested. The gene expression values ​​in the sample are then converted into cumulative probabilities P. i (x ir If any gene g i and gj If the linear combination of genes follows a one-dimensional normal distribution, then the joint distribution between two genes follows a bivariate normal distribution, and its joint probability is Q. i (g i ,g j ):

[0051]

[0052]

[0053] Where, x ir For gene g i Gene expression values ​​of (i = 1, 2, ..., m) in sample r (r = 1, 2, ..., n). and Gene g i and g j The average expression value of gene g in n samples at time point T, where ρ is the expression value of gene g. i and g j The correlation coefficient at time point T, μ i and σ i (i = 1, 2, ..., m) represents gene g. i The mean expression value and standard deviation of n samples at time point T.

[0054] Step 2: Construct the mutual information network MIN at each time point T. T ;

[0055] MIN Interconnected Information Network T The edge weights in the algorithm can quantitatively characterize the degree of association between genes, where gene g i With gene g j The network edge weights between them are determined by MI T (g i ,g j Indicators determined:

[0056]

[0057] From an information perspective, the degree of correlation between genes is described as follows: when there is a certain degree of correlation between genes, the lower the randomness between genes, the higher the mutual information (MI). T (g i ,g j The larger the value, the better.

[0058] Step 3: Extract the local network from the global network;

[0059] From the global network MIN at time point T T Extracting local networks Each local network contains a central gene g.k and its first-order neighboring genes in These are the edge weights in a local network.

[0060] By introducing network edge weights when calculating the local network entropy, network information is fully utilized to accurately reflect the dynamics and complexity of system changes, thus improving effectiveness.

[0061] Step 4: Calculate the differential entropy of neighborhood genes in the local network;

[0062] Time T represents a point in time, and for each local network at time T... Neighborhood genes The differential entropy is defined as:

[0063]

[0064]

[0065] in, For genes The average expression value of n samples at time point T, where f(x) is the gene expression value. The probability density function, Genes The mean and standard deviation of the expression values ​​of n samples at time point T.

[0066] Step 5: Calculate the mutual information weighted entropy (MIWE) of the global network. T Identify the critical point signal for an outbreak;

[0067] Calculate the weighted entropy score of each local network at time T. Right now:

[0068]

[0069] The weighted entropy score of the global network is then:

[0070]

[0071] When a complex dynamic system undergoes a critical transition, biosignaling molecules exhibit significant collective behavior and strong fluctuations. The weighted entropy of a local network containing biosignaling molecules at the critical state differs significantly from that before the transition. If the entropy value increases sharply at a certain stage, that stage can be considered a critical point. This method considers genes with the top 5% weighted entropy scores at the critical stage as signaling genes, i.e., dynamic network biomarkers (DNBs).

[0072] Figure 1In the diagram, A represents fitting the Gaussian distribution of each gene at different time points, B represents constructing a global mutual information network and extracting local networks, and C represents calculating the weighted differential entropy of the global network. This method uses continuous variables when dealing with complex data structures and nonlinear relationships, and it can capture subtle changes and trends, exhibiting strong robustness. It is suitable for both batch expression data and single-cell expression data, fully utilizing network information to accurately reflect the dynamics and complexity of system changes, thus improving effectiveness.

[0073] Example 2

[0074] This application proposes a method for detecting the critical state of complex biological systems. It constructs a mutual information weighted entropy (MIWE) and uses the differential entropy information of each stage to detect the critical state. First, gene expression is converted into a probability distribution, and a mutual information network is constructed at each stage. Then, based on the weights between genes in the network at each stage, the weighted differential entropy of each local network is calculated to quantitatively characterize the fluctuation of the system at each stage, thereby detecting the critical state in complex biological systems.

[0075] This method was applied to a numerical simulation dataset and two real-world datasets, including batch and single-cell expression datasets. Numerical simulations validated the robustness of the method under varying noise levels. Specifically, the implementation used a single-cell omics dataset from the NCBI GEO database: mouse embryonic fibroblast differentiation into neurons (MEF toneurons; GEO: GSE67310), and a bulk sequencing omics dataset from the Cancer Genome Atlas (TCGA) database: colorectal adenocarcinoma (COAD). The method's performance is tested as follows:

[0076] 1. Differentiation of mouse embryonic fibroblasts into neurons

[0077] This method uses MIWE score curves across time points to represent the fluctuations in cell differentiation at each stage. For data on the differentiation of mouse embryonic fibroblasts into neurons, the MIWE score significantly increased from day 5 to day 20. Figure 2 This provides an early warning signal that the cells are about to differentiate into neurons, indicating that a cell fate transition begins on day 22. The algorithmic detection results of the dataset are consistent with the original experimental observations.

[0078] Furthermore, to demonstrate the robustness of this method, box plots of the local network weighted entropy at each stage are presented based on samples at each time point. The median of the box plot provides a clear signal of the critical point, and the uncertainty error of the samples has a weak impact on the MIWE score.

[0079] This method selects genes with the highest local MIWE scores in the top 5% of the critical phase as signaling genes, which may be highly correlated with the cell differentiation process. The landscape plot shows the dynamic changes in the local MIWE scores of signaling genes in a global view. Figure 3 The local MIWE value of the signaling gene increased sharply on day 20.

[0080] 2. Colon adenocarcinoma

[0081] Healthy samples were used as a reference group in the entropy calculation at each stage. In the second stage, the global MIWE score of the colon adenocarcinoma data significantly increased ( Figure 4 This can be identified as a critical state of disease progression. The landscape plot shows the dynamic changes in local MIWE values ​​for all genes. Figure 5 This also indicates that an anomaly occurred in the system during the second phase;

[0082] Kaplan-Meier survival analysis was used to perform prognostic survival analysis on clinical samples of colon adenocarcinoma. By comparing the survival rates and their standard errors, a significant difference in prognosis was observed between patients diagnosed before the critical stage and those diagnosed after the critical stage (P < 0.05). Figure 6 Patients treated before disease progression have higher survival rates and longer survival times. Detecting the critical point before disease deterioration or metastasis helps in timely clinical intervention for subsequent treatment. The MIWE method can provide early warning signals during disease development, which is helpful for disease treatment.

[0083] 3. Demonstration of dynamic changes in gene regulatory networks

[0084] Signaling genes were mapped to protein-protein association networks, revealing the dynamic changes in these networks at different stages. For a dataset of mouse embryonic fibroblast differentiation into neurons, significant changes in network structure occurred on day 20 (…). Figure 7 This also indicates that a shift in cell fate determination is imminent at this point in time;

[0085] For colorectal adenocarcinoma data, a network diagram was drawn using genes that had the highest local MIWE values ​​in the top 5% of the critical phase. Figure 8 It is clear that the edges also become thicker when the nodes turn red, which indicates that the model can determine the critical state of disease deterioration, meaning that the system is abnormal in the second stage and is about to deteriorate.

[0086] 4. Performance Evaluation

[0087] This method uses a theoretical model to verify the robustness of the MIWE method, and constructs a 10-node supervision network based on the Michaelis-Menten equation, which can generate a dataset for numerical simulation. The parameter p is set to vary in the range of -0.5 to 0.25, and the system experiences a critical transition at the parameter value p = 0.

[0088] A gene regulatory network consisting of 10 nodes with positive and negative regulatory relationships ( Figure 9 Before the system reaches the critical point, the MIWE score is relatively stable and at a low level for each parameter. As it approaches the critical point, the MIWE score tends to rise. When the parameter value p = 0, the MIWE score increases sharply, providing an early warning signal for the impending state transition. Figure 10 ).

[0089] Considering the uncertainty and interference factors in real data, this method was validated under four different noise conditions. Figure 11 As shown, a is the prediction result of the numerical simulation under the influence of 0.01 noise, b is the prediction result of the numerical simulation under the influence of 0.06 noise, c is the prediction result of the numerical simulation under the influence of 0.2 noise, and d is the prediction result of the numerical simulation of the present invention under the influence of 0.5 noise. The results show that the MIWE score can successfully identify the critical state under different levels of noise influence, which shows that the method has strong robustness.

[0090] 5. Applying the detection method proposed in this invention to detect critical states in complex biological systems, the results obtained from the above experimental data in this embodiment are as follows:

[0091] 1) Identify transcription factors based on this method;

[0092] Transcription factors are important molecules controlling gene expression and can be considered key molecules controlling or driving cell fate commitment. Identifying transcription factors using a weighted entropy algorithm can explore the role of signaling genes in cell fate commitment processes within cell differentiation datasets. Specifically, the weighted entropy of the global network at each stage of mouse embryonic fibroblast differentiation into neurons is calculated using the weighted entropy algorithm to identify critical stages. Then, the top 5% of genes with the highest local weighted entropy scores at each critical stage are selected as signaling genes. The transcription factors regulating these signaling genes are ranked according to a comprehensive evaluation; this method selected the top 20 transcription factors with the highest average comprehensive ranking as the main research focus. In mouse embryonic fibroblast differentiation into neurons data, transcription factors regulate 74% of signaling genes at the critical point (…). Figure 12 ).

[0093] In the analysis of transcription factors in data on the differentiation of mouse embryonic fibroblasts into neurons, this method identified two relatively key transcription factors, CREB1 and CREB3. These two transcription factors contribute to a deeper understanding of the molecular mechanisms of embryonic development and have important implications for the treatment and prevention of related diseases. CREB1 plays a role in pathways related to cell proliferation and myoblast differentiation. CREB3 is involved in embryonic development and the differentiation of other tissues and organs, such as osteoblast differentiation, and plays an important role in cell growth and development, metabolic regulation, and stress response. Combined with the transcription factors and the signaling genes they regulate, this method found that they participate in several signaling pathways related to embryonic differentiation. Figure 13 The left side of the outer ring represents the signaling genes detected by MIWE, and the right side represents the various biological processes these genes participate in. In the inner ring, the color and width of the connections represent different enrichment pathways and significant gene function levels, respectively. The TNF signaling pathway plays an important role in various physiological and pathological processes, including cell proliferation, differentiation, apoptosis, regulation of immune responses, and induction of inflammation. Activation of the TNF signaling pathway can trigger activation of the PI3K-Akt signaling pathway. Phosphorylated PKA can further phosphorylate CREB3 and activate its transcriptional activity. CREB3 participates in the regulation of various cellular physiological processes by binding to CBP and regulating the transcription of specific genes.

[0094] 2) This method reveals the potential signaling mechanism of dark genes;

[0095] Differential expression not only helps to reveal the mysteries of biological processes but also provides important theoretical basis for gene diagnosis and treatment. In many clinical trials and biological studies, differentially expressed genes are used as markers or drug targets; however, some non-differentially expressed genes are often overlooked. Non-differentially expressed genes also play important roles in biological processes and may be potential therapeutic biomarkers. In this method, genes that are non-differentially expressed but sensitive to MIWE scores are defined as dark genes. Specifically, in the analysis of data on the differentiation of mouse embryonic fibroblasts into neurons, the top 5% of genes with the highest local weighted entropy scores are selected at the critical stage, and then the definition of dark genes is used to analyze the selected genes. Each selected gene, i.e., a dark gene, shows relatively stable expression values ​​at each stage, but its MIWE score varies significantly at each stage. Figure 14 ).

[0096] This method was used to perform dark gene enrichment analysis on mouse embryonic fibroblast differentiation data into neurons. Figure 15This study aimed to investigate the potential signaling mechanisms revealed by the mouse dark gene and its neighboring genes. HSP90B1 participates in the Thyroidhormone synthesis pathway, synthesizing thyroid hormones that can bind to nuclear receptors and regulate many genes involved in cell cycle control and cell differentiation. In the prostate cancer pathway, HSP90AB1 and HSP90B1 indirectly affect cell proliferation and survival by activating Ar and binding to DNA sites. The PI3K-Akt signaling pathway is a crucial node controlling cell growth, proliferation, and metabolism in mammalian cells.

[0097] Figure 16 This study investigates the potential role of the dark gene and its neighboring genes in signaling pathways during mouse embryonic fibroblast differentiation into neurons. High expression of GNB1 during embryonic differentiation activates PI3K, which then co-activates AKT, a downstream target of PI3K, with HSP90. HSP90 has been shown to regulate various biological processes, including cell growth, differentiation, and survival. AKT kinase translates various signals into intracellular signals controlling cell survival, proliferation, metabolism, and differentiation, transmitting these signals to downstream genes and thus influencing cell proliferation and differentiation. Significant changes in dark gene expression were observed between day 5 and day 22, further validating that the identified critical point may be a crucial timeframe guiding mouse embryonic fibroblast differentiation into neurons.

[0098] 3) Based on this method, signaling genes related to the development of colorectal cancer are identified;

[0099] In the analysis of colorectal adenocarcinoma data, we used a weighted entropy algorithm to identify the critical stage in the development of colorectal adenocarcinoma that is about to worsen. Genes ranking in the top 5% of the local network weighted entropy scores at this critical stage were selected as signaling genes. To understand the participation mechanism of signaling genes in disease development, this method performed functional enrichment analysis on common signaling genes in colorectal adenocarcinoma. GO analysis results showed that signaling genes are mainly involved in chemical reactions that form proteins in the cytoplasm, macromolecular modification processes such as the synthesis or assembly of ribonucleoprotein complexes, and regulating the rate at which ubiquitin groups are added to proteins. Figure 17 The deficiency of many of these ribosomal proteins can directly affect the overall translation process and global expression of proteins, leading to various diseases, including cancer. Figure 18 As a link between genes and biological processes, HSP90AB1 is upregulated in many solid tumors and is believed to induce angiogenesis and promote cancer metastasis. HSPA5 can serve as a diagnostic and prognostic biomarker for various malignant tumors. P4HB can regulate tumor development in a collagen-dependent or collagen-independent manner.

[0100] In addition, some pathways involving signaling genes are also associated with cancer development. Figure 19 MHC class I and II antigen processing and presentation pathways present peptides to circulating CD8+ cytotoxic T cells and CD4+ helper T cells, respectively, to recognize pathogens and transformed cells. Immune surveillance by transformed cells or tumor cells drives alterations in antigen processing and presentation pathways to evade immune responses, which is a crucial process in tumor development. Figure 20 The relevant pathways involved for each gene are listed, with the numbers representing the ENTREZ number of each gene. B2M plays a physiological and pathological role in tumor cells. In antigen processing and presentation, the B2M and HLA-B / C complex activate downstream signaling, upregulating and triggering or enhancing T-cell immunity, playing an important role in controlling the growth of colorectal cancer. Studies have shown that B2M is a potential tumor suppressor gene in COAD and has been identified as a potential biomarker for THCA. Protein processing, modification, and folding in the endoplasmic reticulum are tightly regulated processes that determine cell function, fate, and survival, and aberrant activation of its downstream signaling pathways has been proven to be a key regulator of tumor growth and metastasis. Estrogen can influence tumor progression by regulating the tumor microenvironment and plays a crucial role in the development and progression of THCA. These signaling genes are likely to become key biomarkers for studying cancer development risk, helping to design individualized treatment plans and early clinical interventions.

[0101] In summary, this invention proposes a method for detecting critical states in complex biological systems. It transforms gene expression into a probability distribution and constructs a mutual information network at each stage to quantitatively characterize system fluctuations at each stage. This method detects critical states before critical transitions occur in complex biological systems and identifies signaling genes in these critical states. It accurately describes the interactions between genes and can capture minute changes and trends when dealing with complex data structures and nonlinear relationships, exhibiting strong robustness.

[0102] The foregoing has shown and described the main features, basic principles, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention based on actual circumstances without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for detecting the critical state of a complex biological system, characterized in that, This method is implemented entirely by computer and includes the following steps: Step 1: Fit a Gaussian distribution for each gene at each stage; based on the given samples at each time point, convert gene expression into a probability distribution; Step 2: Construct the mutual information network for each time point. The process is as follows: Use mutual information to measure the amount of information contained in one random variable by another, and construct the gene mutual information network for each time point based on the calculated mutual information between genes as edge weights. Step 3: Extract the local network from the global network at each time point, and use the mutual information between genes as the edge weights of the local network; Step 4: Calculate the time T The differential entropy of neighborhood genes in each local network; Step 5: Calculate the mutual information weighted entropy of the global network to identify the critical point signal, defined as follows: Based on the edge weights of the local network and the differential entropy of the first-order neighborhood genes, calculate the signal at time [time value missing]. T The weighted entropy score is expressed as: in, These are the edge weights in a local network. It is the differential entropy of the neighboring nodes; If the entropy value increases sharply at a certain stage, that stage is considered to be the critical point.

2. The method for detecting the critical state of a complex biological system according to claim 1, characterized in that, In step one, based on genes At the point of time T of n Sample The expression values ​​are fitted with a Gaussian distribution, and the goodness-of-fit of the fitted Gaussian distribution is tested.

3. The method for detecting the critical state of a complex biological system according to claim 1, characterized in that, Step two describes the degree of association between genes from an information perspective. When there is a certain degree of association between variables, the less randomness between variables, the greater the mutual information.

4. The method for detecting the critical state of a complex biological system according to claim 3, characterized in that, Using edge weights to quantitatively characterize the degree of association between genes, where genes With genes The network edge weights are determined by mutual information. Indicators determined.

5. A method for detecting the critical state of a complex biological system according to claim 1, characterized in that, In step three, local networks are extracted from the global network obtained in step two at each stage. Each local network contains a central gene and its first-order neighboring genes.

6. The method for detecting the critical state of a complex biological system according to claim 1, characterized in that, In step four, the uncertainty information in the probability distribution of continuous random variables is quantified. Gene expression is treated as a continuous random variable, and the probability distribution is fitted. During the quantification stage, the dynamic changes in the association between genes in the network are observed. The higher the entropy value, the greater the uncertainty.

7. A method for detecting the critical state of a complex biological system according to claim 1, characterized in that, The determination of the critical point in step five is as follows: When a complex dynamic system undergoes a critical transition, biological signal molecules exhibit significant collective behavior and strong fluctuations. The weighted entropy of the local network containing biological signal molecules in the critical state is significantly different from the weighted entropy in the state before the transition. If the entropy value increases sharply in a certain stage, that stage is considered to be the critical point.

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