Network entropy, method and application for evaluating critical state of biological system

Abstract

The invention relates to a network entropy for evaluating a critical state of a biological system, a method and application, and relates to the technical field of information generation. The network entropy is a global SNE value of an individual sample, and an early warning signal of a critical state or phase change can be identified based on the network entropy, so that the critical state of the biological system is evaluated.

Description

Technical Field

[0001] The present invention relates to the field of bioinformatics technology, and particularly to network entropy, methods, and applications for evaluating the critical state of biological systems. Background Art

[0002] The dynamic evolution process of biological systems can generally be regarded as a time-dependent nonlinear dynamical system, where the critical state is regarded as a qualitative transition at the bifurcation point (Scheffer et al., 2001). The evolution of the system usually goes through three stages (Chen et al., 2012; Liu et al., 2012): (1) a relatively stable normal stage with high robustness; (2) a critical stage highly sensitive to perturbations; and (3) a stage that returns to high robustness after a critical transition. However, the traditional dynamic network biomarker (DNB) method requires multiple samples at each time point to evaluate statistical indicators. Summary of the Invention

[0003] In view of the above problems, the present invention provides a network entropy for evaluating the critical state of biological systems. Based on this network entropy, early warning signals of critical states or phase transitions can be identified, and thus the critical state of biological systems can be evaluated.

[0004] The present invention provides a network entropy for evaluating the critical state of biological systems. The network entropy is the global SNE value of an individual sample, and the formula for the global SNE value is as follows:

[0005] Wherein, is the local SNE value, is the number of genes of a predetermined gene, is a measure of the perturbation of the individual sample to the overall system.

[0006] In view of the inconvenience of the traditional dynamic network biomarker (DNB) method, the inventor of the present invention proposes the above network entropy to evaluate whether a biological system reaches a critical state through the global SNE value. The reason why the global SNE value can detect early warning signals of critical states is as follows in the theoretical derivation of this calculation method: The calculation method of sample-specific network entropy (SNE) is based on the dynamic evolution process of complex biological systems, aiming to capture characteristic changes before the critical transition of the system. Compared with the traditional dynamic network biomarker (DNB) method, SNE detects the critical state by quantitatively analyzing the gene expression perturbation of a single sample. To characterize this process, we use a nonlinear discrete-time dynamical system to describe: Wherein, is the state vector of the system at time and represents the dynamic variables inside the system, represents slowly varying external parameters (such as genetic factors, epigenetic factors, or environmental factors). The function is the non - linear relationship between the system state and the external parameters. The system satisfies the following assumptions: (i) is the fixed point of the equation, satisfying

[0007] (ii) At a certain regulatory parameter , the Jacobian matrix of the system has a pair of eigenvalues with modulus 1 at the fixed point , indicating that the system is close to the critical point here.

[0008] (iii) When , the modulus of the system eigenvalues is not 1.

[0009] When the system is at the fixed point , if the parameter reaches a certain critical value , the system will undergo a critical phase transition. This phase transition is usually manifested as the drastic fluctuations of some key variables and their strong correlations with each other. During the critical transition of the biological system, a set of variables called "dynamic network markers" within the system will show significant changes, which satisfy the following statistical characteristics: (i) The variance of this set of variables increases rapidly; (ii) The correlation between variables within the group increases rapidly; (iii) The correlation between variables outside the group and variables within the group decreases rapidly.

[0010] Therefore, based on this theory, the present inventors capture the changes when the system approaches the critical state by calculating the local network entropy and conditional entropy of a single sample in the protein - protein interaction network, calculate the global SNE value, and use this to evaluate whether the biological system reaches the critical state.

[0011] In one embodiment, the predetermined genes are the top 3 - 7% of the genes ranked from high to low in terms of the local SNE value in the individual sample; the local SNE value is the local SNE value of the differential local network.

[0012] Select the adjustable parameter N as the number of biomolecules in the top 3 - 7% with the highest local SNE value, which can not only improve the accuracy of the calculation results but also effectively reduce the complexity of the calculation and analysis.

[0013] In one embodiment, the formula for the local SNE value is as follows:

[0014] Where, is the number of neighbor genes in the differential local network, which is used to measure the perturbation degree of the central gene in the differential local network and the neighbor genes of the central gene in individual samples, is the difference in standard deviation, and is the difference in Pearson correlation coefficient.

[0015] In one embodiment, the method for constructing the differential local network includes: mapping the genes of individual samples to a protein - protein interaction network to construct a global background network , and based on each gene 's neighbor genes , extract the local network ; in each local network , calculate the difference between the reference sample and the individual sample to construct a differential local network.

[0016] In one embodiment, the step of extracting the local network includes: using the gene as the central node, and the genes , as the first - order neighbor nodes, and extracting the local network .

[0017] The above - mentioned central node is the central gene, and the neighbor nodes are the neighbor genes.

[0018] In one embodiment, the differences include: the difference in standard deviation , the difference in Pearson correlation coefficient ; The , calculation formulas are as follows:

[0019]

[0020] Among them, respectively represent the standard deviation and Pearson correlation coefficient based on reference samples, where there are n reference samples and 1 individual sample.

[0021] The present invention also provides a method for evaluating the critical state of a biological system, including the following steps: using the sample to be tested as an individual sample, calculating the network entropy, and analyzing the biological system of the sample to be tested according to the network entropy.

[0022] In one embodiment, the analysis includes: when the global SNE value significantly increases, it indicates that the biological system of the sample to be tested reaches a critical state.

[0023] The above detection index Appears mutation or sharp increase, as a warning of an impending critical transition, or indicates that the complex biological system is about to enter the critical state of phase transition. It can be understood that the above significant increase can be judged by those skilled in the art according to the technical knowledge in the art. For example, if the global SNE value is more than twice the global SNE value of the previous time point, it is judged as a significant increase.

[0024] In one embodiment, the number of the reference samples ≥ 4.

[0025] In one embodiment, the reference sample is a sample from an individual or tissue that has not reached the critical state or whose biological system has not undergone a phase transition, or a sample far from the bifurcation point in numerical simulation.

[0026] The present invention also provides a method for evaluating cancer risk for non-therapeutic purposes, including the following steps: evaluating the biological system of the person to be tested by using the above method, if the biological system of the person to be tested reaches the critical state, it indicates that the person to be tested has a higher risk of cancer.

[0027] The above method can solve the limitation of relying on multiple samples to evaluate the critical state of diseases in the prior art. This method analyzes through the gene expression data of a single sample, uses the change of dynamic network entropy to detect the critical transition of the system, and provides a basis for the early warning of diseases.

[0028] The present invention also provides the application of the above method in evaluating the critical state of a biological system.

[0029] Compared with the prior art, the present invention has the following beneficial effects: The network entropy, method and application for evaluating the critical state of a biological system of the present invention. This network entropy is obtained by mining the rich dynamic information in high-throughput data and using the dynamic characteristic differences between the normal state and the critical state to quantify the interference of a single sample on the distribution of the reference group samples. Based on this network entropy, the early warning signals of the critical state or phase transition can be identified, and then the critical state of the biological system can be evaluated. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a schematic flow chart for judging whether a complex biological system is in the critical state of phase transition through the SNE index of a single sample; Figure 2 It is a schematic diagram of a regulatory network including eight nodes, and this regulatory network is used to generate a numerical simulation data set; Figure 3It is a result graph showing that the SNE value curve increases sharply near the critical point (bifurcation point p = 0) in the numerical simulation experiment; Figure 4 It is a result graph showing the dynamic changes of the SNE values of each local network from a global perspective. The dynamic changes of the local SNE values of 8 local networks ( ) are shown in the global view; Figure 5 It is a result graph showing the evolution of the network standard deviation and Pearson correlation coefficient before the transition and near the critical point; Figure 6 It is a graph of the SNE value curve of colon adenocarcinoma; Figure 7 It is a result graph comparing the survival rates before and after the critical point of colon adenocarcinoma; Figure 8 It is a graph of the SNE value curve of hepatocellular carcinoma; Figure 9 It is a result graph comparing the survival rates before and after the critical point of hepatocellular carcinoma; Figure 10 It is a graph of the SNE value curve of embryonic cells. Detailed implementation manner

[0031] To facilitate the understanding of the present invention, the present invention will be described more comprehensively below with reference to the relevant drawings. Preferred embodiments of the present invention are shown in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, these embodiments are provided to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0032] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs. The terms used in the description of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "and / or" used herein includes any and all combinations of one or more of the related listed items.

[0033] Unless otherwise specified, the reagents, materials, and equipment used in this embodiment are all commercially available sources; unless otherwise specified, the test methods are all conventional test methods in the art.

[0034] Example 1 1. A network entropy for evaluating the critical state of a biological system and a method for obtaining the same.

[0035] 1. Genes are mapped into a protein - protein interaction (PPI) network to construct a global background network . This network contains the interactions between genes in all samples and removes isolated nodes to form the network basis. For each gene , based on its neighboring genes , Extract the local network , specific operation: using gene as the central node (i.e., the central gene), genes , as the first-order neighbor nodes (i.e., neighboring genes), and extract the local network .

[0036] 2. A group of samples in a relatively normal state are selected as reference samples to characterize the network features of gene expression in a healthy state. These samples provide a reference for judging the perturbation of individual samples in subsequent calculations. Samples from relatively healthy people can be selected as reference samples; in numerical simulations, samples far from the critical point are used as reference samples; for real datasets, samples from relatively normal tissues are selected. The number of reference samples ≥ 4.

[0037] 3. In each local network , calculate the differences between the reference samples and the individual test samples. By the differences in the standard deviation (SD) and Pearson correlation coefficient (PCC) of gene expression, construct the differential local network. Specifically, calculate the changes in the standard deviation and correlation between the reference samples and the test samples to evaluate the degree of gene perturbation. The difference formula is as follows:

[0038]

[0039] where, and represent the standard deviation and Pearson correlation coefficient based on reference samples respectively, including the individual test samples.

[0040] 4. For each differential local network, calculate the local SNE value to quantify the perturbation of genes in the network. The formula for the local SNE value is as follows:

[0041] where, is the number of neighboring genes in the local network, used to measure the perturbation degree of the central gene and its neighboring genes in the test samples.

[0042] 5. By selecting the top 5% genes with the highest local SNE values, calculate the global SNE value of the individual samples to judge the overall perturbation degree of the system. A sharp increase in the global SNE value indicates that the system is approaching the critical state, predicting the approaching of a critical transition. The formula for the global SNE value is as follows:

[0043] Among them, is the number of genes with the highest top 5% SNE values, which is used to quantify the perturbation of an individual sample to the overall system.

[0044] II. A method for evaluating the critical state of a biological system.

[0045] The steps of this method are as follows: Taking the sample to be tested as an individual sample, calculating the network entropy of the sample to be tested by using the method in step one of this embodiment, analyzing the biological system of the sample to be tested based on the network entropy. If the global SNE value of the sample to be tested increases significantly, it indicates that the biological system of the sample to be tested reaches the critical state.

[0046] The method for evaluating the critical state of a biological system aims to identify impending critical transitions. It should be noted that the present invention detects early warning signals before the critical state to judge the arrival or occurrence of the phase transition critical state, rather than merely looking for signs of qualitative changes that have already occurred. Compared with traditional biomarkers for diagnosing the "deterioration stage" based on molecular expression differences, the method provided by the present invention can more accurately reflect the changes in the critical state during the development of complex biological systems. This method can identify the critical state of a complex system by relying on a single sample, while the traditional dynamic network biomarker DNB method requires multiple samples at each time point to evaluate statistical indicators.

[0047] The method of the present invention for judging the critical state through the single-sample SNE index aims to quantify the statistical perturbation of each sample to a set of reference samples, so as to accurately detect the early warning signals of key transitions at the single-sample level. This innovation not only simplifies the complexity of data collection and analysis, but also provides important technical support for early intervention and personalized medicine.

[0048] Example 2 Research and verification based on numerical simulation Figure 1 Shown is an implementation method for judging whether a complex biological system is in the phase transition critical state through the SNE index of a single sample.

[0049] To verify the effectiveness of this method, this example uses a regulatory network model with eight nodes ( Figure 2). The model is constructed by a set of variables controlled by eight stochastic differential equations and is described in the Michaelis-Menten form, which is very common in the study of gene regulatory mechanisms (such as transcription, diffusion, translation, translocation, etc.). The value range of parameter p is between -0.5 and 0.15, and based on this, a numerical simulation dataset is generated. The reference sample data is extracted from the range of -0.5 to -0.45 of the p-value interval to ensure being far from the key point p = 0.

[0050] From Figure 3 It can be seen that when the parameter p approaches the specific value 0, the single-sample SNE index increases significantly, indicating that the system is about to undergo a critical transition, and this specific value is regarded as the bifurcation point. Further analysis shows that the median of the SNE index also verifies the stability of this method in early warning of the critical state. Figure 4 provides the dynamic changes of the SNE values of each local network from a global perspective. Obviously, near p = 0, the SNE values of some local networks increase significantly, and the SNE value of the DNB variable at the center of the local network ( ) increases sharply, marking the upcoming critical transition. Figure 5 shows the evolution of the network standard deviation and Pearson correlation coefficient before the transition and near the critical point. Near the critical point (p = 0), the network structure changes significantly, indicating that there are significant differences between individual case samples and reference samples in the critical stage, and the system is about to undergo a major transition.

[0051] Through numerical simulation studies, the effectiveness and reliability of the method for judging the critical state of phase transitions in complex biological systems by the single-sample SNE index are verified. This method can effectively detect signals indicating critical state transitions, thereby enabling the judgment of whether the system is about to reach or has already undergone the critical state of phase transitions.

[0052] Example 3 Predict the critical points of real datasets.

[0053] In this example, the single-sample SNE index is applied to detect the critical states of three different real experimental datasets, including the critical states of two different types of tumors (liver hepatocellular carcinoma (LIHC) and colon adenocarcinoma (COAD)) from the TCGA database, and the critical state of embryonic cell differentiation.

[0054] I. To verify the effectiveness of the method proposed in this study for judging the critical state of phase transitions in complex biological systems by the single-sample SNE index, the method of Example 1 is applied to two tumor datasets in The Cancer Genome Atlas, namely liver hepatocellular carcinoma and colon adenocarcinoma.

[0055] Using tumor adjacent tissue samples representing a relatively healthy state (i.e., the samples are taken from non-cancerous tissues / regions) as reference samples, calculate the SNE value for each tumor sample, and use the average SNE value at different stages to quantitatively evaluate the critical stage of the tumor.

[0056] The research results show that the single-sample SNE index can identify stage III of colorectal adenocarcinoma and stage II of hepatocellular carcinoma as the critical stages ( Figure 6 , Figure 8 ). To verify the accuracy of the identified critical stages, the prognostic results of samples before and after the critical state are compared and analyzed through Kaplan-Meier survival analysis (log-rank test).

[0057] Specifically, in colorectal adenocarcinoma, as Figure 6 shown, there is a significant increase in the SNE value at stage III. Figure 7 It shows that the survival time of samples before the critical state (stages I-III) is significantly longer than that of samples after the critical state (stage IV), and the difference between the two survival curves is statistically significant (P = 0). Similarly, for hepatocellular carcinoma, Figure 8 it shows that the SNE value reaches a peak at stage II. Figure 9 It indicates that there is a significant difference in the survival curves between samples before the critical state (stages I-II) and after the critical state (stages III-IV) (P = 0.0251), and the samples before the critical state show a longer survival time.

[0058] The above results verify the effectiveness of the single-sample SNE index in identifying the critical state of tumors through survival analysis, indicating that this method can accurately predict the phase transition critical state of tumors and provide reliable prognostic information.

[0059] II. Detecting the critical state of embryonic cell differentiation based on the single-sample SNE index.

[0060] To verify the effectiveness of the method provided by the present invention for judging the critical state of phase transition in complex biological systems through the single-sample SNE index, the method of Example 2 is applied to the single-cell dataset (GSE102066) of the differentiation process of progenitor cells into nerve cells.

[0061] In the original experiment, a total of 483 single-cell samples were collected at 6 time points during embryonic development, as follows: day 0 (80 cells), day 1 (78 cells), and day 5 (85 cells), day 7 (80), day 10 (79 cells), and day 30 (81 cells). Using the cells at the first time point (i.e., day 0) as the reference sample, according to Figure 10It can be seen that a sudden increase in the SNE value was detected during the period from day 0 to day 1, indicating that there was a critical transition around day 1, which is considered to predict that progenitor cells will transform into neuronal cells after day 1.

[0062] This result is consistent with the observations of the original experiment, that is, progenitor cells began to differentiate and transform into neuronal cells after day 1 and continued until day 30. This result verifies the accuracy of the single-sample SNE index. In summary, the SNE value can detect the warning signal generated by the critical state, so as to accurately judge the arrival and / or occurrence of the critical state of the biological system, can detect the warning signal of the key transition at the single-sample level, and judge the critical state of the phase transition of the biological system based on a single sample.

[0063] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0064] The above-described embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention patent shall be subject to the appended claims.

Claims

1. A network entropy for evaluating the critical state of a biological system, characterized in that: The network entropy is the global SNE value of the individual sample, and the formula of the global SNE value is as follows: in, is the local SNE value, is the number of genes of the predetermined gene, To measure the disturbance of individual samples to the whole system.

2. The network entropy according to claim 1, characterized in that: The predetermined genes are the top 3-7% genes after the local SNE values ​​in the individual samples are sorted from high to low; the local SNE value is the local SNE value of the local differential local network.

3. The network entropy according to claim 2, characterized in that: The formula for the local SNE value is as follows: in, is the number of neighbor genes in the differential local network, It is used to measure the disturbance degree of the central gene of the differential local network and its neighboring genes in individual samples. is the difference in standard deviation, is the difference of Pearson correlation coefficient.

4. The network entropy according to claim 3, characterized in that: The method for constructing the differential local network includes: mapping the genes of individual samples to a protein-protein interaction network, and constructing a global background network. , based on each gene Neighbor gene , Extracting local networks (In each local network In , the difference between the reference sample and the individual sample is calculated to construct a differential local network.

5. The network entropy according to claim 4, characterized in that: The differences include: differences in standard deviations , the difference of Pearson correlation coefficient ; Said , The calculation formula is as follows: in, Respectively based on The standard deviation and Pearson correlation coefficient of the reference samples, There are n reference samples and 1 individual sample.

6. A method for assessing the critical state of a biological system, characterized in that The following steps are involved: The sample to be tested is taken as an individual sample, the network entropy according to any one of claims 1 to 5 is calculated, and the biological system of the sample to be tested is analyzed according to the network entropy.

7. The method according to claim 6, characterized in that The analysis includes: when the global SNE value increases significantly, it indicates that the biological system of the sample to be tested has reached a critical state.

8. The method according to claim 6, characterized in that The number of the reference samples is ≥4.

9. A method for assessing cancer risk for non-therapeutic purposes, characterized in that: The method comprises the following steps: using the method described in any one of claims 6 to 8 to evaluate the biological system of the person to be tested, and if the biological system of the person to be tested reaches a critical state, it indicates that the person to be tested has a higher risk of cancer.

10. Use of the method according to any one of claims 6 to 8 in assessing the criticality of a biological system.

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