A method for identifying key proteins based on weak consistency model

Abstract

The present invention discloses a method for identifying key proteins based on a weak consistency model, comprising the following steps: 1) setting weak consistency conditions; 2) weak consistency model evaluation. This method has high recognition efficiency and practical value, and provides a new idea for the identification of key proteins.

Description

Technical Field

[0001] The present invention relates to the field of bioinformatics, and involves multiple biological features of fusion proteins, which are used to identify key proteins, and specifically is a method for identifying key proteins based on a weak consistency model. Background Art

[0002] There are thousands of proteins in nature, and each protein has different functions. Some of them are crucial and are the essential material basis for cell survival or reproduction. Killing them will cause cell death or stop reproduction. These proteins are called key proteins or lethal proteins. Due to the important role of key proteins, studying key proteins has become a hot topic. Studies have shown that key proteins are also related to pathogenic genes, and identifying key proteins can also help in disease research. In addition, the identification of key proteins can also help in the development of new therapies and antibiotics and promote the development of synthetic biology.

[0003] At present, the methods for identifying key proteins are mainly divided into biological experimental methods and computational methods. Although biological experimental methods such as gene knockout, RNA interference, conditional gene knockout and gene editing technology have identified the gold standard set of key proteins in multiple species, they are not only long-term, inefficient and expensive, but also subject to strict ethical constraints when conducting experiments on humans or other primates. Therefore, it is urgent to develop new methods for identifying key proteins.

[0004] With the emergence of high-throughput technology and the accumulation of protein-protein interaction (PPI) network data, it has become a trend to use computational methods to identify key proteins. In recent years, some methods based on the topological characteristics of PPI networks have been proposed, such as degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), subgraph centrality (SC), eigenvector centrality (EC), information centrality (IC) and neighbor centrality (NC).

[0005] The prediction accuracy of this type of centrality method depends on the reliability of PPI network data. However, PPI data contains many false positives and false negatives, which affect the accuracy of key protein identification. Therefore, researchers have gradually developed methods that integrate multiple protein features. For example, Li et al. combined the topological features of the PPI network with gene expression data to propose the PeC method. Peng et al. used orthologous information to measure the conservative characteristics of proteins, used the edge clustering coefficient (ECC) to reflect the topological characteristics of the PPI network, and then used the random walk model to combine them to design the ION method. Li et al. proposed neighbor proximity centrality based on the topological characteristics of the PPI network, and then used the EXPOC model to combine orthologous data and NCC to design the NCCO method; Li et al. designed the E_POC method by using an improved POC model combined with the ECC coefficient, orthologous data and the Pearson correlation coefficient (PCC). Zhong et al. proposed a new metric called JDC, which provides a dynamic threshold method to binarize gene expression data and combines the jaccard similarity index and ECC to predict essential proteins.

[0006] The above methods are all based on multi-feature fusion to identify key proteins, and have improved recognition accuracy to a certain extent. Among them, both NCCO and E_POC methods found that there is a consistency relationship between the two types of features. After a large number of observations and statistical analyses, the present invention found that the two types of features are more likely to satisfy a weak consistency relationship, and on this basis, a weak consistency model is proposed to identify key proteins. Summary of the invention

[0007] The present invention aims at the deficiencies in the binding models of the existing representative methods and proposes a weak consistency model to identify key proteins. This method has high recognition efficiency and practical value and provides a new idea for the identification of key proteins.

[0008] The technical solution for achieving the purpose of the present invention is:

[0009] The method for identifying key proteins based on the weak consistency model includes the following steps:

[0010] 1) Set the weak consistency condition: Assume that protein u and protein v satisfy weak consistency, that is, u<<v, which means that u weakly suppresses v. The weak consistency condition is as follows:

[0011] A(u)>A(v)-ξand B(u)>B(v)-ξ,

[0012] Where u and v represent proteins; A and B represent two feature scores; ξ is the tolerance factor, which is a positive number;

[0013] The PPI network is represented by a graph G(V,E), where V is a set of protein nodes and E is a set of edges. After determining the weak repression relationship between proteins, the binding model is defined as:

[0014]

[0015] DM u,v Indicates whether protein u and protein v satisfy the weak suppression relationship, which is further defined as follows:

[0016]

[0017] Where α is an adjustable parameter between [0,1];

[0018] 2) Weak consistency model evaluation:

[0019] In order to test the ability of the weak consistency model to identify key proteins, the weak consistency model was used to replace the binding model in the following representative methods to observe whether it has a higher key protein recognition rate than the original method; 2-1) The PeC method uses the edge clustering coefficient to measure the tightness of the connection between two proteins, and uses the Pearson correlation coefficient based on the gene expression spectrum to measure the reliability of the connection between proteins. Then, the edge clustering coefficient and the Pearson correlation coefficient are combined by multiplication. The calculation formula of PeC is:

[0020]

[0021] where ecc(u,v) represents the edge aggregation coefficient between protein u and protein v respectively; N v represents the neighborhood of protein v; pcc(u,v) represents the Pearson correlation coefficient between protein u and protein v. The formulas of ecc(u,v) and pcc(u,v) are as follows:

[0022]

[0023]

[0024] Where N u and N v are the neighborhoods of protein u and protein v respectively; D u and D vRepresent the degrees of protein u and protein v respectively; s represents the number of samples of gene expression data; G(u,i) and G(v,i) represent the gene expression levels of protein u and protein v in sample i respectively; G(u) and G(v) are the means of the gene expression levels of protein u and protein v respectively; σ(u) and σ(v) represent the standard deviations of the gene expression levels of protein u and protein v respectively. The weak consistency model of formula (1) is used to replace formula (3), and then the method after replacing the combined model is named FPeC. FPeC satisfies the following conditions:

[0025] ecc(u)>ecc(v)-ξand pcc(u)>pcc(v)-ξ,

[0026] Where ecc(u) and ecc(v) represent the edge aggregation coefficients of protein u and protein v, respectively; pcc(u) and pcc(v) represent the Pearson correlation coefficients of protein u and protein v, respectively; ξ is the tolerance factor, which is a positive number. The combined model is used to give the final score, and the calculation formula is as follows:

[0027]

[0028] Where α is an adjustable parameter between [0,1], N u represents the neighborhood of protein u;

[0029] 2-2) The ION method uses orthologous information to measure the conservative characteristics of proteins, uses the edge clustering coefficient to reflect the topological characteristics of the PPI network, and then uses the random walk model to combine the edge clustering coefficient and orthologous information. The calculation formula of ION is:

[0030] PR t+1 =(1-α)D+α*H*PR t (7), where PR represents the ranking score, t is the number of iterations, D represents the orthologous matrix, H is the normalized ECC matrix, and the formula of D is as follows:

[0031]

[0032] Where O(u) is the number of reference species with orthologous proteins of protein u in the reference organism, and the formula of H is as follows:

[0033]

[0034] Where N u is the neighborhood of protein u, and the formula of ECC(u,v) is as follows:

[0035]

[0036] Among them, Z u,v is the number of triangles containing edge (u, v), k u and k v are the degrees of protein u and protein v respectively; min() is the minimum value function. The weak consistency model of formula (1) is used to replace formula (7), and then the method after replacing the combined model is named FION. The conditions satisfied by FION are:

[0037] D(u)>D(v)-ξandHR(u)>HR(v)-ξ,

[0038] Where D(u) represents the orthologous score of protein u; HR represents H*PR t ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score. The calculation formula is as follows:

[0039]

[0040] Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u;

[0041] 2-3) The NCCO method proposed the neighbor closeness centrality (NCC) based on the topological characteristics of the PPI network, and then combined the orthologous data and NCC using the EXPOC model. The calculation formula of NCCO is:

[0042] FS(u)=∑ u＜v (NCC(u)-NCC(v))+(Os(u)-Os(v)) (12), Where uξv means u suppresses v; NCC(u) means the neighbor proximity centrality score of protein u; Os means the orthologous score, the formula of Os is consistent with formula (8), and the calculation formula of NCC is:

[0043] CC(u)=(N-1) / ∑ v P(u,v)

[0044]

[0045] Where N is the total number of proteins in the PPI network, P(u,v) represents the shortest path between proteins u and v; D u and D v represents the degree of protein u and protein v; min() is the minimum function; N u represents the neighborhood of protein u; T u，vis the set of points of all triangles containing protein u and protein v. The weak consistency model of formula (1) is used to replace formula (12), and then the method after replacing the combined model is named FNCCO. The conditions satisfied by FNCCO are:

[0046] NCC(u)>NCC(v)-ξand Os(u)>Os(v)-ξ,

[0047] Where ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score. The calculation formula is as follows:

[0048]

[0049] Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u;

[0050] 2-4) The E_POC method uses the edge clustering coefficient to measure the degree of protein aggregation; uses the Pearson correlation coefficient to represent the gene expression level of two proteins to measure the reliability of the edge; uses the orthologous information to measure the importance of the protein itself; finally, the extended POC model is used to integrate the Pearson correlation coefficient, edge clustering coefficient, and orthologous information. The calculation formula of E_POC is:

[0051]

[0052]

[0053] Where P s represents the orthologous score, P s The formula is the same as formula (8); α is an adjustable parameter between [0,1]; P n Represents the sum of the edge clustering coefficient and the Pearson correlation coefficient, and its formula is as follows:

[0054] P n (u)=ECC(u)+pcc(u) (16),

[0055] Where ECC represents the edge clustering coefficient, and the formula of ECC is the same as formula (10). PCC represents the Pearson correlation coefficient, and the formula of PCC is consistent with formula (5). The weak consistency model of formula (1) is used to replace formula (15), and then the method after replacing the combined model is named FE_POC. FE_POC satisfies the following conditions:

[0056] P n (u)>P n (v)-ξand P s (u)>P s (v) -ξ,

[0057] Where ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score. The calculation formula is as follows:

[0058]

[0059] Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u;

[0060] 2-5) The JDC method uses a dynamic threshold method to binarize gene expression data and uses multiplication to combine the Jaccard similarity index and edge clustering coefficient to predict key proteins. The calculation formula of JDC is:

[0061]

[0062] Where N u represents the neighborhood of protein u; jaccard(u, v) represents the jaccard similarity of edge (u, v); ECC(u, v) represents the edge clustering coefficient of edge (u, v), ECC is the same as formula (10), and the calculation formula of jaccard similarity is as follows:

[0063]

[0064] Among them, S u and S v The Boolean value representing the gene expression data of protein u and protein v, the jaccard similarity coefficient is between 0 and 1, the weak consistency model of formula (1) is used to replace formula (18), and then the method after replacing the combined model is named FJDC. FJDC satisfies the following conditions:

[0065] jaccard(u)>jaccard(v)-ξand ECC(u)>ECC(v)-ξ,

[0066] Where jaccard(u) and jaccard(v) represent the jaccard similarity coefficients of protein u and protein v, respectively; ECC(u) and ECC(v) represent the edge aggregation coefficients of protein u and protein v, respectively; ξ is the fault tolerance factor, which is a small positive number. The combined model is used to give the final score, and the calculation formula is as follows:

[0067]

[0068] Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u.

[0069] Advantages of this technical solution:

[0070] (1) This technical solution first proposed that there is a weak suppression relationship between different feature scores, and proteins that meet this relationship are more likely to be key proteins;

[0071] (2) Based on the weak suppression relationship between features, this technical solution designs a weak consistency model to integrate different feature scores;

[0072] (3) The weak consistency model is applied to five classic algorithms. The results show that the weak consistency model has higher recognition rate and practical value.

[0073] This method has high recognition rate and practical value, and provides new ideas for the identification of key proteins. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A schematic diagram of comparative experimental results based on a bar graph in the embodiment;

[0075] Figure 2 This is a schematic diagram of the experimental results based on the Precision-Recall curve comparison in the embodiment;

[0076] Figure 3 It is a schematic diagram of the experimental results based on the jackknife curve comparison in the embodiment. DETAILED DESCRIPTION

[0077] The invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, but the invention is not limited thereto.

[0078] Example:

[0079] This experiment was conducted on a computer (Intel(R) Core(TM) i5-6500 3.20GHz CPU, 16G memory), the operating system was Windows 10, and the compilation and running tool was Matlab2021.

[0080] This example uses the dataset of S.cerevisiae species as test data. The PPI dataset comes from three databases: BioGRID, IntAct, MINT and the Consolidated PPI dataset downloaded in January 2014, which contains 6099 proteins and 560702 interactions. The key protein dataset integrates data from four databases: MIPS, SGD, DEG and SGDP, and contains 1285 key proteins. The orthologous protein dataset is extracted from the 7th version of InParanoid, which is generated by the INPARANIOD program and contains protein comparisons between the whole genomes of 100 reference species. The gene expression data was constructed by Tu et al., with a total of 6777 gene products and 36 samples.

[0081] In order to verify the performance of the weak consistency model, this example uses five representative methods, PeC, ION, NCCO, E_POC, and JDC, as test methods and conducts experiments on the S. cerevisiae dataset. Among these five representative methods, ION and E_POC both contain the parameter α, and their α values ​​on the S. cerevisiae dataset are shown in Table 1.

[0082] In this example, after replacing the combined model of PeC, ION, NCCO, E_POC and JDC with the weak consistency model, the parameters ξ and α were introduced. The optimal parameter values ​​of FPeC, FION, FNCCO, FE_POC and FJDC on the S. cerevisiae dataset are shown in Table 2.

[0083] Table 1 Parameters of ION and E_POC on S. cerevisiae

[0084]

[0085] The method for identifying key proteins based on the weak consistency model includes the following steps:

[0086] 1) Set the weak consistency condition: Assume that protein u and protein v satisfy weak consistency, that is, u<<v, indicating that u weakly suppresses v. The weak consistency condition is as follows:

[0087] A(u)>A(v)-ξand B(u)>B(v)-ξ,

[0088] Where u and v represent proteins; A and B represent two feature scores; ξ is the tolerance factor, which is a small positive number;

[0089] The PPI network is represented by a graph G(V,E), where V is a set of protein nodes and E is a set of edges. After determining the weak repression relationship between proteins, the binding model is defined as:

[0090]

[0091] DM u,v Indicates whether protein u and protein v satisfy the weak suppression relationship, which is further defined as follows:

[0092]

[0093] Where α is an adjustable parameter between [0,1];

[0094] 2) Weak consistency model evaluation:

[0095] In order to test the ability of the weak consistency model to identify key proteins, this example replaced the binding models in the following representative methods with the weak consistency model to observe whether it has a higher key protein recognition rate than the original method;

[0096] 2-1) The PeC method uses the edge clustering coefficient to measure the tightness of the connection between two proteins, and uses the Pearson correlation coefficient based on the gene expression spectrum to measure the reliability of the connection between proteins. The edge clustering coefficient and the Pearson correlation coefficient are then combined by multiplication. The calculation formula of PeC is:

[0097]

[0098] where ecc(u,v) represents the edge aggregation coefficient between protein u and protein v respectively; N v represents the neighborhood of protein v; pcc(u,v) represents the Pearson correlation coefficient between protein u and protein v. The formulas of ecc(u,v) and pcc(u,v) are as follows:

[0099]

[0100]

[0101] Where N u and N v are the neighborhoods of protein u and protein v respectively; D u and D v Represent the degrees of protein u and protein v respectively; s represents the number of samples of gene expression data; G(u,i) and G(v,i) represent the gene expression levels of protein u and protein v in sample i respectively; G(u) and G(v) are the means of the gene expression levels of protein u and protein v respectively; σ(u) and σ(v) represent the standard deviations of the gene expression levels of protein u and protein v respectively. In this example, the weak consistency model of formula (1) is used to replace formula (3), and then the method after replacing the combined model is named FPeC. FPeC satisfies the following conditions:

[0102] ecc(u)>ecc(v)-ξandpcc(u)>pcc(v)-ξ,

[0103] Where ecc(u) and ecc(v) represent the edge aggregation coefficients of protein u and protein v, respectively; pcc(u) and pcc(v) represent the Pearson correlation coefficients of protein u and protein v, respectively; ξ is the tolerance factor, which is a small positive number. The combined model is used to give the final score, and the calculation formula is as follows:

[0104]

[0105] Where α is an adjustable parameter between [0,1], N u Represents the neighborhood of protein u. The specific process is as follows:

[0106]

[0107]

[0108] 2-2) The ION method uses orthologous information to measure the conservative characteristics of proteins, uses the edge clustering coefficient to reflect the topological characteristics of the PPI network, and then uses the random walk model to combine the edge clustering coefficient and orthologous information. The calculation formula of ION is:

[0109] PR t+1 =(1-α)D+α*H*PR t (7)

[0110] Where PR represents the ranking score, t is the number of iterations, D represents the orthologous matrix, H is the normalized ECC matrix, and the formula of D is as follows:

[0111]

[0112]

[0113] Where O(u) is the number of reference species with orthologous proteins of protein u in the reference organism, and the formula of H is as follows:

[0114]

[0115] Where N u is the neighborhood of protein u, and the formula of ECC(u,v) is as follows:

[0116]

[0117] Among them, Z u,v is the number of triangles containing edge (u, v), ku and k v are the degrees of protein u and protein v respectively; min() is the minimum value function. In this example, the weak consistency model of formula (1) is used to replace formula (7), and then the method after replacing the combined model is named FION. The conditions satisfied by FION are:

[0118] D(u)>D(v)-ξandHR(u)>HR(v)-ξ,

[0119] Where D(u) represents the orthologous score of protein u; HR represents H*PR t ξ is the fault tolerance factor, which is a small positive number. The combined model is used to give the final score. The calculation formula is as follows:

[0120]

[0121] Where α is an adjustable parameter between [0,1]; N u Represents the neighborhood of protein u. The specific process is as follows:

[0122]

[0123] 2-3) The NCCO method proposed the neighbor closeness centrality (NCC) based on the topological characteristics of the PPI network, and then combined the orthologous data and NCC using the EXPOC model. The calculation formula of NCCO is:

[0124] FS(u)=∑ u＜v (NCC(u)-NCC(v))+(Os(u)-Os(v)) (12),

[0125] Where u<v means u suppresses v; NCC(u) represents the neighbor proximity centrality score of protein u; Os represents the orthologous score, and the formula of Os is consistent with formula (8). The calculation formula of NCC is:

[0126] CC(u)=(N-1) / ∑ v P(u,v)

[0127]

[0128] Where N is the total number of proteins in the PPI network, P(u,v) represents the shortest path between proteins u and v; D u and D v represents the degree of protein u and protein v; min() is the minimum function; N u represents the neighborhood of protein u; T u，vis the set of points of all triangles containing protein u and protein v. In this example, the weak consistency model of formula (1) is used to replace formula (12), and then the method after replacing the combined model is named FNCCO. The conditions satisfied by FNCCO are:

[0129] NCC(u)>NCC(v)-ξand Os(u)>Os(v)-ξ,

[0130] Where ξ is the fault tolerance factor, which is a small positive number. The combined model is used to give the final score. The calculation formula is as follows:

[0131]

[0132] Where α is an adjustable parameter between [0,1]; N u Represents the neighborhood of protein u. The specific process is as follows:

[0133]

[0134] 2-4) The E_POC method uses the edge clustering coefficient to measure the degree of protein aggregation; uses the Pearson correlation coefficient to represent the gene expression level of two proteins to measure the reliability of the edge; uses the orthologous information to measure the importance of the protein itself; finally, the extended POC model is used to integrate the Pearson correlation coefficient, edge clustering coefficient, and orthologous information. The calculation formula of E_POC is:

[0135]

[0136]

[0137] Where P s represents the orthologous score, P s The formula is the same as formula (8); α is an adjustable parameter between [0,1]; P n Represents the sum of the edge clustering coefficient and the Pearson correlation coefficient, and its formula is as follows:

[0138] P n (u)=ECC(u)+pcc(u) (16),

[0139] Where ECC represents the edge clustering coefficient, and the formula of ECC is the same as formula (10). PCC represents the Pearson correlation coefficient, and the formula of PCC is consistent with formula (5). In this example, the weak consistency model of formula (1) is used to replace formula (15), and then the method after the replacement and combination model is named FE_POC. FE_POC satisfies the following conditions:

[0140] P n (u)>P n(v)-ξand P s (u)>P s (v) -ξ,

[0141] Where ξ is the fault tolerance factor, which is a small positive number. The combined model is used to give the final score. The calculation formula is as follows:

[0142]

[0143] Where α is an adjustable parameter between [0,1]; N u Represents the neighborhood of protein u. The specific process is as follows:

[0144]

[0145]

[0146] 2-5) The JDC method uses a dynamic threshold method to binarize gene expression data and uses multiplication to combine the Jaccard similarity index and edge clustering coefficient to predict key proteins. The calculation formula of JDC is:

[0147]

[0148] Where N u represents the neighborhood of protein u; jaccard(u, v) represents the jaccard similarity of edge (u, v); ECC(u, v) represents the edge clustering coefficient of edge (u, v), ECC is the same as formula (10), and the calculation formula of jaccard similarity is as follows:

[0149]

[0150] Among them, S u and S v The Boolean value representing the gene expression data of protein u and protein v. The jaccard similarity coefficient is between 0 and 1. In this example, the weak consistency model of formula (1) is used to replace formula (18), and then the method after replacing the combined model is named FJDC. FJDC meets the following conditions:

[0151] jaccard(u)>jaccard(v)-ξand ECC(u)>ECC(v)-ξ,

[0152] Where jaccard(u) and jaccard(v) represent the jaccard similarity coefficients of protein u and protein v, respectively; ECC(u) and ECC(v) represent the edge aggregation coefficients of protein u and protein v, respectively; ξ is the fault tolerance factor, which is a small positive number. The combined model is used to give the final score, and the calculation formula is as follows:

[0153]

[0154] Where α is an adjustable parameter between [0,1]; N u Represents the neighborhood of protein u. The specific process is as follows:

[0155]

[0156]

[0157] The comparison results between this example and the existing method are as follows Figure 1-Figure 3 As shown, after replacing the binding model using this method, the efficiency of identifying key proteins is significantly higher than that of existing methods.

Claims

1. A method for identifying key proteins based on a weak consistency model, characterized in that: The steps include: 1) Set the weak consistency condition: Assume that protein u and protein v satisfy weak consistency, that is, u<<v, indicating that u weakly suppresses v. The weak consistency condition is as follows: A(u)>A(v)-ξand B(u)>B(v)-ξ, Where u and v represent proteins; A and B represent two feature scores; ξ is the tolerance factor, which is a positive number; The PPI network is represented by a graph G(V,E), where V is a set of protein nodes and E is a set of edges. After determining the weak repression relationship between proteins, the binding model is defined as: DM u,v Indicates whether protein u and protein v satisfy the weak suppression relationship, which is further defined as follows: Where α is an adjustable parameter between [0,1]; 2) Weak consistency model evaluation: In order to test the ability of the weak consistency model to identify key proteins, the weak consistency model was used to replace the binding model in the following representative methods to observe whether it has a higher key protein recognition rate than the original method; 2-1) The PeC method uses the edge clustering coefficient to measure the tightness of the connection between two proteins, and uses the Pearson correlation coefficient based on the gene expression spectrum to measure the reliability of the connection between proteins. Then, the edge clustering coefficient and the Pearson correlation coefficient are combined by multiplication. The calculation formula of PeC is: where ecc(u,v) represents the edge aggregation coefficient between protein u and protein v respectively; N v represents the neighborhood of protein v; pcc(u,v) represents the Pearson correlation coefficient between protein u and protein v. The formulas of ecc(u,v) and pcc(u,v) are as follows: Where N u and N v are the neighborhoods of protein u and protein v respectively; D u and D v Represent the degrees of protein u and protein v respectively; s represents the number of samples of gene expression data; G(u,i) and G(v,i) represent the gene expression levels of protein u and protein v in sample i respectively; G(u) and G(v) are the means of the gene expression levels of protein u and protein v respectively; σ(u) and σ(v) represent the standard deviations of the gene expression levels of protein u and protein v respectively. The weak consistency model of formula (1) is used to replace formula (3), and then the method after replacing the combined model is named FPeC. FPeC satisfies the following conditions: ecc(u)>ecc(v)-ξand pcc(u)>pcc(v)-ξ, Where ecc(u) and ecc(v) represent the edge aggregation coefficients of protein u and protein v, respectively; pcc(u) and pcc(v) represent the Pearson correlation coefficients of protein u and protein v, respectively; ξ is the tolerance factor, which is a positive number. The combined model is used to give the final score, and the calculation formula is as follows: Where α is an adjustable parameter between [0,1], N u represents the neighborhood of protein u; 2-2) The ION method uses orthologous information to measure the conservative characteristics of proteins, uses the edge clustering coefficient to reflect the topological characteristics of the PPI network, and then uses the random walk model to combine the edge clustering coefficient and orthologous information. The calculation formula of ION is: PR t+1 =(1-α)D+α*H*PR t (7), Where PR represents the ranking score, t is the number of iterations, D represents the orthologous matrix, H is the normalized ECC matrix, and the formula of D is as follows: Where O(u) is the number of reference species with orthologous proteins of protein u in the reference organism, and the formula of H is as follows: Where N u is the neighborhood of protein u, and the formula of ECC(u,v) is as follows: Among them, Z u,v is the number of triangles containing edge (u, v), k u and k v are the degrees of protein u and protein v respectively; min() is the minimum value function. The weak consistency model of formula (1) is used to replace formula (7), and then the method after replacing the combined model is named FION. The conditions satisfied by FION are: D(u)>D(v)-ξand HR(u)>HR(v)-ξ, Where D(u) represents the orthologous score of protein u; HR represents H*PR t ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score. The calculation formula is as follows: Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u; 2-3) The NCCO method proposed the neighbor closeness centrality (NCC) based on the topological characteristics of the PPI network, and then combined the orthologous data and NCC using the EXPOC model. The calculation formula of NCCO is: FS(u)=∑ u＜v (NCC(u)-NCC(v))+(Os(u)-Os(v)) (12), Where u<v means u suppresses v; NCC(u) represents the neighbor proximity centrality score of protein u; Os represents the orthologous score, and the formula of Os is consistent with formula (8). The calculation formula of NCC is: CC(u)=(N-1) / ∑ v P(u,v) Where N is the total number of proteins in the PPI network, P(u,v) represents the shortest path between proteins u and v; D u and D v represents the degree of protein u and protein v; min() is the minimum function; N u represents the neighborhood of protein u; T u，v is the set of points of all triangles containing protein u and protein v. The weak consistency model of formula (1) is used to replace formula (12), and then the method after replacing the combined model is named FNCCO. The conditions satisfied by FNCCO are: NCC(u)>NCC(v)-ξand Os(u)>Os(v)-ξ, Where ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score. The calculation formula is as follows: Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u; 2-4) The E_POC method uses the edge clustering coefficient to measure the degree of protein aggregation; uses the Pearson correlation coefficient to represent the gene expression level of two proteins to measure the reliability of the edge; uses the orthologous information to measure the importance of the protein itself; finally, the extended POC model is used to integrate the Pearson correlation coefficient, edge clustering coefficient, and orthologous information. The calculation formula of E_POC is: Where P s represents the orthologous score, P s The formula is the same as formula (8); α is an adjustable parameter between [0,1]; P n Represents the sum of the edge clustering coefficient and the Pearson correlation coefficient, and its formula is as follows: P n (u)=ECC(u)+pcc(u) (16), Where ECC represents the edge clustering coefficient, and the formula of ECC is the same as formula (10). PCC represents the Pearson correlation coefficient, and the formula of PCC is consistent with formula (5). The weak consistency model of formula (1) is used to replace formula (15), and then the method after replacing the combined model is named FE_POC. FE_POC satisfies the following conditions: P n (u)>P n (v)-ξand P s (u)>P s (v)-ξ, Where ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score. The calculation formula is as follows: Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u; 2-5) The JDC method uses a dynamic threshold method to binarize gene expression data and uses multiplication to combine the Jaccard similarity index and edge clustering coefficient to predict key proteins. The calculation formula of JDC is: Where N u represents the neighborhood of protein u; jaccard(u, v) represents the jaccard similarity of edge (u, v); ECC(u, v) represents the edge clustering coefficient of edge (u, v), ECC is the same as formula (10), and the calculation formula of jaccard similarity is as follows: Among them, S u and S v The Boolean value representing the gene expression data of protein u and protein v, the jaccard similarity coefficient is between 0 and 1, the weak consistency model of formula (1) is used to replace formula (18), and then the method after replacing the combined model is named FJDC. FJDC satisfies the following conditions: jaccard(u)>jaccard(v)-ξand ECC(u)>ECC(v)-ξ, Where jaccard(u) and jaccard(v) represent the jaccard similarity coefficients of protein u and protein v, respectively; ECC(u) and ECC(v) represent the edge aggregation coefficients of protein u and protein v, respectively; ξ is the fault tolerance factor, which is a positive number. The combined model is used to give the final score, and the calculation formula is as follows: Where α is an adjustable parameter between [0,1]; N u represents the neighborhood of protein u.

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