A method for predicting protein interaction relationships based on non-negative matrix factorization framework

Abstract

The present invention discloses a computational method for predicting protein interaction relationships based on a non-negative matrix decomposition framework. This method effectively integrates the topological structural characteristics of protein interaction data and the ontological semantic similarity information of proteins. These two types of information are integrated into the framework of the non-negative matrix decomposition method. By iteratively solving the results of the non-negative matrix decomposition, a similarity matrix of the connectivity relationships between proteins is obtained. Finally, the similarity values ​​between proteins with unknown connectivity relationships are obtained by filtering through the subcellular localization information matrix. The greater the similarity, the greater the possibility of interaction between the two proteins. Tests have verified that the method proposed by the present invention can significantly improve the accuracy and efficiency of predicting unknown protein interaction relationships.

Description

Technical Field

[0001] The present invention relates to the interdisciplinary research field of mathematics and biology, and in particular to a method for predicting unknown interaction relationships between proteins based on known protein interaction relationship data. Background Art

[0002] Proteins are the material basis of cells, and the physiological activities of cells are mainly regulated by protein-protein interactions. Studying protein-protein interactions helps to reveal the regulatory relationships and protein functions at the molecular level. Biological research has shown that the prediction of protein-protein interactions has important applications in drug design targeting protein interactions and personalized medicine for complex diseases. Effective prediction of unknown interactions between proteins helps to elucidate intermolecular regulatory mechanisms, providing assistance for further drug molecular target design and research on disease pathogenic mechanisms.

[0003] Traditional biological experiments typically use techniques such as co-immunoprecipitation, yeast two-hybrid, and fluorescence resonance energy transfer to detect protein-protein interactions. However, these methods are often time-consuming, expensive, and inefficient. Furthermore, these methods also have inherent limitations. For example, yeast two-hybrid methods are not applicable to all proteins, only effective for fusion proteins, and have a high false-positive rate. Therefore, there is an urgent need for rapid methods to detect protein-protein interactions. With the rapid development of high-throughput biological technologies in recent years, a large amount of high-throughput data, such as protein interaction data, gene function annotation data, and protein subcellular localization data, has become available. This has provided the opportunity to computationally predict protein-protein interactions. Based on this data, effectively exploring the inherent properties inherent in this data and designing mathematical methods to computationally predict protein-protein interactions are currently hot research areas.

[0004] In recent years, scholars at home and abroad have proposed many computational methods for predicting interactions between unknown proteins. For example, Zhang et al. proposed a method based on protein domain interactions to predict interactions between unknown proteins, based on protein domain information. Wang, Krishna et al. proposed a matrix decomposition-based method, R-NMTF, to predict protein interactions, transforming the prediction of unknown protein interactions into the problem of filling in elements in the matrix of existing protein interaction relationships. More recently, Wang and Tang et al. (2018) proposed a non-negative matrix factorization method (SASNMF) based on non-negative matrix factorization that incorporates internal and external information for link prediction. Although Wang et al. also expanded the non-negative matrix factorization method by incorporating multiple data sources and adding regularization terms to effectively improve prediction accuracy, this method relies on the construction of regularization terms in the objective function and the selection of the iteration format, and it is difficult to ensure the smoothness and accuracy of the solution.

[0005] Because protein-protein connectivity can be viewed as a classification problem, determining whether a pair of proteins interacts or not, many researchers have, in recent years, transformed the problem of predicting unknown protein-protein connectivity into a classification problem, employing machine learning methods to predict unknown protein-protein connectivity. For example, Martin et al. proposed a method based on support vector machines (SVMs) with different kernel functions to predict protein-protein interactions; Ding et al. proposed a method based on random forests to predict unknown protein-protein interactions; and recently, Tian et al. proposed a multi-information fusion method to effectively extract protein sequence features, followed by a SVM approach to predict unknown protein-protein interactions. However, these machine learning-based methods rely on negative samples, and the selection of reliable negative samples largely determines the prediction accuracy and efficiency of the algorithms. Reliable negative sample data for protein-protein interaction relationships in unknown species is difficult to find, and even for widely studied species such as yeast, obtaining accurate negative sample data remains extremely challenging.

[0006] In summary, although some work has been done on predicting unknown protein interaction relationships, the accuracy and efficiency of methods for predicting protein interaction relationships still need to be improved. Summary of the Invention

[0007] The present invention provides a method for predicting protein interaction relationships based on a non-negative matrix factorization framework, the method comprising the following steps:

[0008] (1) Obtain existing protein interaction relationship data (also known as protein interaction network data), gene ontology semantic annotation information (Gene Ontology annotation) and protein subcellular localization (Protein Subcellular Localization) data;

[0009] (2) Construct an adjacency matrix A based on the existing protein interaction relationship data, construct a protein-protein gene function similarity matrix S based on the gene ontology semantic annotation information data, and construct a subcellular localization information adjacency matrix SL_adj between proteins based on the protein subcellular localization data;

[0010] (3) Define an objective function based on the non-negative matrix factorization framework:

[0011] (1)

[0012] Where A represents the adjacency matrix, , and , S represents the gene function similarity matrix, represents the Frobenius norm, Tr(A) represents the trace of matrix A, represents the weight parameter, are regularization parameters to prevent overfitting, p is a parameter between 1 and 2, L=DC, C is the cosine similarity matrix of matrix A, ;

[0013] (4) Establish an augmented Lagrangian function and use an iterative optimization method to optimize the objective function value;

[0014] (5) Obtain W and H1 after iterative optimization and calculate the connection similarity value between proteins with unknown connection relationships;

[0015] (6) Sort the similarity values ​​between proteins with unknown connectivity relationships from large to small, and the connectivity relationships corresponding to the top k (k is an integer, usually 100 or 200) with the largest similarity values ​​are the predicted protein interaction relationships.

[0016] Furthermore, the existing protein interaction relationship data, gene ontology semantic annotation information data and protein subcellular localization data in step (1) are obtained from a public database.

[0017] Furthermore, the step (2) specifically includes:

[0018] (2.1) Obtain the adjacency matrix A of the relationships between proteins from the protein interaction relationship data;

[0019] (2.2) Based on the gene ontology semantic annotation information data, find the pair of gene ontology term numbers (GO-id(u), GO-id(v)) corresponding to each pair of interacting proteins (u, v) under the biological process information; use the statistical software R toolbox Gosim to calculate the semantic similarity of the protein pair (u, v) under the biological process. , thereby obtaining the semantic similarity between all protein pairs, and constructing the gene ontology semantic similarity matrix S;

[0020] (2.3) Based on the protein subcellular localization information data and the existing protein interaction relationship data, count each edge in the network Corresponding protein Subcellular localization information And calculate their intersection to determine whether the two interacting proteins are in the same subcellular localization, and obtain the adjacency matrix data SL_adj of the corresponding subcellular localization information:

[0021]

[0022] Where SL(u) represents the subcellular localization information data of protein u, and SL(v) represents the subcellular localization information data of protein v.

[0023] Furthermore, the steps of establishing the augmented Lagrangian function in step (4) are as follows:

[0024] Introduction , and For constraints , and The Lagrange multiplier of , the augmented Lagrange function is as follows:

[0025]

[0026] Based on the above augmented Lagrangian function L, , and By taking partial derivatives and applying KKT conditions, we can obtain the following iterative method to optimize the objective function in step (3):

[0027] (2)

[0028] (3)

[0029] (4)

[0030] When the number of iterations meets certain conditions (such as more than 100 iterations), the iteration is terminated and the optimized W and H1 are obtained.

[0031] Furthermore, the steps of calculating the connection similarity values ​​between proteins with unknown connection relationships in step (5) are as follows:

[0032] Based on the iteratively optimized W and H1 obtained in step (4), the connection similarity value S_prediction between proteins with unknown connection relationships is calculated according to the following formula:

[0033] , (5)

[0034] in , Represents the multiplication of corresponding matrix elements, where i is the only matrix of all elements.

[0035] The technical effect of the present invention is that, compared with existing technologies, the present invention effectively integrates semantic similarity information between proteins and the topological structural similarity of known protein interactions into a non-negative matrix factorization framework. This is combined with subcellular localization information for filtering, assuming that proteins in different subcellular locations will not interact with each other, thus proposing a new computational method for predicting protein interactions. The method proposed by the present invention has significant advantages in prediction accuracy over existing methods, effectively solving the problems of high costs and long time periods associated with biological experiments, and can provide a reliable basis for biologists to conduct biological verification. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] FIG1 is a comparison chart of the results of the method of the present invention and the R-NMTF method under five-fold cross validation on the test data DIP Core, where the X-axis represents FPR and the Y-axis represents TPR.

[0037] FIG2 is a comparison diagram of the results of the method of the present invention and the R-NMTF method under five-fold cross validation on the test data Collins 2007, where the X-axis represents FPR and the Y-axis represents TPR.

[0038] Figure 3 This is a comparison chart of the results of the method of the present invention and the R-NMTF method under five-fold cross validation on the test data Krogan2006, where the X-axis represents FPR and the Y-axis represents TPR. DETAILED DESCRIPTION

[0039] The algorithm flow and beneficial effects of the present invention will be described in detail below with reference to examples, in order to help readers better understand the essence of the present invention, but it does not constitute any limitation on the implementation and protection scope of the present invention.

[0040] The present invention aims to provide a new computational method for predicting unknown interactions between proteins based on existing protein interaction relationship data. The prediction of protein interaction relationships is regarded as a matrix missing data filling problem. The existing protein interaction relationship data is used to construct a protein interaction adjacency matrix, a gene ontology semantic similarity matrix, and a protein subcellular localization information matrix. These three types of information are effectively integrated into the non-negative matrix factorization framework to predict unknown protein interactions. The specific operation is carried out according to the following steps:

[0041] 1) Based on the known protein interaction relationship data, obtain the adjacency matrix A of the connection relationship between proteins;

[0042] 2) For any pair of proteins in the protein interaction data, find the GO-id of the two proteins in the corresponding gene ontology (GO). Then, calculate the functional similarity between this pair of proteins using the gene semantic similarity calculation method. Similarly, calculate the functional similarity values ​​of all protein pairs and obtain the adjacency matrix data S of the semantic similarity information between all proteins.

[0043] 3) Count the subcellular localization information data of each protein in the protein interaction network. If any two proteins have the same subcellular localization, the corresponding element in the subcellular localization information adjacency matrix is ​​1, otherwise it is 0. Thus, the subcellular localization information adjacency matrix SL_adj based on the protein interaction relationship is constructed;

[0044] 4) Substitute the network adjacency matrix A, gene ontology semantic similarity matrix S, and subcellular localization information adjacency matrix SL_adj obtained from the above steps into the above formula (1), randomly initialize W, H1, and H2, and solve the optimized W and H1 according to the iterative method in formulas (2), (3), and (4). The connection similarity value between proteins with unknown connection relationships is calculated by formula (5). The larger the value, the greater the probability of interaction between the two proteins.

[0045] To verify the effectiveness of the algorithm, we used yeast protein interaction data, which is currently under extensive research, for testing and analysis. The yeast protein interaction data used in this study was derived from the core data of the DIP database in May 2017. After removing duplicate and self-interaction data, we obtained a protein interaction network data containing 2339 proteins and 5182 edges.

[0046] Download yeast GO annotation semantic information data from the Gene Ontology Consortium database. The deadline is March 4, 2015.

[0047] The subcellular localization data of yeast proteins are derived from the COMPARTMENTS database, in which yeast proteins are annotated with 11 subcellular localizations, namely cytoskeleton, nucleus, endoplasmic reticulum, cytoplasm, Golgi apparatus, mitochondria, endosomes, cell membrane, lysosomes, extracellular matrix and vacuole.

[0048] The prediction of unknown interaction relationships between proteins can be abstracted as the completion of the connection relationship matrix between proteins, and the completion of the matrix is ​​achieved through matrix decomposition. The traditional non-negative matrix decomposition method only relies on the topological structure information of the known protein interaction relationship, and it is difficult to accurately predict the unknown connection relationship between proteins. In view of this, the present invention proposes a new calculation method for predicting unknown interaction relationships between proteins based on the non-negative matrix decomposition framework by integrating the PPI network topology, GO semantic annotation information, and protein subcellular localization data. Under the given test yeast protein interaction network data, the connection relationship similarity value between two proteins with unknown connection relationship is calculated, and the specific implementation steps are as follows:

[0049] Step 1. Based on the existing protein interaction relationship data, first find the number of proteins m in it, and then construct an m*m matrix. If there is an interaction relationship between two corresponding proteins, the corresponding element in the matrix is ​​1, otherwise it is 0. In this way, the adjacency relationship matrix A between proteins is constructed.

[0050] Step 2. In order to characterize the functional similarity between two proteins, we use the semantic similarity of the annotated terms in Gene Ontology (GO) to measure the similarity between the functions of two connected proteins. Gene Ontology consists of three independent parts: biological process (BP), cellular component (CC), and molecular function (MF). Previous studies have shown that biological process information is more advantageous than the other two types of information in predicting key proteins. Therefore, only the semantic similarity under the biological process is considered. The functional similarity between two connected proteins u and v is calculated using the R toolbox GOsim based on the calculation method proposed by James Z Wang et al. (Wang JZ, Du Z, PayattakoolR, Yu PS, Chen CF: A new method to measure the semantic similarity of GOterms. Bioinformatics 2007, 23(10):1274-1281). , and the semantic similarity matrix S between any two proteins is calculated.

[0051] Step 3. Based on the protein subcellular localization information data, taking yeast data as an example, there are 11 types of subcellular localization information data for yeast proteins, namely nucleus (NS), cytosol (CL), cytoskeleton (CN), peroxisome (PE), lysosome (LE), endoplasmic reticulum (EC), Golgi apparatus (GI), plasma (PA), endosome (EE), extracellular protein (ER), and mitochondrion (MN). It is assumed that proteins in different subcellular locations will not interact with each other. Based on the existing protein interaction relationship data, the subcellular localization information data SL(u) corresponding to each protein u is found, and a matrix is ​​constructed to determine whether any two proteins have common subcellular localization information. The corresponding matrix elements between two proteins with common subcellular localization are 1, and otherwise 0. The adjacency matrix SL_adj of the subcellular localization information is defined as follows:

[0052]

[0053] Where SL(u) represents the subcellular localization information data of protein u.

[0054] Step 4. Based on the adjacency matrix A, gene ontology semantic similarity matrix S, and protein subcellular localization information matrix SL_adj calculated in the above steps, define the optimization function based on the non-negative matrix factorization framework as follows:

[0055] (1)

[0056] Where A represents the adjacency matrix, S represents the gene ontology semantic similarity matrix, represents the Frobenius norm, Indicates seeking trace, represents the weight parameter, are regularization parameters to prevent overfitting. .

[0057] First randomly initialize , , , use the following iterative format to solve the above function

[0058]

[0059]

[0060]

[0061] When the number of iterations is greater than 100, the iteration is terminated and the optimized W and H1 are obtained.

[0062] Step 5. Based on the optimized W and H1, calculate the connection similarity matrix S_prediction between proteins with unknown connection relationships as follows. It is believed that the larger the predicted value of the corresponding element in the similarity matrix, the greater the possibility of interaction between the two proteins.

[0063] (in , Represents the multiplication of corresponding elements of the matrix, i is the only matrix of all elements)

[0064] To evaluate the effectiveness of the proposed method, we used two metrics: the area under the curve (AUC) and the prediction accuracy. The AUC represents the probability that a randomly selected edge in the test dataset will have a higher score than a randomly selected edge that does not exist. The AUC calculation method is defined as follows:

[0065]

[0066] in It means randomly taking an edge from the test set, and then randomly selecting an edge from the non-existent edges, and repeating times, if there is The edge score value in the test set is greater than the edge score that does not exist. The two scores are equal.

[0067] The definition of accuracy ACC is as follows:

[0068]

[0069] Where k represents the number of correct edges predicted after sorting the predicted values ​​of the unknown connection relationship from large to small, and then selecting the first k edges as the predicted correct edges. Indicates the number of correctly predicted edges.

[0070] Comparison of the area under the curve (AUC) and accuracy (ACC) of the method of the present invention with other matrix decomposition methods for predicting protein interaction relationships:

[0071] Table 1. Mean and variance results of prediction accuracy (ACC) and area under the curve (AUC) of the new method under three test data

[0072] Dataset AUC mean AUC std ACC mean ACC std DIP Core 0.9637 0.0057 0.674 0.0402 Collins2007 0.9738 0.0042 0.958 0.0185 Krogan2006 0.8541 0.0076 0.8202 0.0388

[0073] Table 2. Mean and variance results of the prediction accuracy (ACC) and area under the curve (AUC) of the R-NMTF method in the literature under three test data

[0074] Dataset AUC mean AUC std ACC mean ACC std DIP Core 0.8921 0.0099 0.345 0.0672 Collins2007 0.9443 0.007 0.5802 0.0606 Krogan2006 0.8308 0.0071 0.3944 0.0737

[0075] From the comparison of Table 1 and Table 2 above, it can be seen that the results of the method of the present invention in calculating the two metrics AUC and ACC under the three test data are significantly better than the method R-NMTF in the literature.

[0076] The above description is merely a description of the embodiments of the present invention and does not limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solution of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for predicting protein interaction relationships based on a non-negative matrix factorization framework, the method comprising the following steps: (1) Obtain existing protein interaction relationship data, gene ontology semantic annotation information data, and protein subcellular localization data; (2) Construct an adjacency matrix A based on the existing protein interaction relationship data, construct a protein-protein gene function similarity matrix S based on the gene ontology semantic annotation information data, and construct a subcellular localization information adjacency matrix SL_adj between proteins based on the protein subcellular localization data; (3) Define an objective function based on the non-negative matrix factorization framework: （1） Where A represents the adjacency matrix, , and , S represents the gene function similarity matrix, represents the Frobenius norm, (A) means finding the trace of matrix A, represents the weight parameter, are regularization parameters to prevent overfitting, p is a parameter between 1 and 2, L=DC, C is the cosine similarity matrix of the adjacency matrix A, ; (4) Establish an augmented Lagrangian function and use an iterative optimization method to optimize the objective function value; (5) Obtain W and H1 after iterative optimization and calculate the connection similarity value between proteins with unknown connection relationships; (6) The similarity values ​​between proteins with unknown connectivity relationships are sorted from large to small, and the connectivity relationships corresponding to the top k largest similarity values ​​are the predicted protein interaction relationships.

2. The method according to claim 1, characterized in that The existing protein interaction relationship data, gene ontology semantic annotation information data and protein subcellular localization data in step (1) are obtained from public databases.

3. The method according to claim 1, characterized in that The step (2) specifically includes: (2.1) Obtain the adjacency matrix A of the relationships between proteins from the protein interaction relationship data; (2.2) Based on the Gene Ontology semantic annotation information data, find the pair of Gene Ontology term numbers (GO-id(u), GO-id(v)) corresponding to each pair of interacting proteins (u, v) under the biological process information; use the statistical software R toolbox Gosim to calculate the semantic similarity of the protein pair (u, v) under the biological process. , thereby obtaining the semantic similarity between all protein pairs, and constructing the gene ontology semantic similarity matrix S; (2.3) Based on the protein subcellular localization information data and the existing protein interaction relationship data, count each edge in the network Corresponding protein Subcellular localization information And calculate their intersection to determine whether the two interacting proteins are in the same subcellular localization, and obtain the adjacency matrix data SL_adj of the corresponding subcellular localization information: , where SL(u) represents the subcellular localization information data of protein u, and SL(v) represents the subcellular localization information data of protein v.

4. The method according to claim 1, wherein The steps of establishing the augmented Lagrangian function in step (4) are as follows: Introduction , and For constraints , and The Lagrange multiplier of , the augmented Lagrange function is as follows: , based on the above augmented Lagrangian function L, we can respectively , and By taking partial derivatives and applying KKT conditions, we can obtain the following iterative method to optimize the objective function in step (3): （2） （3） （4） When the number of iterations meets certain conditions, the iteration is terminated and the optimized W and H1 are obtained.

5. The method according to claim 1, characterized in that The steps for calculating the connection similarity values ​​between proteins with unknown connection relationships in step (5) are as follows: Based on the iteratively optimized W and H1 obtained in step (4), the connection similarity value S_prediction between proteins with unknown connection relationships is calculated according to the following formula: ， （5） in , Represents the multiplication of corresponding matrix elements, where i is the only matrix of all elements.

6. The method according to claim 1, characterized in that In the step (6), k is a positive integer between 100 and 200.

7. The method according to claim 4, characterized in that The certain condition refers to the number of iterations being greater than 100.

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