A pairwise protein interaction network alignment method based on a divide-and-conquer integration strategy

Abstract

The present invention discloses a paired protein interaction network comparison method based on a divide-and-conquer integration strategy, comprising: step 1: reading a source network, a target network and a BLAST similarity file; step 2: using a method based on a combination of nodes and paths to respectively calculate the similarity scores of nodes in the two networks, and dividing the two networks into modules based on the similarity scores; step 3: obtaining homologous protein pairs, respectively calculating the similarity between modules from different networks based on the homologous protein pairs and BLAST similarity; and matching the modules from different networks one-to-one based on the similarity. The beneficial effects of the present invention: using node-based and path-based similarity calculation methods instead of self-similarity files, the problem of dependence on self-similarity files is solved.

Description

Technical Field

[0001] The present invention relates to the field of protein interaction network comparison, and in particular to a method for comparing paired protein interaction networks based on a divide-and-conquer integration strategy. Background Art

[0002] With the development of bioinformatics, people's research is focused on biological macromolecules such as proteins and DNA. Protein molecules perform various important tasks in organisms, and protein interactions are the basis for maintaining cell structure and function. Therefore, the study of protein interaction networks is of great significance. One of the important research tasks is to compare and analyze protein interaction networks. Through network comparison, protein function prediction and conserved functional module mining can be carried out.

[0003] Traditional technologies have the following technical problems:

[0004] The "SPINAL: scalable protein interaction network aligment" (Journal Source: Bioinformatics. 2013, 4 (29): 917–924) algorithm uses a two-pass alignment algorithm consisting of coarse-grained and fine-grained steps. The coarse-grained stage iteratively improves the matrix P of the estimated matching confidence of each pair of nodes by considering the confidence of matching with adjacent nodes calculated in the previous iteration. After P converges, the fine-grained stage begins, which uses a seed-and-expand algorithm to construct the alignment. In addition, in each iteration of the seed-and-expand process, a local search is performed to directly increase the number of conserved edges. The problem with this algorithm is that it takes into account too much topological information, resulting in low quality of biological functions in the final alignment.

[0005] The algorithm "ModuleAlign: module-based global alignment of protein-protein interaction networks" (Journal Source: Bioinformatics, 2016, 32(17): 658-664) proposed a homology score function, which relies on module similarity to calculate the homology score of the node, and uses the dynamic Hungarian algorithm to solve it. Problems with this algorithm: Improper selection of modularization method This algorithm uses a cumbersome and improper calculation method through module similarity calculation, resulting in an erroneous biological similarity score, which makes its biological function quality poor.

[0006] The algorithm "AligNet: alignment of protein-protein interaction networks" (Journal source: BMC Bioinformatics, 2020, 21 (Suppl 6): 1-22) adopts a modular approach. First, the network is divided into several modules, the modules are enumerated and aligned, and finally all the alignment results are merged into the final alignment. The problem with this algorithm is that all modules need to be enumerated and aligned, which greatly increases the time complexity.

[0007] The algorithm "HubAlign: an accurate and efficient method for global alignment of protein-protein interaction networks" (Journal source: Bioinformatics, 2014, 30(17): 438-444) believes that proteins that act as hubs in PPI networks are more important in terms of function and topology, proposes Importance centrality, and uses a greedy seed-extension algorithm to sort proteins based on a combination of their Importance scores and sequence similarity. The problem with this algorithm is that the algorithm randomly selects nodes as the starting point for edge splitting, and different starting points may result in alignment results of different quality.

[0008] The algorithm "MAGNA++: Maximizing accuracy in global network alignment via both node and edge conservation" (Journal source: Bioinformatics, 2015, 31(14): 2409-2411) uses the idea of ​​genetic algorithm to perform network alignment, and generates new solutions through continuous iteration and crossover mutation. This effectively solves the problem of the algorithm falling into the local optimal solution. The problem with this algorithm is that it requires thousands of iterations and takes a long time.

[0009] "INDEX: Incremental depth extension approach for protein-protein interaction networks alignment" Journal source: BioSystems, 2017, 162 (2017): 24-34) The algorithm proposes a new alignment strategy that takes into account the growth of the alignment score and the alignment kernel, so that the obtained common connected subgraph has a larger number of edges than previous methods. The problem with this algorithm is that the biological quality of the alignment is poor and a good balance between biological and topological quality is not achieved. Summary of the invention

[0010] The technical problem to be solved by the present invention is to provide a paired protein interaction network comparison method based on a divide-and-conquer integration strategy, which solves the problem of dependence on similarity files between nodes in the same network; uses the matching relationship of existing protein pairs to predict the matching relationship of modules, thereby calculating module similarity, solving the problem of module similarity calculation; uses degree centrality and eigenvector centrality to capture the topological characteristics of nodes, thereby improving the biological quality and topological quality of the algorithm.

[0011] In order to solve the above technical problems, the present invention provides a method for comparing paired protein interaction networks based on a divide-and-conquer integration strategy, comprising:

[0012] Step 1: Read the source network, target network and BLAST similarity file;

[0013] Step 2: Calculate the similarity scores of the nodes in the two networks by combining the node-based and path-based methods, and divide the two networks into modules based on the similarity scores;

[0014] Step 3: Obtain homologous protein pairs, calculate the similarity between modules from different networks based on the homologous protein pairs and BLAST similarity, and perform one-to-one matching of modules from different networks based on the similarity;

[0015] Step 4: Calculate the similarity between nodes in each pair of matched modules based on feature vector centrality and BLAST similarity, perform intra-module alignment, and merge the obtained sub-alignment results into a candidate result set;

[0016] Step 5: Use the hypergraph matching algorithm on the candidate result set to obtain the final one-to-one comparison result.

[0017] In one embodiment, in step 2, the similarity score is calculated as follows:

[0018] The degree and shortest path length are used to measure the similarity between two nodes. The node similarity is calculated as shown in formula (1):

[0019]

[0020] Where G is the network, u and v are nodes in G, and deg u Refers to the degree of node u, deg G refers to the maximum degree in the graph G, D(G) refers to the diameter of the graph G, d G (u,v) refers to the shortest path length between nodes u and v.

[0021] In one embodiment, in step 2, the module division steps are as follows:

[0022] (1) Use formula (1) to calculate the similarity of the source network G and obtain the similarity matrix S;

[0023] (2) For each row in the matrix S, the nodes with similarity in the top 75% are formed into a module according to the numerical value, and the center of the module is the row name of the matrix.

[0024] In one embodiment, step 3 is as follows:

[0025] Generate homologous protein pairs, and calculate the homology similarity of the module based on the collective behavior of the protein pairs in the module. Use formula (2) to convert the homologous protein pair file into a homology matrix π, where i and j are proteins from the two networks respectively;

[0026]

[0027] Then the homology similarity scores of modules m1 and m2 obtained according to the matrix π are:

[0028]

[0029] Formula (3) is subject to formula (4):

[0030]

[0031] The module similarity calculation formula is:

[0032] S(m1,m2)=HS(m1,m2)+BLAST(c1,c2) ​​(5)

[0033] Where c1 and c2 are the cluster centers of modules m1 and m2 respectively; BLAST is sequence similarity;

[0034] According to formula (5), we get the module similarity matrix S. By solving S using the Hungarian algorithm, we can get a one-to-one module matching relationship.

[0035] In one embodiment, step 4 is specifically as follows: for each pair of matched modules obtained in the module comparison phase, firstly calculate the similarity matrix of the nodes in the modules, and then compare the nodes in the two modules; the more specific process is as follows:

[0036] The similarity between two nodes in different modules is calculated based on the feature vector centrality and sequence similarity, see formula (6)

[0037]

[0038] Where T(u,v) represents the eigenvector centrality similarity score of nodes u and v, and its calculation method is shown in formula (7):

[0039]

[0040] where c u Refers to the eigenvector centrality of node u;

[0041] The sub-alignments generated by all pairing modules are merged into a candidate set. At this time, a node in the candidate set may form an alignment relationship with multiple nodes from another network, so the candidate set is a many-to-many matching set.

[0042] In one embodiment, the steps of performing intra-module comparison according to formula (6) are as follows: (1) first compare the module centers c1 and c2 of modules m1 and m2; (2) obtain the neighbors of c1 and c2, Deg(c1) and Deg(c2) respectively; (3) extract the submatrix with row names and column names in Deg(c1) and Deg(c2) from F, and use the Hungarian algorithm to compare the nodes Deg(c1) and Deg(c2); (4) remove the expanded node (c1, c2), and repeat steps (2) and (3) for the remaining compared node pairs.

[0043] In one of the embodiments, step 5 is specifically as follows: abstracting the candidate set into a hypergraph, wherein the nodes in the source network are the source nodes of the hypergraph, the nodes in the target network are the target nodes of the hypergraph, and each sub-matching corresponds to a hyperarc of the hypergraph; using a weighted bipartite hypergraph matching algorithm, the hypergraph is extracted into a bipartite graph containing only one-to-one matching relationships, thereby obtaining the final node matching relationship.

[0044] Based on the same inventive concept, the present application also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any one of the methods when executing the program.

[0045] Based on the same inventive concept, the present application also provides a computer-readable storage medium on which a computer program is stored, and when the program is executed by a processor, the steps of any one of the methods are implemented.

[0046] Based on the same inventive concept, the present application also provides a processor, which is used to run a program, wherein the program executes any one of the methods described when it is run.

[0047] Beneficial effects of the present invention:

[0048] Node-based and path-based similarity calculation methods are used instead of self-similarity files to solve the problem of dependence on self-similarity files; homologous protein pairs are obtained from PrimAlign, and the matching relationship of existing protein pairs is used to predict the matching relationship of modules, thereby calculating module similarity and solving the problem of module similarity calculation; the eigenvector centrality is further optimized, and the centrality of the node itself and the centrality difference between two nodes are captured at the same time, so as to better capture the topological characteristics of the node and improve the quality of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 Flowchart of a pairwise protein interaction network alignment method based on a divide-and-conquer integration strategy.

[0050] Figure 2 This is a schematic diagram of the EC, ICS, S3, and FC scores of different algorithms on the ISOBASE dataset.

[0051] Figure 3 Schematic diagram of EC, ICS, S3 and FC scores of different algorithms on synthetic datasets (DMC, DMR).

[0052] Figure 4 It is a schematic diagram of EC, ICS, S3 and FC scores when the present invention uses the existing algorithm to obtain homologous pairs and its original algorithm.

[0053] Figure 5 It is a schematic diagram of the time required for the present invention to obtain homologous pairs for comparison using different existing algorithms. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0055] See also Figures 1 to 5 , a pairwise protein interaction network alignment method based on a divide-and-conquer integration strategy, including:

[0056] Step 1: Read the source network, target network and BLAST similarity files.

[0057] Step 2: Calculate the similarity scores of the nodes in the two networks using a method based on combining nodes and paths, and divide the two networks into modules based on the similarity scores.

[0058] In order to more fully explore the similarity information of nodes in the same network, a combination of node-based and path-based methods is used to calculate the similarity between nodes, that is, the degree and the shortest path length are used to measure the similarity between two nodes. The node similarity calculation is shown in formula (1).

[0059]

[0060] Where G is the network, u and v are nodes in G, and deg u Refers to the degree of node u, deg G refers to the maximum degree in the graph G, D(G) refers to the diameter of the graph G, d G (u,v) refers to the shortest path length between nodes u and v.

[0061] The steps for module division are as follows:

[0062] (1) Use formula (1) to calculate the similarity of the source network G and obtain the similarity matrix S;

[0063] (2) For each row in the matrix S, the nodes with similarity in the top 75% are formed into a module according to the numerical value, and the center of the module is the row name of the matrix.

[0064] Step 3: Obtain homologous protein pairs, calculate the similarity between modules from different networks based on the homologous protein pairs and BLAST similarity, and perform one-to-one matching of modules from different networks based on the similarity.

[0065] Homologous protein pairs were generated using PrimAlign, and the homology similarity of the module was calculated based on the collective behavior of the protein pairs in the module. The homologous protein pair files were converted into a homology matrix π using formula (2), where i and j are proteins from the two networks, respectively.

[0066]

[0067] Then the homology similarity scores of modules m1 and m2 obtained according to the matrix π are:

[0068]

[0069] Formula (3) is subject to formula (4):

[0070]

[0071] The module similarity calculation formula is:

[0072] S(m1,m2)=HS(m1,m2)+BLAST(c1,c2) ​​(5)

[0073] Where c1 and c2 are the cluster centers of modules m1 and m2 respectively. BLAST is sequence similarity.

[0074] According to formula (5), we get the module similarity matrix S. By solving S using the Hungarian algorithm, we can get a one-to-one module matching relationship.

[0075] Step 4: Calculate the similarity between nodes in each pair of matched modules based on feature vector centrality and BLAST similarity, perform intra-module alignment, and merge the obtained sub-alignment results into a candidate result set;

[0076] For each pair of matched modules obtained in the module comparison phase, the similarity matrix of the nodes in the modules is first calculated, and then the nodes in the two modules are compared. The specific process is as follows:

[0077] The similarity between two nodes in different modules is calculated based on the feature vector centrality and sequence similarity, see formula (6)

[0078]

[0079] Where T(u,v) represents the eigenvector centrality similarity score of nodes u and v, and its calculation method is shown in formula (7):

[0080]

[0081] where c u Refers to the eigenvector centrality of node u. Formula (6) not only considers the difference in the eigenvector centrality of nodes u and v, but also considers the centrality value of the node itself. This design helps to first align proteins with a strong central position and similar centrality in the module.

[0082] According to formula (6), the steps for intra-module comparison are as follows:

[0083] (1) First, align the module centers c1 and c2 of modules m1 and m2;

[0084] (2) Get the neighbors of c1 and c2, Deg(c1) and Deg(c2) respectively;

[0085] (3) Extract the submatrices with row and column names in Deg(c1) and Deg(c2) from F, and use the Hungarian algorithm to compare the nodes of Deg(c1) and Deg(c2);

[0086] (4) Remove the expanded node (c1, c2) and repeat steps (2) and (3) for the remaining matched node pairs.

[0087] The sub-alignments generated by all pairing modules are merged into a candidate set. At this time, a node in the candidate set may form an alignment relationship with multiple nodes from another network, so the candidate set is a many-to-many matching set.

[0088] Step 5: Use the hypergraph matching algorithm on the candidate result set to obtain the final one-to-one comparison result.

[0089] The candidate set is abstracted into a hypergraph, where the nodes in the source network are the source nodes of the hypergraph, the nodes in the target network are the target nodes of the hypergraph, and each sub-matching corresponds to a hyperarc of the hypergraph. The weighted bipartite hypergraph matching algorithm is used to extract the hypergraph into a bipartite graph containing only one-to-one matching relationships, that is, to obtain the final node matching relationship.

[0090] A specific application scenario of the present invention is given below:

[0091] Take the SCE and HSA networks in the ISOBASE database as examples:

[0092] 1. Read SCE network, HSA network and BLAST similarity files;

[0093] 2. Calculate the similarity values ​​of nodes in the SCE and HSA networks respectively according to formula (1);

[0094] 3. Divide the SCE and HSA networks into modules respectively;

[0095] 4. Use PrimAlign to obtain homologous protein pairs

[0096] 5. Calculate the similarity between different network modules according to formula (5);

[0097] 6. One-to-one matching of modules from different networks based on similarity;

[0098] 7. Calculate the similarity between nodes in each pair of matched modules according to formula (6) and perform intra-module comparison;

[0099] 8. Combine the sub-alignment results obtained in step 7 into a candidate result set;

[0100] 9. Use the hypergraph matching algorithm on the candidate result set to obtain the final one-to-one comparison result.

[0101] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A method for pairwise protein interaction network comparison based on a divide-and-conquer integration strategy, characterized in that: include: Step 1: Read the source network, target network and BLAST similarity file; Step 2: Calculate the similarity scores of the nodes in the two networks by combining the node-based and path-based methods, and divide the two networks into modules based on the similarity scores; Step 3: Obtain homologous protein pairs, calculate the similarity between modules from different networks based on the homologous protein pairs and BLAST similarity, and perform one-to-one matching of modules from different networks based on the similarity; Step 4: Calculate the similarity between nodes in each pair of matched modules based on feature vector centrality and BLAST similarity, perform intra-module alignment, and merge the obtained sub-alignment results into a candidate result set; Step 5: Use the hypergraph matching algorithm to obtain the final one-to-one comparison result for the candidate result set; In step 2, the similarity score is calculated as follows: The degree and shortest path length are used to measure the similarity between two nodes. The node similarity is calculated as shown in formula (1): Where G is the network, u and v are nodes in G, and deg u Refers to the degree of node u, deg G refers to the maximum degree in the graph G, D(G) refers to the diameter of the graph G, d G (u,v) refers to the shortest path length between nodes u and v; The steps for module division are as follows: (1) Use formula (1) to calculate the similarity of the source network G and obtain the similarity matrix S; (2) For each row in the matrix S, the nodes with similarity in the top 75% are formed into a module according to the numerical value, and the center of the module is the row name of the matrix in that row; Step 3 is as follows: Generate homologous protein pairs, and calculate the homology similarity of the module based on the collective behavior of the protein pairs in the module. Use formula (2) to convert the homologous protein pair file into a homology matrix π, where i and j are proteins from the two networks respectively; Then the homology similarity scores of modules m1 and m2 obtained according to the matrix π are: Formula (3) is subject to formula (4): The module similarity calculation formula is: S(m1,m2)=HS(m1,m2)+BLAST(c1,c2) 5) Where c1 and c2 are the cluster centers of modules m1 and m2 respectively; BLAST is sequence similarity; According to formula (5), the module similarity matrix S is obtained. The Hungarian algorithm is used to solve S, and a one-to-one module matching relationship can be obtained. Step 4 is as follows: for each pair of matched modules obtained in the module comparison phase, first calculate the similarity matrix of the nodes in the modules, and then compare the nodes in the two modules; the more specific process is as follows: The similarity between two nodes in different modules is calculated based on the feature vector centrality and sequence similarity, see formula (6) Where T(u,v) represents the eigenvector centrality similarity score of nodes u and v, and its calculation method is shown in formula (7): where c u Refers to the eigenvector centrality of node u; The sub-alignments generated by all pairing modules are merged into a candidate set. At this time, a node in the candidate set may form an alignment relationship with multiple nodes from another network, so the candidate set is a many-to-many matching set.

2. The method for comparing paired protein interaction networks based on a divide-and-conquer integration strategy according to claim 1, characterized in that: The steps for intra-module comparison according to formula (6) are as follows: (1) First, compare the module centers c1 and c2 of modules m1 and m2; (2) Obtain the neighbors of c1 and c2, Deg(c1) and Deg(c2) respectively; (3) Extract the submatrix with row names and column names in Deg(c1) and Deg(c2) from F, and use the Hungarian algorithm to compare the nodes of Deg(c1) and Deg(c2); (4) Remove the expanded node (c1, c2), and repeat steps (2) and (3) for the remaining compared node pairs.

3. The method for pairwise protein interaction network comparison based on the divide-and-conquer integration strategy according to claim 1, characterized in that: Step 5 is as follows: abstract the candidate set into a hypergraph, where the nodes in the source network are the source nodes of the hypergraph, the nodes in the target network are the target nodes of the hypergraph, and each sub-matching corresponds to a hyperarc of the hypergraph; use the weighted bipartite hypergraph matching algorithm to extract the hypergraph into a bipartite graph containing only one-to-one matching relationships, and obtain the final node matching relationship.

4. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the method according to any one of claims 1 to 3 are implemented.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 3 are implemented.

6. A processor, characterized in that: The processor is used to run a program, wherein the program executes the method according to any one of claims 1 to 3 when running.

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