Methods for reconstructing weighted protein interaction networks and predicting protein complexes
By reconstructing the weight information of the weighted protein interaction network and using the weight perturbation model and latent factor model, the network structure was optimized, the prediction effect of protein complexes was improved, and the problem of network noise affecting prediction was solved.
Patent Information
- Application Number
- CN202311609447.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-29
- Publication Date
- 2025-10-03
- Estimated Expiration
- 2043-11-29
AI Technical Summary
Existing protein interaction networks contain a lot of noise, which affects the prediction effect of complexes, especially because false positive and false negative edges and binary relationships cannot distinguish the importance of incorrect edges from correct edges.
By checking the weight consistency index of the link weight matrix, a link weight prediction algorithm based on the weight perturbation model and the latent factor model is used to reconstruct the weighted protein interaction network, keeping the edge situation unchanged and optimizing the weight information in the network.
Data enhancement of protein interaction networks was achieved, which improved the prediction effect of protein complexes, especially when using the WMCODE and WIPCA algorithms, significantly improving the prediction accuracy and recall rate.
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Figure CN117976062B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of bioinformatics, and in particular to a method for reconstructing a weighted protein interaction network and its application. Background Art
[0002] In bioinformatics, a protein interaction network is first constructed based on experimental data of protein interactions. Then, community structures or dense subgraphs are mined based on this network to predict protein complexes. Existing protein complex prediction algorithms can be roughly divided into two categories: prediction algorithms for unweighted networks and prediction algorithms for weighted networks. Prediction algorithms for unweighted networks are relatively basic and are based only on the original protein interaction network, which can be regarded as a clustering problem. Prediction algorithms for weighted networks have been a hot topic of research in recent years. This is mainly due to the fact that the original protein interaction network has a certain proportion of false positives and false negatives. Therefore, researchers have begun to focus on integrating more structural and functional characteristics to improve the confidence of the network, including: protein amino acid sequence, protein function, network topology, etc.
[0003] Therefore, the quality of protein interaction networks directly affects the effectiveness of complex prediction. Furthermore, most existing complex prediction algorithms directly mine community structures from unprocessed interaction networks, which inevitably compromises prediction performance for two reasons. First, protein interaction data inherently contain some false-positive and false-negative edges. Second, the binary value of 0-1 (representing "unconnected" and "connected," respectively) cannot distinguish between incorrect and correct edges, nor can it distinguish the importance of different correct edges. Therefore, it is necessary to first optimize and reconstruct the protein interaction network before applying appropriate methods to complex prediction.
[0004] Therefore, the existing technology has the problem that the protein interaction network has large noise, which affects the prediction effect of the complex. Summary of the Invention
[0005] In order to overcome the above technical deficiencies, the first aspect of the present invention provides a method for reconstructing a weighted protein interaction network, comprising:
[0006] Step S1: Check the weight consistency index of the link weight matrix W of a given weighted protein interaction network, the weight consistency index σ w The calculation formula is:
[0007]
[0008] Among them, N ΔW represents the mean of all elements in the ΔW matrix, Represents the disturbance weight matrix ΔW and its corresponding prediction weight matrix The root mean square error between
[0009] Step S2: Keeping the edges of the original weighted protein interaction network unchanged, the entire original weighted protein interaction network is selected as the training set, and only the weight information in the edges of the original weighted protein interaction network is reconstructed by the link weight prediction algorithm based on the weight perturbation model and the latent factor model to obtain a new weighted protein interaction network.
[0010] The link weight prediction algorithm based on the weight perturbation model and the latent factor model is:
[0011]
[0012] Among them, α=τ·arctan(υ·σ w ), τ and υ are two hyperparameters used to control the weight consistency index;
[0013] Among them, the weight perturbation model is: λ1 is the matrix W r The jth eigenvalue of
[0014] ΔW is the weight matrix corresponding to the link perturbation set, x i is the eigenvector corresponding to this eigenvalue, Represents the matrix W r The transpose of the eigenvector corresponding to the j-th eigenvalue;
[0015] Among them, the latent factor model is:
[0016] The weight consistency metric primarily reflects the difference between the predicted weights in the perturbed network and the original weights of the network. A larger difference indicates poor consistency, and the weight perturbation model will have a relatively low weight in our overall model (i.e., the link weight prediction algorithm based on the weight perturbation model and the latent factor model). The opposite is true.
[0017] Furthermore, in step S2, the latent factor model infers the corresponding latent factors by fitting the known weight matrix and multiplies the latent factors to predict the missing weight information in the network. The loss function corresponding to the latent factor model is as follows:
[0018]
[0019] Among them, U and V are two latent factor matrices, W o is the adjacency matrix of a known weighted network, n and k represent the number of nodes and potential factors respectively, W ij Representative node v i and v jThe weight of the link between ir and v rj are two hyperparameters of the latent factor model, where u ir Representative node v i The correlation between the rth latent factor, v rj Represents the rth latent factor and node v j the correlation between It is a regularization term to suppress the optimization process of the algorithm from falling into the overfitting state and to reduce the time complexity of the algorithm. Among them, λ is the regularization parameter; the optimization process of the loss function is mainly achieved by the stochastic gradient descent method, that is, by calculating u ir and v rj The partial derivatives of the factors are used to search for the fastest descent direction.
[0020] A second aspect of the present application provides a system for reconstructing a weighted protein interaction network, comprising:
[0021] A checking module is used to check the weight consistency index of the link weight matrix W of a given weighted protein interaction network, wherein the weight consistency index σ w The calculation formula is:
[0022]
[0023] Among them, N ΔW represents the mean of all elements in the ΔW matrix, Represents the disturbance weight matrix ΔW and its corresponding prediction weight matrix The root mean square error between
[0024] The weight reconstruction module is used to keep the edges of the original weighted protein interaction network unchanged. The entire original weighted protein interaction network is selected as the training set. Only the link weight prediction algorithm based on the weight perturbation model and the latent factor model is used to reconstruct the weight information in the edges of the original weighted protein interaction network to obtain a new weighted protein interaction network.
[0025] The link weight prediction algorithm based on the weight perturbation model and the latent factor model is:
[0026]
[0027] Where α=τ•arctan(υ•σ w ), τ and υ are two hyperparameters used to control the weight consistency index;
[0028] Among them, the weight perturbation model is: λ i is the matrix Wr The jth eigenvalue of
[0029] ΔW is the weight matrix corresponding to the link perturbation set, x i is the eigenvector corresponding to this eigenvalue, Represents the matrix W r The transpose of the eigenvector corresponding to the j-th eigenvalue;
[0030] Among them, the latent factor model is:
[0031] The third aspect of the present application provides a method for predicting protein complexes, which predicts protein complexes based on the WMCODE algorithm or the WIPCA algorithm according to a new weighted protein interaction network obtained by the above-mentioned weighted protein interaction network reconstruction method.
[0032] Compared with the existing technology, the above technical solution has the following beneficial effects:
[0033] The present invention reconstructs the weight information in the links of the original weighted protein interaction network through a link weight prediction algorithm (WPLF) based on a weight perturbation model and a latent factor model, obtains a new weighted protein interaction network, realizes data enhancement of the protein interaction network, optimizes the protein interaction network, and thus improves the prediction effect of protein complexes. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 Four different types of disclosed Saccharomyces cerevisiae protein interaction networks are used to reconstruct the network using the weighted protein interaction network reconstruction method of the present invention in an embodiment of the present invention, namely, Collins weighted network (see Figure 1 a), Gavin weighted network (see Figure 1 b), Krogan weighted network (see Figure 1 c), WI-PHI weighted network (see Figure 1 d) in the
[0035] Figure 2 Flowchart for weighted protein interaction network reconstruction and schematic diagram for predicting protein complexes for this application;
[0036] Figure 3 Recall comparison value of the WMCODE algorithm on the original network and the reconstructed network;
[0037] Figure 4 is the Precision comparison value of the WMCODE algorithm on the original network and the reconstructed network;
[0038] Figure 5 It is the F1 comparison value of the WMCODE algorithm on the original network and the reconstructed network;
[0039] Figure 6 Recall comparison value of the WIPCA algorithm on the original network and the reconstructed network;
[0040] Figure 7 Precision comparison value of the WIPCA algorithm on the original network and the reconstructed network;
[0041] Figure 8 This is the F1 comparison value of the WIPCA algorithm on the original network and the reconstructed network. DETAILED DESCRIPTION
[0042] The advantages of the present invention are further described below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that the following specific description is illustrative rather than restrictive and should not be used to limit the scope of protection of the present invention.
[0043] Example 1 Optimization of weighted protein interaction network
[0044] This embodiment provides a system for reconstructing a weighted protein interaction network, including a checking module and a weight reconstruction module. The checking module is used to check the weight consistency index of the link weight matrix of a given weighted protein interaction network. The weight reconstruction module is used to keep the edges of the original weighted protein interaction network unchanged, select the entire original weighted protein interaction network as a training set, and reconstruct the weight information in the edges of the original weighted protein interaction network using only a link weight prediction algorithm based on a weight perturbation model and a latent factor model to obtain a new weighted protein interaction network.
[0045] For example, this example is based on four different types of published Saccharomyces cerevisiae protein interaction networks, namely: Collins weighted network (see Figure 1 a), Gavin weighted network (see Figure 1 b), Krogan weighted network (see Figure 1 c) and WI-PHI weighted network (see Figure 1 d), the method for network reconstruction using the above-mentioned weighted protein interaction network reconstruction system includes steps S1 and S2:
[0046] Step S1: Check the weight consistency index of the link weight matrix W of a given weighted protein interaction network.
[0047] Before predicting link weights in a weighted network, the algorithm proposed in this invention first checks the network's weight consistency index. If the network's link weights exhibit certain regularity and consistency, then the weight information lost in the network can be well restored.
[0048] The weight consistency index σ w The calculation formula is:
[0049]
[0050] Among them, N ΔW represents the mean of all elements in the ΔW matrix, Represents the disturbance weight matrix ΔW and its corresponding prediction weight matrix The root mean square error between
[0051] Step S2: Keeping the edge connections of the original weighted protein interaction network unchanged, the entire original weighted protein interaction network is selected as the training set, and only the weight information in the edges of the original weighted protein interaction network is reconstructed through the link weight prediction algorithm based on the weight perturbation model and the latent factor model to obtain a new weighted protein interaction network.
[0052] A link weight prediction algorithm is constructed by linearly fusion weight perturbation model and latent factor model, thereby realizing the recovery of weight information in the network.
[0053] 1) Weight perturbation model
[0054] The weight perturbation model proposed in this paper takes the existing link weight information in the network as known information and randomly selects a portion of the links to perturb the weight matrix. Assuming that after the perturbation, if the corresponding eigenvectors of the network remain basically consistent, then the perturbed weight matrix can be used as the final predicted weight matrix. The formal definition of the algorithm is as follows:
[0055] Given a weighted network G(N, E, W), where N, E, and W represent the set of nodes, the set of links, and the set of link weights in the network, respectively. Randomly select a part of the links to form the perturbation set ΔE, and define the set of the remaining links as E γ =E-ΔE. At the same time, the weight matrices corresponding to these two sets are W r and ΔW, then the weight matrix of the network is W=W r +ΔW. Due to W r is a real symmetric matrix that can be diagonalized, that is:
[0056]
[0057] Among them, λ i is the matrix W rThe i-th eigenvalue, x i is the eigenvector corresponding to this eigenvalue, Represents the matrix W r The transpose of the eigenvector corresponding to the i-th eigenvalue of .
[0058] In addition, this algorithm defines the matrix ΔW as the perturbation matrix. The perturbation process leads to the weight matrix W r The eigenvalue λ i Produced Δλ i The corresponding eigenvector x i Produced Δx i That is:
[0059] (W r +ΔW)(x i +Δx i )=(λ i +Δλ i )(x i +Δx i ) (2)
[0060] Then use the factor Multiply both sides of the above formula and ignore the second-order terms in the calculation process and The eigenvalue increment can be obtained:
[0061]
[0062] If for any i, assuming Δx i The values of are small and can be omitted. Then the perturbation weight matrix can be expressed as:
[0063]
[0064] In this case, the prediction weight matrix can be considered It is a linear approximation of the known weight matrix W.
[0065] In addition, before using the weight perturbation algorithm to predict the link weight, the weight predictability of each network is first checked. At the same time, the present invention proposes a weight consistency index σ w ,Right now:
[0066]
[0067] Among them, N ΔW represents the mean of all elements in the ΔW matrix, Represents the disturbance weight matrix ΔW and its corresponding prediction weight matrix The root mean square error between .
[0068] 2) Latent Factor Model
[0069] The latent factor model proposed in this paper mainly extracts the latent features of network weights by low-rank decomposition.
[0070] Among them, the solution process of the latent factor model is basically an optimization process, and the corresponding loss function is as follows:
[0071]
[0072] Among them, U and V are two latent factor matrices, W o is the adjacency matrix of a known weighted network, n and k represent the number of nodes and potential factors respectively, W ij Representative node v i and v j The weight of the link between ir and v rj are two hyperparameters of the latent factor model, where u ir Representative node v i The correlation between the rth latent factor, v rj Represents the rth latent factor and node v j In addition, It is a regularization term that prevents the optimization process of the algorithm from falling into an overfitting state and can reduce the time complexity of the algorithm. Where λ is the regularization parameter.
[0073] In this model, the optimization process of the above loss function is mainly achieved through the stochastic gradient descent method, that is, by calculating u ir and v rj The partial derivative of the factor is used to search for the fastest descent direction. In order to avoid the phenomenon of infinite iterations due to the failure of convergence of the objective function, this algorithm pre-sets the iteration threshold to N c Finally, the final prediction weight matrix is obtained by multiplying the two latent factor matrices, namely:
[0074]
[0075] 3) Algorithm Framework
[0076] First, input a link weight matrix W of a weighted network G, and q H and p H Represent the proportion of training set and perturbation set respectively, Q is composed of W r The matrix composed of the eigenvectors of r The final predicted link weight matrix can be obtained by the following formula:
[0077]
[0078] Among them, α=τ·arctan(υ·σ w ), and τ and υ are two hyperparameters used to control the weight consistency index. The hyperparameters τ and υ are mainly optimized through the grid search method.
[0079] The weighted protein interaction network is optimized and reconstructed by the WPLF algorithm described above, and is ultimately used as a reconstructed network endowed with new weight information.
[0080] Example 2 Prediction of protein complexes
[0081] like Figure 2 As shown, this embodiment considers acyclic networks within the entire protein interaction network. For four different types of Saccharomyces cerevisiae protein interaction networks (i.e., the Collins, Gavin, Krogan, and WI-PHI weighted networks), the original protein interaction networks and the reconstructed new protein interaction networks were used to predict protein complexes based on classic protein complex prediction algorithms (e.g., the WMCODE algorithm and the WIPCA algorithm, both of which are publicly available. WMCODE: Weighted Molecular Complex Detection is a weighted molecular complex prediction algorithm, and WIPCA: Weighted Improvement Development Clustering Algorithm is a weighted improved and extended clustering algorithm). A comparative analysis was performed. Two publicly available standard complex datasets, CYC2008 and MIPS (see Table 1), were used for validation, and accuracy, recall, and F1 value were selected as evaluation metrics to ultimately assess the prediction performance before and after the reconstruction of the network weight information.
[0082] Table 1 CYC2008 and MIPS standard complex data sets
[0083]
[0084] (1) Analysis of experimental results
[0085] Figure 3 、 Figure 4 and Figure 5 This is the comparative analysis result of the WMCODE algorithm on the original network and the network after the weight information is reconstructed based on the WPLF algorithm. The two standard data sets CYC2008 and MIPS are used for verification. Figure 3 、 Figure 4 and Figure 5It can be seen that based on the three evaluation indicators of Recall, Precision and F1, the prediction results of the WMCODE algorithm on the optimized network are significantly better than those on the original network.
[0086] Figure 6 、 Figure 7 and Figure 8 This is the comparative analysis result of the WIPCA algorithm on the original network and the network after the weight information is reconstructed based on the WPLF algorithm. The two standard data sets CYC2008 and MIPS are also used for verification. Figure 7 and Figure 8 It can be seen that based on the two evaluation indicators of Precision and F1, the prediction results of the WIPCA algorithm on the optimized network are significantly better than those on the original network. Based on the Recall evaluation indicator, the prediction results of the WIPCA algorithm on the original network are better than those on the reconstructed network.
[0087] (2) Experimental conclusions
[0088] The experiments in this section validated that, when considering the F1 metric, which more comprehensively reflects the accuracy of prediction algorithms, the WPLF algorithm, after reconstructing the weight information of four weighted protein interaction networks, significantly improved the prediction performance of two classic weighted complex prediction algorithms, WMCODE and WIPCA. This conclusion strongly validates the effectiveness of the WPLF algorithm in improving complex prediction.
[0089] It should be noted that the embodiments of the present invention have better practicability and do not impose any form of limitation on the present invention. Any technician familiar with the field may use the technical content disclosed above to change or modify it into an equivalent effective embodiment. However, any modification or equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.
Claims
1. A method for predicting a protein complex, characterized in that: Predict protein complexes based on the new weighted protein interaction network obtained by the weighted protein interaction network reconstruction method using the WMCODE algorithm or the WIPCA algorithm; The weighted protein interaction network reconstruction method comprises: Step S1: Check the link weight matrix of a given weighted protein interaction network The weight consistency index, the weight consistency index The calculation formula is: ； in, represent The mean of all elements in the matrix, Represents the perturbation weight matrix And its corresponding prediction weight matrix The root mean square error between Step S2: Keeping the edges of the original weighted protein interaction network unchanged, the entire original weighted protein interaction network is selected as the training set, and only the weight information in the edges of the original weighted protein interaction network is reconstructed by the link weight prediction algorithm based on the weight perturbation model and the latent factor model to obtain a new weighted protein interaction network. The link weight prediction algorithm based on the weight perturbation model and the latent factor model is: ； in, , and are two hyperparameters used to control the weight consistency index; Among them, the weight perturbation model is: , is a matrix No. eigenvalues, , , is the weight matrix corresponding to the link perturbation set, is the eigenvector corresponding to this eigenvalue, Representative Matrix No. The transpose of the eigenvector corresponding to the eigenvalue; Among them, the latent factor model is: ; In step S2, the latent factor model infers the corresponding latent factors by fitting the known weight matrix and multiplying the latent factors to predict the missing weight information in the network. The loss function corresponding to the latent factor model is as follows: ； in, and are two latent factor matrices, is the adjacency matrix of a known weighted network, and Represent the number of nodes and latent factors respectively, Representative Node and The weight of the link between and are two hyperparameters of the latent factor model, where Representative Node Hedi The correlation between the potential factors Representative latent factors and nodes the correlation between It is a regular term to suppress the optimization process of the algorithm from falling into the overfitting state and to reduce the time complexity of the algorithm. is the regularization parameter; the optimization process of the loss function is mainly achieved through the stochastic gradient descent method, that is, by calculating and The partial derivatives of the factors are used to search for the fastest descent direction.