Improving protein-protein interactions prediction accuracy using protein evolutionary information and relevance vector machine model.

Predicting protein-protein interactions (PPIs) is a challenging task and essential to construct the protein interaction networks, which is important for facilitating our understanding of the mechanisms of biological systems. Although a number of high-throughput technologies have been proposed to predict PPIs, there are unavoidable shortcomings, including high cost, time intensity, and inherently high false positive rates. For these reasons, many computational methods have been proposed for predicting PPIs. However, the problem is still far from being solved. In this article, we propose a novel computational method called RVM-BiGP that combines the relevance vector machine (RVM) model and Bi-gram Probabilities (BiGP) for PPIs detection from protein sequences. The major improvement includes (1) Protein sequences are represented using the Bi-gram probabilities (BiGP) feature representation on a Position Specific Scoring Matrix (PSSM), in which the protein evolutionary information is contained; (2) For reducing the influence of noise, the Principal Component Analysis (PCA) method is used to reduce the dimension of BiGP vector; (3) The powerful and robust Relevance Vector Machine (RVM) algorithm is used for classification. Five-fold cross-validation experiments executed on yeast and Helicobacter pylori datasets, which achieved very high accuracies of 94.57 and 90.57%, respectively. Experimental results are significantly better than previous methods. To further evaluate the proposed method, we compare it with the state-of-the-art support vector machine (SVM) classifier on the yeast dataset. The experimental results demonstrate that our RVM-BiGP method is significantly better than the SVM-based method. In addition, we achieved 97.15% accuracy on imbalance yeast dataset, which is higher than that of balance yeast dataset. The promising experimental results show the efficiency and robust of the proposed method, which can be an automatic decision support tool for future proteomics research. For facilitating extensive studies for future proteomics research, we developed a freely available web server called RVM-BiGP-PPIs in Hypertext Preprocessor (PHP) for predicting PPIs. The web server including source code and the datasets are available at http://219.219.62.123:8888/BiGP/.

Introduction

In an organism, proteins are fundamental molecules, which participate in many cellular functions. Especially, proteins seldom perform their roles alone, so it is much important for PPIs detection. Thus, PPIs detection is an essential step for basic research and practical application, which can provide insight into molecular functions biological processes, and bring about a deep understanding of disease mechanisms, and suggest novel methods for practical medical applications. Until now, many high‐throughput approaches, such as yeast two‐hybrid (Y2H) screening methods,1, 2 immunoprecipitation,3 and protein chips,4 have been used to detect PPIs. However, these experimental methods have some disadvantages, such as time‐intensiveness and high cost. Besides, the aforementioned methods suffer from high rates of false positives and false negatives. For the sake of these reasons, it is difficult for predicting unknown PPIs only using biological experimental approaches. Therefore, developing computational methods for PPIs becomes more and more important.

Up to now, variously computational methods5, 6 for PPIs detection have been proposed from different sources of information, including tertiary structures, phylogenetic profiles, protein domains, and secondary structures. However, if it is not available for prior‐knowledge about a protein of interest, these methods cannot be used. With the rapid growth of protein sequence data, protein sequence‐based method7, 8 is becoming the most widely used tool for predicting PPIs. Consequently, large quantities of protein sequence‐based methods for predicting PPIs have been exploited.9, 10, 11, 12, 13, 14 Such as, Sylvain et al.15 proposed a novel protein–protein interaction prediction engine called PIPE, which can detect PPIs for any target pair of the yeast Saccharomyces cerevisiae proteins. Xia et al.16 proposed a sequence‐based method that selected rotation forest as classifier and employed autocorrelation descriptor as feature extraction method for predicting PPIs. Hamed et al.17 proposed a novel approach to predict interaction of two proteins solely by analyzing their coding sequences. Ming et al.12 proposed a sequence‐based method that using support vector machine (SVM) combined with correlation coefficient (CC) transformation. In spite of this, there has still space to improve the accuracy and efficiency of the existing methods.

In this article, we proposed a novel computational method that can be used to predict PPIs only using protein sequence data. Improving the accuracy of PPIs detection is the main purpose in the study. The major novelty of our proposed method includes (1) protein sequences are represented using the Bi‐gram probabilities (BiGP) feature representation on a position specific scoring matrix (PSSM), (2) For reducing the influence of noise, principal component analysis (PCA) method is used to reduce the dimension of BiGP vector, (3) using the relevance vector machine (RVM) based classifier. First, each protein sequence is represented using a PSSM. Second, the Bi‐gram probabilities (BiGP) descriptor is used to capture useful information from each protein sequence PSSM and generate a 400‐dimensional feature vector. Third, The PCA method is employed to reduce the dimensions of the BiGP vector. Finally, the RVM model is employed as the machine learning approach to perform classification. The proposed method was carried out by using two different PPIs datasets (yeast and Helicobacter pylori). The experimental results are found to be superior to SVM and other previous methods. In addition, to further evaluate the feasibility and efficiency of the proposed method, imbalance yeast dataset consists of 5594 positive protein pairs and 16,782 negative protein pairs used to execute using the proposed method. Thus, we compared the prediction accuracy between balance yeast and imbalance yeast, the prediction accuracy of imbalance yeast is higher that of balance yeast. Experimental results demonstrate that the proposed method is suitable for predicting PPIs. It proved that the proposed method performs incredibly well for PPIs detection.

Materials and Methodology

Dataset

In this article, yeast and Helicobacter pylori protein sequence dataset have been used. The two datasets can be obtained from the publicly available database of interaction proteins (DIP).18 The yeast contains 5594 positive protein pairs and 5594 negative protein pairs. Similarly, the Helicobacter pylori consist of 1458 positive protein pairs and 1458 negative protein pairs. The description of Yeast and Helicobacter pylori protein sequence dataset were shown in Table 1.

Table 1

Description of Yeast and Helicobacter pylori Protein Sequence Dataset

Organisms	Number of positive pairs	Number of negative pairs
Yeast	5594	5594
Helicobacter pylori	1458	1458

In addition, for further evaluating the proposed method, we created imbalance yeast dataset. First, we count the number of without repetition protein sequences on yeast dataset, where contain 2530 without repetition protein sequences. A total of 6,400,900 protein pairs were created from 2530 protein. Here, we removed 5594 positive protein pairs from 6,400,900 protein pairs. As a result, we obtained 6,395,306 negative protein pairs. Finally, 5594 positive protein pairs were selected to build the positive pairs and 16,782 negative protein pairs random selected from 6395306 negative protein pairs to build the negative pairs. As a result, the balance yeast dataset contains 11,188 protein pairs, the imbalance yeast dataset consist of 22,376 protein pairs, and the Helicobacter pylori dataset contains 2916 protein pairs.

Position‐specific scoring matrix

Position specific scoring matrix (PSSM) was originally employed to detect distantly related proteins, which can be generated from a set of protein sequences.19 For a given protein sequence, PSSM can be defined as an M × 20 matrix where L is a protein sequence length, and 20 represents 20 amino acids. A score for the amino acid in the position of the query protein sequence is assigned by PSSM. The score can be expressed as , where represents the amino acid appearing frequency ratio at position of the probe, and is the value of Dayhoff's mutation matrix between and amino acids. As a result, a high score represents a largely conserved position and a small score represents a weakly conserved position.

PSSM is very useful to predict protein quaternary structural attributes, disulfide connectivity, and folding patterns.20, 21 Thus, it is used to predict PPIs in this work. The Position Specific Iterated BLAST (PSI‐BLAST)22 has been employed to build each protein sequence PSSM. To obtain broadly and highly homologous sequences, the e‐value parameter of PSI_BLAST was selected as 0.001 and three iterations were chosen. The resulting PSSM can be represented as 20‐dimensional matrices. Each matrix contains L× 20 elements, where L is the total number of residues in a protein. The rows of the matrix represent the protein residues, and the columns of the matrix represent the 20 amino acids.

Bi‐gram probabilities

In this section, the Bi‐gram probabilities (BiGP) feature extraction method using PSSM linear probabilities is expressed. The characteristics of the Bi‐gram probabilities was originally described in the literature.23 The Bi‐gram probabilities (BiGP) represents the given protein sequence by using its PSSM and the Bi‐gram features is calculated using the PSSM probability information. Let P represent the PSSM of a given protein. PSSM has been mentioned in the Position‐specific Scoring Matrix section of the article. Thus, the matrix P contains L rows and 20 columns, where L is a protein sequence length. A PSSM element for the amino acid in the position for a protein sequence can be interpreted as the relative probability of amino acid at the location of the primary protein sequence, which can be expressed as . The frequency of occurrence of transition from amino acid to amino acid can be defined as follows:

The Eq. (1) gives 400 frequencies of occurrences for 400 bi‐gram transitions, the matrix BiGP is called as the bi‐gram occurrence matrix and its 400 elements define our bi‐gram feature vector23 as follows:

These bi‐gram features can also be represented as follows:

Where is the dimensionality of the feature vector the can be represented as follows:

Finally, each protein sequence of yeast and Helicobacter pylori was converted into a 400‐dimensional vector using the Bi‐gram Probabilities feature extraction method.

Principal component analysis

Principal component analysis (PCA) is widely used to reduce the dimensional of sample data. In such a way, high‐dimensional sample data can be projected to a low‐dimensional subspace. At the same time, the useful information can be retained. Suppose a multivariate sample data can be represented as

Where represents the number of variables, and represents the number of each variable sampling. PCA closely related to singular value decomposition (SVD) of matrix and the singular value decomposition of matrix can be expressed as

Where represents feature vector of and represents feature vector of , and is singular value. If there are m linear relationships between variables, then singular values is zero. Any line of P can be defined as feature vector

Where represents the projection of on feature vector is load vector, and is score.

If there are certain degrees of linear correlation between the variables of matrix, then the projection of final several load vectors of matrix P will become enough small, which resulting from measurement noise. Consequently, the principal decomposition of matrix represented as

Where E is error matrix and can be ignored. This not brings about the obvious loss of useful information of data.

In the study, in order to reduce the influence of noise and improve the prediction accuracy, the dimensional of balance yeast and imbalance yeast and Helicobacter pylori have been reduced from 400 to 350 using PCA.

Relevance vector machine

The characteristics of the Relevance Vector Machine described in the literature.24 We can assume that , is the training sample for binary classification problems, where represents the training sample label, represents the label of testing sample, and , where is the classification model; represents additional noise, with a mean value of zero and a variance of , where . It is assumed that the training datasets are independent identically distributed; the vector obeys the following distribution:

Where φ is defined as follows:

The sample label is used to predict the testing sample label , given by

For making the value of most components of the weight vector zero and reducing the amount of calculation of the kernel function, additional conditions is attached to the weight vector . Assuming that obeys a distribution with a mean value of zero and a variance of , the mean , , where is a hyper‐parameters vector of the prior distribution of the weight vector .

Because cannot be obtained by an integral. Thus, it must be resolved using a Bayesian formula, given by

The integral of the product of and is given by

Because ) and ) cannot be solved by means of integration, the solution is approximated using the maximum likelihood method, represented by

The iterative process of and is as follows:

Here is element on the diagonal of , and the initial value of and can be decided via the approximation of and using formula (22) continuously renewal. After enough iterations, most of will be close to infinity, the corresponding parameters in will be zero, and other values will be close to finite. The resulting corresponding parameters of are now referred to as the relevance vector.

Procedure of the proposed method

In the work, the proposed method consists of three steps: feature extraction, dimensionality reduction using PCA, and sample classification. The feature extraction method includes two steps: (1) each protein sequence is represented as a PSSM matrix; (2) representing each protein sequence PSSM as a 400‐dimensional vector by taking advantage of Bi‐gram probabilities. Each 400‐dimensional vector was converted into 350 dimensional using the PCA method. Finally, sample classification occurs in two steps: (1) the RVM model is employed to execute classification on balance yeast and imbalance yeast and Helicobacter pylori datasets; (2) the SVM model is used to perform classification on yeast dataset. The flow chart of the proposed method is shown in Figure 1.

Figure 1

The flow chart of the proposed method.

Performance evaluation

In this article, for evaluating the feasibility and effectiveness of the proposed method, four parameters include (1) Accuracy (Ac), (2) Sensitivity (Sn), (3) Precision (Pe), (4) Matthews's correlation coefficient (Mcc), which were calculated. They are represented as follows:

Where TN represents true negatives, TP represents true positives, FN represents false negatives and FP represents false positives respectively. True positives represent the count of true interacting pairs correctly predicted. True negatives are the number of true noninteracting pairs predicted correctly. False positives defined as the count of true noninteracting pairs falsely predicted, and false negatives represent true interacting pairs falsely predicted to be noninteracting pairs. Moreover, a receiver operating curve (ROC) was generated to evaluate the performance of our proposed method.

Results and Discussion

Performance of the proposed method

For averting the over‐fitting and verifying the efficacy and stability of our proposed method, fivefold cross validation was employed in the experiment. More specifically, we divided into the whole dataset five parts; four parts were selected as training dataset and one part was selected as test dataset. For the sake of ensuring fairness, there are several parameters for RVM model, which were set up the same for the balance yeast and imbalance yeast and Helicobacter pylori datasets. Thus, we chose the Gaussian function as the kernel function. Meanwhile, we set up the three parameters: width = 2.8, initapla = 1/N and beta = 0, where width represents the width of Gaussian function, N represents the count of training samples, and beta represents classification or regression. Hear, “beta = 0” represents classification. The experimental results of the RVM classifier combined with Bi‐gram probabilities and PSSM and PCA, which based on the protein sequence information from balance yeast and imbalance yeast and Helicobacter pylori datasets are shown in Tables 2, 3, 4.

Table 2

Fivefold Cross Validation Results Shown Using Our Proposed Method on Yeast

Testing set	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
1	94.32	94.88	93.79	89.29
2	95.22	95.04	95.46	90.89
3	94.81	93.62	96.00	90.17
4	94.73	94.59	94.59	90.00
5	93.79	93.20	94.45	88.36
Average	94.57 ± 0.005	94.27 ± 0.0.008	94.86 ± 0.009	89.74 ± 0.010

Table 3

Fivefold Cross Validation Results Shown Using Our Proposed Method on Helicobacter pylori

Testing set	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
1	91.77	93.15	90.67	84.88
2	89.37	92.12	87.34	80.96
3	91.42	92.74	90.94	84.28
4	91.08	90.22	90.88	83.70
5	89.21	91.19	87.90	80.73
Average	90.57 ± 0.012	91.88 ± 0.012	89.55 ± 0.018	82.91 ± 0.020

Table 4

Fivefold Cross Validation Results Shown Using Our Proposed Method on Imbalance Yeast

Testing set	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
1	97.79	95.06	95.85	94.12
2	97.05	93.45	94.79	92.38
3	97.25	94.40	94.97	93.03
4	97.09	93.02	95.23	92.41
5	96.56	93.15	92.81	91.02
Average	97.15 ± 0.004	93.82 ± 0.009	94.73 ± 0.011	92.59 ± 0.011

We performed computational experiments on balance yeast and imbalance yeast and Helicobacter pylori datasets to verify the efficacy and stability of the propose method. We obtained the results of average accuracy, sensitivity, precision, and Mcc of 94.57, 94.27, 94.86, and 89.74% and the standard deviations of them of 0.005, 0.008, 0.009, and 0.01% on yeast dataset, respectively. At the same time, good results of average accuracy, sensitivity, precision, and Mcc of 97.15, 93.82, 94.73, and 92.59% were obtained on imbalance yeast dataset and the standard deviations of them of 0.004, 0.009, 0.011, and 0.019% achieved, respectively. Similarly we also achieved good results of average accuracy, sensitivity, precision, and Mcc of 90.57, 91.88, 89.55, and 82.91% on Helicobacter pylori dataset and the standard deviations of them of 0.012, 0.012, 0.018, and 0.020%, respectively.

It can be found from Tables 2–IV that the proposed method is accurate, robust, and effective for predicting PPIs. The better prediction accuracy achieved may be attributed to feature extraction method and choice of classifier. This feature extraction approach is novel and effective, and the choice of the classifier is accurate. The major improvement of the proposed feature extraction method lies in three reasons: (1) the PSSM matrix is a much useful tool for representing protein sequence, which can not only describes the order information but also retains sufficient prior information for the protein sequence. As a result, each protein sequence represented as a PSSM that contains all the useful information for predicting PPIs. (2) The Bi‐gram probabilities represented each protein sequence by its PSSM and calculated the Bi‐gram feature using the probability information contained in PSSM. The Bi‐grams features from PSSMs can significantly reduce the sparsity level which helps in improving the recognition performance.23 (3) Under the condition of guaranteeing the integrity of the information of feature vector, for reducing the influence of noise, each Bi‐gram vector was reduced dimensional using PCA method. The experiments results demonstrated that the feature vector extracted using the proposed feature extraction method is very fit for predicting PPIs. In addition, it can be observed from Tables 2 and IV, the prediction accuracy of imbalance yeast is higher than that of balance yeast using the proposed method, which further proved that the proposed prediction model is accurate, robust, and effective for PPIs detection.

Comparison with the SVM‐based method

To further validate the effectiveness of the proposed approach, we compared the prediction accuracies with that of the state‐of‐the‐art support vector machine (SVM) classifier. More specifically, the classification performance was compared between SVM and RVM model on the yeast dataset using Bi‐gram probabilities feature extraction method. The LIBSVM tool25 was used to carry out classification in SVM. For the classifier, SVM is used with a radial basis function (RBF).The RBF kernel parameters are c = 0.5 and g = 0.6 optimized by using a grid search method.

The obtained prediction results of the RVM are compared with that of the SVM and shown in Table 5 on yeast dataset. At the same time, the ROC curves are compared between RVM and SVM and displayed in Figure 2. It can be observed from Table 5, the SVM classifier achieved 86.60% average Accuracy, 84.33% average sensitivity, 88.34% average precision, and 76.76% average Mcc. However, the RVM classifier of the proposed method achieved 94.57% average accuracy, 94.27% average sensitivity, 94.86%, average precision, and 89.74% average Mcc. It can be seen from these prediction results that the RVM classifier is significantly better than the SVM classifier. Similarly, it is shown in Figure 2 that the ROC curves of RVM classifier is also significantly better than that of SVM classifier. This clearly demonstrated that the RVM classifier employed the proposed method is an accurate and robust classifier. The better classification performance of RVM classifier may be attributed to two reasons: (1) The obvious advantage of RVM classifier is that the amount of calculation of the kernel function is greatly reduced; (2) The RVM classifier overcomes the disadvantage that the kernel function required to meet the condition of Mercer. For the sake of these reasons, the RVM classifier used our proposed method is obviously better than the SVM classifier. At the same time, it is proved that the proposed prediction model can obtain higher accuracy for detecting PPIs.

Table 5

Five‐fold Cross Validation Results Shown by Using Our Proposed Method on Yeast

Testing set	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
SVM+PSSM+BiGP
1	85.96	83.60	87.55	75.83
2	86.90	83.68	88.81	77.15
3	87.04	85.34	88.62	77.42
4	86.81	84.21	88.89	77.07
5	86.29	84.82	87.83	76.34
Average	86.60 ± 0.005	84.33 ± 0.007	88.34 ± 0.006	76.76 ± 0.007
RVM+PSSM+BiGP
1	94.32	94.88	93.79	89.29
2	95.22	95.04	95.46	90.89
3	94.81	93.62	96.00	90.17
4	94.73	94.59	94.59	90.00
5	93.79	93.20	94.45	88.36
Average	94.57 ± 0.005	94.27 ± 0.0.008	94.86 ± 0.009	89.74 ± 0.010

Figure 2

Comparison of ROC curves between RVM and SVM on yeast dataset.

Comparison with other methods

To demonstrate the effectiveness of the propose method, some state‐of‐the‐art methods for PPIs detection were selected to compare with the proposed method that uses a RVM model combined with PSSM, Bi‐gram probabilities, and PCA on yeast and Helicobacter pylori datasets. Experimental results of various methods on yeast and Helicobacter pylori datasets were shown in Tables 6 and VII. As we can see from Table 6 that the average prediction accuracy of the proposed method is variously higher that of the other five methods on yeast dataset. Similarly, the precision and sensitivity of our proposed method are also superior to those of the other five methods. At the same time, it can be seen from Table 7 that the average prediction accuracy of the proposed method is also significantly higher than that of the five different methods on Helicobacter pylori dataset. From Tables 6 and 7, it can be observed that the proposed method obtained obviously better prediction results compared to other existing methods. All experiment results proved that the RVM classifier combined with BiGP and the PSSM and PCA can improve the prediction accuracy relative to current state‐of‐the‐art methods. The improvement of prediction accuracy of the proposed method lies in using a correct classifier and a novel feature extraction method.

Table 6

Predicting Ability of Different Methods on Yeast

Model	Testing set	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
Guo's work26	ACC	89.33 ± 2.67	89.93 ± 3.60	88.77 ± 6.16	N/A
	AC	87.36 ± 1.38	87.30 ± 4.68	87.82 ± 4.33	N/A
Zhou's work27	SVM + LD	88.56 ± 0.33	87.37 ± 0.22	89.50 ± 0.60	77.15 ± 0.68
Yang's work28	Cod1	75.08 ± 1.13	75.81 ± 1.20	74.75 ± 1.23	N/A
	Cod2	80.04 ± 1.06	76.77 ± 0.69	82.17 ± 1.35	N/A
	Cod3	80.41 ± 0.47	78.14 ± 0.90	81.66 ± 0.99	N/A
	Cod4	86.15 ± 1.17	81.03 ± 1.74	90.24 ± 1.34	N/A
You's work29	PCA‐EELM	87.00 ± 0.29	86.15 ± 0.43	87.59 ± 0.32	77.36 ± 0.44
Proposed method	RVM	94.57 ± 0.005	94.27 ± 0.0.008	94.86 ± 0.009	89.74 ± 0.010

Table 7

Predicting Ability of Different Methods on Helicobacter pylori

Model	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
Nanni30	83	86	85.1	N/A
Nanni31	84	86	84	N/A
Nanni and Lumini32	86.6	86.7	85	N/A
Z‐H You29	87.5	88.95	86.15	78.13
L Nanni31	84	84	86	N/A
Proposed method	90.57	91.88	89.55	82.91

Performance of the proposed method on HPRD dataset

To further illustrate the effectiveness of the propose method, we carry out the experiment on HPRD dataset. The HPRD dataset contains 36,480 positive protein pairs and 36,630 negative protein pairs. As a result, HPRD dataset contains 73,110 protein pairs. Experimental results on HPRD dataset were shown in Table 1, 8. It can be seen from Table 8 that the proposed method achieved good prediction accuracy. The experiment results further demonstrated that the improvement of prediction accuracy of the proposed method lies in using a correct classifier and a novel feature extraction method.

Table 8

Fivefold Cross Validation Results Shown Using Our Proposed Method on HPRD

Testing set	Ac (%)	Sn (%)	Pe (%)	Mcc (%)
1	98.92	99.12	98.78	97.87
2	98.50	98.91	98.14	97.04
3	98.70	98.88	98.48	97.43
4	99.00	99.45	98.56	98.02
5	98.82	99.29	98.35	97.68
Average	98.79 ± 0.002	99.13 ± 0.002	98.46 ± 0.019	97.61 ± 0.004

Conclusion

In this article, we explore a novel computational method for predicting PPIs, called RVM‐BiGP. It was constructed by combining an RVM classifier with Bi‐gram probabilities and Position Specific Scoring Matrix. Experimental results on two widely used yeast and Helicobacter pylori datasets showed that the prediction accuracy of the proposed method is significantly higher than that of the previous methods. Compared with some other state‐of‐the‐art methods, the proposed method achieved the best performance. Furthermore, by carrying out the proposed approach on imbalance yeast dataset, the prediction accuracy is better than that of balance yeast dataset, which further proved that the proposed prediction model is very powerful for imbalanced data classification. The major improvements of the proposed method lie in employing an effective feature extraction method that can capture useful evolutionary information and significantly reduce the sparsity level which helps in improving the recognition performance. Moreover, PCA can integrate the useful information and reduce the influence of noise, which helps in improving the prediction accuracy. In addition, the experimental results demonstrated that the RVM classifier model is very suitable for PPIs detection. In conclusion, the proposed method is an efficient, reliable, and powerful prediction model and can be a useful tool for future proteomics research. For the future study, more effective feature extraction methods and machine learning techniques will be explored for prediction PPIs.