Introduction

The concept of protein structure classes, which was introduced by Levitt and Chothia in 1976, was initially based on a visual inspection of polypeptide chain topologies in a dataset of 31 globular proteins (Levitt and Chothia 1976). According Levitt and Chothia's definition (1976), a protein of known structure can generally be categorized into one of four structural classes: all-α, all-β, α/β, and α + β. Since the implementation of this classification, the structural class has become one of the most important features for characterizing the overall folding type of a protein, and it has played an important role in molecular biology, cell biology, pharmacology, rational drug design, and many other related fields (Chen et al. 2006a; Chou 1992, 2004; Chou 2000; Feng et al. 2005; Kedariseti et al. 2006).

During the past three decades, many methods have been proposed for predicting protein structure class, such as the Mahalanobis distance approach (Chou 1995; Chou and Zhang 1994), covariant discrimination approach (Chou and Maggiora 1998), information theory (Jin et al. 2003), artificial neural network (Cai and Zhou 2000; Metfessel et al. 1993), fuzzy clustering (Shen et al. 2005), support vector machine (SVM) (Cai et al. 2002, 2001; Chen et al. 2006a, b; Sun and Huang 2006) and boosting (Cai et al. 2006; Feng et al. 2005). The successes in predicting protein structural classification have, in particular, greatly stimulated the development of predicting other attributes of proteins (Chou 2005), such as subcellular localization (Cedano et al. 1997; Chou and Elrod 1999; Chou and Shen 2007d, 2008), among many others (Chou and Elrod 2002, 2003; Guo et al. 2006; Kuric 2007; Liu et al. 2005a; Shen and Chou 2007c; Shen et al. 2007a, b; Wang et al. 2004, 2005b, 2006; Zhang SW et al. 2006). Many predictors have been proposed to predict protein structure classes with their amino acid composition (Bahar et al. 1997; Chou 1995; Chou and Zhang 1992; Zhang and Chou 1992; Zhang et al. 1995; Zhou and Assa-Munt 2001; Zhou et al. 1992). However, one of the reasons for the lower successful prediction rate may be the complete lack of sequence-order effects in the primary sequence. To take into account the sequence-order effects, a diverse set of descriptors were proposed for enhancing the prediction quality; these include pair-coupled amino acid composition (Chou 1999a), polypeptide composition (Luo et al. 2002), pseudo-amino acid composition (Chen et al. 2006a, b; Chou 2001; Xiao et al. 2006b), various auto-correlation descriptors (Feng and Zhang 2000; Lin and Pan 2001; Horne 1988), and other composition factors (Du et al. 2003, 2006). Since the concept of Chou’s pseudo-amino acid composition was introduced, various pseudo-amino acid composition approaches have been developed to deal with the varieties of problems encountered in proteins and protein-related systems (Aguero-Chapin et al. 2006; Caballero et al. 2007; Cai and Chou 2006; Chen and Li 2007a, b; Chen et al. 2006a, b; Chou and Shen 2008; Diao et al. 2007; Du and Li 2006; Fang et al. 2008; Gao et al. 2005; Gonzalez-Diaz et al. 2006, 2007a, b, c; Kurgan et al. 2007; Li and Li 2007; Lin and Li 2007a, b; Liu et al. 2005a, b; Mondal et al. 2006; Mundra et al. 2007; Pan et al. 2003; Pu et al. 2007; Shen and Chou 2005a, b, 2006, 2007c; Shen et al. 2006, 2007a, b; Shi et al. 2007, 2008; Wang et al. 2004, 2006; Xiao et al. 2006a, b; Zhang SW et al. 2006, 2007; Zhang TL et al. 2006; Zhang and Ding 2007; Zhou et al. 2007; ). Due to its wide usage, a very flexible pseudo-amino acid composition generator, called “PseAAC” (Shen and Chou 2008), was recently made available at the website http://chou.med.harvard.edu/bioinf/PseAAC/, enabling users ton generate 63 different kinds of PseAA composition. Chou and Cai (2002) proposed a completely different approach, the so-called functional domain composition, to incorporate the information of various function types. The validity of their approach has been tested by numerous previous investigations (Cai and Chou 2005a, b; Chou and Cai 2004). Unfortunately, most of the existing methods are based on a group of features that only possesses a kind of discriminative information for the prediction of protein structure class. However, different types of discriminative information associated with primary sequence have been completely missed, which undoubtedly has reduced the success rate of prediction. Empirical studies have demonstrated that the merging of descriptors should increase the predictive accuracy if the descriptors represent different types of discriminative information. Alternatively, the merging of descriptors will simultaneously increase the information redundancy that could, in turn, decrease the predictive accuracy (Kohavi and John 1997). Therefore, there is a need to explore whether an effective combination of descriptors could help to enhance predictive performance.

The SVM, firstly proposed by Cortes and Vapnik (1995), is an excellent machine learning method. Compared with other machine learning systems, SVM has many attractive features, including the absence of local minima, speed and scalability, and the ability to condense information contained in the training set (Chen et al. 2006b). In recent years, SVMs have performed well in predicting protein secondary structure (Hua and Sum 2001), subcellular localization (Chou and Cai 2002; Kim et al. 2006; Yu et al. 2006; Zhang ZH et al. 2006), membrane protein types (Cai et al. 2004; Wang et al. 2004), among others. When using a SVM for predicting protein diverse attributes, two problems are encountered, namely the choice of the optimal features subset and the set of the kernel parameters. The choice of the optimal features subset is how to choose the optimal feature subset that is relevant to protein attributes. Large numbers of features fed to SVM can increase computational complexity and cost (Shen et al. 2007a, b), suffer from the curse of dimensionality and the risk of overfitting and also impede the identification of some biologically mechanism that describe the relationship between the protein and its attributes. In contrast, when a small feature set that is not relevant to protein attributes is used, the result can be bad generalization performance and accurateness. Consequently, the selection of an optimized feature subset is necessary to speed up computation and to improve the generalization performance of the SVM. The choice of the set of the kernel parameters involves how to set the kernel parameters so that the performance of SVM can be brought into full play. These parameters include the penalty constant C and the parameters in the kernel function (width parameter σ of radial basis function, etc.), and they affect more or less the performance of the SVM (Yuan and Chu 2007). Providing adequate solutions to these two problems is crucial because the feature subset choice influences the appropriate kernel parameters, and vice versa (Huang et al. 2008).

Unfortunately, SVMs do not offer the option of a free choice of the optimal features subset and the set of the kernel parameters. In practice, we usually choose a kernel function and set the kernel parameters by experience when a SVM system is constructed. Furthermore, the grid search algorithm is often utilized to find the best kernel parameters when the radial basis function is used; however, the algorithm is time consuming and does not perform well (Hsu and Lin 2002; LaValle and Branicky 2002). The principal component analysis (PCA) and t test are also applied when choosing the optimal features subset when a SVM is used, and although the efficiency of the filter approach of PCA and the t test is high, the results of these methods are poor. In fact, a number of different heuristic algorithms, such as the particle swarm optimization algorithm (Shen et al. 2007a, b), ant colony optimization algorithm (Sivagaminathan and Ramakrishnan 2007), artificial immunization algorithm (Yuan and Chu 2007), and genetic algorithm (GA), have been applied for feature selection. The basic idea of GA is to imitate life evolution in nature according to Darwinian survival of the fittest principle (Jalali-Heravi and Kyani 2007; Lv et al. 2003). GA can effectively search the interesting space and easily solve complex problems without requiring a priori knowledge about the space and the problem. These characteristics of GA make it possible to simultaneously optimize the feature subset and the SVM parameters.

The objective of the research reported here was to develop an effective approach by combining existing descriptors for protein structure class prediction based on an improved GA and SVM. The improved GA was used to simultaneously optimize the kernel parameters of the SVM and to determine the optimized features subset. The prediction quality evaluated by the jackknife cross-validation test exhibited a significant improvement compared to those obtained with several published methods.

Materials and methods

Data sets

In order to facilitate the comparison, the dataset constructed by Chou (1999b) and other two datasets constructed by Zhou (1998) were used as the working dataset. The dataset constructed by Chou (1999b) contains 204 proteins, of which 52 are all-α, 61 are all-β, 45 are α/β, and 46 are α + β. Of the two datasets constructed by Zhou, one consists of 277 domains (70 all-α domains, 61 all-β domains, 81 α/β domains, and 65 α + β domains); the other consists of 498 domains (107 all-α domains, 126 all-β domains, 136 α/β domains, and 129 α + β domains).

Protein primary sequence representation

An important issue in the prediction of protein structure class is to represent the primary sequence of proteins with certain encoding scheme. In this work, six feature groups are composed of ten structural and physicochemical features of proteins and peptides from amino acid sequences, and 1447 features were used to represent the protein samples. These features can be easily computed by the PROFEAT web server (Li et al. 2006). PROFEAT is accessible at http://jing.cz3.nus.edu.sg/cgi-bin/prof/prof.cgi. The ten features are summarized in Table 1.

Table 1 List of structural and physicochemical features of proteins and peptides
Full size table

Couple the improved genetic algorithm with SVMs

The publicly available LIBSVM software (Chang and Lin 2001), which can be downloaded freely from http://www.csie.ntu.edu.tw/~cjlin/libsvm, was used to process the SVM classification. The radial basis function was selected as the kernel function. Prediction of protein structure class is a multi-class classification problem. In general, the most commonly used approach for solving multi-class problems is to reduce a single multi-class problem into multiple binary problems known as the one-versus-one and one-versus-rest. However, the one-versus-rest strategy has the well-known ‘false positives’ problem (Ding and Dubchak 2001). Consequently, we adopt here the one-versus-one method to transfer the multi-class problem into a two-class problem. The GA based on chaos (Lv et al. 2003) was used to simultaneously select the feature subset and optimize kernel parameters. In the improved GA, the mutation method based on the chaotic system is used to maintain the population diversity and prevent the incest leading to misleading local optima (Eshelmen and Schaffer 1991). The chromosome representations, fitness function, selection, crossover and mutation operator are described in the following sections.

Chromosome representation

There are three parts to the chromosome: C, γ and the features mask. The chromosome was represented as the binary and decimal coding systems. The hybrid chromosome-encoding method is illustrated in Fig. 1. The hybrid chromosome consists of 1447 binary genes for the selection of features and two decimal genes, C and γ, for the optimization of parameters. If g n  = 0, the feature with index n is excluded from the given feature set. Otherwise, the feature with index n is included.

Fig. 1
figure 1

The chromosome coding

Full size image

Fitness function

A good fitness function is the key to assessing the performance of each chromosome and to obtaining a high classification accuracy. Two objectives must be considered when designing the fitness function. One is to maximize the classification accuracy of fivefold cross-validation, and the other is to minimize the number of selected features. The performances of these two objectives can be evaluated by Eq. (1),

$$ {\text{fitness}} = {\text{SVM}}\_{\text{accuracy}} + (1 - N/1447) $$
(1)

Where SVM_accuracy is the SVM classification accuracy by fivefold cross-validation, and N is the number of selected features.

Selection, crossover and mutation operator

Elitist strategy was used to select the operation. The elitist model guarantees that the chromosome with the highest fitness value is always replicated in the next generation of chromosome. Hence, the function of maximal fitness versus the number of generated chromosome is a monotonous increasing function (Handels et al. 1999). Once a pair of chromosome has been selected for crossover, five random selected positions are assigned to the crossover operator of the binary coding part. The crossover operator was determined according to Eqs. (2) and (3) for the decimal coding part, where p is the random number of (0, 1).

$$ {\text{Child}}_{1} = p \times {\text{parent}}_{1} + (1 - p) \times {\text{parent}}_{2} $$
(2)
$$ {\text{Child}}_{2} = p \times {\text{parent}}_{2} + (1 - p) \times {\text{parent}}_{1} $$
(3)

The GA based on the chaotic method was applied to the mutation operator and to the part of decimal coding in the chromosome. Mutation to the part of binary coding in the chromosome is the same as traditional GA.

In the study described here, the population size of improved GA was 30, and the termination condition was that the generation number was 30,000. The whole procedure of GA/SVM-coupled GA with SVM is illustrated in Fig. 2, and the steps were as follows:

  • Step 1. Produce all of the initial chromosome of GA randomly with an appropriate size of the population.

  • Step 2. Run SVM and calculate the fitness values of each chromosome in the population using the fitness function. If the generation number reaches 30,000, stop the process with the output of results, otherwise, go to the next step.

  • Step 3. Select a given percentage of the fittest chromosomes from the current generation based on their fitness value. The selected chromosomes as a part of the next generation are used as parent chromosomes to produce new chromosomes in the next step.

  • Step 4. Produce a given percentage of new chromosomes of the next generation by the mating and mutating operation based on the parents.

  • Step 5. Go back to the second step to run SVM and calculate the fitness values of the renewed population.

Fig. 2
figure 2

The chart of the improved genetic algorithm/support vector machine (GA/SVM) scheme

Full size image

Results and discussion

Analysis of the convergence processes for current method

Figures 3 and 4 illustrate the convergence processes for the improved GA to optimize kernel parameters and to select the feature subset based on the working datasets constructed by Chou (1999b). The better fitness value, higher classification accuracy, and optimized features subset can be obtained from about 15,000 generations, 8000 generations, and 15,000 generations, respectively. Initially, improved GA selected approximate 700 features into SVM and achieved a predictive accuracy about 90%, which is a distinct symptom of overfitting. Along with the implementation of the process, the number of selected features gradually decreased while fitness value and classification accuracy were improved. Classification accuracy was invariable when the number of generations gradually increased from 7000 to 15,000. Fewer than 100 features were fed to SVM at this time. The results indicate that our method has the ability to overcome the overfitting problem and to achieve a high success rate by searching the optimized features subset and kernel parameters.

Fig. 3
figure 3

Convergence curves for improved GA/SVM. Curve 1 Fitness value was obtained from the most fitted member of each generation, curve 2 classification accuracy was obtained from the most fitted member of each generation)

Full size image
Fig. 4
figure 4

The relationship between the number of features and the number of generations using improved GA/SVM

Full size image

Analysis of the optimized features subset

The results of the best features subset are summarized in Table 2. From Table 2 we can see that the optimized features subset contains nine composition, transition, and distribution descriptors; five sequence order descriptors; three amino acid and dipeptide composition descriptors; one autocorrelation descriptors. The results appear to suggest that the order of these feature groups that contributed to the prediction of protein structural class were: composition, transition, and distribution > sequence order descriptors > amino acid and dipeptide composition > autocorrelation descriptors.

Table 2 Results of the selection of the best features subset
Full size table

In fact, there are two compositions of polarity and polarizability, one transition of charge, three distributions of hydrophobicity, and three distributions of polarity, polarizability, and charge in the group of composition, transition, and distribution descriptors. The five sequence order descriptors include two sequence-order-coupling numbers based on Schneider–Wrede distance and three sequence-order-coupling numbers based on normalized Grantham chemical distance. The three amino acid and dipeptide composition are alanine, leucine, and lysine–arginine composition. One autocorrelation descriptor was the Moran autocorrelation hydrophobicity scale. These results suggest that factors such as hydrophobicity, polarizability, polarity, charge, and composition of alanine, leucine, lysine–arginine are important to protein structure class. We therefore expect that if a new encoding scheme can integrate with (1) composition, transition, and distribution, (2) sequence order, (3) amino acid and dipeptide composition, and (4)autocorrelation information, it would be of great significance in terms of predicting the attributes of protein.

Comparison with different methods

In statistical prediction, the most widely used cross-validation methods for examining the accuracy of a predictor are the sub-sampling test and jackknife test (Chou and Shen 2008; Chou and Zhang 1995). However, as demonstrated by Eq. 50 in a recent comprehensive review by Chou and Shen (2007d), the sub-sampling (e.g., fivefold cross-validation) test cannot avoid arbitrariness even for a very simple benchmark dataset. Accordingly, the jackknife test has been increasingly and widely adopted by investigators (Chen et al. 2006a, b, 2007; Chou and Shen 2006a, b, 2007a, b, c, e; Diao et al. 2008; Ding et al. 2007; Du and Li 2006; Fang et al. 2008; Gao et al. 2005; Guo et al. 2006; Kedarisetti et al. 2006; Li and Li 2007; Lin and Li 2007a, b; Liu et al. 2007; Mondal et al. 2006; Niu et al. 2006; Shen and Chou 2007a, b, c, d; Shen et al. 2007a, b; Shi et al. 2007, 2008; Sun and Huang 2006; Tan et al. 2007; Wang et al. 2005a; Wen et al. 2006; Xiao and Chou 2007; Xiao et al. 2005a, b, 2006a; Zhang and Ding 2007; Zhang SW et al. 2006, 2007; Zhou 1998; Zhou and Doctor 2003; Zhou et al. 2007) to test the power of various predictors. To facilitate a comparison with previous studies for the dataset constructed by Chou (1999b), the optimized kernel parameters and features subsets were utilized to perform jackknife cross-validation test. The success rates by the jackknife test are listed in Table 3 and compared with several published results for the same dataset.

Table 3 Comparison of different methods by the jackknife test for 204 proteins
Full size table

The reliability of the optimized features subset was further evaluated by the two datasets constructed by Zhou (1998). We performed the jackknife cross-validation based on the optimized features subset. Grid searches strategy was adopted to find the best C and γ for obtaining maximal jackknife-tested overall rates. The success rates by the jackknife cross-validation test are listed in Tables 4 and 5.

Table 4 Comparison of different methods by the jackknife test for 277 proteins
Full size table
Table 5 Comparison of different methods by the jackknife test for 498 proteins
Full size table

Table 3 shows that the overall rates by the current approach were 99.5% with the one-versus-one method. The results indicate that our method was about 24 and 14% higher than other two SVMs, which were based on amino acid composition and pseudo-amino acid composition respectively. The results also reveal that our improvements can be attributed to the adoption of the optimized features subset and kernel parameters. It is worth noting that the success rates were improved markedly to 100% for all-α, all-β and—the most difficult case—α + β. Consequently, our proposed method is superior to other methods in identifying the structural classification for the Chou’s (1999b) dataset. Table 4 shows that the overall success rate by the our approach was 84.5% for the 277 dataset, which is about 5% higher than that obtained with the SVM method, which was performed with the conventional amino acid composition as the input. In addition, the result is only 3% lower than the SVM fusion, which had the highest overall predictive rate for the dataset. Table 5 shows that the overall success rate by our method was 94.2% for the 498 dataset, which indicates that our method is superior to other existing methods and comparable to LogitBoost. Accordingly, it can be expected that the current method and the SVM fusion or the LogitBoost, if complemented, may further improve the overall rate for the 277 and 498 dataset, respectively. In short, based on both the rationality of the testing procedure and the present success rates, as shown here by our test results, we believe that the optimized features subset may be used to explore the protein folding mechanism by using abundant discriminative information related to protein structure class.

Conclusion

We have proposed a strategy based on improved GA to simultaneously select the feature subset and optimize the parameters of SVM for predicting protein structure class. The results indicate that the proposed method is very effective for the optimal combination of different features. Moreover, it can be anticipated that this method may also have a great impact by improving the success rates for many other protein attributes, such as subcellular localization, membrane types, enzymes family and subfamily classes, and G-protein-coupled receptor classification.