Currently proposed methods widely use low-similarity benchmark datasets named 1189, FC699, 640 and 25PDB.The sequence similarity of 25PDB [10], 1189 [11], FC699 [1] and 640[12] are lower than 25%, 40%, 40% and 25% respectively. In order to compare with other methods, we choose 25PDB dataset as training set for SVM classifier, while the other datasets 1189, FC699 and 640 are test sets.

Nowadays, a lot of methods are used to predict amino acids sequences into secondary structural sequences (SSS) constructed by three secondary structural elements, -helix (H), -strand (E), and random coil(C). Firstly, we obtain corresponding secondary structural sequences by PSI-PRED (version 2.6) [6]. It’s difficult to distinguish and classes for both of them contain -helices and -strands. -helices and -strands are usually separated in class, while they are usually interspersed in class. In order to better represent the distribution of -helices and -strands, every segment H, E and in secondary structure sequence(SSS) is replaced by, and respectively, the new sequence is secondary structure segment sequence(SS), all element are removed from SS to form a new sequence represented by SSW[13].

Our novel method mapped each protein sequence into a 14-dimentional vector that can be defined as

where T is a transpose symbol, () is one of the features in feature vector P. The elements of Equation (1) are based on super- secondary structure information and are first proposed in this paper. What’s more, are proposed specially to make a distinction between and classes. A number of secondary structure elements interact with each other and form a regular combination of secondary structure, which acts as a structural member of tertiary structure in much protein and is known as super-secondary structure (motif). Some super-secondary structures are related to specific functions and there are three basic forms of combination:, and. In order to tap the structural characteristics of each class, we extract several typical features of folds and combinations.

1) The easiest structure is hairpin motif which is connected by a short loop. Multiple hairpin motifs together will form a stable and widespread -turns, so extracting the number of hairpin motifs (defined as) are very meaningful. Super-secondary structure is a helix bundle and is often formed by two intertwined spiral parallel or ant parallel?helices. Structure named Rossman folds is one of the most special structures of class. So we extract the number of super-secondary structure () and () as features. Then the corresponding features can be defined as, ,.

2) In proteins of class, -strands and -helices are parallel, -helix and - sheets appear alternatively, such as. Proteins of class are two types. Such as “-plaits” in which -helices and -strands appear alternatively, this characteristic is same to proteins in class. In -plaits, the alternative form of -helices and -strands is or . In another type -helices and -strands are separated. Therefore the number of occurrences of segments () and () segments is an obvious characteristic to distinguish proteins in and classes.

Features mentioned above can be represented as:

,

where and are the maximal lengths of segments and segments in SSW.

3) In proteins of the class, -helices and -strands alternate more frequently than in proteins of the class. Based on this characteristic, we can design a feature, where is the alternating frequency of -helices and -strands in SSS.

4) Because the length of the secondary structural segments will affect the assignment of the structural class, we define new features

and

where and are the maximal lengths of -helix and -strand segments in SSS.

5) Position information of SS is also the deciding factor. Herein, the position of a segment is defined as a starting position of the segment. The corresponding features can be defined as

,

where () is the starting order of the -helix (-strand) segment in SSS, and are the occurrences of -helix and -strand segments in SSS.

6) To reflect the position information of protein secondary structure, two features can be defined as

where and are the j-th order of H and E in SSS, and are the number of H and E in protein secondary structure sequence (SSS).

7) The probability of content C can be ignored due to the sum of the three probabilities of H, E and C is 1 [1]. Hence, the two features are expressed as

where,.

Protein secondary structure prediction is a multiclass classification problem. With high prediction accuracy, support vector machine (SVM) has been widely used for protein secondary structure classification [4] [5]. Here we use of the "one to one" multiclass classification method that construct a multiclass classifier by combining six binary classifiers. We choose Gaussian radial basis function (RBF) as the kernel function for SVM [14]. Using a grid search on the training set (25PDB) by tenfold cross-validation, we can find out the penalty parameter and kernel parameter, the final parameters are,.

In this paper, we use an independent testing dataset cross-validation. There are many indicators to evaluate model’s performance, sensitivity (Sens), specificity (Spec), Matthew’s correlation coefficient (MCC) and overall accuracy (OA) are widely used in protein structure prediction [15]. The total number of proteins, classes and proteins in k-th

class are denoted by N, k and respectively, so. Usually, four parameters are used by studies for examining a predictor’s effectiveness:

The number of proteins which is correctly predicted as kth class and non-kth class are denoted by and. The number of proteins which is incorrectly predicted as kth class and non-kth class are denoted by and. Where,. Using these parameters, we can obtain Equation (2):

(2)

In our experiment, we use 25PDB dataset as a training set and other three datasets as testing sets. We not only report the values of Sens, Spec, MCC and overall accuracy (OA) of every structural class of testing set, but also report the average of Sens, Spec, MCC and overall accuracy (OA). The detail results can be seen in Table 1. The overall accuracy is more than 84% for each test set and it reaches 90% for FC699 dataset. What’s more, the average overall accuracy of 3 test sets is up to 86.6%. The Sens and

MCC values of class are the lowest. This is not strange because class is complicated and it not only contains and classes but also contains -plaits structure, so the prediction accuracy of class is lower.

To better verify the effect of the new proposed seven features, we do the following experiment with FC699, 1189 and 640 datasets. The comparison of obtained accuracies between our method including 14 features and our method including 7 features can be seen in Table 2. After added new features, the average overall accuracy increases by 2.6% up to 86.6%. For FC699 dataset, the overall accuracy and accuracies of All-, All- and classes are improved by 2.7%, 1.5%, 4.4% and 2.7% respectively. For 1189 and 640 datasets, the overall accuracy increases by 2.6% and 2.3%, respectively. However, the results of and classes are not obvious because of the interference of other classes [13].

To further validate effect of super-secondary structure features, we do experiment just on proteins in and classes with a 14-dimensional feature vectors. The 25PDBS, FC699S, 1189S and 640S sets are the subsets formed by removing all the proteins in the All- and All- classes from 25PDB, FC699, 1189 and 640 datasets respectively. Hence, we use the 25PDBS to train SVM classifier and other subsets to test. The parameters and (,) are selected by tenfold cross-validation on 25PDBS with a grid search method. The corresponding experimental results are shown in Table 3. In Table 3, the overall accuracies of all datasets predicted by our method are higher than 80%. The overall accuracies and accuracies of class predicted by our method are the highest compared with other competitive methods. The prediction accuracies of all structural classes are higher than 90% on FC699S subset. The accuracies of class and the overall accuracy are increased by 9.2% - 27.4% and 2.4% - 7.3% on 1189S respectively. For 640S, the accuracies of class and the overall accuracy are improved by 2.9% - 11.7% and 0.6% - 5.2%

respectively, however, the accuracy of class is consistent with the result produced by PKS-PPSC model. Experimental results show that our method for predicting proteins in and classes is very effective.

It’s known to all, SCPRED [2] and MODAS [7] are famous in predicting protein secondary structure and are often used as baseline for comparison. From Table 4 we can see, our method improves the overall accuracies by 0.9% - 3.8% and 0.5% - 4.2% on 1189 and 640 datasets compared with other competing prediction methods including SCPRED and MODAS. And only for FC699 dataset, the overall accuracy is lower than Kong et al. and is not the highest, but it is increased by 0.8% - 2.9% compared with the rest methods. Compared with model SCPRED and the method of Liu and Jia, the overall accuracy predicted by our method is improved by 2.9% and 0.8% on FC699 dataset, respectively, besides the accuracy of class is increased by 4.8% and 19.5%. Our method obtains the highest accuracies for the All- and classes which reach to 87.8% and 79.3% on 1189 dataset and the overall accuracy is the highest than other exiting methods. For 640 dataset, the overall accuracy and the accuracy of All- class are the highest.

Therefore our method extracting features based on super-secondary structure has the ability to reflect the realistic characteristics of proteins more accurately. Specially, our method improved the accuracies of and classes greatly. According Table 4, we find our method is not always the best. The reason is that some methods not only extract features based on protein secondary structure but also combine other information. In contrast, our method is aimed to predict secondary structural classes by extracting features more effectively just on the basis of secondary structure.