BACKGROUND
the biological function of a protein is essentially associated with its tertiary structure, which is believed to be determined by its amino acid sequence via the process of protein folding  <cit> .
therefore, the prediction of protein's tertiary structure from amino acid sequences is a very important while challenging task in computational biology and proteomics.
the tertiary structure can be broadly categorized into four structural classes based on the types and arrangements of their secondary structural elements  <cit> .
they are the α class in which proteins contain mainly helices, the β class containing mainly strands, and the other two classes with a mixture of α helices and β strands - the α + β class having β strands mainly antiparallel and the α/β class having β strands mainly parallel.
it is of great value to predict protein structural classes as it is beneficial to study protein function, regulation and interactions.
for instance, the searching scope of conformation will be significantly reduced for proteins whose structural classes are known  <cit> .
a number of methods have been proposed to predict protein structural classes from amino acid sequences  <cit> .
they mainly differ in the selection of feature sets used for prediction.
the most common features are on the basis of the amino acid composition, which generally represent a protein as a twenty-dimensional vector corresponding to the frequencies of twenty amino acids in a given protein amino acid sequence  <cit> .
however, these features ignored the important sequence order information which has been shown beneficial to the predictions.
to overcome this limitation, various new features were developed on the basis of a so-called pseudo amino acid  composition  <cit> , and have been shown very successful in the prediction of protein structural classes  <cit> , especially for high-homology protein datasets.
however, when low-homology datasets with pairwise sequence identity below 40% were tested, these methods were not effective any more.
for instance, for the widely used dataset 25pdb whose sequence homology is about 25%, the reported overall accuracies with these methods were about 60% only  <cit> .
recently, kurgan et al.
<cit>  proposed to extract features from the predicted secondary structure content rather than directly from the protein's amino acid sequence, and reported that the higher prediction accuracy can be consequently achieved, for instance, the overall accuracy of  <dig> % for the dataset 25pdb  <cit> .
in this study, we would like to introduce a new comprehensive feature set that was also constructed from the predicted secondary structure, and demonstrate by experiments on three benchmark datasets that the prediction of protein structural classes can be further improved for low-homology amino acid sequences.
RESULTS
the proposed method
in the first step, we use the tool psipred to predict the protein secondary structure for an amino acid sequence of interest.
then, the chaos game representation is employed to represent a predicted secondary structure as two time series, from which we generate a comprehensive set of  <dig> features using recurrence quantification analysis, k-string based information entropy and segment-based analysis.
the recurrence quantification analysis aims to capture the sequence order information of the time series  <cit> , the k-string based information entropy to reflect certain local interactions along the secondary structure  <cit> , and the segment-based analysis to characterize the spacial arrangements of α helices and β strands .
finally, the resulting 24-dimensional feature vector is fed into a simple yet powerful fisher's discriminant algorithm  <cit>  to make prediction of its protein structural class.
please see the section methods for the details on the feature construction.
a web server that implements the proposed method is freely available at  <cit> .
prediction accuracies for three benchmark datasets
the proposed method is tested on three benchmark datasets in low homology, including 25pdb that comprises  <dig> proteins of about 25% sequence identity,  <dig> that comprises  <dig> proteins of about 25% sequence identity and  <dig> that comprises  <dig> proteins of about 40% sequence identity.
the resulting prediction accuracies are listed in table  <dig>  it can be seen that the overall accuracies for the three datasets are all above 80%.
to be specific, the overall accuracies of  <dig> %,  <dig> % and  <dig> % are achieved for the datasets 25pdb,  <dig> and  <dig>  respectively.
if comparing the four structural classes to each other, the predictions of proteins in the α classes are always the best .
the accuracies are evaluated by jackknife test and measured by the percentage of correctly predicted proteins.
the best results are highlighted in bold face.
we also obtained satisfactory prediction accuracies  for proteins in the β and α/β classes.
however, it seems very challenging to predict proteins in α + β classes as their prediction accuracies are relatively low  when compared with the other classes.
as a previous study pointed out  <cit> , the low prediction accuracy of the α + β class might be due to its non-negligible overlap with the other classes.
comparison with existing methods
the proposed method were compared with ten existing methods  <cit> , and the experimental results are listed in table  <dig>  except for the method scpred  <cit> , the listed accuracy values are taken directly from their respective references.
because some inconsistencies were found between our test dataset 25pdb and the one used in  <cit>  to test scpred , the direct comparison with the accuracy values reported in  <cit>  would not be fair.
therefore, to ensure a fair comparison, we re-implemented the method scpred by following the details presented in the reference paper, trained its classifier with the same version of psipred used for our method, and then applied it to our test dataset 25pdb.
it turns out that, the obtained accuracy values  for predicting proteins in the α, β, α + β and α/β classes are  <dig> %,  <dig> %,  <dig> % and  <dig> %, respectively, giving rise to the improvements of  <dig> %  <dig> % and  <dig> % for the first three classes over those given in the reference paper.
the overall prediction accuracy hence increases by  <dig> % with our test dataset as well.
these new accuracy values are listed in table  <dig>  and we use them as the performance measurements of the method scpred for comparison.
from table  <dig>  we can see that the proposed method achieved the highest overall prediction accuracies among all the tested methods.
by compared to the second highest accuracy values that were obtained with the method scpred, there are improvements of  <dig> %,  <dig> %, and 3% for the three test datasets, respectively.
we also notice that significant improvements were made in particular for the α + β class and the α/β class.
for example, the proposed method obtained the  <dig> % accuracy for predicting proteins of the α/β class from the dataset 25pdb, which is  <dig> % higher than that given by the method scpred.
when the dataset  <dig> is tested, the accuracy for predicting proteins of the α + β class is  <dig> % higher than that given by the method scpred.
bear in mind that both scpred and our proposed method use features that are extracted from the secondary structure predicted with psipred.
the prediction improvements hence clearly indicate that our features are more comprehensive and informative than those used by scpred.
contribution of features
to represent a protein, we used three different approaches to extract features from the predicted secondary structure sequences -- recurrence quantification analysis, k-string based information entropy, and segment-based analysis.
for brevity, let r, k and s denote the feature subsets generated by these three approaches, respectively.
below, we investigate how these feature subsets contribute to the prediction results.
r
k
s
see text for the notations of r, k and s.
differentiating between the α + β and α/β classes
because the segment-based features  are aimed to mainly differentiate between the α + β and α/β classes, it is very interesting to know how effective they are.
to avoid any potential outside effects, we would like to make tests on  datasets that comprise proteins only from the α + β and α/β classes.
for this purpose, we generate a subset for each benchmark dataset by removing all the proteins in the α class or the β class, and then train the classifier  on these reduced subsets instead of the whole datasets.
the datasets comprise only proteins in the α + β and α/β classes.
CONCLUSIONS
to predict structural classes for low-homology protein sequences for which the pairwise sequence identity lies between 20% and 40%, existing methods work very poorly with only relatively low accuracies obtained.
in this paper, we aim to develop a new method so as to improve the prediction accuracy.
to do so, we first use psipred to predict the secondary structure sequence from a given amino acid sequence.
then, the chaos game representation  is employed to represent the predicted secondary structure as two time series, from which a comprehensive set of  <dig> features are generated by three different approaches -- that is, the recurrence quantification analysis, k-string based information entropy, and segment-based analysis.
the resulting feature vectors, each representing one protein, are fed into fisher's discriminant algorithm for the final prediction of protein structural classes.
experimental results showed that all these features can make their own positive and complementary contributions so that higher prediction accuracies are achieved.
for example, to predict structural classes of proteins in the dataset 25pdb, it achieved the accuracies of  <dig> %,  <dig> %,  <dig> % and  <dig> % for the α, β, α + β and α/β classes, respectively, and the overall accuracy of  <dig> %, which is  <dig> % higher than that given by the state-of-the-art method scpred.
by comparisons with ten existing methods, we may attribute the high prediction accuracy of the proposed method to the superior performance of psipred in predicting secondary structures and the comprehensive set of features that we constructed.
the first attribution can be seen from the comparison with the method proposed in  <cit> , which used the secondary structure prediction tool developed in  <cit>  instead of psipred.
a previous study  <cit>  showed that psipred is superior to other competing secondary structure prediction methods.
the second attribution can be seen from the comparison with the method scpred, which differs from our proposed method mainly in the selection of features.
we used three different approaches to extract a comprehensive set of features from the predicted secondary structures, where the recurrence quantification analysis is used to capture the sequence order information of the time series, the k-string based information entropy to reflect certain local interactions along the secondary structure, and the segment-based features to characterize the spacial arrangements of α helices and β strands.
thus, our proposed method may provide a promising tool for the accurate prediction of protein structural classes, in particular for low-homology amino acid sequences.

 the biological function of a protein is essentially associated with its tertiary structure, which is believed to be determined by its amino acid sequence via the process of protein folding. therefore, the prediction of protein's tertiary structure from amino acid sequences is a very important while challenging task in computational biology and proteomics. the tertiary structure can be broadly categorized into four structural classes based on the types and arrangements of their secondary structural elements. they are the α class in which proteins contain mainly helices, the β class containing mainly strands, and the other two classes with a mixture of α helices and β strands - the α + β class having β strands mainly antiparallel and the α/β class having β strands mainly parallel. it is of great value to predict protein structural classes as it is beneficial to study protein function, regulation and interactions. for instance, the searching scope of conformation will be significantly reduced for proteins whose structural classes are known. a number of methods have been proposed to predict protein structural classes from amino acid sequences. they mainly differ in the selection of feature sets used for prediction. the most common features are on the basis of the amino acid composition, which generally represent a protein as a twenty-dimensional vector corresponding to the frequencies of twenty amino acids in a given protein amino acid sequence. however, these features ignored the important sequence order information which has been shown beneficial to the predictions. to overcome this limitation, various new features were developed on the basis of a so-called pseudo amino acid composition, and have been shown very successful in the prediction of protein structural classes, especially for high-homology protein datasets. however, when low-homology datasets with pairwise sequence identity below 40% were tested, these methods were not effective any more. for instance, for the widely used dataset 25pdb whose sequence homology is about 25%, the reported overall accuracies with these methods were about 60% only. recently, kurgan et al. proposed to extract features from the predicted secondary structure content rather than directly from the protein's amino acid sequence, and reported that the higher prediction accuracy can be consequently achieved, for instance, the overall accuracy of % for the dataset 25pdb. in this study, we would like to introduce a new comprehensive feature set that was also constructed from the predicted secondary structure, and demonstrate by experiments on three benchmark datasets that the prediction of protein structural classes can be further improved for low-homology amino acid sequences.  the proposed method in the first step, we use the tool psipred to predict the protein secondary structure for an amino acid sequence of interest. then, the chaos game representation is employed to represent a predicted secondary structure as two time series, from which we generate a comprehensive set of features using recurrence quantification analysis, k-string based information entropy and segment-based analysis. the recurrence quantification analysis aims to capture the sequence order information of the time series, the k-string based information entropy to reflect certain local interactions along the secondary structure, and the segment-based analysis to characterize the spacial arrangements of α helices and β strands. finally, the resulting 24-dimensional feature vector is fed into a simple yet powerful fisher's discriminant algorithm to make prediction of its protein structural class. please see the section methods for the details on the feature construction. a web server that implements the proposed method is freely available at. prediction accuracies for three benchmark datasets the proposed method is tested on three benchmark datasets in low homology, including 25pdb that comprises proteins of about 25% sequence identity, that comprises proteins of about 25% sequence identity and that comprises proteins of about 40% sequence identity. the resulting prediction accuracies are listed in table it can be seen that the overall accuracies for the three datasets are all above 80%. to be specific, the overall accuracies of %, % and % are achieved for the datasets 25pdb, and respectively. if comparing the four structural classes to each other, the predictions of proteins in the α classes are always the best. the accuracies are evaluated by jackknife test and measured by the percentage of correctly predicted proteins. the best results are highlighted in bold face. we also obtained satisfactory prediction accuracies for proteins in the β and α/β classes. however, it seems very challenging to predict proteins in α + β classes as their prediction accuracies are relatively low when compared with the other classes. as a previous study pointed out, the low prediction accuracy of the α + β class might be due to its non-negligible overlap with the other classes. comparison with existing methods the proposed method were compared with ten existing methods, and the experimental results are listed in table except for the method scpred, the listed accuracy values are taken directly from their respective references. because some inconsistencies were found between our test dataset 25pdb and the one used in to test scpred, the direct comparison with the accuracy values reported in would not be fair. therefore, to ensure a fair comparison, we re-implemented the method scpred by following the details presented in the reference paper, trained its classifier with the same version of psipred used for our method, and then applied it to our test dataset 25pdb. it turns out that, the obtained accuracy values for predicting proteins in the α, β, α + β and α/β classes are %, %, % and %, respectively, giving rise to the improvements of % % and % for the first three classes over those given in the reference paper. the overall prediction accuracy hence increases by % with our test dataset as well. these new accuracy values are listed in table and we use them as the performance measurements of the method scpred for comparison. from table we can see that the proposed method achieved the highest overall prediction accuracies among all the tested methods. by compared to the second highest accuracy values that were obtained with the method scpred, there are improvements of %, %, and 3% for the three test datasets, respectively. we also notice that significant improvements were made in particular for the α + β class and the α/β class. for example, the proposed method obtained the % accuracy for predicting proteins of the α/β class from the dataset 25pdb, which is % higher than that given by the method scpred. when the dataset is tested, the accuracy for predicting proteins of the α + β class is % higher than that given by the method scpred. bear in mind that both scpred and our proposed method use features that are extracted from the secondary structure predicted with psipred. the prediction improvements hence clearly indicate that our features are more comprehensive and informative than those used by scpred. contribution of features to represent a protein, we used three different approaches to extract features from the predicted secondary structure sequences -- recurrence quantification analysis, k-string based information entropy, and segment-based analysis. for brevity, let r, k and s denote the feature subsets generated by these three approaches, respectively. below, we investigate how these feature subsets contribute to the prediction results. r k s see text for the notations of r, k and s. differentiating between the α + β and α/β classes because the segment-based features are aimed to mainly differentiate between the α + β and α/β classes, it is very interesting to know how effective they are. to avoid any potential outside effects, we would like to make tests on datasets that comprise proteins only from the α + β and α/β classes. for this purpose, we generate a subset for each benchmark dataset by removing all the proteins in the α class or the β class, and then train the classifier on these reduced subsets instead of the whole datasets. the datasets comprise only proteins in the α + β and α/β classes.  to predict structural classes for low-homology protein sequences for which the pairwise sequence identity lies between 20% and 40%, existing methods work very poorly with only relatively low accuracies obtained. in this paper, we aim to develop a new method so as to improve the prediction accuracy. to do so, we first use psipred to predict the secondary structure sequence from a given amino acid sequence. then, the chaos game representation is employed to represent the predicted secondary structure as two time series, from which a comprehensive set of features are generated by three different approaches -- that is, the recurrence quantification analysis, k-string based information entropy, and segment-based analysis. the resulting feature vectors, each representing one protein, are fed into fisher's discriminant algorithm for the final prediction of protein structural classes. experimental results showed that all these features can make their own positive and complementary contributions so that higher prediction accuracies are achieved. for example, to predict structural classes of proteins in the dataset 25pdb, it achieved the accuracies of %, %, % and % for the α, β, α + β and α/β classes, respectively, and the overall accuracy of %, which is % higher than that given by the state-of-the-art method scpred. by comparisons with ten existing methods, we may attribute the high prediction accuracy of the proposed method to the superior performance of psipred in predicting secondary structures and the comprehensive set of features that we constructed. the first attribution can be seen from the comparison with the method proposed in, which used the secondary structure prediction tool developed in instead of psipred. a previous study showed that psipred is superior to other competing secondary structure prediction methods. the second attribution can be seen from the comparison with the method scpred, which differs from our proposed method mainly in the selection of features. we used three different approaches to extract a comprehensive set of features from the predicted secondary structures, where the recurrence quantification analysis is used to capture the sequence order information of the time series, the k-string based information entropy to reflect certain local interactions along the secondary structure, and the segment-based features to characterize the spacial arrangements of α helices and β strands. thus, our proposed method may provide a promising tool for the accurate prediction of protein structural classes, in particular for low-homology amino acid sequences. 
prediction of protein structural classes from amino acid sequences is of great importance, as it is beneficial to study protein function, regulation and interactions. we propose a new method to predict protein structural classes on the basis of features extracted from the predicted secondary structures of proteins rather than directly from their amino acid sequences. thus, it is a valuable method to predict protein structural classes particularly for low-homology amino acid sequences. the high prediction accuracy achieved by our proposed method is attributed to the design of a comprehensive feature set on the predicted secondary structure sequences, which is capable of characterizing the sequence order information, local interactions of the secondary structural elements, and spacial arrangements of α helices and β strands. we tested the proposed method on three benchmark datasets in low homology and achieved the overall prediction accuracies of %, % and %, respectively. then, the chaos game representation is employed to represent the predicted secondary structure as two time series, from which we generate a comprehensive set of features using recurrence quantification analysis, k-string based information entropy and segment-based analysis. however, for low-homology sequences whose average pairwise sequence identity lies between 20% and 40%, they perform relatively poorly, yielding the prediction accuracy often below 60%. a web server that implements the proposed method is freely available at http://www spms.ntu.edu.sg/~chenxin/rks_ppsc/. many methods have been developed for high-homology protein sequences, and the prediction accuracies can achieve up to 90%. it first uses psipred to predict the secondary structure for each protein sequence. the resulting feature vectors are finally fed into a simple yet powerful fisher's discriminant algorithm for the prediction of protein structural classes.
 prediction of protein structural classes from amino acid sequences is of great importance, as it is beneficial to study protein function, regulation and interactions. many methods have been developed for high-homology protein sequences, and the prediction accuracies can achieve up to 90%. however, for low-homology sequences whose average pairwise sequence identity lies between 20% and 40%, they perform relatively poorly, yielding the prediction accuracy often below 60%.  we propose a new method to predict protein structural classes on the basis of features extracted from the predicted secondary structures of proteins rather than directly from their amino acid sequences. it first uses psipred to predict the secondary structure for each protein sequence. then, the chaos game representation is employed to represent the predicted secondary structure as two time series, from which we generate a comprehensive set of features using recurrence quantification analysis, k-string based information entropy and segment-based analysis. the resulting feature vectors are finally fed into a simple yet powerful fisher's discriminant algorithm for the prediction of protein structural classes. we tested the proposed method on three benchmark datasets in low homology and achieved the overall prediction accuracies of %, % and %, respectively. comparisons with ten existing methods showed that our method consistently performs better for all the tested datasets and the overall accuracy improvements range from % to %. a web server that implements the proposed method is freely available at http://www spms.ntu.edu.sg/~chenxin/rks_ppsc/.  the high prediction accuracy achieved by our proposed method is attributed to the design of a comprehensive feature set on the predicted secondary structure sequences, which is capable of characterizing the sequence order information, local interactions of the secondary structural elements, and spacial arrangements of α helices and β strands. thus, it is a valuable method to predict protein structural classes particularly for low-homology amino acid sequences. 18- january the eighth asia pacific bioinformatics conference bangalore, india 