BACKGROUND
secondary protein structure information provides useful input for a wide range of applications including prediction of solvent accessibility  <cit> , fold type  <cit> , folding rate  <cit> , beta-turns  <cit> , alpha-turns  <cit> , contact order  <cit> , tertiary structure  <cit> , and in fold recognition  <cit> .
the secondary structures include helices, strands, tight turns, bulges, and random coils structures.
helices and strands are repetitive motifs that stabilize the protein structure and which are classified as regular secondary structures.
the remaining secondary structures, which are generally designated as random coil regions, are non-repetitive motifs that are regarded as irregular secondary structures  <cit> .
the tight turns can be further divided into α-, β-, γ-, δ-, and π-turns depending on the number of the constituent residues.
the β-turns consist of four consecutive residues.
the distance between the first, ith, and the last, ith+ <dig>  residue in a β-turn must be less than  <dig> Å  <cit> .
this distance implies a particular geometry of the corresponding backbone, which turns back on itself or, more generally, which corresponds to a change of direction.
the β-turns are usually described as orienting structure because they orient α-helices, β-sheets, indirectly defining the topology of proteins.
they are one of the most abundant secondary structures, i.e., on average about 25% residues in all protein chains form β-turns  <cit> .
the β-turns play several significant biological roles in proteins and peptides.
they tend to be more solvent exposed than buried and as a result they were found helpful in the context of molecular recognition and in modeling interactions between peptide substrates and receptors  <cit> .
β-turns are also involved in the biological activity of peptides as the bioactive structures that interact with other molecules such as receptors, enzymes, or antibodies.
recent years have seen interest in mimicking β-turns for the synthesis of medicines  <cit> .
formation of β-turns is also a vital stage during the process of protein folding  <cit> .
as a result, development of accurate prediction methods to identify β-turns in protein sequences would provide valuable insights and inputs for the fold recognition and drug design.
the β-turn prediction methods can be divided into those based on statistics and based on machine learning.
statistical methods utilize probabilities computed using information concerning preferences of individual amino acid types at each position in β-turns.
they include chou-fasman method  <cit> , thornton's algorithm  <cit> , gorbturn  <cit> , 1– <dig> & 2– <dig> correlation model  <cit> , sequence-coupled model  <cit> , and coudes method  <cit> .
the first five methods use the sequence as the input, while the coudes is based on propensities of individual residues augmented with the multiple alignment.
the position-specific scoring matrix , which is calculated with psi-blast  <cit> , was used to weigh propensities for a given residue, so that all the residues present in the multiple alignment at this position are taken into account.
secondary structure predicted by psipred  <cit> , sspro <dig>  <cit> , and prof  <cit>  and the flanking residues around the β-turn tetrapeptide were also utilized by coudes to improve the prediction accuracy.
machine learning based methods include btpred  <cit> , betatpred <dig>  <cit> , and molebrnn  <cit>  which are based on artificial neural networks , kim's method  <cit>  which utilizes k-nearest neighbor , and four methods based on support vector machines   <cit> .
btpred encodes the sequence using a large window of  <dig> residues centered over the predicted residue together with secondary structure predicted with phdsec  <cit>  for the central  residue to perform predictions.
betatpred <dig> is an improved neural network design, in which two networks are used.
the molebrnn is based on a bidirectional elman-type recurrent neural network and uses pssm profiles as the input.
the latter method predicts β-turns and their types.
in kim's method, the protein sequence encoded using a window of up to  <dig> residues is used as the input to knn, which is combined with a filter that uses secondary structure predicted with psipred for the central residue.
the btsvm method by pham and colleagues  applies position-specific frequent matrix  and pssm, both computed with psi-blast, to encode input for svm classifier  <cit> .
the svm based method proposed by zhang and colleagues  <cit>  uses pssm over a 7-residue window and the secondary structure of the central residue predicted by psipred as the input.
both, this method and kim's method also utilize a filtering stage based on 'state-flipping' rules  <cit> .
the newest smv-based predictor that was developed by hu and li combines the increment of diversity, position conservation scoring function, and secondary structures predicted with psipred to compute the inputs for prediction of β-turns and γ-turns  <cit> .
performance of six β-turn prediction methods, including chou-fasman method, thornton's method, 1– <dig> & 2– <dig> correlation, sequence-coupled method, gorbturn, and btpred was compared using a benchmark database of  <dig> nonredundant  proteins  <cit> .
this dataset was later used to compare and evaluate the subsequently proposed methods and is also adopted in this work.
we observe that although information coming from the sequence  was encoded using a window, the existing methods did not use the window when processing information coming from the predicted secondary structure.
moreover, the existing methods apply only one predicted secondary structure at the time, when different predictors are shown to provide complementary predictions  <cit> .
to this end, we combine the pssm values with information obtained by utilizing an ensemble of four secondary structure prediction methods that was processed using a window to improve the β-turn predictions.
we also perform feature selection that allows identifying which information  is useful for the predictions.
our main goal is to create a prediction model that improves the overall prediction accuracy, qtotal.
the highest reported qtotal obtained based on the cross-validation on the benchmark dataset of  <dig> sequences equals  <dig> %  <cit> .
since 25% of residues are β-turns, the above result translates in just  <dig> / <dig> = 19% error rate reduction over a naïve method that would classify all residues as not β-turns.
we note that the percentage of correct predictions among all predicted β-turns, qpredicted, that is reported for the existing methods ranges between  <dig>  and 56%.
this means that about half or more of the residues predicted as β-turns are in fact not β-turns.
to this end, our goal is also to provide prediction method characterized by low false positive predictions that would correspond to higher qpredicted values, when providing favorable qtotal values.
methods
datasets
we apply three different nonredundant protein databases, which were proposed in  <cit> , to validate the proposed method.
the dataset of  <dig> protein sequences , which was developed by guruprasad and rajkumar   <cit> , is the most widely used benchmark dataset.
the two other datasets contain  <dig>  and  <dig>  protein sequences.
they were constructed using pdbselect list published in june  <dig> and october  <dig>  <cit> , respectively, by fuchs and alix   <cit> .
the three datasets share several characteristics, such as that the β-turns are assigned using promotif  <cit> , the pairwise sequence identity between any two protein chains is below 25%, the protein structure is determined by x-ray crystallography with at least  <dig>  Å resolution, and that each chain contains at least one β-turn.
the total number of residues in the bt <dig>  bt <dig>  and bt <dig> datasets equals  <dig>   <dig>  and  <dig>  respectively.
to facilitate computationally expensive parameterization of the classifier and feature selection that were performed in this paper we created another, smaller dataset.
we selected three out of the predefined seven folds in the bt <dig> dataset  <cit> , and in each of these three folds we randomly selected 20% of residues; the corresponding dataset is named bt426- <dig>  we note that the parameterization with the bt426- <dig> dataset is equivalent to the parameterizations performed by the competing methods, which was based on the original bt <dig> dataset, i.e., the same division into training and test sets is used.
design of the proposed prediction method
the overall architecture of the proposed system is shown in figure  <dig>  the protein sequence is converted into a feature vector that incorporates information from the pssm matrix generated with psi-blast  <cit>  and secondary structure predicted with four prediction methods  <cit> .
the feature vector, which is computed using a window over the pssm and the predicted secondary structures that is centered on the predicted residue, is fed into support vector machine classifier to compute the predictions.
feature vector
the pssm indicates whether a given residue in the query sequence is conserved  <cit> .
since the conservation is usually indicative of the formation of repetitive motifs such as the secondary structures, this information was found useful in prediction of β-turns  <cit> .
the pssm is computed using multiple alignment that requires use of a window, and thus the input of the above β-turn predictors was also encoded using a window.
the pssm, which is a matrix of  <dig> × m elements, where m is the size of the window, was generated with the psi-blast  <cit>  against the nr  ncbi database  <cit>  using default parameters.
similarly as in  <cit> , standard logistic function was used to normalize the pssm values to < <dig>  1> interval.
a sliding window of seven residues, i.e., m =  <dig>  was used to extract features from the pssm, and the matrix was filled with 0's for positions outside of the sequence, i.e., where the window is located at the sequence termini.
the size of  <dig> is sufficient to account for the coupling effect of residues within β-turns since the turns involve  <dig> residues and thus they should not stretch beyond ith+ <dig> and ith- <dig> positions, where the ith position corresponds to the center of the window.
the size of  <dig> or  <dig> was reported by shepherd et al.
to achieve the best predictions with btpred  <cit>  and the two most recent svm based methods also apply 7-residue window  <cit> .
four secondary structure prediction methods, psipred v <dig>   <cit> , jnet  <cit> , transsec  <cit>  and proteus <dig>  <cit>  were employed to produce features.
the motivation to use psipred comes from the work of the authors of the coudes β-turn predictor, which concluded that predictions when using psipred were better than when using sspro <dig> and prof secondary structure prediction methods  <cit> .
this also motivated exclusion of the two latter secondary structure prediction methods.
we note that psipred was used to predict β-turns in several other methods  <cit> .
proteus <dig> is a recently developed secondary structure prediction method that was selected due to its reported favorable performance when compared with eight competing secondary structure predictors  <cit> .
the main reason to select the other two methods was their unique architectural design that could potentially lead to generation of complementary predictions.
transsec uses two-tier neural network architecture in which the first network is fed with multiple alignment generated with psi-blast and the second network operates on the secondary structure determined via the first network  <cit> .
jnet utilizes a consensus neural network design, in which several different multiple sequence alignment profiles  are combined using a "jury" neural network.
the four secondary structure prediction methods output the 3-state, i.e., helix , strand , and coil , predictions and the confidence score with values between  <dig> and  <dig>  these values together with the normalized pssm scores over the  <dig> residues window were used to compute the following  <dig> features for each predicted residue:
- pssmij is the normalized pssm value where i =  <dig>   <dig>  ...,  <dig> denotes the position in the sliding window and j =  <dig>   <dig>  ...,  <dig> denotes the position in the pssm .
we assume pssm values of  <dig> for the positions in the window that are outside of the sequence.
- sspk is a binary value denoting the prediction of a given secondary structure method for the central residue, where ssp = {psi , jne , tra , pro } and k = {c, e, h} denotes the predicted secondary structure .
- scoressp = confidence score/ <dig> is the confidence value  obtained for the central residue by the ssp prediction method .
- 3patternm, k, ssp is a binary value denoting a specific configuration of the secondary structure predicted with ssp method for the central and the two adjacent residues where m =  <dig>   <dig>   <dig>   <dig> denotes a pattern type.
for m =  <dig> and k = c the secondary structure prediction would be ccc, and for m =  <dig>   <dig>  and  <dig> the prediction would be ccx, xcc, and xcx, respectively, where x = {e, h}.
we assume coils for the positions outside of the sequence, i.e., when computing at the sequence termini.
the total number of these features equals  <dig> .
they encode whether the central  residue is located inside a secondary structure segment or at the interface between two segments.
- contentk, ssp is the content of the secondary structure k predicted with method ssp over a  <dig> residues window .
the content is defined as the ratio between the number of residues in a given secondary structure and the window size.
the window size is shortened when the central residue is at the termini of the sequence.
the first two feature sets are consistent with the inputs used by the competing prediction methods  <cit> , except that sspk is computed for four  secondary structure prediction methods.
the latter three feature sets are proposed in this paper in an attempt to incorporate window based information concerning the predicted secondary structure and the confidence scores that are provided together with the predictions.
prediction method
the support vector machine   <cit>  classifier was applied to predict β-turns.
given a training set of data point pairs , i =  <dig>   <dig>  ... n, where xi denotes the feature vector, ci ={- <dig>  1} denotes binary class label , n is the number of training data points, finding the optimal svm is achieved by solving:
min⁡‖w‖2+c∑iξisuch thatci≥1−ξi and 1≤i≤n
where w is a vector perpendicular to wx - b =  <dig> hyperplane that separates the two classes, c is a user defined complexity constant, ξi are slack variables that measure the degree of misclassification of xi for a given hyperplane, b is an offset that defines the size of a margin that separates the two classes, and z = φ where k = φ·φ is a user defined kernel function.
the svm classifier was trained using platt's sequential minimal optimization algorithm  <cit> , which was optimized by keerthi et al   <cit> .
the radial basis functions  was used as kernel function
k=e−γ‖x−x'‖ <dig>
where γ is the user defined constant.
the svm classification algorithm and feature selection algorithms  used to build and test our prediction method were implemented in weka  <cit> .
the selection of the classifier and the kernel type was motivated by the best β-turn predictions reported to date on the bt <dig> dataset that were obtained using rbf-kernel based svm classifier  <cit> .
the proposed classifier is parameterized, i.e., the values of c and γ are selected, based on the procedure described in the next section.
features selection and parameterization of svm
since total of  <dig> features were generated for each predicted residue and we expect that some of them would not contribute to the prediction, a feature selection was performed to reduce the dimensionality.
this allows for reduction of the time necessary to compute the prediction model and for finding and discussing which of the proposed features are related to the prediction of β-turns.
three feature selection approaches were employed.
the first, hybrid approach combines the information-gain   <cit>  and the chi-squared   <cit>  feature selection methods.
the two methods were selected based on their successful application in  <cit>  and  <cit> , respectively, where they were used to rank protein sequence based features.
we also applied a filter-based feature selection method which removes features based on the inconsistency criterion  <cit>  and a wrapper-based algorithm  <cit>  that applies flexible naïve bayes classifier  <cit> .
in the case of the filter-based and the wrapper-based methods, we used best first search that starts with empty set of features to search through possible subsets of features.
the selection of this search method and the selection of the flexible naïve bayes to evaluate feature sets in the wrapper-based method were motivated by their good scalability, which was necessary due to the large size of the datasets, i.e., the search method is linear with respect to the number of features and the naïve bayes is linear with respect to the number of data points.
in the hybrid feature selection , we used two different selection methods to reduce bias introduced by each of the methods.
in both algorithms, each feature is ranked based on its merit , and next they were sorted by their average rank across the two algorithms.
the measurement of the merit for the two selection methods is defined below.
ig measures the decrease in entropy when a given feature is used to group values of another feature.
the entropy of a feature x is defined as:
h=−∑iplog⁡2)
where {xi} is a set of values of x and p is the prior probability of xi.
the conditional entropy of x, given another feature y  is defined as:
h=−∑jp∑iplog⁡2)
where p is the posterior probability of x given the value yi of y. the amount by which the entropy of x decreases reflects additional information about x provided by y and is called information gain
ig = h - h
according to this measure, y has stronger correlation with x than with z if ig > ig.
chi method is based on a common statistical test that measures divergence from the expected distribution assuming that the occurrence of a given feature is independent of the class value.
let x be a discrete random variable  with m =  <dig> possible outcomes x <dig> = β-turn, x <dig> = non β-turn, and with probability of each outcome p = pi.
pearson-chi-squared statistic is defined as:
χ2=∑i=1m2npi
where ni is the number of instances which will result the outcome xi.
a feature that obtains higher χ value receives lower rank.
to avoid overfitting, the  <dig> features were ranked on the bt <dig> dataset using 7-fold cross validation.
in the case of the hybrid method, the average ranks  were computed for each of the  <dig> training datasets separately, and next they were averaged over the  <dig> datasets.
after the features are ranked, we performed β-turn prediction in order to decide how many of the features should be kept.
this was performed in two steps.
first, we selected the top  <dig> features to perform parameterization of the svm classifier.
next, we used the parameterized svm to select the desired number of features.
in step  <dig> we perform greedy search for optimal c and γ parameters:
- we freeze c =  <dig> and find the optimal γ based on 3-fold cross validation on the bt426- <dig> dataset using the top  <dig> features, see figure 2a.
we observe that highest accuracy  is achieved for γ equal  <dig>  or  <dig> .
the optimal γ =  <dig>  is the same as the value used in  <cit> .
- next, we use the γ =  <dig>  and we optimize c, see figure 2b.
the best accuracy is achieved for c =  <dig>
we did not apply the grid-based parameterization, which could potentially lead to better parameters, since this would be computationally expensive and since figure  <dig> shows that the svm is not sensitive to the parameters, i.e., the qtotal values change by only up to  <dig> % by varying γ and c.
in the second step, the svm classifier with the optimized parameters  was used to select the desired number of the top ranked features.
the selection was again based on 3-fold cross validation on the bt426- <dig> dataset, see figure  <dig>  the results show that selection of the top  <dig> features provides the best accuracy, although we note that the differences are relatively small.
this indicates that only a small fraction of the original features is necessary to provide accurate β-turn predictions.
since the wrapper- and filter-based feature selections directly select a set of features, rather than ranking the features as it is done by the hybrid method, there was no need to decide how many features should be kept.
instead, each method was used to select a set of features for each of the  <dig> training folds from the bt <dig> dataset, and next these features were combined together.
this resulted in selection of  <dig> and  <dig> features in the case of the filter-based and wrapper-based algorithms, respectively.
these two feature sets were used with svm parameterized using the above procedure where the top  <dig> ranked features were applied.
we did not re-parameterize the svm for the other two sets of features because the above parameterization shows that the svm is not sensitive to the parameters, the  <dig> features used in the parameterization overlap with features used in the other two sets, and since such parameterization is computationally expensive.
evaluation procedure and measures
7-fold cross validation was used to perform tests on the three datasets .
the folds were created by randomly selecting equal number of sequences.
the quality of prediction is evaluated using four measures, qtotal, qpredicted, qobserved, and mcc.
this is consistent with the test procedures and measures applied to evaluate modern competing methods  <cit> .
given that tp  is the number of correctly classified β-turn residues, tn  is the number of correctly classified non-β-turn residues, fp  if the number of non-β-turn incorrectly classified as β-turn residues, and fn  is the number of β-turn incorrectly classified as non-β-turn residues, qtotal  is defined as the percentage of correctly classified residues.
qtotal=tp+tntp+tn+fp+fn× <dig>
probability of correct prediction, qpredicted, is the percentage of correctly predicted β-turns among the predicted β-turns
qpredicted=tptp+fp× <dig>
sensitivity or coverage, qobserved, is the percentage of correctly predicted β-turns among the observed  β-turns
qobserved=tptp+fn× <dig>
we observe that approximately 24% to  <dig> % β-turn residues are observed in the three datasets, and therefore qtotal = 75%  could be obtained by merely regarding all residues as non β-turns.
therefore, qtotal values can result in misleading information , which was pointed out in  <cit> .
this is especially evident when tn values are large, compared to tp, fn, and fp values.
as a result matthews correlation coefficient  is computed
mcc=tp×tn−fp×fn×××× <dig>
the value of mcc is confined to <- <dig> > interval.
if the mcc value is close to  <dig> then the prediction method is not better than a random classification.
higher mcc value corresponds to better performance of the prediction method.
we also report receiver-operator characteristics  curves that present a graphical plot of the tp rate = qobserved against fp rate = fp/.
RESULTS
comparison of different feature selection strategies
the three employed feature selection methods produce different feature sets which are summarized in figure  <dig>  in all three cases majority of the features are based on pssm.
among the features that are computed from the predicted secondary structures, the largest fraction is derived from the structures predicted by proteus <dig>  we also observe that all four predicted secondary structures are used to derive features in each of the feature sets.
this consistency supports the need for multiple predicted secondary structures.
each of the three set of features was used as the input to the optimized svm classifier with c =  <dig> and γ =  <dig>  to perform prediction of β-turns.
the evaluation of the quality of these predictions was performed based on 7-fold cross validation on the bt <dig> datasets, see table  <dig>  the table shows that usage of the  <dig> features selected using the hybrid methods results in the highest mcc value.
these features also lead to the highest qobserved and qtotal.
at the same time, we note that the features selected using the filter-based method correspond to the highest qpredicted value.
we observe that the differences are relatively small as all three designs provide the accuracy which is close to 80%.
the roc curves shown in figure  <dig> allow for a more detailed analysis of the differences.
the  <dig> features generated by the hybrid method are shown to provide favorable prediction quality for low values of ft rate , while the  <dig> features based sequence representation developed with wrapper-based method provides higher tp rate for the higher values of the fp rate.
the most interesting part of the curves corresponds to relative high tp rates that are coupled with low values of fp rate.
since the ratio of positive to negative samples is 1: <dig>  the ratio between the true positives and false positives would be even at fp rate of approximately  <dig> .
for higher fp rate, the number of false positives would be higher than the number of true positives.
as a result, we conclude that the  <dig> features provide better predictions than the other two feature sets and this feature set is used to build the proposed prediction method.
the tests are based on  <dig> fold cross validation on the bt <dig> dataset
comparison with competing prediction methods
the  <dig> selected features and svm with c =  <dig> and γ =  <dig>  were applied in the proposed prediction model.
the 7-fold cross validation test results on the bt <dig> dataset are summarized and compared with over a dozen of competing methods in table 2; the results are organized in the descending order by the values of mcc.
<dig> results reported on a different dataset with  <dig> chains.
we investigate the impact of the proposed features extracted from the predicted secondary structure on the prediction quality.
when excluding the  <dig> features that are based on pssm , the predictions performed with the remaining  <dig> secondary-structure features are characterized by qtotal =  <dig> %, qpredicted =  <dig> %, qobserved =  <dig> , and mcc =  <dig> .
although removal of the pssm features results in slightly worse predictions, we observe that the features computed from the predicted secondary structures provide valuable input.
we also experimented with the design in which only one of the four secondary structure predictions is used.
we used output of the proteus <dig> that is characterized by a favorable performance when compared with the other three secondary structure prediction methods  <cit> .
the predictions that use only the  <dig> pssm based features and  <dig> features generated from secondary structure predicted by proteus result in qtotal =  <dig> %, qpredicted =  <dig> %, qobserved =  <dig> , and mcc =  <dig> .
we observe that these results are again slightly worse than the results obtained with the proposed method; the usage of all  <dig> features improves qtotal, qpredicted, and mcc.
the simplified architecture that uses only one predicted secondary structure is equivalent to the design of the recent method by zhang and colleagues  <cit> .
we note that our results are better than the results of this method, i.e., qtotal =  <dig> % vs. qtotal =  <dig> %, which stems from using different secondary structure prediction method and the novel features.
our method uses features computed from a window over the predicted secondary structure, while the zhang's method uses only the secondary structure of the predicted residue.
results obtained based on the 7-fold cross validation with the bt <dig> and bt <dig> datasets are given in table  <dig>  they show that for the bt <dig> dataset the proposed method obtains  <dig> % higher qtotal, 2% higher mcc, 14% better qpredicted, and 16% lower qobserved when compared with the second-best svm based method  <cit> .
similarly, for the bt <dig> dataset, our method obtains  <dig> % and  <dig> % increase in qtotal and qpredicted, respectively, and  <dig> % decrease in qobserved.
we observe that the proposed method obtains consistent  quality of predictions for all three datasets.
the qtotal values range between  <dig> % and  <dig> %, qpredicted values range between  <dig> % and  <dig> %, qobserved between  <dig> % and  <dig> %, and mcc between  <dig>  and  <dig> , see tables  <dig> and  <dig>  this rules out possibility of overfitting the bt <dig> dataset due to the performed design.
the tests are based on the  <dig> fold cross validation test on the bt <dig> and bt <dig> datasets
analysis of the proposed feature based sequence representation
the proposed method applies  <dig> features, which constitutes 86% reduction of the dimensionality of the input vector when compared with the method by hu and li  that applies  <dig> features .
the dimensionality reduction of 62% and 37% is achieved when compared with the two third-best performing, i.e., with the third best mcc value, svm-based predictors by pham and colleagues , which uses  <dig> features   <cit> , and the method by zhang and coworkers  that applies  <dig> features , respectively.
the top  <dig> ranked features that were used to implement the proposed prediction method are shown in table  <dig>  we observe that  <dig> out of  <dig> features are the newly proposed features, which are based on the sliding window over the secondary structure predicted by three prediction methods, proteus <dig>  <cit> , psipred  <cit> , and jnet  <cit> .
the remaining  <dig> features concern the predicted secondary structure for the predicted residue.
<dig> out of  <dig> features are computed using the predicted coils, while the remaining  <dig> concern predicted helices.
the former is likely due to β-turns being a coil subtype and due to the favorable accuracy that the secondary structure prediction methods obtain for coils and helices when compared with the accuracy for strands  <cit> .
we note that  <dig> out of  <dig> features are extracted from the predictions performed with proteus <dig>  which confirms high quality of this method.
finally, table  <dig> reveals the top  <dig> features were based on the predicted secondary structure, i.e., none of them was based on pssm  <cit> , which signifies the novelty of the proposed approach.
furthermore, we analyzed the composition of the top  <dig> selected features.
the highest scoring pssmij feature was ranked  <dig> and total of  <dig> out of  <dig> features were derived from the pssm.
among the remaining  <dig> features,  <dig> concern structure predicted for the central residue ,  <dig> concern the prediction confidence score for the central residue ,  <dig> are based on the  <dig> residue window pattern over the predicted secondary structure , and  <dig> concern secondary structure content over the  <dig> residue window .
this shows that all proposed feature sets were utilized to perform the prediction.
CONCLUSIONS
we propose a novel method for the prediction of β-turns that uses features extracted from a window over the three-state secondary structure predicted by an ensemble of four methods.
we use feature selection to reduce the dimensionality of the proposed feature vector.
the proposed feature set is smaller by  <dig> to 86% when compared with the best performing competing methods.
the analysis of the selected features reveals that:
- information from all four predicted secondary structures is useful for the prediction of β-turns,
- the most useful information extracted from the predicted three-state secondary structure are the structure of the predicted residue, content of the secondary structures over  <dig> residues window centered on the predicted residue, and features that indicate whether the predicted residue is inside a secondary structure segment,
- pssm values of asn , asp , gly , ile , leu , met , pro , and val , were among the top ranked features; similar conclusions, i.e., high potential of asn, asp, gly, and pro, and low potential of ile, leu, met, and val, to form β-turns were shown in  <cit> .
in our case, asn, asp, gly, and pro are likely associated with potential β-turns, while the remaining four amino acids predict non β-turns.
empirical evaluation using three nonredundant datasets shows that our predictions provide favorable qtotal, qpredicted, and mcc values when compared with over a dozen of modern competing methods.
our method is the first to break the 80% qtotal barrier and is characterized by  <dig> % qtotal,  <dig>  mcc, and qpredicted higher by over 6% when compared with the second best method using a benchmark dataset of  <dig> nonredundant sequences.
this shows that our method not only constitutes an improvement over the competition, but also that the proposed prediction model can better discriminate between β-turns and non β-turns since it generates lower numbers of false positive predictions.
abbreviations
ann: artificial neural networks; chi: chi-squared; fn: false negatives; fp: false positives; ig: information-gain; knn: k-nearest neighbor; mcc: matthews correlation coefficient; pdb: protein data bank; psfm: position specific frequent matrix; pssm: position specific scoring matrix; roc: receiver-operator characteristics; svm: support vector machine; tn: true negatives; tp: true positives.
authors' contributions
cz helped with the preparation of the datasets, computed the features, performed feature selection, generated the prediction model, performed experimental comparison, and helped with evaluation of the results.
lk contributed to the conception and design of the prediction method, helped with the preparation of the datasets, designed the experimental study, helped with the evaluation of the results, prepared the revision, drafted the manuscript, and coordinated the project.
both authors have corrected and approved the manuscript.

 secondary protein structure information provides useful input for a wide range of applications including prediction of solvent accessibility, fold type, folding rate, beta-turns, alpha-turns, contact order, tertiary structure, and in fold recognition. the secondary structures include helices, strands, tight turns, bulges, and random coils structures. helices and strands are repetitive motifs that stabilize the protein structure and which are classified as regular secondary structures. the remaining secondary structures, which are generally designated as random coil regions, are non-repetitive motifs that are regarded as irregular secondary structures. the tight turns can be further divided into α-, β-, γ-, δ-, and π-turns depending on the number of the constituent residues. the β-turns consist of four consecutive residues. the distance between the first, ith, and the last, ith+ residue in a β-turn must be less than Å. this distance implies a particular geometry of the corresponding backbone, which turns back on itself or, more generally, which corresponds to a change of direction. the β-turns are usually described as orienting structure because they orient α-helices, β-sheets, indirectly defining the topology of proteins. they are one of the most abundant secondary structures, i.e., on average about 25% residues in all protein chains form β-turns. the β-turns play several significant biological roles in proteins and peptides. they tend to be more solvent exposed than buried and as a result they were found helpful in the context of molecular recognition and in modeling interactions between peptide substrates and receptors. β-turns are also involved in the biological activity of peptides as the bioactive structures that interact with other molecules such as receptors, enzymes, or antibodies. recent years have seen interest in mimicking β-turns for the synthesis of medicines. formation of β-turns is also a vital stage during the process of protein folding. as a result, development of accurate prediction methods to identify β-turns in protein sequences would provide valuable insights and inputs for the fold recognition and drug design. the β-turn prediction methods can be divided into those based on statistics and based on machine learning. statistical methods utilize probabilities computed using information concerning preferences of individual amino acid types at each position in β-turns. they include chou-fasman method, thornton's algorithm, gorbturn, 1– & 2– correlation model, sequence-coupled model, and coudes method. the first five methods use the sequence as the input, while the coudes is based on propensities of individual residues augmented with the multiple alignment. the position-specific scoring matrix, which is calculated with psi-blast, was used to weigh propensities for a given residue, so that all the residues present in the multiple alignment at this position are taken into account. secondary structure predicted by psipred, sspro, and prof and the flanking residues around the β-turn tetrapeptide were also utilized by coudes to improve the prediction accuracy. machine learning based methods include btpred, betatpred, and molebrnn which are based on artificial neural networks, kim's method which utilizes k-nearest neighbor, and four methods based on support vector machines. btpred encodes the sequence using a large window of residues centered over the predicted residue together with secondary structure predicted with phdsec for the central residue to perform predictions. betatpred is an improved neural network design, in which two networks are used. the molebrnn is based on a bidirectional elman-type recurrent neural network and uses pssm profiles as the input. the latter method predicts β-turns and their types. in kim's method, the protein sequence encoded using a window of up to residues is used as the input to knn, which is combined with a filter that uses secondary structure predicted with psipred for the central residue. the btsvm method by pham and colleagues applies position-specific frequent matrix and pssm, both computed with psi-blast, to encode input for svm classifier. the svm based method proposed by zhang and colleagues uses pssm over a 7-residue window and the secondary structure of the central residue predicted by psipred as the input. both, this method and kim's method also utilize a filtering stage based on'state-flipping' rules. the newest smv-based predictor that was developed by hu and li combines the increment of diversity, position conservation scoring function, and secondary structures predicted with psipred to compute the inputs for prediction of β-turns and γ-turns. performance of six β-turn prediction methods, including chou-fasman method, thornton's method, 1– & 2– correlation, sequence-coupled method, gorbturn, and btpred was compared using a benchmark database of nonredundant proteins. this dataset was later used to compare and evaluate the subsequently proposed methods and is also adopted in this work. we observe that although information coming from the sequence was encoded using a window, the existing methods did not use the window when processing information coming from the predicted secondary structure. moreover, the existing methods apply only one predicted secondary structure at the time, when different predictors are shown to provide complementary predictions. to this end, we combine the pssm values with information obtained by utilizing an ensemble of four secondary structure prediction methods that was processed using a window to improve the β-turn predictions. we also perform feature selection that allows identifying which information is useful for the predictions. our main goal is to create a prediction model that improves the overall prediction accuracy, qtotal. the highest reported qtotal obtained based on the cross-validation on the benchmark dataset of sequences equals %. since 25% of residues are β-turns, the above result translates in just / = 19% error rate reduction over a naïve method that would classify all residues as not β-turns. we note that the percentage of correct predictions among all predicted β-turns, qpredicted, that is reported for the existing methods ranges between and 56%. this means that about half or more of the residues predicted as β-turns are in fact not β-turns. to this end, our goal is also to provide prediction method characterized by low false positive predictions that would correspond to higher qpredicted values, when providing favorable qtotal values. methods datasets we apply three different nonredundant protein databases, which were proposed in, to validate the proposed method. the dataset of protein sequences, which was developed by guruprasad and rajkumar, is the most widely used benchmark dataset. the two other datasets contain and protein sequences. they were constructed using pdbselect list published in june and october, respectively, by fuchs and alix. the three datasets share several characteristics, such as that the β-turns are assigned using promotif, the pairwise sequence identity between any two protein chains is below 25%, the protein structure is determined by x-ray crystallography with at least Å resolution, and that each chain contains at least one β-turn. the total number of residues in the bt bt and bt datasets equals and respectively. to facilitate computationally expensive parameterization of the classifier and feature selection that were performed in this paper we created another, smaller dataset. we selected three out of the predefined seven folds in the bt dataset, and in each of these three folds we randomly selected 20% of residues; the corresponding dataset is named bt426- we note that the parameterization with the bt426- dataset is equivalent to the parameterizations performed by the competing methods, which was based on the original bt dataset, i.e., the same division into training and test sets is used. design of the proposed prediction method the overall architecture of the proposed system is shown in figure the protein sequence is converted into a feature vector that incorporates information from the pssm matrix generated with psi-blast and secondary structure predicted with four prediction methods. the feature vector, which is computed using a window over the pssm and the predicted secondary structures that is centered on the predicted residue, is fed into support vector machine classifier to compute the predictions. feature vector the pssm indicates whether a given residue in the query sequence is conserved. since the conservation is usually indicative of the formation of repetitive motifs such as the secondary structures, this information was found useful in prediction of β-turns. the pssm is computed using multiple alignment that requires use of a window, and thus the input of the above β-turn predictors was also encoded using a window. the pssm, which is a matrix of × m elements, where m is the size of the window, was generated with the psi-blast against the nr ncbi database using default parameters. similarly as in, standard logistic function was used to normalize the pssm values to < 1> interval. a sliding window of seven residues, i.e., m = was used to extract features from the pssm, and the matrix was filled with 0's for positions outside of the sequence, i.e., where the window is located at the sequence termini. the size of is sufficient to account for the coupling effect of residues within β-turns since the turns involve residues and thus they should not stretch beyond ith+ and ith- positions, where the ith position corresponds to the center of the window. the size of or was reported by shepherd et al. to achieve the best predictions with btpred and the two most recent svm based methods also apply 7-residue window. four secondary structure prediction methods, psipred v, jnet, transsec and proteus were employed to produce features. the motivation to use psipred comes from the work of the authors of the coudes β-turn predictor, which concluded that predictions when using psipred were better than when using sspro and prof secondary structure prediction methods. this also motivated exclusion of the two latter secondary structure prediction methods. we note that psipred was used to predict β-turns in several other methods. proteus is a recently developed secondary structure prediction method that was selected due to its reported favorable performance when compared with eight competing secondary structure predictors. the main reason to select the other two methods was their unique architectural design that could potentially lead to generation of complementary predictions. transsec uses two-tier neural network architecture in which the first network is fed with multiple alignment generated with psi-blast and the second network operates on the secondary structure determined via the first network. jnet utilizes a consensus neural network design, in which several different multiple sequence alignment profiles are combined using a "jury" neural network. the four secondary structure prediction methods output the 3-state, i.e., helix, strand, and coil, predictions and the confidence score with values between and these values together with the normalized pssm scores over the residues window were used to compute the following features for each predicted residue: - pssmij is the normalized pssm value where i =..., denotes the position in the sliding window and j =..., denotes the position in the pssm. we assume pssm values of for the positions in the window that are outside of the sequence. - sspk is a binary value denoting the prediction of a given secondary structure method for the central residue, where ssp = {psi, jne, tra, pro } and k = {c, e, h} denotes the predicted secondary structure. - scoressp = confidence score/ is the confidence value obtained for the central residue by the ssp prediction method. - 3patternm, k, ssp is a binary value denoting a specific configuration of the secondary structure predicted with ssp method for the central and the two adjacent residues where m = denotes a pattern type. for m = and k = c the secondary structure prediction would be ccc, and for m = and the prediction would be ccx, xcc, and xcx, respectively, where x = {e, h}. we assume coils for the positions outside of the sequence, i.e., when computing at the sequence termini. the total number of these features equals. they encode whether the central residue is located inside a secondary structure segment or at the interface between two segments. - contentk, ssp is the content of the secondary structure k predicted with method ssp over a residues window. the content is defined as the ratio between the number of residues in a given secondary structure and the window size. the window size is shortened when the central residue is at the termini of the sequence. the first two feature sets are consistent with the inputs used by the competing prediction methods, except that sspk is computed for four secondary structure prediction methods. the latter three feature sets are proposed in this paper in an attempt to incorporate window based information concerning the predicted secondary structure and the confidence scores that are provided together with the predictions. prediction method the support vector machine classifier was applied to predict β-turns. given a training set of data point pairs, i =... n, where xi denotes the feature vector, ci ={- 1} denotes binary class label, n is the number of training data points, finding the optimal svm is achieved by solving: min⁡‖w‖2+c∑iξisuch thatci≥1−ξi and 1≤i≤n where w is a vector perpendicular to wx - b = hyperplane that separates the two classes, c is a user defined complexity constant, ξi are slack variables that measure the degree of misclassification of xi for a given hyperplane, b is an offset that defines the size of a margin that separates the two classes, and z = φ where k = φ·φ is a user defined kernel function. the svm classifier was trained using platt's sequential minimal optimization algorithm, which was optimized by keerthi et al. the radial basis functions was used as kernel function k=e−γ‖x−x'‖ where γ is the user defined constant. the svm classification algorithm and feature selection algorithms used to build and test our prediction method were implemented in weka. the selection of the classifier and the kernel type was motivated by the best β-turn predictions reported to date on the bt dataset that were obtained using rbf-kernel based svm classifier. the proposed classifier is parameterized, i.e., the values of c and γ are selected, based on the procedure described in the next section. features selection and parameterization of svm since total of features were generated for each predicted residue and we expect that some of them would not contribute to the prediction, a feature selection was performed to reduce the dimensionality. this allows for reduction of the time necessary to compute the prediction model and for finding and discussing which of the proposed features are related to the prediction of β-turns. three feature selection approaches were employed. the first, hybrid approach combines the information-gain and the chi-squared feature selection methods. the two methods were selected based on their successful application in and, respectively, where they were used to rank protein sequence based features. we also applied a filter-based feature selection method which removes features based on the inconsistency criterion and a wrapper-based algorithm that applies flexible naïve bayes classifier. in the case of the filter-based and the wrapper-based methods, we used best first search that starts with empty set of features to search through possible subsets of features. the selection of this search method and the selection of the flexible naïve bayes to evaluate feature sets in the wrapper-based method were motivated by their good scalability, which was necessary due to the large size of the datasets, i.e., the search method is linear with respect to the number of features and the naïve bayes is linear with respect to the number of data points. in the hybrid feature selection, we used two different selection methods to reduce bias introduced by each of the methods. in both algorithms, each feature is ranked based on its merit, and next they were sorted by their average rank across the two algorithms. the measurement of the merit for the two selection methods is defined below. ig measures the decrease in entropy when a given feature is used to group values of another feature. the entropy of a feature x is defined as: h=−∑iplog⁡2) where {xi} is a set of values of x and p is the prior probability of xi. the conditional entropy of x, given another feature y is defined as: h=−∑jp∑iplog⁡2) where p is the posterior probability of x given the value yi of y. the amount by which the entropy of x decreases reflects additional information about x provided by y and is called information gain ig = h - h according to this measure, y has stronger correlation with x than with z if ig > ig. chi method is based on a common statistical test that measures divergence from the expected distribution assuming that the occurrence of a given feature is independent of the class value. let x be a discrete random variable with m = possible outcomes x = β-turn, x = non β-turn, and with probability of each outcome p = pi. pearson-chi-squared statistic is defined as: χ2=∑i=1m2npi where ni is the number of instances which will result the outcome xi. a feature that obtains higher χ value receives lower rank. to avoid overfitting, the features were ranked on the bt dataset using 7-fold cross validation. in the case of the hybrid method, the average ranks were computed for each of the training datasets separately, and next they were averaged over the datasets. after the features are ranked, we performed β-turn prediction in order to decide how many of the features should be kept. this was performed in two steps. first, we selected the top features to perform parameterization of the svm classifier. next, we used the parameterized svm to select the desired number of features. in step we perform greedy search for optimal c and γ parameters: - we freeze c = and find the optimal γ based on 3-fold cross validation on the bt426- dataset using the top features, see figure 2a. we observe that highest accuracy is achieved for γ equal or. the optimal γ = is the same as the value used in. - next, we use the γ = and we optimize c, see figure 2b. the best accuracy is achieved for c = we did not apply the grid-based parameterization, which could potentially lead to better parameters, since this would be computationally expensive and since figure shows that the svm is not sensitive to the parameters, i.e., the qtotal values change by only up to % by varying γ and c. in the second step, the svm classifier with the optimized parameters was used to select the desired number of the top ranked features. the selection was again based on 3-fold cross validation on the bt426- dataset, see figure the results show that selection of the top features provides the best accuracy, although we note that the differences are relatively small. this indicates that only a small fraction of the original features is necessary to provide accurate β-turn predictions. since the wrapper- and filter-based feature selections directly select a set of features, rather than ranking the features as it is done by the hybrid method, there was no need to decide how many features should be kept. instead, each method was used to select a set of features for each of the training folds from the bt dataset, and next these features were combined together. this resulted in selection of and features in the case of the filter-based and wrapper-based algorithms, respectively. these two feature sets were used with svm parameterized using the above procedure where the top ranked features were applied. we did not re-parameterize the svm for the other two sets of features because the above parameterization shows that the svm is not sensitive to the parameters, the features used in the parameterization overlap with features used in the other two sets, and since such parameterization is computationally expensive. evaluation procedure and measures 7-fold cross validation was used to perform tests on the three datasets. the folds were created by randomly selecting equal number of sequences. the quality of prediction is evaluated using four measures, qtotal, qpredicted, qobserved, and mcc. this is consistent with the test procedures and measures applied to evaluate modern competing methods. given that tp is the number of correctly classified β-turn residues, tn is the number of correctly classified non-β-turn residues, fp if the number of non-β-turn incorrectly classified as β-turn residues, and fn is the number of β-turn incorrectly classified as non-β-turn residues, qtotal is defined as the percentage of correctly classified residues. qtotal=tp+tntp+tn+fp+fn× probability of correct prediction, qpredicted, is the percentage of correctly predicted β-turns among the predicted β-turns qpredicted=tptp+fp× sensitivity or coverage, qobserved, is the percentage of correctly predicted β-turns among the observed β-turns qobserved=tptp+fn× we observe that approximately 24% to % β-turn residues are observed in the three datasets, and therefore qtotal = 75% could be obtained by merely regarding all residues as non β-turns. therefore, qtotal values can result in misleading information, which was pointed out in. this is especially evident when tn values are large, compared to tp, fn, and fp values. as a result matthews correlation coefficient is computed mcc=tp×tn−fp×fn×××× the value of mcc is confined to <- > interval. if the mcc value is close to then the prediction method is not better than a random classification. higher mcc value corresponds to better performance of the prediction method. we also report receiver-operator characteristics curves that present a graphical plot of the tp rate = qobserved against fp rate = fp/.  comparison of different feature selection strategies the three employed feature selection methods produce different feature sets which are summarized in figure in all three cases majority of the features are based on pssm. among the features that are computed from the predicted secondary structures, the largest fraction is derived from the structures predicted by proteus we also observe that all four predicted secondary structures are used to derive features in each of the feature sets. this consistency supports the need for multiple predicted secondary structures. each of the three set of features was used as the input to the optimized svm classifier with c = and γ = to perform prediction of β-turns. the evaluation of the quality of these predictions was performed based on 7-fold cross validation on the bt datasets, see table the table shows that usage of the features selected using the hybrid methods results in the highest mcc value. these features also lead to the highest qobserved and qtotal. at the same time, we note that the features selected using the filter-based method correspond to the highest qpredicted value. we observe that the differences are relatively small as all three designs provide the accuracy which is close to 80%. the roc curves shown in figure allow for a more detailed analysis of the differences. the features generated by the hybrid method are shown to provide favorable prediction quality for low values of ft rate, while the features based sequence representation developed with wrapper-based method provides higher tp rate for the higher values of the fp rate. the most interesting part of the curves corresponds to relative high tp rates that are coupled with low values of fp rate. since the ratio of positive to negative samples is 1: the ratio between the true positives and false positives would be even at fp rate of approximately. for higher fp rate, the number of false positives would be higher than the number of true positives. as a result, we conclude that the features provide better predictions than the other two feature sets and this feature set is used to build the proposed prediction method. the tests are based on fold cross validation on the bt dataset comparison with competing prediction methods the selected features and svm with c = and γ = were applied in the proposed prediction model. the 7-fold cross validation test results on the bt dataset are summarized and compared with over a dozen of competing methods in table 2; the results are organized in the descending order by the values of mcc. results reported on a different dataset with chains. we investigate the impact of the proposed features extracted from the predicted secondary structure on the prediction quality. when excluding the features that are based on pssm, the predictions performed with the remaining secondary-structure features are characterized by qtotal = %, qpredicted = %, qobserved =, and mcc =. although removal of the pssm features results in slightly worse predictions, we observe that the features computed from the predicted secondary structures provide valuable input. we also experimented with the design in which only one of the four secondary structure predictions is used. we used output of the proteus that is characterized by a favorable performance when compared with the other three secondary structure prediction methods. the predictions that use only the pssm based features and features generated from secondary structure predicted by proteus result in qtotal = %, qpredicted = %, qobserved =, and mcc =. we observe that these results are again slightly worse than the results obtained with the proposed method; the usage of all features improves qtotal, qpredicted, and mcc. the simplified architecture that uses only one predicted secondary structure is equivalent to the design of the recent method by zhang and colleagues. we note that our results are better than the results of this method, i.e., qtotal = % vs. qtotal = %, which stems from using different secondary structure prediction method and the novel features. our method uses features computed from a window over the predicted secondary structure, while the zhang's method uses only the secondary structure of the predicted residue. results obtained based on the 7-fold cross validation with the bt and bt datasets are given in table they show that for the bt dataset the proposed method obtains % higher qtotal, 2% higher mcc, 14% better qpredicted, and 16% lower qobserved when compared with the second-best svm based method. similarly, for the bt dataset, our method obtains % and % increase in qtotal and qpredicted, respectively, and % decrease in qobserved. we observe that the proposed method obtains consistent quality of predictions for all three datasets. the qtotal values range between % and %, qpredicted values range between % and %, qobserved between % and %, and mcc between and, see tables and this rules out possibility of overfitting the bt dataset due to the performed design. the tests are based on the fold cross validation test on the bt and bt datasets analysis of the proposed feature based sequence representation the proposed method applies features, which constitutes 86% reduction of the dimensionality of the input vector when compared with the method by hu and li that applies features. the dimensionality reduction of 62% and 37% is achieved when compared with the two third-best performing, i.e., with the third best mcc value, svm-based predictors by pham and colleagues, which uses features, and the method by zhang and coworkers that applies features, respectively. the top ranked features that were used to implement the proposed prediction method are shown in table we observe that out of features are the newly proposed features, which are based on the sliding window over the secondary structure predicted by three prediction methods, proteus, psipred, and jnet. the remaining features concern the predicted secondary structure for the predicted residue. out of features are computed using the predicted coils, while the remaining concern predicted helices. the former is likely due to β-turns being a coil subtype and due to the favorable accuracy that the secondary structure prediction methods obtain for coils and helices when compared with the accuracy for strands. we note that out of features are extracted from the predictions performed with proteus which confirms high quality of this method. finally, table reveals the top features were based on the predicted secondary structure, i.e., none of them was based on pssm, which signifies the novelty of the proposed approach. furthermore, we analyzed the composition of the top selected features. the highest scoring pssmij feature was ranked and total of out of features were derived from the pssm. among the remaining features, concern structure predicted for the central residue, concern the prediction confidence score for the central residue, are based on the residue window pattern over the predicted secondary structure, and concern secondary structure content over the residue window. this shows that all proposed feature sets were utilized to perform the prediction.  we propose a novel method for the prediction of β-turns that uses features extracted from a window over the three-state secondary structure predicted by an ensemble of four methods. we use feature selection to reduce the dimensionality of the proposed feature vector. the proposed feature set is smaller by to 86% when compared with the best performing competing methods. the analysis of the selected features reveals that: - information from all four predicted secondary structures is useful for the prediction of β-turns, - the most useful information extracted from the predicted three-state secondary structure are the structure of the predicted residue, content of the secondary structures over residues window centered on the predicted residue, and features that indicate whether the predicted residue is inside a secondary structure segment, - pssm values of asn, asp, gly, ile, leu, met, pro, and val, were among the top ranked features; similar conclusions, i.e., high potential of asn, asp, gly, and pro, and low potential of ile, leu, met, and val, to form β-turns were shown in. in our case, asn, asp, gly, and pro are likely associated with potential β-turns, while the remaining four amino acids predict non β-turns. empirical evaluation using three nonredundant datasets shows that our predictions provide favorable qtotal, qpredicted, and mcc values when compared with over a dozen of modern competing methods. our method is the first to break the 80% qtotal barrier and is characterized by % qtotal, mcc, and qpredicted higher by over 6% when compared with the second best method using a benchmark dataset of nonredundant sequences. this shows that our method not only constitutes an improvement over the competition, but also that the proposed prediction model can better discriminate between β-turns and non β-turns since it generates lower numbers of false positive predictions. abbreviations ann: artificial neural networks; chi: chi-squared; fn: false negatives; fp: false positives; ig: information-gain; knn: k-nearest neighbor; mcc: matthews correlation coefficient; pdb: protein data bank; psfm: position specific frequent matrix; pssm: position specific scoring matrix; roc: receiver-operator characteristics; svm: support vector machine; tn: true negatives; tp: true positives. authors' contributions cz helped with the preparation of the datasets, computed the features, performed feature selection, generated the prediction model, performed experimental comparison, and helped with evaluation of the results. lk contributed to the conception and design of the prediction method, helped with the preparation of the datasets, designed the experimental study, helped with the evaluation of the results, prepared the revision, drafted the manuscript, and coordinated the project. both authors have corrected and approved the manuscript. 
empirical evaluation using three nonredundant datasets shows favorable qtotal, qpredicted and mcc values when compared with over a dozen of modern competing methods. β-turn is a secondary protein structure type that plays significant role in protein folding, stability, and molecular recognition. we show that all four predicted secondary structures are useful; the most useful information extracted from the predicted secondary structure includes the structure of the predicted residue, secondary structure content in a window around the predicted residue, and features that indicate whether the predicted residue is inside a secondary structure segment; the pssm values of asn, asp, gly, ile, leu, met, pro, and val were among the top ranked features, which corroborates with recent studies. we use feature selection to reduce the dimensionality of the feature vector used as the input for the proposed prediction method. experiments show that the proposed method constitutes an improvement over the competing prediction methods. to date, several methods for prediction of β-turns from protein sequences were developed, but they are characterized by relatively poor prediction quality. the asn, asp, gly, and pro indicate potential β-turns, while the remaining four amino acids are useful to predict non-β-turns. the proposed prediction model can better discriminate between β-turns and non-β-turns due to obtaining lower numbers of false positive predictions. our method is the first to break the 80% qtotal barrier and achieves qtotal = %, mcc =, and qpredicted higher by over 6% when compared with the second best method. the prediction model and datasets are freely available at. the novelty of the proposed sequence-based β-turn predictor stems from the usage of a window based information extracted from four predicted three-state secondary structures, which together with a selected set of position specific scoring matrix values serve as an input to the support vector machine predictor.
 β-turn is a secondary protein structure type that plays significant role in protein folding, stability, and molecular recognition. to date, several methods for prediction of β-turns from protein sequences were developed, but they are characterized by relatively poor prediction quality. the novelty of the proposed sequence-based β-turn predictor stems from the usage of a window based information extracted from four predicted three-state secondary structures, which together with a selected set of position specific scoring matrix values serve as an input to the support vector machine predictor.  we show that all four predicted secondary structures are useful; the most useful information extracted from the predicted secondary structure includes the structure of the predicted residue, secondary structure content in a window around the predicted residue, and features that indicate whether the predicted residue is inside a secondary structure segment; the pssm values of asn, asp, gly, ile, leu, met, pro, and val were among the top ranked features, which corroborates with recent studies. the asn, asp, gly, and pro indicate potential β-turns, while the remaining four amino acids are useful to predict non-β-turns. empirical evaluation using three nonredundant datasets shows favorable qtotal, qpredicted and mcc values when compared with over a dozen of modern competing methods. our method is the first to break the 80% qtotal barrier and achieves qtotal = %, mcc =, and qpredicted higher by over 6% when compared with the second best method. we use feature selection to reduce the dimensionality of the feature vector used as the input for the proposed prediction method. the applied feature set is smaller by and 37% when compared with the second and two third-best competing methods, respectively.  experiments show that the proposed method constitutes an improvement over the competing prediction methods. the proposed prediction model can better discriminate between β-turns and non-β-turns due to obtaining lower numbers of false positive predictions. the prediction model and datasets are freely available at. 