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Predicting and analyzing DNA-binding domains using a systematic approach to identifying a set of informative physicochemical and biochemical properties

Background Existing methods of predicting DNA-binding proteins used valuable features of physicochemical properties to design support vector machine (SVM) based classifiers. Generally, selection of physicochemical properties and determination of their corresponding feature vectors rely mainly on known properties of binding mechanism and experience of designers. However, there exists a troublesome problem for designers that some different physicochemical properties have similar vectors of representing 20 amino acids and some closely related physicochemical properties have dissimilar vectors. Results This study proposes a systematic approach (named Auto-IDPCPs) to automatically identify a set of physicochemical and biochemical properties in the AAindex database to design SVM-based classifiers for predicting and analyzing DNA-binding domains/proteins. Auto-IDPCPs consists of 1) clustering 531 amino acid indices in AAindex into 20 clusters using a fuzzy c-means algorithm, 2) utilizing an efficient genetic algorithm based optimization method IBCGA to select an informative feature set of size m to represent sequences, and 3) analyzing the selected features to identify related physicochemical properties which may affect the binding mechanism of DNA-binding domains/proteins. The proposed Auto-IDPCPs identified m=22 features of properties belonging to five clusters for predicting DNA-binding domains with a five-fold cross-validation accuracy of 87.12%, which is promising compared with the accuracy of 86.62% of the existing method PSSM-400. For predicting DNA-binding sequences, the accuracy of 75.50% was obtained using m=28 features, where PSSM-400 has an accuracy of 74.22%. Auto-IDPCPs and PSSM-400 have accuracies of 80.73% and 82.81%, respectively, applied to an independent test data set of DNA-binding domains. Some typical physicochemical properties discovered are hydrophobicity, secondary structure, charge, solvent accessibility, polarity, flexibility, normalized Van Der Waals volume, pK (pK-C, pK-N, pK-COOH and pK-a(RCOOH)), etc. Conclusions The proposed approach Auto-IDPCPs would help designers to investigate informative physicochemical and biochemical properties by considering both prediction accuracy and analysis of binding mechanism simultaneously. The approach Auto-IDPCPs can be also applicable to predict and analyze other protein functions from sequences.

Background DNA-binding domains/proteins are functional proteins in a cell, which plays a vital role in various essential biological activities, such as DNA transcription, replication, packaging, repair and rearrangement [1]. In past, numerous computational methods predict DNA-binding domains/proteins using informative features from protein structure and amino acid sequence. The structurebased prediction methods such as [2,3] are accurate, but not capable for high throughput annotation. In this study, the sequence-based prediction methods for DNAbinding domains/proteins are investigated.
The computational methods using support vector machine (SVM) in conjunction with evolutionary information of amino acid sequence in terms of their position-specific scoring matrices (PSSMs) for predicting DNA-binding sites were successfully developed [4]. Several methods of using machine learning approaches were developed to predict DNA-binding domains/proteins from given sequences of variable lengths [5][6][7][8][9], shown in Table 1.
Due to different design aims and data sets used, it is difficult to assess which feature type is the most informative cooperated with SVM by comparing with prediction accuracies only. The PSSM profile was first used with SVM to successfully predict DNA-binding domains and proteins from query amino acid sequences in the method PSSM-400 [7]. The PSSM is an effective feature type of representing DNA-binding sequences, but its ability of interpretability is not satisfactory enough in analyzing the binding mechanism. Besides PSSMs, physicochemical properties with characteristics of high interpretability were commonly used [5,6,8,9]. Some issues are concerned in designing prediction methods, described below.
1) Selection of physicochemical properties. Generally, effective physicochemical properties of amino acids are selected as prediction features by using known properties of DNA-binding mechanism and binding knowledge [5,6,8,9]. However, it is desirable to explore undiscovered properties by machine learning approaches to further advance prediction accuracy and understand the binding mechanism.
2) Representation of sequences. How to effectively represent sequences of variable lengths as a feature vector using physicochemical properties plays an important role in advancing prediction accuracy. The pseudoamino acid composition is an efficient representation method of coupling physicochemical properties, which was used to represent a sequence as a 40-dimensional feature vector for discriminating DNA-binding from non-binding proteins [5]. The combined descriptor was proposed using amino acid composition and a series of associated physicochemical properties to form a 132dimensional feature vector [9]. The conjoint triad descriptor of using a 343-dimensional feature vector was proposed that 20 amino acids were clustered into seven classes according to their dipoles and volumes of side chains [8].
3) Values of amino acids for specific physicochemical properties. The AAindex database [10,11] collected 531 physicochemical and biochemical properties (ignoring 13 properties without available values) with corresponding values of amino acids. How to select an effective feature vector of 20 amino acid values to represent a given property by using experience of designers is not straightforward. Recently, some computational methods of predicting protein functions were successfully developed by mining informative physicochemical properties with their corresponding values from AAindex [12,13]. 4) Tradeoffs between prediction accuracy and knowledge acquisition. Besides pursuit of high prediction accuracy, discovering potential properties to further understand the binding mechanism should be also taken into account. Although ensemble classifiers with hybrid feature types and boosting techniques are commonly used to improve prediction performance, it is more desirable to find effective, interpretable physicochemical properties with strong discrimination abilities under using a simple SVM classifier.
This study presents a troublesome problem in using the AAindex database and proposes an effective method to solve. We found that some different physicochemical properties have similar vectors of representing 20 amino acids and some closely related physicochemical properties have dissimilar vectors. For example, several dissimilar vectors in AAindex are available in coupling the hydrophobicity property to represent a sequence and their corresponding performance is significantly different. Similarly, if a different property with a similar vector replaces the known one without significantly degrading prediction performance, it means that the replaced property may be also relative to the binding mechanism from the viewpoint of machine learning. The detailed explanation by using a real quantization example is described below. Figure 1 shows an illustration example. The 402 properties in AAindex were classified into six groups according to their biological meanings classified by Tomii and Kanehisa [11], as shown in Fig. 2 obtained from [10]. According to the numerical indices representing 531 properties of amino acids, we clustered them into 20 clusters by using a fuzzy c-means algorithm based on their Euclidean distances between two indices [14]. The properties H88 and A392 are two different properties belonging to the same cluster 7, but their distance of 0.0178 is relatively small. On the other hand, H88 and H178 belonging to the same group, named Hydrophobicity in AAindex, have a large distance of 0.0877 belonging to clusters 7 and 18, respectively. Although H88 and H151 (used in [5]) are in the same group Hydrophobicity and the same cluster 7, their distance 0.0299 is also larger than that between H88 and A392.
For the aim of designing accurate prediction methods, the major concern is to identify feature vectors with high discrimination abilities for classifying positive and negative samples. This task can be done well for computational methods by using an optimization approach to feature selection from a large set of candidate features. If the feature vectors were identified by predetermined properties based on prior knowledge, the selected vectors of representing amino acids may be not the best. Considering the other aim of discovering potential properties to further look insight the binding mechanism, we propose a systematic, optimization approach (named Auto-IDPCPs) to automatically identify a set of feature vectors and analyze the feature vectors to find properties of affecting the DNA-binding mechanism.
The proposed approach Auto-IDPCPs can identify a small number m of feature vectors cooperated with a single SVM classifier, and discover the related hydrophobicity properties with comparable performance, compared with the PSSM feature. Auto-IDPCPs would help designers to investigate informative physicochemical and biochemical properties by considering both prediction accuracy and analysis of binding mechanism simultaneously. Auto-IDPCPs can be also applicable to predict and analyze other protein functions from sequences.

Methods
The flowchart of the proposed approach Auto-IDPCPs is shown in Fig. 3. The input of the method comprises the AAindex database and three data sets, including DNA-binding domains and sequences, and one independent test data set. The output has two parts: 1) a predictor for DNA-binding domains/proteins with a set of m informative feature vectors and the parameter setting of SVM by using an efficient feature selection algorithm IBCGA, and 2) an analyzer with a set of promising physicochemical and biochemical properties in the AAindex database for analyzing the DNA-binding mechanism.

Data sets
To evaluate effectiveness of the identified physicochemical properties by comparing with the famous PSSM features, we used the benchmark data sets used in the PSSM-400 method [7], as shown in Table 2. Figure 1 An illustration example. The properties H88 and A392 are two different properties but their distance 0.0178 is relatively small. On the other hand, H88 and H178 belonging to the same group Hydrophobicity in AAindex have a large distance 0.0877. H88 and H151 in the same group have a larger distance 0.0299 than that between H88 and A392.
The data set DNAset has 146 non-redundant DNAbinding domains (or protein chains) and 250 nonbinding domains. No two domains have similarity more than 25%. The data set DNAaset consists of 1153 DNA-binding proteins and 1153 non-binding proteins. No two proteins have similarity more than 25%. An independent data set DNAiset is additionally used, having 92 DNA-binding domains and 100 non-DNA-binding proteins [7].

Feature vector representation
All the domains/sequences have a variable length l. A sequence forms an l-dimensional profile where the value of each amino acid is obtained from the AAindex database for encoding a specific physicochemical property. The l-dimensional profiles are transformed into vectors with the same constant length L for utilizing SVM. The transformation can be any known effective representation provided that the L features can  effectively classify the l-dimensional profiles of positive and negative sequences. The simplest feature is the mean of the profile that L=1 [12,13]. Therefore, the sequences with m properties are represented as an mdimensional feature vectors. Finally, all values of the feature vectors are normalized into [-1, 1] to apply SVM.

Feature selection by IBCGA
Selecting a minimal number of informative features while maximizing prediction accuracy is a bi-objective 0/1 combinatorial optimization problem. An efficient inheritable bi-objective combinatorial genetic algorithm IBCGA [15] bases on an intelligent genetic algorithm IGA [16] is utilized to solve this optimization problem. IGA based on orthogonal experimental design uses a divide-and-conquer strategy and a systematic reasoning method instead of the conventional generate-and-go method to efficiently solve the combinatorial optimization problem C(n, m) having a huge search space of size n!/(m!(n-m)!)), where n=531 in this study. IBCGA can efficiently search the space of C(n, r±1) by inheriting a good solution in the space of C(n, r) [15]. Therefore, IBCGA can economically obtain a complete set of high-quality solutions in a single run.
The chromosome encoding scheme of IGA consists of n binary IGA-genes g i for selecting informative features (physicochemical properties) and two 4-bit IGA-genes for encoding g and C of SVM parameters, where g {2 -7 , 2 -6 …, 2 8 } and C {2 -7 , 2 -6 …, 2 8 } [12]. The i th feature is used in the SVM classifier if g i =1; otherwise, the i th feature is excluded (g i =0). The performance of selected properties associated with the parameter values of SVM is measured by five-fold cross-validation (5-CV) for comparing with the method PSSM-400 [7]. IBCGA with the fitness function f(X) of 5-CV prediction accuracy can simultaneously obtain a set of solutions, X r , where r=r start , r start +1, …, r end in a single run. In this study, the parameter settings r start =10, r end =30, N pop =50, p c =0.8, and p m =0.05. The output contains a set of m selected properties from AAindex and an SVM classifier with associated parameter settings g and C. The customized IBCGA algorithm used in Auto-IDPCPs is given below.
Step 1: (Initiation) Randomly generate an initial population of N pop individuals. All the n binary genes have r 1's and n-r 0's where r = r start .
Step 2: (Evaluation) Evaluate the fitness values of all individuals using f(X).
Step 3: (Selection) Use the traditional tournament selection that selects the winner from two randomly selected individuals to form a mating pool.
Step 4: (Crossover) Select p c ·N pop parents from the mating pool to perform orthogonal array crossover on the selected pairs of parents where p c is the crossover probability.
Step 5: (Mutation) Apply the mutation operator to the randomly selected p m ·N pop individuals in the new population where p m is the mutation probability. To prevent the best fitness value from deteriorating, mutation is not applied to the best individual.
Step 6: (Termination test) If the stopping condition for obtaining the solutions X r is satisfied, output the best individual as X r . Otherwise, go to Step 2.
Step 7: (Inheritance) If r <r end , randomly change one bit in the binary genes for each individual from 0 to 1; increase the number r by one, and go to Step 2.
Step 8: (System uncertainty) Perform Steps 1-7 for R (=30 in this study) independent runs and obtain the best one of R solutions. The best solution can be determined by considering the most accurate one S a with the highest prediction accuracy or the robust one S r with the highest score, where the scores S t , t=1, …, R are derived using the following procedure Appscore.
The procedure Appscore is described as follows: Step 1: Calculate the appearance frequency f(p i ) of each feature p i from all features in the R sets, where i=1, …, m t . There are m Â¬t features in the t-th set.
Step 2: Calculate score S t, t=1, …, R for each of R solutions:

Clustering properties by fuzzy c-means
The physicochemical properties can be classified into six groups according to their biological meanings [11]. From the viewpoint of machine learning, two properties are similar if the distance between their feature vectors is small. To identify informative physicochemical properties and obtain effective feature vectors with strong discriminative abilities, we cluster the 531 vectors of physicochemical properties into 20 clusters using a fuzzy c-means (FCM) method [14].
A feature vector of amino acids is a set of 20 numerical values representing a physicochemical property of amino acids. To apply the FCM method, all data were normalized in such a way that every physicochemical  Table 3 The 20 clusters and their corresponding physicochemical and biochemical properties in the AAindex database property had an averaged profile value of zero and a standard deviation equal to 1. The FCM method has an objective functional of the form [14]: where n=531 is the number of data vectors, K is the number of clusters to be found, u ij [0, 1] is the membership degree of j th data vector x j in the i th cluster, the i th cluster represented by the cluster prototype v i , s [1,∞) is a weighting exponent called the fuzzifier and d(v i , x j ) is the distance of x j from the cluster prototype v i . Dembélé and Kastner [17] suggested the parameters setting s=1.12 and K=20 clusters, adopted in this study.

Identifying physicochemical properties
It is not easy to discover related physicochemical properties for analyzing DNA-binding mechanism by computational methods using relatively small-size data sets. Therefore, we present a hybrid method by combining evidences from the viewpoints of both machine learning and biological meanings. Auto-IDPCPs identifies m properties belong to c out of 20 clusters. We examine each property P1 of the 531 properties and each property P2 of the identified m properties. If they satisfy the following two criteria, P1 is a promising property to be further investigated: 1) the distance between the feature vectors of P1 and P2 is small, and 2) P2 is replaced with P1 one at a time and the prediction accuracy is not significantly decreased.
Only 402 of 531 properties were classified into six groups [11] Table S1 (see Additional File 1). The 20 clusters and their corresponding physicochemical and biochemical properties belonging to six groups in the AAindex database are given in Table 3. The statistical result of the 531 physicochemical properties distributed upon the 20 clusters and six groups is given in Table 4. The large clusters 7, 9 and 10 have properties belonging to six groups. The valuable information in Tables 3 and 4 integrating classification results of both biological meanings and similarity measure is very helpful in identifying informative properties. The statistical results of property distribution in the six groups for 531 and 402 amino acid indices are given in Fig. 4. The largest group is Hydrophobicity having 149 indices and the second largest group is Alpha and turn propensities having 118 indices (Fig. 4b). The sizes of the other four groups are relatively small.

Identified properties by IBCGA
The statistical result of S t in selecting property sets from R =30 independent runs on DNAset and DNAaset is given in Fig. 5. The 18 th and 6 th runs having the highest scores for DNAset and DNAaset respectively are selected, and their prediction accuracies for various numbers of selected features are given in Fig. 6. The robust solutions S 18 and S 6 having m=22 and 28 features with accuracies of 87.12% and 75.50% for DNAset and DNAaset, respectively, are given in Tables 5 and 6, where the AAindex identity numbers and their property descriptions are provided.
An efficient way to study effects of several factors simultaneously is to utilize orthogonal experimental design used in IGA [16]. The main effect difference (MED) of orthogonal experimental design can estimate effects of individual features according to the value of MED [12,16]. The most effective property has the largest value of MED. The m properties ranked by using MED are shown in Fig. 7. The properties of rank 1 are identity numbers H86 (FAUJ880109, Number of hydrogen bond donors) and B39 (CHOP780202, Normalized    frequency of beta-sheet) for DNAset and DNAaset, belonging to the groups Hydrophobicity and Beta propensity, respectively.

Prediction performance evaluation
To evaluate the effectiveness of the identified m informative feature vectors (PCPs), we implemented the predictor using the same single classifier SVM with the feature types, amino acid composition (AAC) and PSSM [7]. Additionally, the selected PCPs combined with AAC and PSSM were also evaluated, as shown in Table 7. AAC is a 20-dimensional vector of amino acid composition. PSSM is the feature representation of 400 features. PCPs +AAC and PCPs +PSSM are two hybrid feature types.
Considering the DNA-binding domain data set DNAset, the set of m=22 informative properties (PCPs) identified by Auto-IDPCPs performs best where the robust solution S r with accuracy of 87.12% is used. The four compared methods AAC, PSSM, PCPs+AAC, and PCPs +PSSM have accuracies of 80.30%, 86.62%, 81.82% and 86.62%, respectively. For the DNA-binding protein data set DNAaest, the method using PCPs with m=28 informative properties (75.50%) is slightly better than the PSSM-400 (74.22%). However, PCPs+PSSM can improve both PCPs and PSSM to the accuracy of 80.27%. When the method using the trained SVM with PCPs was evaluated by the independent test data set DNAiset, the method using selected PCPs has the accuracy of 80.73% (=155/192), slightly worse than the method PSSM-400 with the accuracy of 82.81% (=159/192) [7].
A small, high-performance features set of size c that one property is selected from each of the identified c clusters using the optimization algorithm IGA is given in Table 8, where c=5 and 8 for DNAset and DNAaset, respectively. The accuracies of the robust solutions using the c features with SVM are 83.59% and 73.24% for DNAset and DNAaset, respectively. The properties and their descriptions are given in Tables 9 and 10.
The experimental results reveal that the identified small set of m physicochemical properties with a simple sequence representation and a single SVM classifier is promising, compared with the PSSM feature type. However, the identified physicochemical properties are interpretable for further understanding the DNA-binding mechanism.

Analyzing physicochemical properties for binding mechanism
The selected features of the conducted 30 runs are very different in terms of feature ID from 531 properties. The appearance frequency of each identified cluster in Table 5 The robust solution S 18 with a set of m=22 features for DNAset the 30 runs is shown in Fig. 8. From the statistic result, the clusters 7, 9, 10, 16 and 18 with very high selection frequencies are more informative for predicting DNAbinding domains and proteins. The selected clusters of the 30 runs are very similar in terms of cluster ID from 20 clusters. The m=22 properties (Table 5) belong to five clusters which are the same with the five clusters 7, 9, 10, 16 and 18. For predicting DNA-binding proteins, the m=28 properties (Table 6) belong to eight clusters, which are the same five clusters and additional three clusters 3, 14 and 17. The results reveal that the identified features of the robust solution S r belong to  informative clusters. Therefore, the informative clusters can provide informative properties to be further investigated if these properties were not selected by the feature selection method. An illustration example for exploring promising properties is given in Fig. 9. The both feature sets S1 (H88, H86, H67, C209, H178) and S2 (A392, A303, A307, C440, H178) are selected for predicting DNAbinding domains in DNAset that one property is selected from one of five clusters 7, 9, 10, 16 and 18. The identified properties H88 and A392 belong to the Hydrophobicity, and Alpha and turn propensities groups respectively, but they belong to the same cluster 7 with a relatively small distance 0.0178. The prediction accuracy of S3 by replacing H88 with H151 is 81.05 %. On the other hand, H151 belonging to the cluster 7 and Hydrophobicity group used in [5] can be inferred from feature sets S1 and S2. After analyzing all candidate properties, we identify some properties in the five identified clusters for analyzing DNA-binding domains, shown in Table 11. Some typical properties discovered are hydrophobicity, secondary structure, charge, solvent accessibility, polarity, flexibility, normalized Van Der Waals volume, pK (pK-C, pK-N, pK-COOH and pK-a(RCOOH)), etc.
Most of identified properties were used in previous works [5,6,8,9], but a few properties such as the flexibility property H8: BHAR880101 in cluster 7 "Average flexibility indices (Bhaskaran-Ponnuswamy, 1988)" are not utilized yet in existing method of predicting DNAbinding domains. The correlation between protein flexibility and protein function suggests a link between DNA-binding activity and the conformational freedom of the DNA-binding domain [18].   Table 9 The m=5 features selected from the five clusters identified from DNAset that one best feature is selected from one cluster by IGA  Although most identified properties were mentioned in literature, it is not easy to know which amino acid index is the best feature in designing accurate prediction method. For example, the two feature vectors of properties H8: BHAR880101 and A:124 KARP850101 "Flexibility parameter for no rigid neighbours (Karplus-Schulz, 1985)" belonging to different clusters 7 and 9 are dissimilar. From Table 11, it can be found that the four clusters 7, 9, 10 and 16 has properties, H115: HOPT810101 (Hydrophilicity value (Hopp-Woods, 1981)), H355: ROSM880101 (Side chain hydropathy, uncorrected for solvation (Roseman, 1988)), H398: ZIMJ680101 (Hydrophobicity (Zimmerman et al., 1968)), and H252: PRAM900101 (Hydrophobicity (Prabhakaran, 1990)), respectively, belonging to the  An illustration example for exploring promising properties. H151 can be inferred from feature sets S1 and S2. Hydrophobicity group. The scenario reveals that more than one feature vectors may be needed in utilizing one physicochemical property to advance prediction accuracy.

Discussion
To avoid from overfitting the small-scale data sets in identifying physicochemical properties using an optimization approach, this study proposes a hybrid computational method of combining evidences by considering robust features and biological meanings from literature. These discovered properties in predicting and analyzing the DNA-binding mechanism can be further investigated.
In this study, the proposed approach Auto-IDPCPs aims to identify an informative feature set of physicochemical and biochemical properties, rather than proposing an accurate method for predicting DNA-binding domains/ proteins. Some techniques can be used to improve the prediction accuracy such as using ensemble classifiers with hybrid feature types and boosting techniques.

Conclusions
This study has proposed a systematic approach Auto-IDPCPs to automatically identify an informative set of physicochemical and biochemical properties in the AAindex database to design SVM-based classifiers for predicting and analyzing DNA-binding domains/proteins. Since the AAindex database contains 531 physicochemical and biochemical properties of 20 naturally occurring amino acids that are the building-blocks of proteins, the proposed approach Auto-IDPCPs using an optimization method of feature selection can be useful and efficient for selecting informative physicochemical and biochemical properties, which is helpful in designing prediction methods for protein functions from sequences.

Additional material
Additional file 1: Table S1 -The 531 feature IDs used in this study and their corresponding AAindex IDs.