A weighting method for predicting protein structural class from amino acid composition.

A protein is generally classified into one of the following four structural classes: all alpha, all beta, alpha+beta and alpha/beta. In this paper, based on the weighting to the 20 constituent amino acids, a new method is proposed for predicting the structural class of a protein according to its amino acid composition. The 20 weighting parameters, which reflect the different properties of the 20 constituent amino acids, have been obtained from a training set of proteins through the linear-programming approach. The rate of correct prediction for a training set of proteins by means of the new method was 100%, whereas the highest rate of previous methods was 82.8%. Furthermore, the results showed that the more numerous training proteins, the more effective the new method.     

How good is prediction of protein structural class by the component-coupled method?

Proteins of known structures are usually classified into four structural classes: all-alpha, all-beta, alpha+beta, and alpha/beta type of proteins. A number of methods to predicting the structural class of a protein based on its amino acid composition have been developed during the past few years. Recently, a component-coupled method was developed for predicting protein structural class according to amino acid composition. This method is based on the least Mahalanobis distance principle, and yields much better predicted results in comparison with the previous methods. However, the success rates reported for structural class prediction by different investigators are contradictory. The highest reported accuracies by this method are near 100%, but the lowest one is only about 60%. The goal of this study is to resolve this paradox and to determine the possible upper limit of prediction rate for structural classes. In this paper, based on the normality assumption and the Bayes decision rule for minimum error, a new method is proposed for predicting the structural class of a protein according to its amino acid composition. The detailed theoretical analysis indicates that if the four protein folding classes are governed by the normal distributions, the present method will yield the optimum predictive result in a statistical sense. A non-redundant data set of 1,189 protein domains is used to evaluate the performance of the new method. Our results demonstrate that 60% correctness is the upper limit for a 4-type class prediction from amino acid composition alone for an unknown query protein. The apparent relatively high accuracy level (more than 90%) attained in the previous studies was due to the preselection of test sets, which may not be adequately representative of all unrelated proteins.     

An optimization approach to predicting protein structural class from amino acid composition.

Proteins are generally classified into four structural classes: all-alpha proteins, all-beta proteins, alpha + beta proteins, and alpha/beta proteins. In this article, a protein is expressed as a vector of 20-dimensional space, in which its 20 components are defined by the composition of its 20 amino acids. Based on this, a new method, the so-called maximum component coefficient method, is proposed for predicting the structural class of a protein according to its amino acid composition. In comparison with the existing methods, the new method yields a higher general accuracy of prediction. Especially for the all-alpha proteins, the rate of correct prediction obtained by the new method is much higher than that by any of the existing methods. For instance, for the 19 all-alpha proteins investigated previously by P.Y. Chou, the rate of correct prediction by means of his method was 84.2%, but the correct rate when predicted with the new method would be 100%! Furthermore, the new method is characterized by an explicable physical picture. This is reflected by the process in which the vector representing a protein to be predicted is decomposed into four component vectors, each of which corresponds to one of the norms of the four protein structural classes.     

Generality of the structurally constrained protein evolution model: assessment on representatives of the four main fold classes

The Structurally Constrained Protein Evolution (SCPE) model simulates protein evolution by introducing random mutations into the evolving sequences and selecting them against too much structural perturbation. Given a single protein structure, the SCPE model can be used to obtain a whole set of site-dependent amino acid substitution matrices. The set of SCPE substitution matrices for a given protein family can be seen as an independent-sites model of evolution for that family. Thus, these matrices can be compared with other substitution-matrix-based models of evolution. So far, SCPE has been tested only on left-handed parallel beta helix (LbetaH) proteins. Here, we address the question of generality by assessing the SCPE model on representatives of the four main classes of folds: alpha, beta, alpha+beta, and alpha/beta. We compare with other models using the likelihood ratio test with parametric bootstrapping. We show that SCPE performs better than the popular JTT model for all cases considered. Furthermore, by considering the relative contributions of mutation and selection, we found that the key to the success of the SCPE model is the selection step.     

Structural class prediction: an application of residue distribution along the sequence

Deciphering the native conformation of proteins from their amino acid sequences is one of the most challenging problems in molecular biology. Information on the secondary structure of a protein can be helpful in understanding its native folded state. In our earlier work on molecular chaperones, we have analyzed the hydrophobic and charged patches, short-, medium- and long-range contacts and residue distributions along the sequence. In this article, we have made an attempt to predict the structural class of globular and chaperone proteins based on the information obtained from residue distributions. This method predicts the structural class with an accuracy of 93 and 96%, respectively, for the four- and three-state models in a training set of 120 globular proteins, and 90 and 96%, respectively, for a test set of 80 proteins. We have used this information and methodology to predict the structural classes of chaperones. Interestingly most of the chaperone proteins are predicted under alpha/beta or mixed folding type.     

Hydrophobicity and structural classes in proteins.

The bulk hydrophobic character for the 20 natural amino acid residues, has been obtained from a database of 60 protein structures, grouped in the four structural classes alpha alpha, beta beta, alpha + beta and alpha/beta. The hydrophobicity coefficients thus obtained are compared with Ponnuswamy's original values using scales normalized to average = 0.0 and standard deviation = 1.0. Even though most of the amino acid residues do not change their hydropathic character in the different structural classes, their behaviour suggests the convenience that averaging methods should only consider proteins of the same structural class and that this information should be included in the secondary structure methods.     

Proteins of the same fold and unrelated sequences have similar amino acid composition

It is well established that there is a relationship between the amino acid composition of a protein and its structural class (i.e., alpha, beta, alpha + beta, or alpha/beta). Several studies have even shown the power of amino acid composition in predicting the secondary structure class of a protein. Herein, we show that significant similarity in amino acid composition exists not only between proteins of the same class, but even between proteins of the same fold. To test conjectural explanations for this phenomenon, we analyzed a set of structurally similar proteins that are dissimilar in sequence. Based on this analysis, we suggest that specific residues that are involved in intramolecular interactions may account for this surprising relationship between composition and structure.     

Prediction of protein structural class by amino acid and polypeptide composition.

A new approach of predicting structural classes of protein domain sequences is presented in this paper. Besides the amino acid composition, the composition of several dipeptides, tripeptides, tetrapeptides, pentapeptides and hexapeptides are taken into account based on the stepwise discriminant analysis. The result of jackknife test shows that this new approach can lead to higher predictive sensitivity and specificity for reduced sequence similarity datasets. Considering the dataset PDB40-B constructed by Brenner and colleagues, 75.2% protein domain sequences are correctly assigned in the jackknife test for the four structural classes: all-alpha, all-beta, alpha/beta and alpha + beta, which is improved by 19.4% in jackknife test and 25.5% in resubstitution test, in contrast with the component-coupled algorithm using amino acid composition alone (AAC approach) for the same dataset. In the cross-validation test with dataset PDB40-J constructed by Park and colleagues, more than 80% predictive accuracy is obtained. Furthermore, for the dataset constructed by Chou and Maggiona, the accuracy of 100% and 99.7% can be easily achieved, respectively, in the resubstitution test and in the jackknife test merely taking the composition of dipeptides into account. Therefore, this new method provides an effective tool to extract valuable information from protein sequences, which can be used for the systematic analysis of small or medium size protein sequences. The computer programs used in this paper are available on request.     

Structural analysis based on state-space modeling.

A new method has been developed to compute the probability that each amino acid in a protein sequence is in a particular secondary structural element. Each of these probabilities is computed using the entire sequence and a set of predefined structural class models. This set of structural classes is patterned after Jane Richardson''s taxonomy for the domains of globular proteins. For each structural class considered, a mathematical model is constructed to represent constraints on the pattern of secondary structural elements characteristic of that class. These are stochastic models having discrete state spaces (referred to as hidden Markov models by researchers in signal processing and automatic speech recognition). Each model is a mathematical generator of amino acid sequences; the sequence under consideration is modeled as having been generated by one model in the set of candidates. The probability that each model generated the given sequence is computed using a filtering algorithm. The protein is then classified as belonging to the structural class having the most probable model. The secondary structure of the sequence is then analyzed using a "smoothing" algorithm that is optimal for that structural class model. For each residue position in the sequence, the smoother computes the probability that the residue is contained within each of the defined secondary structural elements of the model. This method has two important advantages: (1) the probability of each residue being in each of the modeled secondary structural elements is computed using the totality of the amino acid sequence, and (2) these probabilities are consistent with prior knowledge of realizable domain folds as encoded in each model. As an example of the method''s utility, we present its application to flavodoxin, a prototypical alpha/beta protein having a central beta-sheet, and to thioredoxin, which belongs to a similar structural class but shares no significant sequence similarity.     

用离散量预测蛋白质的结构型

基于蛋白质的结构类型决定了它的二级结构序列的概念,用二级结构序列参数Nα,Nβ,Nβaβ,N(βαβ）构成离散源,并计算离散量D（Xα）,D（Xβ）,D（Xα＋β）,利用离散增量预测蛋白质的结构类型,它是由这个蛋白质的离散量D（Xn）与四个标准离散D（Xα）,D（Xβ）,D（Xα／β）,D（Xα＋β）之间离散增量的最小值所决定的,预测结果表明,准确率分别达到84．8％（标准集）和83．3％（检验集）。     

Aligning protein sequence and analysing substitution pattern using a class-specific matrix

Aligning protein sequences using a score matrix has became a routine but valuable method in modern biological research. However, alignment in the ‘twilight zone’ remains an open issue. It is feasible and necessary to construct a new score matrix as more protein structures are resolved. Three structural class-specific score matrices (all-alpha, allbeta and alpha/beta) were constructed based on the structure alignment of low identity proteins of the corresponding structural classes. The class-specific score matrices were significantly better than a structure-derived matrix (HSDM) and three other generalized matrices (BLOSUM30, BLOSUM60 and Gonnet250) in alignment performance tests. The optimized gap penalties presented here also promote alignment performance. The results indicate that different protein classes have distinct amino acid substitution patterns, and an amino acid score matrix should be constructed based on different structural classes. The class-specific score matrices could also be used in profile construction to improve homology detection.     

A quadratic discriminant analysis of protein structure classification based on the Helix/Strand content

Based on the 210 non-homologous proteins (domains) classified manually by Michie et al. (J. Mol. Biol. 262, 168-185, 1996), a new structure classification criterion of globular proteins relying on the content of helix/strand has been proposed, using a quadratic discriminant method. Each protein is classified into one of the three classes, i.e. those of alpha class, beta class and alphabeta class (including alpha/beta and alpha+beta classes). According to the new structure classification criterion, of the 210 proteins in the training set, 207 are correctly classified and thus the accuracy is 207/210=98.57%. Multiple cross-validation tests are performed. The jackknife test shows that of the 210 proteins 207 are correctly classified with an accuracy of 98.57%. To test the method further, of 3577 proteins (domains) extracted from SCOP, 91.39% of them are correctly reclassified by the new classification criterion. On average, the accuracy of the new criterion is about 8 percentage points higher than that of the criterion proposed by Nakashima et al. (J. Biochem. 99, 153-162, 1986). Our result shows that the classification based solely on structures is basically consistent with that combining both structural and evolutionary information. Further complete automated classification scheme should consider both structures and evolutionary relationship. The methodology presented provides an appropriate mathematical format to reach this goal.     

Recognition and architecture of the framework structure of protein

Based on the concept that the framework structure of a protein is determined by its secondary structure sequence, a new method for recognition and prediction of the structural class is suggested. By use of parameters N(alpha), N(beta), and N(beta(alpha)beta) (the number of alpha-helices, beta-strands, and beta(alpha)beta fragments), one can recognize the structural class with an accuracy higher than 90% when applied to the complete set (standard set) published in October 1995 and the structure data newly released before July 1998 (test set). Furthermore, the framework structures of beta, alpha, and alpha/beta protein are studied. It is found that these structures can be built from some basic units and that their architecture obeys some definite rules. Based on the packing of these basic units a set of rules for the recognition of topologies of the framework structure are worked out. When applied to the 1995 standard set and the 1998 test set the rates of correct recognition are higher than 77%. The simplicity and universality of framework structures are indicated which may be related to the evolutionary conservation of these folds. Proteins 2000;39:9-25.     

Dynamics alignment: comparison of protein dynamics in the SCOP database

A novel methodology for comparison of protein dynamics is presented. Protein dynamics is calculated using the Gaussian network model and the modes of motion are globally aligned using the dynamic programming algorithm of Needleman and Wunsch, commonly used for sequence alignment. The alignment is fast and can be used to analyze large sets of proteins. The methodology is applied to the four major classes of the SCOP database: "all alpha proteins," "all beta proteins," "alpha and beta proteins," and "alpha/beta proteins". We show that different domains may have similar global dynamics. In addition, we report that the dynamics of "all alpha proteins" domains are less specific to structural variations within a given fold or superfamily compared with the other classes. We report that domain pairs with the most similar and the least similar global dynamics tend to be of similar length. The significance of the methodology is that it suggests a new and efficient way of mapping between the global structural features of protein families/subfamilies and their encoded dynamics.     

Inter-residue interactions in protein structures exhibit power-law behavior

Inter-residue interactions play an essential role in driving protein folding, and analysis of these interactions increases our understanding of protein folding and stability and facilitates the development of tools for protein structure and function prediction. In this work, we systematically characterized the change of inter-residue interactions at various sequence separation cutoffs using two protein datasets. The first set included 100 diverse, nonredundant and high-resolution soluble protein structures, covering all four major structural classes, all-alpha, alpha/beta, alpha+beta, and all-beta; and the second set included 20 diverse, nonredundant and high-resolution membrane protein structures, representing 19 unique superfamilies. It was shown that the average number of inter-residue interactions in structures of both datasets displays the power-law behavior. Fitting parameters of the power-law function are directly related to the structural classes analyzed. These findings provided further insight into the distribution of short-, medium-, and long-range inter-residue interactions in both soluble and membrane proteins and could be used for protein structure prediction.     

Prediction of protein structural classes by Chou's pseudo amino acid composition: approached using continuous wavelet transform and principal component analysis

A prior knowledge of protein structural classes can provide useful information about its overall structure, so it is very important for quick and accurate determination of protein structural class with computation method in protein science. One of the key for computation method is accurate protein sample representation. Here, based on the concept of Chou’s pseudo-amino acid composition (AAC, Chou, Proteins: structure, function, and genetics, 43:246–255, 2001), a novel method of feature extraction that combined continuous wavelet transform (CWT) with principal component analysis (PCA) was introduced for the prediction of protein structural classes. Firstly, the digital signal was obtained by mapping each amino acid according to various physicochemical properties. Secondly, CWT was utilized to extract new feature vector based on wavelet power spectrum (WPS), which contains more abundant information of sequence order in frequency domain and time domain, and PCA was then used to reorganize the feature vector to decrease information redundancy and computational complexity. Finally, a pseudo-amino acid composition feature vector was further formed to represent primary sequence by coupling AAC vector with a set of new feature vector of WPS in an orthogonal space by PCA. As a showcase, the rigorous jackknife cross-validation test was performed on the working datasets. The results indicated that prediction quality has been improved, and the current approach of protein representation may serve as a useful complementary vehicle in classifying other attributes of proteins, such as enzyme family class, subcellular localization, membrane protein types and protein secondary structure, etc.     

Exploring the environmental preference of weak interactions in (alpha/beta)8 barrel proteins

The environmental preference for the occurrence of noncanonical hydrogen bonding and cation-pi interactions, in a data set containing 71 nonredundant (alpha/beta)(8) barrel proteins, with respect to amino acid type, secondary structure, solvent accessibility, and stabilizing residues has been performed. Our analysis reveals some important findings, which include (a) higher contribution of weak interactions mediated by main-chain atoms irrespective of the amino acids involved; (b) domination of the aromatic amino acids among interactions involving side-chain atoms; (c) involvement of strands as the principal secondary structural unit, accommodating cross strand ion pair interaction and clustering of aromatic amino acid residues; (d) significant contribution to weak interactions occur in the solvent exposed areas of the protein; (e) majority of the interactions involve long-range contacts; (f) the preference of Arg is higher than Lys to form cation-pi interaction; and (g) probability of theoretically predicted stabilizing amino acid residues involved in weak interaction is higher for polar amino acids such as Trp, Glu, and Gln. On the whole, the present study reveals that the weak interactions contribute to the global stability of (alpha/beta)(8) TIM-barrel proteins in an environment-specific manner, which can possibly be exploited for protein engineering applications.     

Accessible surfaces of beta proteins increase with increasing protein molecular mass more rapidly than those of other proteins

Here we present a systematic analysis of accessible surface areas and hydrogen bonds of 2554 globular proteins from four structural classes (all-α, all-β, α/β and α+β proteins) that is aimed to learn in which structural class the accessible surface area increases with increasing protein molecular mass more rapidly than in other classes, and what structural peculiarities are responsible for this effect. The beta structural class of proteins was found to be the leader, with the following possible explanations of this fact. First, in beta structural proteins, the fraction of residues not included in the regular secondary structure is the largest, and second, the accessible surface area of packaged elements of the beta-structure increases more rapidly with increasing molecular mass in comparison with the alpha-structure. Moreover, in the beta structure, the probability of formation of backbone hydrogen bonds is higher than that in the alpha helix for all residues of α+β proteins (the average probability is 0.73±0.01 for the beta-structure and 0.60±0.01 for the alpha-structure without proline) and α/β proteins, except for asparagine, aspartic acid, glycine, threonine, and serine (0.70±0.01 for the beta-structure and 0.60±0.01 for the alpha-structure without the proline residue). There is a linear relationship between the number of hydrogen bonds and the number of amino acid residues in the protein (Number of hydrogen bonds=0.678·number of residues-3.350).     

Predicting protein structure from long-range contacts

Short-range and long-range contacts are important in forming protein structure. The proteins can be grouped into four different structural classes according to the content and topology of alpha-helices and beta-strands, and there are all-alpha, all-beta, alpha/beta and alpha+beta proteins. However, there is much difference in statistical property for those classes of proteins. In this paper, we will discuss protein structure in the view of the relative number of long-range (short-range) contacts for each residue. We find the percentage of residues having a large number of long-range contacts in protein is small in all-alpha class of proteins, and large in all-beta class of proteins. However, the percentage of residues is almost the same in alpha/beta and alpha+beta classes of proteins. We calculate the percentage of residues having the number of long-range contacts greater than or equal to (>/=) N(L)=5, and 7 for 428 proteins. The average percentage is 13.3%, 54.8%, 41.4% and 37.0% for all-alpha, all-beta, alpha/beta and alpha+beta classes of proteins with N(L)=5, respectively. With N(L) increasing, the percentage decreases, especially for all-alpha class of proteins. In the meantime, the percentage of residues having the number of short-range contacts greater than or equal to N(S) (>/=N(S)) in protein samples is large for all-alpha class of proteins, and small for all-beta class of proteins, especially for large N(S). We also investigate the ability of amino residues in forming a large number of long-range and short-range contacts. Cys, Val, Ile, Tyr, Trp and Phe can form a large number of long-range contacts easily, and Glu, Lys, Asp, Gln, Arg and Asn can form a large number of long-range contacts, but with difficulty. We also discuss the relative ability in forming short-range contacts for 20 amino residues. Comparison with Fauchere-Pliska hydrophobicity scale and the percentage of residues having large number of long-range contacts is also made. This investigation can provide some insights into the protein structure.