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.     

Is it a paradox or misinterpretation?

The paradox recently raised by Wang and Yuan (Proteins 2000;38:165-175) in protein structural class prediction is actually a misinterpretation of the data reported in the literature. The Bayes decision rule, which was deemed by Wang and Yuan to be the most powerful method for predicting protein structural classes based on the amino acid composition, and applied by these investigators to derive the upper limit of prediction rate for structural classes, is actually completely the same as the component-coupled algorithm proposed by previous investigators (Chou et al., Proteins 1998;31:97-103). Owing to lack of a complete or near-complete training data set, the upper limit rate thus derived by these investigators might be both invalid and misleading. Clarification of these points will further stimulate investigation of this interesting area.     

Prediction of Protein Structural Classes by Modified Mahalanobis Discriminant Algorithm

We first discuss quantitative rules for determining the protein structural classes based on their secondary structures. Then we propose a modification of the least Mahalanobis distance method for prediction of protein classes. It is a generalization of a quadratic discriminant function to the case of degenerate covariance matrices. The resubstitution tests and leave-one-out tests are carried out to compare several methods. When the class sample sizes or the covariance matrices of different classes are significantly different, the modified method should be used to replace the least Mahalanobis distance method. Two lemmas for the derivation of our new algorithm are proved in an appendix.     

An Intriguing Controversy over Protein Structural Class Prediction

A recent report by Bahar et al. [(1997), Proteins 29, 172–185] indicates that the coupling effects among different amino acid components as originally formulated by K. C. Chou [(1995), Proteins 21, 319–344] are important for improving the prediction of protein structural classes. These authors have further proposed a compact lattice model to illuminate the physical insight contained in the component-coupled algorithm. However, a completely opposite result was concluded by Eisenhaber et al. [(1996), Proteins 25, 169–179], using a different dataset constructed according to their definition. To address such an intriguing controversy, tests were conducted by various approaches for the datasets from an objective database, the SCOP database [Murzin et al. (1995), J. Mol. Biol. 247, 536–540]. The results obtained by both self-consistency and jackknife tests indicate that the overall rates of correct prediction by the algorithm incorporating the coupling effect among different amino acid components are significantly higher than those by the algorithms without counting such an effect. This is fully consistent with the physical reality that the folding of a protein is the result of a collective interaction among its constituent amino acid residues, and hence the coupling effects of different amino acid components must be incorporated in order to improve the prediction quality. It was found by a revisiting the calculation procedures by Eisenhaber et al. that there was a conceptual mistake in constructing the structural class datasets and a systematic mistake in applying the component-coupled algorithm. These findings are informative for understanding and utilizing the component-coupled algorithm to study the structural classes of proteins.     

Support vector machines for prediction of protein domain structural class

The support vector machines (SVMs) method was introduced for predicting the structural class of protein domains. The results obtained through the self-consistency test, jack-knife test, and independent dataset test have indicated that the current method and the elegant component-coupled algorithm developed by Chou and co-workers, if effectively complemented with each other, may become a powerful tool for predicting the structural class of protein domains.     

Prediction of protein (domain) structural classes based on amino-acid index.

A protein (domain) is usually classified into one of the following four structural classes: all-alpha, all-beta, alpha/beta and alpha + beta. In this paper, a new formulation is proposed to predict the structural class of a protein (domain) from its primary sequence. Instead of the amino-acid composition used widely in the previous structural class prediction work, the auto-correlation functions based on the profile of amino-acid index along the primary sequence of the query protein (domain) are used for the structural class prediction. Consequently, the overall predictive accuracy is remarkably improved. For the same training database consisting of 359 proteins (domains) and the same component-coupled algorithm [Chou, K.C. & Maggiora, G.M. (1998) Protein Eng. 11, 523-538], the overall predictive accuracy of the new method for the jackknife test is 5-7% higher than the accuracy based only on the amino-acid composition. The overall predictive accuracy finally obtained for the jackknife test is as high as 90.5%, implying that a significant improvement has been achieved by making full use of the information contained in the primary sequence for the class prediction. This improvement depends on the size of the training database, the auto-correlation functions selected and the amino-acid index used. We have found that the amino-acid index proposed by Oobatake and Ooi, i.e. the average nonbonded energy per residue, leads to the optimal predictive result in the case for the database sets studied in this paper. This study may be considered as an alternative step towards making the structural class prediction more practical.     

Using pseudo amino acid composition and binary-tree support vector machines to predict protein structural classes

Compared with the conventional amino acid composition (AA), the pseudo amino acid composition (PseAA) as originally introduced by Chou can incorporate much more information of a protein sequence; this remarkably enhances the power to use a discrete model for predicting various attributes of a protein. In this study, based on the concept of Chou's PseAA, a 46-D (dimensional) PseAA was formulated to represent the sample of a protein and a new approach based on binary-tree support vector machines (BTSVMs) was proposed to predict the protein structural class. BTSVMs algorithm has the capability in solving the problem of unclassifiable data points in multi-class SVMs. The results by both the 10-fold cross-validation and jackknife tests demonstrate that the predictive performance using the new PseAA (46-D) is better than that of AA (20-D), which is widely used in many algorithms for protein structural class prediction. The results obtained by the new approach are quite encouraging, indicating that it can at least play a complimentary role to many of the existing methods and is a useful tool for predicting many other protein attributes as well.     

Cross-validation of protein structural class prediction using statistical clustering and neural networks.

We present an approach to predicting protein structural class that uses amino acid composition and hydrophobic pattern frequency information as input to two types of neural networks: (1) a three-layer back-propagation network and (2) a learning vector quantization network. The results of these methods are compared to those obtained from a modified Euclidean statistical clustering algorithm. The protein sequence data used to drive these algorithms consist of the normalized frequency of up to 20 amino acid types and six hydrophobic amino acid patterns. From these frequency values the structural class predictions for each protein (all-alpha, all-beta, or alpha-beta classes) are derived. Examples consisting of 64 previously classified proteins were randomly divided into multiple training (56 proteins) and test (8 proteins) sets. The best performing algorithm on the test sets was the learning vector quantization network using 17 inputs, obtaining a prediction accuracy of 80.2%. The Matthews correlation coefficients are statistically significant for all algorithms and all structural classes. The differences between algorithms are in general not statistically significant. These results show that information exists in protein primary sequences that is easily obtainable and useful for the prediction of protein structural class by neural networks as well as by standard statistical clustering algorithms.     

Prediction of recursive convex hull class assignments for protein residues

MOTIVATION: We introduce a new method for designating the location of residues in folded protein structures based on the recursive convex hull (RCH) of a point set of atomic coordinates. The RCH can be calculated with an efficient and parameterless algorithm. RESULTS: We show that residue RCH class contains information complementary to widely studied measures such as solvent accessibility (SA), residue depth (RD) and to the distance of residues from the centroid of the chain, the residues' exposure (Exp). RCH is more conserved for related structures across folds and correlates better with changes in thermal stability of mutants than the other measures. Further, we assess the predictability of these measures using three types of machine-learning technique: decision trees (C4.5), Naive Bayes and Learning Classifier Systems (LCS) showing that RCH is more easily predicted than the other measures. As an exemplar application of predicted RCH class (in combination with other measures), we show that RCH is potentially helpful in improving prediction of residue contact numbers (CN).     

蛋白质序列中的关联规则发现及其应用

随着蛋白质序列-结构分析中使用的机器学习算法越来越复杂,其结果的解释和发现过程也随之复杂化,因此有必要寻找简单且理论上可靠的方法。通过引入原理简单、理论可靠、结果具有很强实际意义的关联规则发现算法,找到了蛋白质序列中数以万计的模式。结合实例演示了如何将这些模式应用于蛋白质序列分析中,如保守区域发现、二级结构预测等。同时根据这些结果构建了一个二级结构规则库和一种简单的二级结构预测算法,实验结果表明,约81%的二级结构可以由至少一条关联规则预测得到。     

Predicting membrane protein types using residue-pair models based on reduced similarity dataset

An algorithm to predict the membrane protein types based on the multi-residue-pair effect in the Markov model is proposed. For a newly constructed dataset of 835 membrane proteins with very low sequence similarity, the overall prediction accuracy has been achieved as high as 81.1% and 71.7% in the resubstitution and jackknife test, respectively, for a prediction of type I single-pass, type II single-pass, multi-pass membrane proteins, lipid chain-anchored and GPI-anchored membrane proteins. The improvement of about 11% in the jackknife test can be achieved compared with the component-coupled algorithm merely based on the amino acid composition (AAC approach). The improvement is also confirmed on a high similarity dataset and the other extrapolating test. The result implies that designing more incisive analysis tools, one should develop algorithms based on the representative dataset with lower sequence similarity. The present algorithm is useful to expedite the determination of the types and functions of new membrane proteins and may be useful for the systematic analysis of functional genome data in a large scale. The computer program is available on request.     

Predicting protein structural class with AdaBoost Learner

The structural class is an important feature in characterizing the overall topological folding type of a protein or the domains therein. Prediction of protein structural classification has attracted the attention and efforts from many investigators. In this paper a novel predictor, the AdaBoost Learner, was introduced to deal with this problem. The essence of the AdaBoost Learner is that a combination of many 'weak' learning algorithms, each performing just slightly better than a random guessing algorithm, will generate a 'strong' learning algorithm. Demonstration thru jackknife cross-validation on two working datasets constructed by previous investigators indicated that AdaBoost outperformed other predictors such as SVM (support vector machine), a powerful algorithm widely used in biological literatures. It has not escaped our notice that AdaBoost may hold a high potential for improving the quality in predicting the other protein features as well, such as subcellular location and receptor type, among many others. Or at the very least, it will play a complementary role to many of the existing algorithms in this regard.     

Will my protein crystallize? A sequence‐based predictor

We propose a machine-learning approach to sequence-based prediction of protein crystallizability in which we exploit subtle differences between proteins whose structures were solved by X-ray analysis [or by both X-ray and nuclear magnetic resonance (NMR) spectroscopy] and those proteins whose structures were solved by NMR spectroscopy alone. Because the NMR technique is usually applied on relatively small proteins, sequence length distributions of the X-ray and NMR datasets were adjusted to avoid predictions biased by protein size. As feature space for classification, we used frequencies of mono-, di-, and tripeptides represented by the original 20-letter amino acid alphabet as well as by several reduced alphabets in which amino acids were grouped by their physicochemical and structural properties. The classification algorithm was constructed as a two-layered structure in which the output of primary support vector machine classifiers operating on peptide frequencies was combined by a second-level Naive Bayes classifier. Due to the application of metamethods for cost sensitivity, our method is able to handle real datasets with unbalanced class representation. An overall prediction accuracy of 67% [65% on the positive (crystallizable) and 69% on the negative (noncrystallizable) class] was achieved in a 10-fold cross-validation experiment, indicating that the proposed algorithm may be a valuable tool for more efficient target selection in structural genomics. A Web server for protein crystallizability prediction called SECRET is available at http://webclu.bio.wzw.tum.de:8080/secret.     

Toward an accurate prediction of inter-residue distances in proteins using 2D recursive neural networks

Background

Protein inter-residue contact maps provide a translation and rotation invariant topological representation of a protein. They can be used as an intermediary step in protein structure predictions. However, the prediction of contact maps represents an unbalanced problem as far fewer examples of contacts than non-contacts exist in a protein structure. In this study we explore the possibility of completely eliminating the unbalanced nature of the contact map prediction problem by predicting real-value distances between residues. Predicting full inter-residue distance maps and applying them in protein structure predictions has been relatively unexplored in the past.

Results

We initially demonstrate that the use of native-like distance maps is able to reproduce 3D structures almost identical to the targets, giving an average RMSD of 0.5Å. In addition, the corrupted physical maps with an introduced random error of ±6Å are able to reconstruct the targets within an average RMSD of 2Å. After demonstrating the reconstruction potential of distance maps, we develop two classes of predictors using two-dimensional recursive neural networks: an ab initio predictor that relies only on the protein sequence and evolutionary information, and a template-based predictor in which additional structural homology information is provided. We find that the ab initio predictor is able to reproduce distances with an RMSD of 6Å, regardless of the evolutionary content provided. Furthermore, we show that the template-based predictor exploits both sequence and structure information even in cases of dubious homology and outperforms the best template hit with a clear margin of up to 3.7Å. Lastly, we demonstrate the ability of the two predictors to reconstruct the CASP9 targets shorter than 200 residues producing the results similar to the state of the machine learning art approach implemented in the Distill server.

Conclusions

The methodology presented here, if complemented by more complex reconstruction protocols, can represent a possible path to improve machine learning algorithms for 3D protein structure prediction. Moreover, it can be used as an intermediary step in protein structure predictions either on its own or complemented by NMR restraints.     

The prediction of the structural class of protein: application of the measure of diversity.

Based on the concept that the structural class of a protein is mainly determined by its secondary structure sequence, a new algorithm for prediction of the structural class of a protein is proposed. By use of the number of alpha -helices, beta -strands, and betaalphabeta fragments, the structural class of a protein can be predicted by an algorithm based on the increment of diversity (ID), in which the sole prediction parameter-the increment of diversity is used as the index of prediction of structural class of a protein. The results indicate that the high rates of correct prediction are obtained for complete set (standard set) from Brookhaven Protein Data Bank-CD ROM (PDB) published in October 1995 and the test set newly released from Brookhaven Protein Data Bank-CD ROM (PDB) before July 1998, respectively.     

Statistical Measures of DNA Sequence Dissimilarity under Markov Chain Models of Base Composition

In molecular biology, the issue of quantifying the similarity between two biological sequences is very important. Past research has shown that word-based search tools are computationally efficient and can find some new functional similarities or dissimilarities invisible to other algorithms like FASTA. Recently, under the independent model of base composition, Wu, Burke, and Davison (1997, Biometrics 53, 1431 1439) characterized a family of word-based dissimilarity measures that defined distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters (i.e., n-words) in the two sequences. Specifically, they introduced the use of Mahalanobis distance and standardized Euclidean distance into the study of DNA sequence dissimilarity. They showed that both distances had better sensitivity and selectivity than the commonly used Euclidean distance. The purpose of this article is to extend Mahalanobis and standardized Euclidean distances to Markov chain models of base composition. In addition, a new dissimilarity measure based on Kullback-Leibler discrepancy between frequencies of all n-words in the two sequences is introduced. Applications to real data demonstrate that Kullback-Leibler discrepancy gives a better performance than Euclidean distance. Moreover, under a Markov chain model of order kQ for base composition, where kQ is the estimated order based on the query sequence, standardized Euclidean distance performs very well. Under such a model, it performs as well as Mahalanobis distance and better than Kullback-Leibler discrepancy and Euclidean distance. Since standardized Euclidean distance is drastically faster to compute than Mahalanobis distance, in a usual workstation/PC computing environment, the use of standardized Euclidean distance under the Markov chain model of order kQ of base composition is generally recommended. However, if the user is very concerned with computational efficiency, then the use of Kullback-Leibler discrepancy, which can be computed as fast as Euclidean distance, is recommended. This can significantly enhance the current technology in comparing large datasets of DNA sequences.     

互信息理论结合决策树算法的土壤质量预测

在充分利用土壤类型、土地利用方式、岩性类型、地形、道路、工业类型等影响土壤质量主要因素,准确获取区域土壤质量的空间分布特征的基础上,采用互信息理论对13个辅助变量（岩性类型、土地利用方式、土壤类型、到城镇的距离、到道路的距离、到工业用地的距离、到河流的距离、相对高程、坡度、坡向、平向曲率、纵向曲率和切线曲率）进行筛选,然后通过决策树See5.0预测研究区土壤质量.结果表明： 影响研究区土壤质量的主要因素包括土壤类型、土地利用方式、岩性类型、到城镇的距离、到水域的距离、相对高程、到道路的距离和到工业用地的距离;以互信息理论选取的因子为预测变量的决策树模型精度明显优于以全部因子为预测变量的决策树模型,在前者的决策树模型中,无论是决策树还是决策规则,分类预测精度均达到80%以上.互信息理论结合决策树的方法在充分利用连续型和字符型数据的基础上,不仅精简了一般决策树算法的输入参数,而且能有效地预测和评价区域土壤质量等级.     

RBRDetector: Improved prediction of binding residues on RNA‐binding protein structures using complementary feature‐ and template‐based strategies

Computational prediction of RNA‐binding residues is helpful in uncovering the mechanisms underlying protein‐RNA interactions. Traditional algorithms individually applied feature‐ or template‐based prediction strategy to recognize these crucial residues, which could restrict their predictive power. To improve RNA‐binding residue prediction, herein we propose the first integrative algorithm termed RBRDetector (RNA‐Binding Residue Detector) by combining these two strategies. We developed a feature‐based approach that is an ensemble learning predictor comprising multiple structure‐based classifiers, in which well‐defined evolutionary and structural features in conjunction with sequential or structural microenvironment were used as the inputs of support vector machines. Meanwhile, we constructed a template‐based predictor to recognize the putative RNA‐binding regions by structurally aligning the query protein to the RNA‐binding proteins with known structures. The final RBRDetector algorithm is an ingenious fusion of our feature‐ and template‐based approaches based on a piecewise function. By validating our predictors with diverse types of structural data, including bound and unbound structures, native and simulated structures, and protein structures binding to different RNA functional groups, we consistently demonstrated that RBRDetector not only had clear advantages over its component methods, but also significantly outperformed the current state‐of‐the‐art algorithms. Nevertheless, the major limitation of our algorithm is that it performed relatively well on DNA‐binding proteins and thus incorrectly predicted the DNA‐binding regions as RNA‐binding interfaces. Finally, we implemented the RBRDetector algorithm as a user‐friendly web server, which is freely accessible at http://ibi.hzau.edu.cn/rbrdetector . Proteins 2014; 82:2455–2471. © 2014 Wiley Periodicals, Inc.     

Protein structures in solution by nuclear magnetic resonance and distance geometry. The polypeptide fold of the basic pancreatic trypsin inhibitor determined using two different algorithms, DISGEO and DISMAN

A set of conformational restraints derived from nuclear magnetic resonance (n.m.r.) measurements on solutions of the basic pancreatic trypsin inhibitor (BPTI) was used as input for distance geometry calculations with the programs DISGEO and DISMAN. Five structures obtained with each of these algorithms were systematically compared among themselves and with the crystal structure of BPTI. It is clear that the protein architecture observed in single crystals of BPTI is largely preserved in aqueous solution, with local structural differences mainly confined to the protein surface. The results confirm that protein conformations determined in solution by combined use of n.m.r. and distance geometry are a consequence of the experimental data and do not depend significantly on the algorithm used for the structure determination. The data obtained further provide an illustration that long intramolecular distances in proteins, which are comparable with the radius of gyration, are defined with high precision by relatively imprecise nuclear Overhauser enhancement measurements of a large number of much shorter distances.     

Prediction of protein structural class using a complexity-based distance measure

Knowledge of structural class plays an important role in understanding protein folding patterns. So it is necessary to develop effective and reliable computational methods for prediction of protein structural class. To this end, we present a new method called NN-CDM, a nearest neighbor classifier with a complexity-based distance measure. Instead of extracting features from protein sequences as done previously, distance between each pair of protein sequences is directly evaluated by a complexity measure of symbol sequences. Then the nearest neighbor classifier is adopted as the predictive engine. To verify the performance of this method, jackknife cross-validation tests are performed on several benchmark datasets. Results show that our approach achieves a high prediction accuracy over some classical methods.