A statistical model for predicting protein folding rates from amino acid sequence with structural class information

Prediction of protein folding rates from amino acid sequences is one of the most important challenges in molecular biology. In this work, I have related the protein folding rates with physical-chemical, energetic and conformational properties of amino acid residues. I found that the classification of proteins into different structural classes shows an excellent correlation between amino acid properties and folding rates of two- and three-state proteins, indicating the importance of native state topology in determining the protein folding rates. I have formulated a simple linear regression model for predicting the protein folding rates from amino acid sequences along with structural class information and obtained an excellent agreement between predicted and experimentally observed folding rates of proteins; the correlation coefficients are 0.99, 0.96 and 0.95, respectively, for all-alpha, all-beta and mixed class proteins. This is the first available method, which is capable of predicting the protein folding rates just from the amino acid sequence with the aid of generic amino acid properties and structural class information.     

Analysis and prediction of protein folding rates using quadratic response surface models

Understanding the relationship between amino acid sequences and folding rates of proteins is an important task in computational and molecular biology. In this work, we have systematically analyzed the composition of amino acid residues for proteins with different ranges of folding rates. We observed that the polar residues, Asn, Gln, Ser, and Lys, are dominant in fast folding proteins whereas the hydrophobic residues, Ala, Cys, Gly, and Leu, prefer to be in slow folding proteins. Further, we have developed a method based on quadratic response surface models for predicting the folding rates of 77 two- and three-state proteins. Our method showed a correlation of 0.90 between experimental and predicted protein folding rates using leave-one-out cross-validation method. The classification of proteins based on structural class improved the correlation to 0.98 and it is 0.99, 0.98, and 0.96, respectively, for all-alpha, all-beta, and mixed class proteins. In addition, we have utilized Baysean classification theory for discriminating two- and three-state proteins, which showed an accuracy of 90%. We have developed a web server for predicting protein folding rates and it is available at http://bioinformatics.myweb.hinet.net/foldrate.htm.     

Importance of native-state topology for determining the folding rate of two-state proteins

Understanding the relationship between amino acid sequences and folding rate of proteins is a challenging task similar to protein folding problem. In this work, we have analyzed the relative importance of protein sequence and structure for predicting the protein folding rates in terms of amino acid properties and contact distances, respectively. We found that the parameters derived with protein sequence (physical-chemical, energetic, and conformational properties of amino acid residues) show very weak correlation (|r| < 0.39) with folding rates of 28 two-state proteins, indicating that the sequence information alone is not sufficient to understand the folding rates of two-state proteins. However, the maximum positive correlation obtained for the properties, number of medium-range contacts, and alpha-helical tendency reveals the importance of local interactions to initiate protein folding. On the other hand, a remarkable correlation (r varies from -0.74 to -0.88) has been obtained between structural parameters (contact order, long-range order, and total contact distance) and protein folding rates. Further, we found that the secondary structure content and solvent accessibility play a marginal role in determining the folding rates of two-state proteins. Multiple regression analysis carried out with the combination of three properties, beta-strand tendency, enthalpy change, and total contact distance improved the correlation to 0.92 with protein folding rates. The relative importance of existing methods along with multiple-regression model proposed in this work will be discussed. Our results demonstrate that the native-state topology is the major determinant for the folding rates of two-state proteins.     

Predicting protein folding rates using the concept of Chou's pseudo amino acid composition

One of the most important challenges in computational and molecular biology is to understand the relationship between amino acid sequences and the folding rates of proteins. Recent works suggest that topological parameters, amino acid properties, chain length and the composition index relate well with protein folding rates, however, sequence order information has seldom been considered as a property for predicting protein folding rates. In this study, amino acid sequence order was used to derive an effective method, based on an extended version of the pseudo-amino acid composition, for predicting protein folding rates without any explicit structural information. Using the jackknife cross validation test, the method was demonstrated on the largest dataset (99 proteins) reported. The method was found to provide a good correlation between the predicted and experimental folding rates. The correlation coefficient is 0.81 (with a highly significant level) and the standard error is 2.46. The reported algorithm was found to perform better than several representative sequence-based approaches using the same dataset. The results indicate that sequence order information is an important determinant of protein folding rates.     

Prediction of protein structural classes by a new measure of information discrepancy

Since it was observed that the structural class of a protein is related to its amino acid composition, various methods based on amino acid composition have been proposed to predict protein structural classes. Though those methods are effective to some degree, their predictive quality is confined because amino acid composition cannot sufficiently include the information of protein sequences. In this paper, a measure of information discrepancy is applied to the prediction of protein structural classes; different from the previous methods, this new approach is based on the comparisons of subsequence distributions; therefore, the effect of residue order on protein structure is taken into account. The predictive results of the new approach on the same data set are better than those of the previous methods. As to a data set of 1401 sequences with no more than 30% redundancy, the overall correctness rates of resubstitution test and Jackknife test are 99.4 and 75.02%, respectively, and to other data sets the similar results are also obtained. All tests demonstrate that the residue order along protein sequences plays an important role on recognition of protein structural classes, especially for alpha/beta proteins and alpha+beta proteins. In addition, the tests also show that the new method is simple and efficient.     

Mechanically untying a protein slipknot: multiple pathways revealed by force spectroscopy and steered molecular dynamics simulations

Protein structure is highly diverse when considering a wide range of protein types, helping to give rise to the multitude of functions that proteins perform. In particular, certain proteins are known to adopt a knotted or slipknotted fold. How such proteins undergo mechanical unfolding was investigated utilizing a combination of single molecule atomic force microscopy (AFM), protein engineering, and steered molecular dynamics (SMD) simulations to show the mechanical unfolding mechanism of the slipknotted protein AFV3-109. Our results reveal that the mechanical unfolding of AFV3-109 can proceed via multiple parallel unfolding pathways that all cause the protein slipknot to untie and the polypeptide chain to completely extend. These distinct unfolding pathways proceed via either a two- or three-state unfolding process involving the formation of a well-defined, stable intermediate state. SMD simulations predict the same contour length increments for different unfolding pathways as single molecule AFM results, thus providing a plausible molecular mechanism for the mechanical unfolding of AFV3-109. These SMD simulations also reveal that two-state unfolding is initiated from both the N- and C-termini, while three-state unfolding is initiated only from the C-terminus. In both pathways, the protein slipknot was untied during unfolding, and no tightened slipknot conformation was observed. Detailed analysis revealed that interactions between key structural elements lock the knotting loop in place, preventing it from shrinking and the formation of a tightened slipknot conformation. Our results demonstrate the bifurcation of the mechanical unfolding pathway of AFV3-109 and point to the generality of a kinetic partitioning mechanism for protein folding/unfolding.     

Using pseudo amino acid composition to predict protein structural class: approached by incorporating 400 dipeptide components

The proteins structure can be mainly classified into four classes: all-alpha, all-beta, alpha/beta, and alpha + beta protein according to their chain fold topologies. For the purpose of predicting the protein structural class, a new predicting algorithm, in which the increment of diversity combines with Quadratic Discriminant analysis, is presented to study and predict protein structural class. On the basis of the concept of the pseudo amino acid composition (Chou, Proteins: Struct Funct Genet 2001, 43, 246; Erratum: Proteins Struct Funct Genet 2001, 44, 60), 400 dipeptide components and 20 amino acid composition are, respectively, selected as parameters of diversity source. Total of 204 nonhomologous proteins constructed by Chou (Chou, Biochem Biophys Res Commun 1999, 264, 216) are used for training and testing the predictive model. The predicted results by using the pseudo amino acids approach as proposed in this paper can remarkably improve the success rates, and hence the current method may play a complementary role to other existing methods for predicting protein structural classification.     

Prediction of protein folding rates from primary sequences using hybrid sequence representation

The ability to predict protein folding rates constitutes an important step in understanding the overall folding mechanisms. Although many of the prediction methods are structure based, successful predictions can also be obtained from the sequence. We developed a novel method called prediction of protein folding rates (PPFR), for the prediction of protein folding rates from protein sequences. PPFR implements a linear regression model for each of the mainstream folding dynamics including two-, multi-, and mixed-state proteins. The proposed method provides predictions characterized by strong correlations with the experimental folding rates, which equal 0.87 for the two- and multistate proteins and 0.82 for the mixed-state proteins, when evaluated with out-of-sample jackknife test. Based on in-sample and out-of-sample tests, the PPFR's predictions are shown to be better than most of other sequence only and structure-based predictors and complementary to the predictions of the most recent sequence-based QRSM method. We show that simultaneous incorporation of several characteristics, including the sequence, physiochemical properties of residues, and predicted secondary structure provides improved quality. This hybridized prediction model was analyzed to reveal the complementary factors that can be used in tandem to predict folding rates. We show that bigger proteins require more time for folding, higher helical and coil content and the presence of Phe, Asn, and Gln may accelerate the folding process, the inclusion of Ile, Val, Thr, and Ser may slow down the folding process, and for the two-state proteins increased beta-strand content may decelerate the folding process. Finally, PPFR provides strong correlation when predicting sequences with low similarity.     

Real value prediction of protein folding rate change upon point mutation

Prediction of protein folding rate change upon amino acid substitution is an important and challenging problem in protein folding kinetics and design. In this work, we have analyzed the relationship between amino acid properties and folding rate change upon mutation. Our analysis showed that the correlation is not significant with any of the studied properties in a dataset of 476 mutants. Further, we have classified the mutants based on their locations in different secondary structures and solvent accessibility. For each category, we have selected a specific combination of amino acid properties using genetic algorithm and developed a prediction scheme based on quadratic regression models for predicting the folding rate change upon mutation. Our results showed a 10-fold cross validation correlation of 0.72 between experimental and predicted change in protein folding rates. The correlation is 0.73, 0.65 and 0.79, respectively in strand, helix and coil segments. The method has been further tested with an extended dataset of 621 mutants and a blind dataset of 62 mutants, and we observed a good agreement with experiments. We have developed a web server for predicting the folding rate change upon mutation and it is available at .     

Structural and functional properties of designed globins

De novo design of artificial proteins is an essential approach to elucidate the principles of protein architecture and to understand specific functions of natural proteins and also to yield novel molecules for medical and industrial aims. We have designed artificial sequences of 153 amino acids to fit the main-chain framework of the sperm whale myoglobin structure based on the knowledge-based energy functions to evaluate the compatibility between protein tertiary structures and amino acid sequences. The synthesized artificial globins bind a single heme per protein molecule as designed, which show well-defined electrochemical and spectroscopic features characteristic of proteins with a low-spin heme. Redox and ligand binding reactions of the artificial heme proteins were investigated and these heme-related functions were found to vary with their structural uniqueness. Relationships between the structural and functional properties are discussed.     

依据氨基酸残基的相关性预测蛋白质的结构类型

作为蛋白质的建筑构件,各种类型的蛋白质的20种氨基酸残基之间存在着特定的相互关联,反映了氨基酸残基之间的制约性,并有深刻的物理和化学的内在因素.某些氨基酸残基对之间的相关系数可以作为一种类型的蛋白质区别于其它类型蛋白质的特征,用于蛋白质结构类型的预测.研究了4种类型的蛋白质204个样品的氨基酸残基对的相关性系数,找出了可作为蛋白质结构类型特征的氨基酸残基的相关对,并用于蛋白质结构类型的预测,对于α型、β型、α/β型和α＋β型蛋白质的204个蛋白质样品的交叉测试,正确率分别为94％、89％、79％和89％,平均为88％,高于简单距离法和欧几里德距离法.     

Improving protein structural class prediction using novel combined sequence information and predicted secondary structural features

Protein structural class prediction solely from protein sequences is a challenging problem in bioinformatics. Numerous efficient methods have been proposed for protein structural class prediction, but challenges remain. Using novel combined sequence information coupled with predicted secondary structural features (PSSF), we proposed a novel scheme to improve prediction of protein structural classes. Given an amino acid sequence, we first transformed it into a reduced amino acid sequence and calculated its word frequencies and word position features to combine novel sequence information. Then we added the PSSF to the combine sequence information to predict protein structural classes. The proposed method was tested on four benchmark datasets in low homology and achieved the overall prediction accuracies of 83.1%, 87.0%, 94.5%, and 85.2%, respectively. The comparison with existing methods demonstrates that the overall improvements range from 2.3% to 27.5%, which indicates that the proposed method is more efficient, especially for low-homology amino acid sequences.     

Classification of protein fold classes by knot theory and prediction of folds by neural networks: A combined theoretical and experimental approach

We present different means of classifying protein structure. One is made rigorous by mathematical knot invariants that coincide reasonably well with ordinary graphical fold classification and another classification is by packing analysis. Furthermore when constructing our mathematical fold classifications, we utilize standard neural network methods for predicting protein fold classes from amino acid sequences. We also make an analysis of the redundancy of the structural classifications in relation to function and ligand binding. Finally we advocate the use of combining the measurement of the VA, VCD, Raman, ROA, EA and ECD spectra with the primary sequence as a way to improve both the accuracy and reliability of fold class prediction schemes.     

Application of principal component analysis in protein unfolding: an all-atom molecular dynamics simulation study

We have performed molecular dynamics (MD) simulation of the thermal denaturation of one protein and one peptide-ubiquitin and melittin. To identify the correlation in dynamics among various secondary structural fragments and also the individual contribution of different residues towards thermal unfolding, principal component analysis method was applied in order to give a new insight to protein dynamics by analyzing the contribution of coefficients of principal components. The cross-correlation matrix obtained from MD simulation trajectory provided important information regarding the anisotropy of backbone dynamics that leads to unfolding. Unfolding of ubiquitin was found to be a three-state process, while that of melittin, though smaller and mostly helical, is more complicated.     

A localized specific interaction alters the unfolding pathways of structural homologues

Reductive unfolding studies of proteins are designed to provide information about intramolecular interactions that govern the formation (and stabilization) of the native state and about folding/unfolding pathways. By mutating Tyr92 to G, A, or L in the model protein, bovine pancreatic ribonuclease A, and through analysis of temperature factors and molecular dynamics simulations of the crystal structures of these mutants, it is demonstrated that the markedly different reductive unfolding rates and pathways of ribonuclease A and its structural homologue onconase can be attributed to a single, localized, ring-stacking interaction between Tyr92 and Pro93 in the bovine variant. The fortuitous location of this specific stabilizing interaction in a disulfide-bond-containing loop region of ribonuclease A results in the localized modulation of protein dynamics that, in turn, enhances the susceptibility of the disulfide bond to reduction leading to an alteration in the reductive unfolding behavior of the homologues. These results have important implications for folding studies involving topological determinants to obtain folding/unfolding rates and pathways, for protein structure-function prediction through fold recognition, and for predicting proteolytic cleavage sites.     

Relative importance of secondary structure and solvent accessibility to the stability of protein mutants. A case study with amino acid properties and energetics on T4 and human lysozymes

Understanding the factors influencing the stability of protein mutants is an important task in molecular and computational biology. In this work, we have approached this problem by examining the relative importance of secondary structure and solvent accessibility of the mutant residue for understanding/predicting the stability of protein mutants. We have used hydrophobic, electrostatic and hydrogen bond free energy terms and nine unique physicochemical, energetic and conformational properties of amino acids in the present study and these parameters have been related with changes in thermal stability (DeltaTm) of all the single mutants of lysozymes based on single and multiple correlation coefficients. As expected the properties reflecting hydrophobicity and hydrophobic free energy play a major role to distinguish stabilizing and destabilizing mutants. The hydrophobic free energy due to carbon and nitrogen atoms distinguish the stability of coil and strand mutations to the accuracy of 100 and 90%, respectively. In agreement with previous results, the subgroup classification based on secondary structure and the information about its location in the structure yielded good relationship with the experimental DeltaTm. We revealed that the secondary structure information is equally or more important than solvent accessibility for understanding the stability of protein mutants. The comparison of amino acid properties with free-energy terms indicate that the energetic contribution explains the mutant stability better in coil region whereas the amino acid properties do better in strand region. Further, the combination of free energies with amino acid properties increased the correlation significantly. The present study demonstrates the importance of classifying the mutants based on secondary structure to the stability of proteins upon mutations.     

Proteins in a shear flow

The conformational dynamics of a single protein molecule in a shear flow is investigated using Brownian dynamics simulations. A structure-based coarse grained model of a protein is used. We consider two proteins, ubiquitin and integrin, and find that at moderate shear rates they unfold through a sequence of metastable states-a pattern which is distinct from a smooth unraveling found in homopolymers. Full unfolding occurs only at very large shear rates. Furthermore, the hydrodynamic interactions between the amino acids are shown to hinder the shear flow unfolding. The characteristics of the unfolding process depend on whether a protein is anchored or not, and if it is, on the choice of an anchoring point.