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

Importance of Inter-residue Contacts for Understanding Protein Folding and Unfolding Rates, Remote Homology, and Drug Design

Inter-residue interactions in protein structures provide valuable insights into protein folding and stability. Understanding these interactions can be helpful in many crucial applications, including rational design of therapeutic small molecules and biologics, locating functional protein sites, and predicting protein-protein and protein-ligand interactions. The process of developing machine learning models incorporating inter-residue interactions has been improved recently. This review highlights the theoretical models incorporating inter-residue interactions in predicting folding and unfolding rates of proteins. Utilizing contact maps to depict inter-residue interactions aids researchers in developing computer models for detecting remote homologs and interface residues within protein-protein complexes which, in turn, enhances our knowledge of the relationship between sequence and structure of proteins. Further, the application of contact maps derived from inter-residue interactions is highlighted in the field of drug discovery. Overall, this review presents an extensive assessment of the significant models that use inter-residue interactions to investigate folding rates, unfolding rates, remote homology, and drug development, providing potential future advancements in constructing efficient computational models in structural biology.

Solution of Levinthal's Paradox and a Physical Theory of Protein Folding Times

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

A novel model-based on FCM-LM algorithm for prediction of protein folding rate

The prediction of protein folding rates is of paramount importance in describing the protein folding mechanism, which has broad applications in fields such as enzyme engineering and protein engineering. Therefore, predicting protein folding rates using the first-order of protein sequence, secondary structure and amino acid properties has become a very active research topic in recent years. This paper presents a new fuzzy cognitive map (FCM) model based on deep learning neural networks which uses data obtained from biological experiments to predict the protein folding rate. FCM extracts the important data features from the protein sequence which then initializes the deep neural networks effectively. It was found that the Levenberg-Marquardt (LM) algorithm for deep neural networks can improve the prediction accuracy of the protein folding rates. The correlation coefficient between the predicted values and those real values obtained from experiments reached 0.94 and 0.9 in two independent numerical tests.

Machine Learning: How Much Does It Tell about Protein Folding Rates?

The prediction of protein folding rates is a necessary step towards understanding the principles of protein folding. Due to the increasing amount of experimental data, numerous protein folding models and predictors of protein folding rates have been developed in the last decade. The problem has also attracted the attention of scientists from computational fields, which led to the publication of several machine learning-based models to predict the rate of protein folding. Some of them claim to predict the logarithm of protein folding rate with an accuracy greater than 90%. However, there are reasons to believe that such claims are exaggerated due to large fluctuations and overfitting of the estimates. When we confronted three selected published models with new data, we found a much lower predictive power than reported in the original publications. Overly optimistic predictive powers appear from violations of the basic principles of machine-learning. We highlight common misconceptions in the studies claiming excessive predictive power and propose to use learning curves as a safeguard against those mistakes. As an example, we show that the current amount of experimental data is insufficient to build a linear predictor of logarithms of folding rates based on protein amino acid composition.

Folding RaCe: a robust method for predicting changes in protein folding rates upon point mutations

MOTIVATION

Protein engineering methods are commonly employed to decipher the folding mechanism of proteins and enzymes. However, such experiments are exceedingly time and resource intensive. It would therefore be advantageous to develop a simple computational tool to predict changes in folding rates upon mutations. Such a method should be able to rapidly provide the sequence position and chemical nature to modulate through mutation, to effect a particular change in rate. This can be of importance in protein folding, function or mechanistic studies.

RESULTS

We have developed a robust knowledge-based methodology to predict the changes in folding rates upon mutations formulated from amino and acid properties using multiple linear regression approach. We benchmarked this method against an experimental database of 790 point mutations from 26 two-state proteins. Mutants were first classified according to secondary structure, accessible surface area and position along the primary sequence. Three prime amino acid features eliciting the best relationship with folding rates change were then shortlisted for each class along with an optimized window length. We obtained a self-consistent mean absolute error of 0.36 s(-1) and a mean Pearson correlation coefficient (PCC) of 0.81. Jack-knife test resulted in a MAE of 0.42 s(-1) and a PCC of 0.73. Moreover, our method highlights the importance of outlier(s) detection and studying their implications in the folding mechanism.

AVAILABILITY AND IMPLEMENTATION

A web server 'Folding RaCe' has been developed and is available at http://www.iitm.ac.in/bioinfo/proteinfolding/foldingrace.html.

CONTACT

gromiha@iitm.ac.in

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Swfoldrate: predicting protein folding rates from amino acid sequence with sliding window method

Protein folding is the process by which a protein processes from its denatured state to its specific biologically active conformation. Understanding the relationship between sequences and the folding rates of proteins remains an important challenge. Most previous methods of predicting protein folding rate require the tertiary structure of a protein as an input. In this study, the long-range and short-range contact in protein were used to derive extended version of the pseudo amino acid composition based on sliding window method. This method is capable of predicting the protein folding rates just from the amino acid sequence without the aid of any structural class information. We systematically studied the contributions of individual features to folding rate prediction. The optimal feature selection procedures are adopted by means of combining the forward feature selection and sequential backward selection method. Using the jackknife cross validation test, the method was demonstrated on the large dataset. The predictor was achieved on the basis of multitudinous physicochemical features and statistical features from protein using nonlinear support vector machine (SVM) regression model, the method obtained an excellent agreement between predicted and experimentally observed folding rates of proteins. The correlation coefficient is 0.9313 and the standard error is 2.2692. The prediction server is freely available at http://www.jci-bioinfo.cn/swfrate/input.jsp.

Predicting protein folding rate from amino acid sequence

Predicting protein folding rate from amino acid sequence is an important challenge in computational and molecular biology. Over the past few years, many methods have been developed to reflect the correlation between the folding rates and protein structures and sequences. In this paper, we present an effective method, a combined neural network--genetic algorithm approach, to predict protein folding rates only from amino acid sequences, without any explicit structural information. The originality of this paper is that, for the first time, it tackles the effect of sequence order. The proposed method provides a good correlation between the predicted and experimental folding rates. The correlation coefficient is 0.80 and the standard error is 2.65 for 93 proteins, the largest such databases of proteins yet studied, when evaluated with leave-one-out jackknife test. The comparative results demonstrate that this correlation is better than most of other methods, and suggest the important contribution of sequence order information to the determination of protein folding rates.

Update of PROFEAT: a web server for computing structural and physicochemical features of proteins and peptides from amino acid sequence

Sequence-derived structural and physicochemical features have been extensively used for analyzing and predicting structural, functional, expression and interaction profiles of proteins and peptides. PROFEAT has been developed as a web server for computing commonly used features of proteins and peptides from amino acid sequence. To facilitate more extensive studies of protein and peptides, numerous improvements and updates have been made to PROFEAT. We added new functions for computing descriptors of protein–protein and protein–small molecule interactions, segment descriptors for local properties of protein sequences, topological descriptors for peptide sequences and small molecule structures. We also added new feature groups for proteins and peptides (pseudo-amino acid composition, amphiphilic pseudo-amino acid composition, total amino acid properties and atomic-level topological descriptors) as well as for small molecules (atomic-level topological descriptors). Overall, PROFEAT computes 11 feature groups of descriptors for proteins and peptides, and a feature group of more than 400 descriptors for small molecules plus the derived features for protein–protein and protein–small molecule interactions. Our computational algorithms have been extensively tested and used in a number of published works for predicting proteins of specific structural or functional classes, protein–protein interactions, peptides of specific functions and quantitative structure activity relationships of small molecules. PROFEAT is accessible free of charge at http://bidd.cz3.nus.edu.sg/cgi-bin/prof/protein/profnew.cgi.

The dynamical contact order: protein folding rate parameters based on quantum conformational transitions

Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain. According to the quantum theory of conformational dynamics, we propose the dynamical contact order (DCO) defined as a characteristic of the contact described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues. Consequently, the protein folding rate can be quantitatively studied from the point of view of dynamics. By comparing theoretical calculations and experimental data on the folding rate of 80 proteins, we successfully validate the view that protein folding is a quantum conformational transition. We conclude that (i) a correlation between the protein folding rate and the contact inertial moment exists; (ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state proteins but with an intermediate delay. We have estimated the order of magnitude of the time delay; (iii) folding can be classified into two types, exergonic and endergonic. Most of the two-state proteins with higher folding rate are exergonic and most of the multi-state proteins with low folding rate are endergonic. The folding speed limit is determined by exergonic folding.

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.

Composition-based effective chain length for prediction of protein folding rates

Folding rate prediction is a useful way to find the key factors affecting folding kinetics of proteins. Structural information is more or less required in the present prediction methods, which limits the application of these methods to various proteins. In this work, an "effective length" is defined solely based on the composition of a protein, namely, the number of specific types of amino acids in a protein. A physical theory based on a minimalist model is employed to describe the relation between the folding rates and the effective length of proteins. Based on the resultant relationship between folding rates and effective length, the optimal sets of amino acids are found through the enumeration over all possible combinations of amino acids. This optimal set achieves a high correlation (with the coefficient of 0.84) between the folding rates and the optimal effective length. The features of these amino acids are consistent with our model and landscape theory. Further comparisons between our effective length and other factors are carried out. The effective length is physically consistent with structure-based prediction methods and has the best predictability for folding rates. These results all suggest that both entropy and energetics contribute importantly to folding kinetics. The ability to accurately and efficiently predict folding rates from composition enables the analysis of the kinetics for various kinds of proteins. The underlying physics in our method may be helpful to stimulate further understanding on the effects of various amino acids in folding dynamics.

Accurate prediction of protein folding rates from sequence and sequence-derived residue flexibility and solvent accessibility

Protein folding rates vary by several orders of magnitude and they depend on the topology of the fold and the size and composition of the sequence. Although recent works show that the rates can be predicted from the sequence, allowing for high-throughput annotations, they consider only the sequence and its predicted secondary structure. We propose a novel sequence-based predictor, PFR-AF, which utilizes solvent accessibility and residue flexibility predicted from the sequence, to improve predictions and provide insights into the folding process. The predictor includes three linear regressions for proteins with two-state, multistate, and unknown (mixed-state) folding kinetics. PFR-AF on average outperforms current methods when tested on three datasets. The proposed approach provides high-quality predictions in the absence of similarity between the predicted and the training sequences. The PFR-AF's predictions are characterized by high (between 0.71 and 0.95, depending on the dataset) correlation and the lowest (between 0.75 and 0.9) mean absolute errors with respect to the experimental rates, as measured using out-of-sample tests. Our models reveal that for the two-state chains inclusion of solvent-exposed Ala may accelerate the folding, while increased content of Ile may reduce the folding speed. We also demonstrate that increased flexibility of coils facilitates faster folding and that proteins with larger content of solvent-exposed strands may fold at a slower pace. The increased flexibility of the solvent-exposed residues is shown to elongate folding, which also holds, with a lower correlation, for buried residues. Two case studies are included to support our findings.

Modular prediction of protein structural classes from sequences of twilight-zone identity with predicting sequences

Background

Knowledge of structural class is used by numerous methods for identification of structural/functional characteristics of proteins and could be used for the detection of remote homologues, particularly for chains that share twilight-zone similarity. In contrast to existing sequence-based structural class predictors, which target four major classes and which are designed for high identity sequences, we predict seven classes from sequences that share twilight-zone identity with the training sequences.

Results

The proposed MODular Approach to Structural class prediction (MODAS) method is unique as it allows for selection of any subset of the classes. MODAS is also the first to utilize a novel, custom-built feature-based sequence representation that combines evolutionary profiles and predicted secondary structure. The features quantify information relevant to the definition of the classes including conservation of residues and arrangement and number of helix/strand segments. Our comprehensive design considers 8 feature selection methods and 4 classifiers to develop Support Vector Machine-based classifiers that are tailored for each of the seven classes. Tests on 5 twilight-zone and 1 high-similarity benchmark datasets and comparison with over two dozens of modern competing predictors show that MODAS provides the best overall accuracy that ranges between 80% and 96.7% (83.5% for the twilight-zone datasets), depending on the dataset. This translates into 19% and 8% error rate reduction when compared against the best performing competing method on two largest datasets. The proposed predictor provides accurate predictions at 58% accuracy for membrane proteins class, which is not considered by majority of existing methods, in spite that this class accounts for only 2% of the data. Our predictive model is analyzed to demonstrate how and why the input features are associated with the corresponding classes.

Conclusions

The improved predictions stem from the novel features that express collocation of the secondary structure segments in the protein sequence and that combine evolutionary and secondary structure information. Our work demonstrates that conservation and arrangement of the secondary structure segments predicted along the protein chain can successfully predict structural classes which are defined based on the spatial arrangement of the secondary structures. A web server is available at http://biomine.ece.ualberta.ca/MODAS/.

An integrated method for cancer classification and rule extraction from microarray data

Different microarray techniques recently have been successfully used to investigate useful information for cancer diagnosis at the gene expression level due to their ability to measure thousands of gene expression levels in a massively parallel way. One important issue is to improve classification performance of microarray data. However, it would be ideal that influential genes and even interpretable rules can be explored at the same time to offer biological insight.

Introducing the concepts of system design in software engineering, this paper has presented an integrated and effective method (named X-AI) for accurate cancer classification and the acquisition of knowledge from DNA microarray data. This method included a feature selector to systematically extract the relative important genes so as to reduce the dimension and retain as much as possible of the class discriminatory information. Next, diagonal quadratic discriminant analysis (DQDA) was combined to classify tumors, and generalized rule induction (GRI) was integrated to establish association rules which can give an understanding of the relationships between cancer classes and related genes.

Two non-redundant datasets of acute leukemia were used to validate the proposed X-AI, showing significantly high accuracy for discriminating different classes. On the other hand, I have presented the abilities of X-AI to extract relevant genes, as well as to develop interpretable rules. Further, a web server has been established for cancer classification and it is freely available at .