Prediction Of Folding Rates Research Articles

Recent advances in the integration of protein mechanics and machine learning

Mechanics underlies protein properties and behavior. From a theoretical standpoint, it is possible to derive these based on physical rules. This is appealing because they provide insights into physiology and disease, as well as aid in protein engineering; however, the convoluted nature of the biological system and current computational speeds limit its feasibility. Machine learning (ML) architectures are known for their ability to make inferences on complex data, such as the relationship between protein mechanics, properties, and behavior. Substantial efforts have been made to learn such correlations in tasks such as the prediction of structure, stability, natural frequency, mechanical strength, folding rate, solubility, and function. Each of these properties is interconnected through protein mechanics, and it is not surprising that the methods used in these tasks overlap highly in model input and architecture. In this review, we evaluate ML methods for the seven aforementioned prediction tasks to identify current trends in ML research in the field of protein sciences, focusing on the input and model architecture of each method. A short overview of de novo protein design is also provided. Finally, we highlight trends in the application of ML methods in the field of protein science, as well as directions for future improvements.

Computational prediction of protein folding rate using structural parameters and network centrality measures

Protein folding is a complex physicochemical process whereby a polymer of amino acids samples numerous conformations in its unfolded state before settling on an essentially unique native three-dimensional (3D) structure. To understand this process, several theoretical studies have used a set of 3D structures, identified different structural parameters, and analyzed their relationships using the natural logarithmic protein folding rate (ln(kf)). Unfortunately, these structural parameters are specific to a small set of proteins that are not capable of accurately predicting ln(kf) for both two-state (TS) and non-two-state (NTS) proteins. To overcome the limitations of the statistical approach, a few machine learning (ML)-based models have been proposed using limited training data. However, none of these methods can explain plausible folding mechanisms. In this study, we evaluated the predictive capabilities of ten different ML algorithms using eight different structural parameters and five different network centrality measures based on newly constructed datasets. In comparison to the other nine regressors, support vector machine was found to be the most appropriate for predicting ln(kf) with mean absolute differences of 1.856, 1.55, and 1.745 for the TS, NTS, and combined datasets, respectively. Furthermore, combining structural parameters and network centrality measures improves the prediction performance compared to individual parameters, indicating that multiple factors are involved in the folding process.

Fuzzy spherical truncation-based multi-linear protein descriptors: From their definition to application in structural-related predictions.

This study introduces a set of fuzzy spherically truncated three-dimensional (3D) multi-linear descriptors for proteins. These indices codify geometric structural information from kth spherically truncated spatial-(dis)similarity two-tuple and three-tuple tensors. The coefficients of these truncated tensors are calculated by applying a smoothing value to the 3D structural encoding based on the relationships between two and three amino acids of a protein embedded into a sphere. At considering, the geometrical center of the protein matches with center of the sphere, the distance between each amino acid involved in any specific interaction and the geometrical center of the protein can be computed. Then, the fuzzy membership degree of each amino acid from an spherical region of interest is computed by fuzzy membership functions (FMFs). The truncation value is finally a combination of the membership degrees from interacting amino acids, by applying the arithmetic mean as fusion rule. Several fuzzy membership functions with diverse biases on the calculation of amino acids memberships (e.g., Z-shaped (close to the center), PI-shaped (middle region), and A-Gaussian (far from the center)) were considered as well as traditional truncation functions (e.g., Switching). Such truncation functions were comparatively evaluated by exploring: 1) the frequency of membership degrees, 2) the variability and orthogonality analyses among them based on the Shannon Entropy’s and Principal Component’s methods, respectively, and 3) the prediction performance of alignment-free prediction of protein folding rates and structural classes. These analyses unraveled the singularity of the proposed fuzzy spherically truncated MDs with respect to the classical (non-truncated) ones and respect to the MDs truncated with traditional functions. They also showed an improved prediction power by attaining an external correlation coefficient of 95.82% in the folding rate modelling and an accuracy of 100% in distinguishing structural protein classes. These outcomes are better than the ones attained by existing approaches, justifying the theoretical contribution of this report. Thus, the fuzzy spherically truncated-based protein descriptors from MuLiMs-MCoMPAs (http://tomocomd.com/mulims-mcompas) are promising alignment-free predictors for modeling protein functions and properties.

FRTpred: A novel approach for accurate prediction of protein folding rate and type

Protein folding rate is an important property that is essential for understanding the protein folding process and is helpful for designing proteins. Predicting such properties from either sequence or structural information is a challenging task in bioinformatics. Although several computational methods have been developed in the past, only one sequence-based method is publicly available that shows limited accuracy when evaluated using a standardized independent dataset. This study proposes a novel approach, called FRTpred, that simultaneously predicts the logarithmic protein folding rate constant, ln(kf), and folding type from the provided sequence. First, 30 baseline models (regression models for ln(kf) and classification models for folding type) were constructed by integrating 10 representative feature extraction methods and three commonly used machine-learning algorithms. Subsequently, the predicted values of the 30 baseline models were combined and inputted into the random forest algorithm to construct the final prediction model. Cross-validation analysis showed that FRTpred achieved mean absolute deviations of 1.491, 2.016, and 1.954 for non-two-state, two-state, and combined models, respectively, when predicting ln(kf). Moreover, FRTpred predicts the folding type with an accuracy of 0.843. Performance comparisons based on independent tests against existing methods showed that FRTpred is more precise for both ln(kf) and folding type prediction. Thus, FRTpred is a powerful tool that may accelerate the characterization of the foldomics protein data and further inspire the development of next-generation predictors. The proposed model is available in the form of a web server that is freely accessible at http://thegleelab.org/FRTpred.

Evidence for new enantiospecific interaction force in chiral biomolecules

Evidence for new enantiospecific interaction force in chiral biomolecules

Study on the Influence of mRNA, the Genetic Language, on Protein Folding Rates.

Many works have reported that protein folding rates are influenced by the characteristics of amino acid sequences and protein structures. However, few reports on the problem of whether the corresponding mRNA sequences are related to the protein folding rates can be found. An mRNA sequence is regarded as a kind of genetic language, and its vocabulary and phraseology must provide influential information regarding the protein folding rate. In the present work, linear regressions on the parameters of the vocabulary and phraseology of mRNA sequences and the corresponding protein folding rates were analyzed. The results indicated that D2 (the adjacent base-related information redundancy) values and the GC content values of the corresponding mRNA sequences exhibit significant negative relations with the protein folding rates, but D1 (the single base information redundancy) values exhibit significant positive relations with the protein folding rates. In addition, the results show that the relationships between the parameters of the genetic language and the corresponding protein folding rates are obviously different for different protein groups. Some useful parameters that are related to protein folding rates were found. The results indicate that when predicting protein folding rates, the information from protein structures and their amino acid sequences is insufficient, and some information for regulating the protein folding rates must be derived from the mRNA sequences.

An Effective Cumulative Torsion Angles Model for Prediction of Protein Folding Rates.

Protein folding rate is mainly determined by the size of the conformational space to search, which in turn is dictated by factors such as size, structure and amino-acid sequence in a protein. It is important to integrate these factors effectively to form a more precisely description of conformation space. But there is no general paradigm to answer this question except some intuitions and empirical rules. Therefore, at the present stage, predictions of the folding rate can be improved through finding new factors, and some insights are given to the above question. Its purpose is to propose a new parameter that can describe the size of the conformational space to improve the prediction accuracy of protein folding rate. Based on the optimal set of amino acids in a protein, an effective cumulative backbone torsion angles (CBTAeff) was proposed to describe the size of the conformational space. Linear regression model was used to predict protein folding rate with CBTAeff as a parameter. The degree of correlation was described by the coefficient of determination and the mean absolute error MAE between the predicted folding rates and experimental observations. It achieved a high correlation (with the coefficient of determination of 0.70 and MAE of 1.88) between the logarithm of folding rates and the (CBTAeff)0.5 with experimental over 112 twoand multi-state folding proteins. The remarkable performance of our simplistic model demonstrates that CBTA based on optimal set was the major determinants of the conformation space of natural proteins.

Tensor Algebra-based Geometrical (3D) Biomacro-Molecular Descriptors for Protein Research: Theory, Applications and Comparison with other Methods

In this report, a new type of tridimensional (3D) biomacro-molecular descriptors for proteins are proposed. These descriptors make use of multi-linear algebra concepts based on the application of 3-linear forms (i.e., Canonical Trilinear (Tr), Trilinear Cubic (TrC), Trilinear-Quadratic-Bilinear (TrQB) and so on) as a specific case of the N-linear algebraic forms. The definition of the kth 3-tuple similarity-dissimilarity spatial matrices (Tensor’s Form) are used for the transformation and for the representation of the existing chemical information available in the relationships between three amino acids of a protein. Several metrics (Minkowski-type, wave-edge, etc) and multi-metrics (Triangle area, Bond-angle, etc) are proposed for the interaction information extraction, as well as probabilistic transformations (e.g., simple stochastic and mutual probability) to achieve matrix normalization. A generalized procedure considering amino acid level-based indices that can be fused together by using aggregator operators for descriptors calculations is proposed. The obtained results demonstrated that the new proposed 3D biomacro-molecular indices perform better than other approaches in the SCOP-based discrimination and the prediction of folding rate of proteins by using simple linear parametrical models. It can be concluded that the proposed method allows the definition of 3D biomacro-molecular descriptors that contain orthogonal information capable of providing better models for applications in protein science.

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.

Predicting protein folding rate change upon point mutation using residue-level coevolutionary information.

Change in folding kinetics of globular proteins upon point mutation is crucial to a wide spectrum of biological research, such as protein misfolding, toxicity, and aggregations. Here we seek to address whether residue-level coevolutionary information of globular proteins can be informative to folding rate changes upon point mutations. Generating residue-level coevolutionary networks of globular proteins, we analyze three parameters: relative coevolution order (rCEO), network density (ND), and characteristic path length (CPL). A point mutation is considered to be equivalent to a node deletion of this network and respective percentage changes in rCEO, ND, CPL are found linearly correlated (0.84, 0.73, and -0.61, respectively) with experimental folding rate changes. The three parameters predict the folding rate change upon a point mutation with 0.031, 0.045, and 0.059 standard errors, respectively.

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.

Prediction of protein folding rates from simplified secondary structure alphabet

Protein folding is a very complicated and highly cooperative dynamic process. However, the folding kinetics is likely to depend more on a few key structural features. Here we find that secondary structures can determine folding rates of only large, multi-state folding proteins and fails to predict those for small, two-state proteins. The importance of secondary structures for protein folding is ordered as: extended β strand>α helix>bend>turn>undefined secondary structure>310 helix>isolated β strand>π helix. Only the first three secondary structures, extended β strand, α helix and bend, can achieve a good correlation with folding rates. This suggests that the rate-limiting step of protein folding would depend upon the formation of regular secondary structures and the buckling of chain. The reduced secondary structure alphabet provides a simplified description for the machine learning applications in protein design.

Using Kinetic Network Models to Understand Folding Mechanisms of GB1 Hairpin and its Trpzip Variants

We used Markov State Model (MSM) approaches to analyze over 9 ms of explicit-solvent simulation trajectories for GB1 hairpin (the 16-residue C-terminal domain of protein G) and its three mutants (trpzip4, trpzip5, and trpzip6) at multiple temperatures, to investigate folding thermodynamics, kinetics, and mechanisms. Our MSM results show predicted folding rates and equilibrium populations that agree well with experimental data. Furthermore, we show how MSMs constructed from combined datasets reveal mechanistic differences resulting from tryptophan mutations. While wild type and trpzip4 hairpins are predicted to be two-state folders, our MSMs predict more complicated kinetics for trpzip5 and trpzip6 due to the presence of non-native traps. We find that changes in the folding landscape can also be revealed by analyzing MSM rate perturbations, provided that metastable states are conserved.

Conservation of inter-residue interactions and prediction of folding rates of domain repeats

Domains are the main structural and functional units of larger proteins. They tend to be contiguous in primary structure and can fold and function independently. It has been observed that 10–20% of all encoded proteins contain duplicated domains and the average pairwise sequence identity between them is usually low. In the present study, we have analyzed the structural similarity between domain repeats of proteins with known structures available in the Protein Data Bank using structure-based inter-residue interaction measures such as the number of long-range contacts, surrounding hydrophobicity, and pairwise interaction energy. We used RADAR program for detecting the repeats in a protein sequence which were further validated using Pfam domain assignments. The sequence identity between the repeats in domains ranges from 20 to 40% and their secondary structural elements are well conserved. The number of long-range contacts, surrounding hydrophobicity calculations and pairwise interaction energy of the domain repeats clearly reveal the conservation of 3-D structure environment in the repeats of domains. The proportions of mainchain–mainchain hydrogen bonds and hydrophobic interactions are also highly conserved between the repeats. The present study has suggested that the computation of these structure-based parameters will give better clues about the tertiary environment of the repeats in domains. The folding rates of individual domains in the repeats predicted using the long-range order parameter indicate that the predicted folding rates correlate well with most of the experimentally observed folding rates for the analyzed independently folded domains.

Towards more accurate prediction of protein folding rates: a review of the existing web-based bioinformatics approaches

The understanding of protein-folding mechanisms is often considered to be an important goal that will enable structural biologists to discover the mysterious relationship between the sequence, structure and function of proteins. The ability to predict protein-folding rates without the need for actual experimental work will assist the research work of structural biologists in many ways. Many bioinformatics tools have emerged in the past decade, and each has showcased different features. In this article, we review and compare eight web-based prediction tools that are currently available and that predominantly predict the protein-folding rate. The prediction performance, usability and utility, together with the prediction tool development and validation methodologies for these tools, are critically reviewed. This article is presented in a comprehensible manner to assist readers in the process of selecting the most appropriate bioinformatics tools to meet their needs.

Capturing protein folding-relevant topology via absolute contact order variants

Absolute contact order is one of the simplest parameters used to predict protein folding rates. Many variants of contact order (CO) have been applied to highlight different aspects of contact neighborhoods and their relationship to folding. However, a systematic study of the influence of CO variants on correlation with folding rate has not been performed for a large combined set of multi- and two-state proteins. We explore different contact neighborhoods and resulting CO by varying the distance thresholds and weighting of sequence separation for heavy atom and residue-based counting methods for a set of 136 proteins diverse across folding and structural classes. We examine the changes in contact neighborhoods and compare correlations with our CO variants and the protein folding rates across our data set as well as by folding type and structural class. Different CO variants lead to the strongest correlations within each protein structural class. Our results demonstrate that backbone topology at a distance beyond where energetic interactions dominate is able to capture folding determinants, and suggest that more sensitive methods of characterizing contact relationships may improve ln kf prediction for diverse protein sets.

Predicting the Protein Folding Rate Based on Sequence Feature Screening and Support Vector Regression

Folding rate prediction plays an important role in clarifying the protein folding mechanism. In this work, we collected 115 protein samples with known folding rates including two-, multi-, and mixed-state proteins.To characterize the primary structure information of the protein molecules more comprehensively, we considered sequence length, residue components with different scales, k-space features for pair residues, and geostatistics association features among different locations of the residues substituted with corresponding physical-chemical properties. Each protein sequence was represented by a numeric vector containing 9357 numbers. We selected23 features with a clear meaning from the above-mentioned high-dimensional features for each sample, after conducting an improved binary matrix shuffling filter and a worst descriptor elimination multi-round method. We constructed a nonlinear support vector regression(SVR) model based on the folding rate and the 23 retained features. The correlation coefficient of the Jackknife cross validation was 0.95. Our prediction accuracy was superior to other results from the literature and other reference feature selection methods. Finally, we established an interpretability system for SVR, and our data showed that the nonlinear regression relationship between the folding rates and the reserved features was highly significant. By further analyzing the effects of each retained descriptor on protein folding rates, the results showed that the protein folding rate might be closely related to the sequence length, the features associated with the medium- and short-range, the triplet residues component features, etc.

Kinetic Monte Carlo approach to RNA folding dynamics using structure-based models

RNA molecules form three-dimensional structures via base pairing that determine the function and biochemical activity of the molecule. Here we introduce a structure-based method for studying the folding dynamics of RNA secondary structures. The approach focuses on native contacts that are parametrized with standard empirical free energies. Kinetic Monte Carlo simulations for free folding of simple hairpins and complex structures such as a tRNA as well as for folding in the presence of an external force show good agreement with experimental data. A systematic comparison of simulated and experimental folding rates for various structures shows a strong correlation, indicating that the approach can predict folding rates within about an order of magnitude.

Progress in the Study on Determinants of Protein Folding Rate and Method of Folding Rate Prediction

Protein folding rate is an important parameter for the study of protein folding mechanisms.In recent years,it was found that protein folding rate is affected by many factors such as amino acid composition in the protein sequence,amino acid properties,contacts between residues,and the sequence order information of amino acids.Based on these findings,many new methods for protein folding rate prediction were proposed and the correlation between the predicted and experimental values of protein folding rates was improved gradually.On the other hand,how to interpret these rate determinants in the protein folding mechanism from a physicochemical viewpoint is another important topic in recent years.Moreover,new progress was also made in the study of the determining factors and prediction methods for the kinetic protein folding types(two-state or multi-state).

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

Retraction: The following article from the Journal of Computational Chemistry, “Predicting Protein Folding Rates Using the Concept of Chou's Pseudo Amino Acid Composition,” by Jianxiu Guo, Nini Rao, Guangxiong Liu, Yong Yang, and Gang Wang,[1] published online on 15 February 2011 in Wiley Online Library (wileyonlinelibrary.com), has been retracted by agreement between the authors, the journal's editors, and Wiley Periodicals, Inc. The retraction has been agreed due to significant overlap with respect to another article, “Predicting Protein Folding Rate from Amino Acid Sequence,” published in Progress in Biochemistry and Biophysics (2010, 37, 1331) and authored by a subset of the present authors.