Local secondary structure content predicts folding rates for simple, two-state proteins

Protein loop structure prediction by community-based deep learning and its application to antibody CDR H3 loop modeling

As of now, more than 60 years have passed since the first determination of protein structures through crystallography, and a significant portion of protein structures can be predicted by computers. This is due to the groundbreaking enhancement in protein structure prediction achieved through neural network training utilizing extensive sequence and structure data. However, substantial challenges persist in structure prediction due to limited data availability, with antibody structure prediction standing as one such challenge. In this paper, we propose a novel neural network architecture that effectively enables structure prediction by reflecting the inherent combinatorial nature involved in protein structure formation. The core idea of this neural network architecture is not solely to track and generate a single structure but rather to form a community of multiple structures and pursue accurate structure prediction by exchanging information among community members. Applying this concept to antibody CDR H3 loop structure prediction resulted in improved structure sampling. Such an approach could be applied in the structural and functional studies of proteins, particularly in exploring various physiological processes mediated by loops. Moreover, it holds potential in addressing various other types of combinatorial structure prediction and design problems.

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.

OUP accepted manuscript

Summary

Motivation. Predicting the native state of a protein has long been considered a gateway problem for understanding protein folding. Recent advances in structural modeling driven by deep learning have achieved unprecedented success at predicting a protein’s crystal structure, but it is not clear if these models are learning the physics of how proteins dynamically fold into their equilibrium structure or are just accurate knowledge-based predictors of the final state.

Results. In this work, we compare the pathways generated by state-of-the-art protein structure prediction methods to experimental data about protein folding pathways. The methods considered were AlphaFold 2, RoseTTAFold, trRosetta, RaptorX, DMPfold, EVfold, SAINT2 and Rosetta. We find evidence that their simulated dynamics capture some information about the folding pathway, but their predictive ability is worse than a trivial classifier using sequence-agnostic features like chain length. The folding trajectories produced are also uncorrelated with experimental observables such as intermediate structures and the folding rate constant. These results suggest that recent advances in structure prediction do not yet provide an enhanced understanding of protein folding.

Availability. The data underlying this article are available in GitHub at https://github.com/oxpig/structure-vs-folding/

Supplementary information

Supplementary data are available at Bioinformatics online.

Topological principles of protein folding

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.

Protein self-entanglement modulates successful folding to the native state: A multi-scale modeling study

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.

Protein folding - seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of β-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

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.

The Influences of Palindromes in mRNA on Protein Folding Rates

BACKGROUND

It is currently believed that protein folding rates are influenced by protein structure, environment and temperature, amino acid sequence and so on. We have been working for long to determine whether and in what ways mRNA affects the protein folding rate. A large number of palindromes aroused our attention in our previous research. Whether these palindromes do have important influences on protein folding rates and what's the mechanism? Very few related studies are focused on these problems.

OBJECTIVE

In this article, our motivation is to find out if palindromes have important influences on protein folding rates and what's the mechanism.

METHODS

In this article, the parameters of the palindromes were defined and calculated, the linear regression analysis between the values of each parameter and the experimental protein folding rates were done. Furthermore, to compare the results of different kinds of proteins, proteins were classified into the two-state proteins and the multi-state proteins. For the two kinds of proteins, the above linear regression analysis were performed respectively.

RESULTS

Protein folding rates were negatively correlated to the palindrome frequencies for all proteins. An extremely significant negative linear correlation appeared in the relationship between palindrome densities and protein folding rates. And the repeatedly used bases by different palindromes simultaneously have an important effect on the relationship between palindrome density and protein folding rate.

CONCLUSION

The palindromes have important influences on protein folding rates, and the repeatedly used bases in different palindromes simultaneously play a key role in influencing the protein folding rates.

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.

How Quickly Do Proteins Fold and Unfold, and What Structural Parameters Correlate with These Values?

The correlations between the logarithm of the unfolding rate of 108 proteins and their structural parameters were calculated. We showed that there is a good correlation between the logarithm of folding and unfolding rates (0.79) and protein stability and unfolding rate (0.79). Thus, the faster the protein folds, the faster it unfolds. Folding and unfolding rates are higher for the proteins with two-state kinetics, in comparison with the proteins with multi-state kinetics. At the same time, two-state bacterial proteins folds and unfolds two orders of magnitude faster than two-state eukaryotic proteins, and multi-state bacterial proteins folds and unfolds slower than multi-state eukaryotic proteins. Despite the fact that the folding rates of thermophilic and mesophilic proteins are close, the unfolding rates of thermophilic proteins is about two orders of magnitude lower than for mesophilic proteins. The correlation between unfolding rate and stability of thermophilic proteins is high (0.90). We also found that the unfolding rate correlates with such structural parameters as: size of the protein, radius of the cross-section, logarithm of absolute contact order, and radius of gyration. This information will be useful for engineering and designing new proteins with desired properties.

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.

Reduced alphabet for protein folding prediction

What are the key building blocks that would have been needed to construct complex protein folds? This is an important issue for understanding protein folding mechanism and guiding de novo protein design. Twenty naturally occurring amino acids and eight secondary structures consist of a 28-letter alphabet to determine folding kinetics and mechanism. Here we predict folding kinetic rates of proteins from many reduced alphabets. We find that a reduced alphabet of 10 letters achieves good correlation with folding rates, close to the one achieved by full 28-letter alphabet. Many other reduced alphabets are not significantly correlated to folding rates. The finding suggests that not all amino acids and secondary structures are equally important for protein folding. The foldable sequence of a protein could be designed using at least 10 folding units, which can either promote or inhibit protein folding. Reducing alphabet cardinality without losing key folding kinetic information opens the door to potentially faster machine learning and data mining applications in protein structure prediction, sequence alignment and protein design.

General mechanism of two-state protein folding kinetics

We describe here a general model of the kinetic mechanism of protein folding. In the Foldon Funnel Model, proteins fold in units of secondary structures, which form sequentially along the folding pathway, stabilized by tertiary interactions. The model predicts that the free energy landscape has a volcano shape, rather than a simple funnel, that folding is two-state (single-exponential) when secondary structures are intrinsically unstable, and that each structure along the folding path is a transition state for the previous structure. It shows how sequential pathways are consistent with multiple stochastic routes on funnel landscapes, and it gives good agreement with the 9 order of magnitude dependence of folding rates on protein size for a set of 93 proteins, at the same time it is consistent with the near independence of folding equilibrium constant on size. This model gives estimates of folding rates of proteomes, leading to a median folding time in Escherichia coli of about 5 s.

Probing the protein-folding mechanism using denaturant and temperature effects on rate constants

Protein folding has been extensively studied, but many questions remain regarding the mechanism. Characterizing early unstable intermediates and the high-free-energy transition state (TS) will help answer some of these. Here, we use effects of denaturants (urea, guanidinium chloride) and temperature on folding and unfolding rate constants and the overall equilibrium constant as probes of surface area changes in protein folding. We interpret denaturant kinetic m-values and activation heat capacity changes for 13 proteins to determine amounts of hydrocarbon and amide surface buried in folding to and from TS, and for complete folding. Predicted accessible surface area changes for complete folding agree in most cases with structurally determined values. We find that TS is advanced (50-90% of overall surface burial) and that the surface buried is disproportionately amide, demonstrating extensive formation of secondary structure in early intermediates. Models of possible pre-TS intermediates with all elements of the native secondary structure, created for several of these proteins, bury less amide and hydrocarbon surface than predicted for TS. Therefore, we propose that TS generally has both the native secondary structure and sufficient organization of other regions of the backbone to nucleate subsequent (post-TS) formation of tertiary interactions. The approach developed here provides proof of concept for the use of denaturants and other solutes as probes of amount and composition of the surface buried in coupled folding and other large conformational changes in TS and intermediates in protein processes.

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.

Template induced conformational change of amyloid-β monomer

Population of aggregation-prone conformers for the monomeric amyloid-β (Aβ) can dramatically speed up its fibrillar aggregation. In this work, we study the effect of preformed template on the conformational distributions of the monomeric Aβ by replica exchange molecular dynamics. Our results show that the template consisting of Aβ peptides with cross-β structure can induce the formation of β-rich conformations for the monomeric Aβ, which is the key feature of the aggregation-prone conformers. Similar effect is observed when the hIAPP peptides and poly alanine peptides were used as templates, suggesting that the template effect is insensitive to the sequence details of the template peptides. In comparison, the template with helical structure has no significant effects on the β-propensity of the monomeric Aβ. Analysis to the interaction details revealed that the template tends to disrupt the intrapeptide interactions of the monomeric Aβ, which are absent in the fibrillar state, suggesting that the preformed template can reorganize the intrapeptide interactions of the monomeric Aβ during the capturing stage and reduce the energy frustrations for the fibrillar aggregations.

Computational methods to predict therapeutic protein aggregation

Protein based biotherapeutics have emerged as a successful class of pharmaceuticals. However, these macromolecules endure a variety of physicochemical degradations during manufacturing, shipping, and storage, which may adversely impact the drug product quality. Of these degradations, the irreversible self-association of therapeutic proteins to form aggregates is a major challenge in the formulation of these molecules. Tools to predict and mitigate protein aggregation are, therefore, of great interest to biopharmaceutical research and development. In this chapter, a number of such computational tools developed to understand and predict the various steps involved in protein aggregation are described. These tools can be grouped into three general classes: unfolding kinetics and native state thermal stability, colloidal stability, and sequence/structure based aggregation liabilities. Chapter sections introduce each class by discussing how these predictive tools provide insight into the molecular events leading to protein aggregation. The computational methods are then explained in detail along with their advantages and limitations.

Bacterial proteins fold faster than eukaryotic proteins with simple folding kinetics

Protein domain frequency and distribution among kingdoms was statistically analyzed using the SCOP structural database. It appeared that among chosen protein domains with the best resolution, eukaryotic proteins more often belong to α-helical and β-structural proteins, while proteins of bacterial origin belong to α/β structural class. Statistical analysis of folding rates of 73 proteins with known experimental data revealed that bacterial proteins with simple kinetics (23 proteins) exhibit a higher folding rate compared to eukaryotic proteins with simple folding kinetics (27 proteins). Analysis of protein domain amino acid composition showed that the frequency of amino acid residues in proteins of eukaryotic and bacterial origin is different for proteins with simple and complex folding kinetics.

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.

Community structure description in amino acid interaction networks

In this paper, we represent proteins by amino acid interaction networks. This is a graph whose vertices are the protein's amino acids and whose edges are the interactions between them. We begin by identifying the main topological properties of these interaction networks using graph theory measures. We observe that the amino acids interact specifically, according to their structural role, and depending on whether they participate or not in the secondary structure. Thus, certain amino acids tend to group together to form local clouds. Then, we study the formation of node aggregations through community structure detections. We observe that the composition of organizations confirms a specific aggregation between loops around a core composed of secondary.

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.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

Simulaid: a simulation facilitator and analysis program

Simulaid performs a large number of simulation-related tasks: interconversion and modification of structure and trajectory files, optimization of orientation, and a large variety of analysis functions. The program can handle structures in PDB (Berman et al., Nucleic Acids Res 2000, 28, 235), Charmm (Brooks et al., J Comput Chem 4, 187) CRD, Amber (Case et al.), Macromodel (Mohamadi et al., J Comput Chem 1990, 11, 440), Gromos/Gromacs (Hess et al.), InsightII (InsightII. Accelrys Inc.: San Diego, 2005), Grasp (Nicholls et al., Proteins: Struct Funct Genet 1991, 11, 281) .crg, Tripos (Tripos International, S. H. R., St. Louis, MO) .mol2 (input only), and in the MMC (Mezei, M.; MMC: Monte Carlo program for molecular assemblies. Available at: http://inka.mssm.edu/~mezei/mmc) formats; and trajectories in the formats of Charmm, Amber, Macromodel, and MMC. Analysis features include (but are not limited to): (1) simple distance calculations and hydrogen-bond analysis, (2) calculation of 2-D RMSD maps (produced both as text file with the data and as a color-coded matrix) and cross RMSD maps between trajectories, (3) clustering based on RMSD maps, (4) analysis of torsion angles, Ramachandran (Ramachandran and Sasiskharan, Adv Protein Chem 1968, 23, 283) angles, proline kink (Visiers et al., Protein Eng 2000, 13, 603) angles, pseudorotational (Altona and Sundaralingam, J Am Chem Soc 1972, 94, 8205; Cremer and Pople, J Am Chem Soc 1975, 97, 1354) angles, and (5) analysis based on circular variance (Mezei, J Mol Graphics Model 2003, 21, 463). Torsion angle evolutions are presented in dial plots (Ravishanker et al., J Biomol Struct Dyn 1989, 6, 669). Several of these features are unique to Simulaid.

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.

iFC²: an integrated web-server for improved prediction of protein structural class, fold type, and secondary structure content

Several descriptors of protein structure at the sequence and residue levels have been recently proposed. They are widely adopted in the analysis and prediction of structural and functional characteristics of proteins. Numerous in silico methods have been developed for sequence-based prediction of these descriptors. However, many of them do not have a public web-server and only a few integrate multiple descriptors to improve the predictions. We introduce iFC² (integrated prediction of fold, class, and content) server that is the first to integrate three modern predictors of sequence-level descriptors. They concern fold type (PFRES), structural class (SCEC), and secondary structure content (PSSC-core). The server exploits relations between the three descriptors to implement a cross-evaluation procedure that improves over the predictions of the individual methods. The iFC² annotates fold and class predictions as potentially correct/incorrect. When tested on datasets with low-similarity chains, for the fold prediction iFC² labels 82% of the PFRES predictions as correct and the accuracy of these predictions equals 72%. The accuracy of the remaining 28% of the PFRES predictions equals 38%. Similarly, our server assigns correct labels for over 79% of SCEC predictions, which are shown to be 98% accurate, while the remaining SCEC predictions are only 15% accurate. These results are shown to be competitive when contrasted against recent relevant web-servers. Predictions on CASP8 targets show that the content predicted by iFC² is competitive when compared with the content computed from the tertiary structures predicted by three best-performing methods in CASP8. The iFC² server is available at http://biomine.ece.ualberta.ca/1D/1D.html .

Is protein folding rate dependent on number of folding stages? Modeling of protein folding with ferredoxin-like fold

Statistical analysis of protein folding rates has been done for 84 proteins with available experimental data. A surprising result is that the proteins with multi-state kinetics from the size range of 50-100 amino acid residues (a.a.) fold as fast as proteins with two-state kinetics from the same size range. At the same time, the proteins with two-state kinetics from the size range 101-151 a.a. fold faster than those from the size range 50-100 a.a. Moreover, it turns out unexpectedly that usually in the group of structural homologs from the size range 50-100 a.a., proteins with multi-state kinetics fold faster than those with two-state kinetics. The protein folding for six proteins with a ferredoxin-like fold and with a similar size has been modeled using Monte Carlo simulations and dynamic programming. Good correlation between experimental folding rates, some structural parameters, and the number of Monte Carlo steps has been obtained. It is shown that a protein with multi-state kinetics actually folds three times faster than its structural homologs.

SeqRate: sequence-based protein folding type classification and rates prediction

BACKGROUND

Protein folding rate is an important property of a protein. Predicting protein folding rate is useful for understanding protein folding process and guiding protein design. Most previous methods of predicting protein folding rate require the tertiary structure of a protein as an input. And most methods do not distinguish the different kinetic nature (two-state folding or multi-state folding) of the proteins. Here we developed a method, SeqRate, to predict both protein folding kinetic type (two-state versus multi-state) and real-value folding rate using sequence length, amino acid composition, contact order, contact number, and secondary structure information predicted from only protein sequence with support vector machines.

RESULTS

We systematically studied the contributions of individual features to folding rate prediction. On a standard benchmark dataset, the accuracy of folding kinetic type classification is 80%. The Pearson correlation coefficient and the mean absolute difference between predicted and experimental folding rates (sec-1) in the base-10 logarithmic scale are 0.81 and 0.79 for two-state protein folders, and 0.80 and 0.68 for three-state protein folders. SeqRate is the first sequence-based method for protein folding type classification and its accuracy of fold rate prediction is improved over previous sequence-based methods. Its performance can be further enhanced with additional information, such as structure-based geometric contacts, as inputs.

CONCLUSIONS

Both the web server and software of predicting folding rate are publicly available at http://casp.rnet.missouri.edu/fold_rate/index.html.

Macromolecular crowding induces polypeptide compaction and decreases folding cooperativity

A cell's interior is comprised of macromolecules that can occupy up to 40% of its available volume. Such crowded environments can influence the stability of proteins and their rates of reaction. Using discrete molecular dynamics simulations, we investigate how both the size and number of neighboring crowding reagents affect the thermodynamic and folding properties of structurally diverse proteins. We find that crowding induces higher compaction of proteins. We also find that folding becomes less cooperative with the introduction of crowders into the system. The crowders may induce alternative non-native protein conformations, thus creating barriers for protein folding in highly crowded media.

The folding trajectory of RNase H is dominated by its topology and not local stability: a protein engineering study of variants that fold via two-state and three-state mechanisms

Proteins can sample a variety of partially folded conformations during the transition between the unfolded and native states. Some proteins never significantly populate these high-energy states and fold by an apparently two-state process. However, many proteins populate detectable, partially folded forms during the folding process. The role of such intermediates is a matter of considerable debate. A single amino acid change can convert Escherichia coli ribonuclease H from a three-state folder that populates a kinetic intermediate to one that folds in an apparent two-state fashion. We have compared the folding trajectories of the three-state RNase H and the two-state RNase H, proteins with the same native-state topology but altered regional stability, using a protein engineering approach. Our data suggest that both versions of RNase H fold through a similar trajectory with similar high-energy conformations. Mutations in the core and the periphery of the protein affect similar aspects of folding for both variants, suggesting a common trajectory with folding of the core region followed by the folding of the periphery. Our results suggest that formation of specific partially folded conformations may be a general feature of protein folding that can promote, rather than hinder, efficient folding.

Coupling between properties of the protein shape and the rate of protein folding

There are several important questions on the coupling between properties of the protein shape and the rate of protein folding. We have studied a series of structural descriptors intended for describing protein shapes (the radius of gyration, the radius of cross-section, and the coefficient of compactness) and their possible connection with folding behavior, either rates of folding or the emergence of folding intermediates, and compared them with classical descriptors, protein chain length and contact order. It has been found that when a descriptor is normalized to eliminate the influence of the protein size (the radius of gyration normalized to the radius of gyration of a ball of equal volume, the coefficient of compactness defined as the ratio of the accessible surface area of a protein to that of an ideal ball of equal volume, and relative contact order) it completely looses its ability to predict folding rates. On the other hand, when a descriptor correlates well with protein size (the radius of cross-section and absolute contact order in our consideration) then it correlates well with the logarithm of folding rates and separates reasonably well two-state folders from multi-state ones. The critical control for the performance of new descriptors demonstrated that the radius of cross-section has a somewhat higher predictive power (the correlation coefficient is −0.74) than size alone (the correlation coefficient is −0.65). So, we have shown that the numerical descriptors of the overall shape-geometry of protein structures are one of the important determinants of the protein-folding rate and mechanism.

What have we learned from the studies of two-state folders, and what are the unanswered questions about two-state protein folding?

Small proteins with globular structures often fold by simple all-or-none mechanisms, both in an equilibrium and a kinetic sense, despite the very large number of partly folded conformations available. This type of 'two-state' folding will be discussed in terms of experimental tests, underlying molecular mechanisms, and limits to two-state behavior. Factors that appear to be important for two-state folding include topology (sequence distance of contacts in the native structure), molecular cooperativity and local energy distribution. Because their local stability distributions and cooperativities can be dissected and analyzed separately from topological features, recent studies of the folding of symmetric proteins will be discussed as a means to better understand the origins of two-state folding.

Defining the TRiC/CCT interactome links chaperonin function to stabilization of newly made proteins with complex topologies

Folding within the crowded cellular milieu often requires assistance from molecular chaperones that prevent inappropriate interactions leading to aggregation and toxicity. The contribution of individual chaperones to folding the proteome remains elusive. We here demonstrate that the eukaryotic chaperonin TRiC/CCT (TCP1-Ring Complex or Chaperonin Containing TCP1) has broad binding specificity in vitro similar to the prokaryotic chaperonin GroEL. However, in vivo TRiC substrate selection is not based solely on intrinsic determinants; instead, specificity is dictated by factors present during protein biogenesis. The identification of cellular substrates revealed that TRiC interacts with folding intermediates of a subset of structurally and functionally diverse polypeptides. Bioinformatics analysis revealed an enrichment in multidomain proteins and regions of beta strand propensity that are predicted to be slow-folding and aggregation-prone. Thus, TRiC may have evolved to protect complex protein topologies within its central cavity during biosynthesis and folding.

Defining the TRiC/CCT interactome links chaperonin function to stabilization of newly made proteins with complex topologies

Folding within the crowded cellular milieu often requires assistance from molecular chaperones that prevent inappropriate interactions leading to aggregation and toxicity. The contribution of individual chaperones to folding the proteome remains elusive. Here we demonstrate that the eukaryotic chaperonin TRiC/CCT (TCP1-ring complex or chaperonin containing TCP1) has broad binding specificity in vitro, similar to the prokaryotic chaperonin GroEL. However, in vivo, TRiC substrate selection is not based solely on intrinsic determinants; instead, specificity is dictated by factors present during protein biogenesis. The identification of cellular substrates revealed that TRiC interacts with folding intermediates of a subset of structurally and functionally diverse polypeptides. Bioinformatics analysis revealed an enrichment in multidomain proteins and regions of beta-strand propensity that are predicted to be slow folding and aggregation prone. Thus, TRiC may have evolved to protect complex protein topologies within its central cavity during biosynthesis and folding.

KineticDB: a database of protein folding kinetics

We propose here KineticDB, a systematically compiled database of protein folding kinetics, which contains about 90 unique proteins. The main goal of the KineticDB is to provide users with a diverse set of protein folding rates determined experimentally. The search for determinants of protein folding is still in progress, aimed at obtaining a new understanding of the folding process. Comparison with experimental protein folding rates has been the main tool for validation of both theoretical models and empirical relationships during the last 10 years. It is, therefore, necessary to provide a researcher with as much data as possible in a simple and easy-to-use way. At present, the KineticDB contains the results of folding kinetics measurements of single-domain proteins and separate protein domains as well as short peptides without disulfide bonds. It includes data on about 90 unique proteins and many mutants that have been systematically accumulated over the last 10 years and is the largest collection of protein folding kinetic data presented as a database. The KineticDB is available at http://kineticdb.protres.ru/db/index.pl.