Origin of unusual phi-values in protein folding: evidence against specific nucleation sites

phi(f)-value analysis is one of the most common methods to characterize the structure of protein folding transition states. It compares the effects of mutations on the folding kinetics with the respective effects on equilibrium stability. The interpretation of the results usually focuses on a few unusual phi(f)-values, which are either particularly high or which are larger than 1 or smaller than 0. These mutations are believed to affect the most important regions for the folding process. A major uncertainty in experimental phi(f)-values is introduced by the commonly used analysis of only a single mutant at various positions in a protein (two-point analysis). To test the reliability of two-point phi(f)-values we used reference data from three positions in two different proteins at which multiple mutations have been introduced. The results show that two-point phi(f)-values are highly inaccurate if the difference in stability between two variants is less than 7 kJ/mol, corresponding to a 20-fold difference in equilibrium constant. Comparison with reported phi(f)-values for 11 proteins shows that most unusual phi(f)-values are observed in mutants which show changes in protein stability that are too small to allow a reliable analysis. The results argue against specific nucleation sites in protein folding and give a picture of transition states as distorted native states for the major part of a protein or for large substructures.     

Compactness determines protein folding type

We have demonstrated here that protein compactness, which we define as the ratio of the accessible surface area of a protein to that of the ideal sphere of the same volume, is one of the factors determining the mechanism of protein folding. Proteins with multi-state kinetics, on average, are more compact (compactness is 1.49 +/- 0.02 for proteins within the size range of 101-151 amino acid residues) than proteins with two-state kinetics (compactness is 1.59 +/- 0.03 for proteins within the same size range of 101-151 amino acid residues). We have shown that compactness for homologous proteins can explain both the difference in folding rates and the difference in folding mechanisms.     

Entropy capacity determines protein folding

Search and study of the general principles that govern kinetics and thermodynamics of protein folding generate a new insight into the factors controlling this process. Here, based on the known experimental data and using theoretical modeling of protein folding, we demonstrate that there exists an optimal relationship between the average conformational entropy and the average energy of contacts per residue-that is, an entropy capacity-for fast protein folding. Statistical analysis of conformational entropy and number of contacts per residue for 5829 protein structures from four general structural classes (all-alpha, all-beta, alpha/beta, alpha+beta) demonstrates that each class of proteins has its own class-specific average number of contacts (class alpha/beta has the largest number of contacts) and average conformational entropy per residue (class all-alpha has the largest number of rotatable angles phi, psi, and chi per residue). These class-specific features determine the folding rates: alpha proteins are the fastest folding proteins, then follow beta and alpha+beta proteins, and finally alpha/beta proteins are the slowest ones. Our result is in agreement with the experimental folding rates for 60 proteins. This suggests that structural and sequence properties are important determinants of protein folding rates.     

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.     

Transition state contact orders correlate with protein folding rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.     

Relationship between protein folding kinetics and amino acid properties

The successful prediction of protein-folding rates based on the sequence-predicted secondary structure suggests that the folding rates might be predicted from sequence alone. To pursue this question, we directly predict the folding rates from amino acid sequences, which do not require any information on secondary or tertiary structure. Our work achieves 88% correlation with folding rates determined experimentally for proteins of all folding types and peptide, suggesting that almost all of the information needed to specify a protein's folding kinetics and mechanism is comprised within its amino acid sequence. The influence of residue on folding rate is related to amino acid properties. Hydrophobic character of amino acids may be an important determinant of folding kinetics, whereas other properties, size, flexibility, polarity and isoelectric point, of amino acids have contributed little to the folding rate constant.     

Global and local prediction of protein folding rates based on sequence autocorrelation information

To understand the folding behavior of proteins is an important and challenging problem in modern molecular biology. In the present investigation, a large number of features representing protein sequences were developed based on sequence autocorrelation weighted by properties of amino acid residues. Genetic algorithm (GA) combined with multiple linear regression (MLR) was employed to select significant features related to protein folding rates, and to build global predictive model. Moreover, local lazy regression (LLR) method was also used to predict the protein folding rates. The obtained results indicated that LLR performed much better than the global MLR model. The important properties of amino acid residues affecting protein folding rates were also analyzed. The results of this study will be helpful to understand the mechanism of protein folding. Our results also demonstrate that the features of amino acid sequence autocorrelation is effective in representing the relationship between protein sequence and folding rates, and the local method is a powerful tool to predict the protein folding rates.     

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.     

Interpretation of protein folding psi values

The structural characterization of transition states is essential for understanding the mechanism of protein folding. Analyzing the effect of mutations on protein stability and folding kinetics in phi-value analysis is commonly used to gain information about the presence of side-chain interactions in transition states. Recently, specific binding of ligands to engineered binding sites was applied to monitor the formation of local structures in transition states (psi analysis). A surprising result from psi analysis was the presence of parallel folding pathways in all reported studies and a major discrepancy between phi and psi values measured in the same protein. Here, we show that psi values cannot be analyzed in the same way as other rate-equilibrium free energy relationships due to the involvement of bimolecular reactions that may have different dissociation constants for the native, unfolded and transition state. As a consequence, psi values reflect the relative binding energy (kappa) of the transition state only for the extreme values of kappa=0 or kappa=1. In all other cases, non-linear rate-equilibrium free-energy relationships (Leffler plots) are observed. This apparently indicates the presence of parallel folding pathways even if folding occurs over a single homogeneous transition state. Consequently, the results from Leffler plots do not yield information about the structural properties of the transition state. This explains the lack of agreement between results from psi analysis and other methods used to characterize protein folding transition states. We further show that the same considerations apply for the analysis of the effect of pH on protein folding.     

Amino acid sequence predicts folding rate for middle-size two-state proteins

The significant correlation between protein folding rates and the sequence-predicted secondary structure suggests that folding rates are largely determined by the amino acid sequence. Here, we present a method for predicting the folding rates of proteins from sequences using the intrinsic properties of amino acids, which does not require any information on secondary structure prediction and structural topology. The contribution of residue to the folding rate is expressed by the residue's Omega value. For a given residue, its Omega depends on the amino acid properties (amino acid rigidity and dislike of amino acid for secondary structures). Our investigation achieves 82% correlation with folding rates determined experimentally for simple, two-state proteins studied until the present, suggesting that the amino acid sequence of a protein is an important determinant of the protein-folding rate and mechanism.     

The folding of an enzyme. I. Theory of protein engineering analysis of stability and pathway of protein folding.

The theory, assumptions and limitations are outlined for a simple protein engineering approach to the problem of the stability and pathway of protein folding. It is a general procedure for analysing structure-activity relationships in non-covalent bonding, including enzyme catalysis, that relates experimentally accessible data to changes in non-covalent bonding. Kinetic and equilibrium measurements on the unfolding and refolding of mutant proteins can be used to map the formation of structure in transition states and folding intermediates. For example, the ratio of the changes in the activation energy of unfolding and the free energy of unfolding on mutation is measured to give a parameter phi. There are two extreme values of phi that are often found in practice and may be interpreted in a simple manner. A value of phi = 0 implies that the structure at the site of mutation is as folded in the transition state as it is in the folded state. Conversely, phi = 1 shows that the structure at the site of mutation is as unfolded in the transition state as it is in the unfolded structure. Fractional values of phi are more difficult to interpret and require a more sophisticated approach. The most suitable mutations involve truncation of side-chains to remove moieties that preferably make few interactions with the rest of the protein and do not pair with buried charges. Fractional values of phi found for this type of mutation may imply that there is partial non-covalent bond formation or a mixture of states. The major assumptions of the method are: (1) mutation does not alter the pathway of folding; (2) mutation does not significantly change the structure of the folded state; (3) mutation does not perturb the structure of the unfolded state; and (4) the target groups do not make new interactions with new partners during the course of reaction energy. Assumptions (2) and (3) are not necessarily essential for the simple cases of phi = 0 or 1, the most common values, since effects of disruption of structure can cancel out. Assumption (4) may be checked by the double-mutant cycle procedure, which may be analysed to isolate the effects of just a pair of interactions against a complicated background. This analysis provides the formal basis of the accompanying studies on the stability and pathway of folding of barnase, where it is seen that the theory holds very well in practice.     

Topology, stability, sequence, and length: defining the determinants of two-state protein folding kinetics

The fastest simple, single domain proteins fold a million times more rapidly than the slowest. Ultimately this broad kinetic spectrum is determined by the amino acid sequences that define these proteins, suggesting that the mechanisms that underlie folding may be almost as complex as the sequences that encode them. Here, however, we summarize recent experimental results which suggest that (1) despite a vast diversity of structures and functions, there are fundamental similarities in the folding mechanisms of single domain proteins and (2) rather than being highly sensitive to the finest details of sequence, their folding kinetics are determined primarily by the large-scale, redundant features of sequence that determine a protein's gross structural properties. That folding kinetics can be predicted using simple, empirical, structure-based rules suggests that the fundamental physics underlying folding may be quite straightforward and that a general and quantitative theory of protein folding rates and mechanisms (as opposed to unfolding rates and thus protein stability) may be near on the horizon.     

Class-specific correlations between protein folding rate, structure-derived, and sequence-derived descriptors

Small single-domain proteins that fold by simple two-state kinetics have been shown to exhibit a wide variation in their folding rates. It has been proposed that folding mechanisms in these proteins are largely determined by the native-state topology, and a significant correlation between folding rate and measures of the average topological complexity, such as relative contact order (RCO), has been reported. We perform a statistical analysis of folding rate and RCO in all three major structural classes (alpha, beta, and alpha/beta) of small two-state proteins and of RCO in groups of analogous and homologous small single-domain proteins with the same topology. We also study correlation between folding rate and the average physicochemical properties of amino acid sequences in two-state proteins. Our results indicate that 1) helical proteins have statistically distinguishable, class-specific folding rates; 2) RCO accounts for essentially all the variation of folding rate in helical proteins, but for only a part of the variation in beta-sheet-containing proteins; and 3) only a small fraction of the protein topologies studied show a topology-specific RCO. We also report a highly significant correlation between the folding rate and average intrinsic structural propensities of protein sequences. These results suggest that intrinsic structural propensities may be an important determinant of the rate of folding in small two-state proteins.     

Native protein sequences are designed to destabilize folding intermediates

Hydrophobic core mutants of sperm whale apomyoglobin were constructed to investigate the amino acid sequence features that determine the folding properties. Replacements of all of the Ile residues with Leu and of all of the Ile and Val residues with Leu decreased the thermodynamic stability of the folded states against the unfolded states but increased the stability of the folding intermediates against the unfolded states, indicating that the amino acid composition of the protein core is important for the protein stability and folding cooperativity. To examine the effect of the arrangement of these hydrophobic residues, mutant proteins were further constructed: 12 sites out of the 18 Leu, 9 Ile, and 8 Val residues of the wild-type myoglobin were randomly replaced with each other so that the amino acid compositions were similar to that of the wild-type protein. Four mutant proteins were obtained without selection of the protein properties. These residue replacements similarly resulted in the stabilization of both the intermediate and folded states against the unfolded states, as compared to the wild-type protein. Thus, the arrangements of the hydrophobic residues in the native amino acid sequence are selected to destabilize the folding intermediate rather than to stabilize the folded state. The present results suggest that the two-state transition of protein folding or the transient formation of the unstable intermediate, which seems to be required for effective production of the functional proteins, has been a major driving force in the molecular evolution of natural globular proteins.     

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 . Proteins 2013. © 2012 Wiley Periodicals, Inc.     

The folding type of a protein is relevant to the amino acid composition

The folding types of 135 proteins, the three-dimensional structures of which are known, were analyzed in terms of the amino acid composition. The amino acid composition of a protein was expressed as a point in a multidimensional space spanned with 20 axes, on which the corresponding contents of 20 amino acids in the protein were represented. The distribution pattern of proteins in this composition space was examined in relation to five folding types, alpha, beta, alpha/beta, alpha + beta, and irregular type. The results show that amino acid compositions of the alpha, beta, and alpha/beta types are located in different regions in the composition space, thus allowing distinct separation of proteins depending on the folding types. The points representing proteins of the alpha + beta and irregular types, however, are widely scattered in the space, and the existing regions overlap with those of the other folding types. A simple method of utilizing the "distance" in the space was found to be convenient for classification of proteins into the five folding types. The assignment of the folding type with this method gave an accuracy of 70% in the coincidence with the experimental data.     

Folding and stability of sweet protein single-chain monellin. An insight to protein engineering

Engineered single-chain monellin (SCM) proteins were constructed by recombinant technology without disrupting the topology and sweet activity of native protein. Data from 8-anilinonaphthalene-1-sulfonic acid fluorescence, size-exclusion chromatography, and heteronuclear NMR strongly suggest the presence of a folding intermediate at 1.5 m GdnHCl for SCM protein. The structural feature of the folding intermediate from NMR data reveals that the secondary structures became mostly unstable, and protein experiences a dynamic equilibrium between native and unfolded state. All backbone amide protons exchange within 10 min, which imply that no stable hydrogen bonds exist in the secondary structural regions in the folding intermediate. From equilibrium unfolding and mutagenesis studies, the unfolding transition midpoints of mutant proteins gradually shifted toward lower denaturant concentration, indicating stability reductions of mutant proteins. Our results suggest that stability and folding pathways of SCM proteins could be regulated by a combined study of spectroscopy and mutagenesis, and these studies will provide useful information for understanding the folding kinetics of novel engineered proteins.     

Mapping the folding pathway of an immunoglobulin domain: structural detail from Phi value analysis and movement of the transition state

BACKGROUND: Do proteins that have the same structure fold by the same pathway even when they are unrelated in sequence? To address this question, we are comparing the folding of a number of different immunoglobulin-like proteins. Here, we present a detailed protein engineering phi value analysis of the folding pathway of TI I27, an immunoglobulin domain from human cardiac titin. RESULTS: TI I27 folds rapidly via a kinetic intermediate that is destabilized by most mutations. The transition state for folding is remarkably native-like in terms of solvent accessibility. We use phi value analysis to map this transition state and show that it is highly structured; only a few residues close to the N-terminal region of the protein remain completely unfolded. Interestingly, most mutations cause the transition state to become less native-like. This anti-Hammond behavior can be used as a novel means of obtaining additional structural information about the transition state. CONCLUSIONS: The residues that are involved in nucleating the folding of TI I27 are structurally equivalent to the residues that form the folding nucleus in an evolutionary unrelated fibronectin type III protein. These residues form part of the common structural core of Ig-like domains. The data support the hypothesis that interactions essential for defining the structure of these beta sandwich proteins are also important in nucleation of folding.     

Evolutionary conservation of the folding nucleus

Here, we present statistical analysis of conservation profiles in families of homologous sequences for nine proteins whose folding nucleus was determined by protein engineering methods. We show that in all but one protein (AcP) folding nucleus residues are significantly more conserved than the rest of the protein. Two aspects of our study are especially important: (i) grouping of amino acid residues into classes according to their physical-chemical properties and (ii) proper normalization of amino acid probabilities that reflects the fact that evolutionary pressure to conserve some amino acid types may itself affect concentration of various amino acid types in protein families. Neglect of any of those two factors may make physical and biological "signals" from conservation profiles disappear.