Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.     

Secondary structure length as a determinant of folding rate of proteins with two- and three-state kinetics

We present a simple method for determining the folding rates of two- and three-state proteins from the number of residues in their secondary structures (secondary structure length). The method is based on the hypothesis that two- and three-state foldings share a common pattern. Three-state proteins first condense into metastable intermediates, subsequent forming of alpha-helices, turns, and beta-sheets at slow rate-limiting step. The folding rate of such proteins anticorrelate with the length of these beta-secondary structures. It is also assumed that in two-state folding, rapidly folded alpha-helices and turns may facilitate formation of fleeting unobservable intermediates and thus show two-state behavior. There is an inverse relationship between the folding rate and the length of beta-sheets and loops. Our study achieves 94.0 and 88.1% correlations with folding rates determined experimentally for 21 three- and 38 two-state proteins, respectively, suggesting that protein-folding rates are determined by the secondary structure length. The kinetic kinds are selected on the basis of a competitive formation of hydrophobic collapse and alpha-structure in early intermediates.     

Effect of multiple prolyl isomerization reactions on the stability and folding kinetics of the notch ankyrin domain: experiment and theory

Studies on the folding kinetics of the Notch ankyrin domain have demonstrated that the major refolding phase is slow, the minor refolding phase is limited by the isomerization of prolyl peptide bonds, and that unfolding is multiexponential. Here, we explore the relationship between prolyl isomerization and folding heterogeneity using a combination of experiment and simulation. Proline residues were replaced with alanine, both singly and in various combinations. These destabilizing substitutions combine to eliminate the minor refolding phase, although unfolding heterogeneity persists even when all seven proline residues are replaced. To test whether prolyl isomerization influences the major refolding phase, we modeled folding and prolyl isomerization as a system of sequential reactions. Simulations that use rate constants of the major folding phase of the Notch ankyrin domain to represent intrinsic folding indicate that even with seven prolyl isomerization reactions, only two significant phases should be observed, and that the fast observed phase provides a good approximation of the intrinsic folding in the absence of prolyl isomerization. These results indicate that the major refolding phase of the Notch ankyrin domain reflects an intrinsically slow folding transition, rather than coupling of fast folding events with slow prolyl isomerization steps. This is consistent with the observation that the single observed refolding phase of a construct in which all proline residues are replaced remains slow. Finally, the simulation fails to produce a second unfolding phase at high urea concentrations, indicating that prolyl isomerization does not play a role in the three-state mechanism that leads to this heterogeneity.     

Comparison of the folding mechanism of highly homologous proteins in the lipid‐binding protein family

The folding mechanism of two closely related proteins in the intracellular lipid‐binding protein family, human bile acid‐binding protein (hBABP), and rat bile acid‐binding protein (rBABP) were examined. These proteins are 77% identical (93% similar) in sequence. Both of these single domain proteins fit well to a two‐state model for unfolding by fluorescence and circular dichroism at equilibrium. Three phases were observed during the unfolding of rBABP by fluorescence but only one phase was observed during the unfolding of hBABP, suggesting that at least two kinetic intermediates accumulate during the unfolding of rBABP that are not observed during the unfolding of hBABP. Fluorine NMR was used to examine the equilibrium unfolding behavior of the W49 side chain in 6‐fluorotryptophan‐labeled rBABP and hBABP. The structure of rBABP appears to be more dynamic than that of hBABP in the vicinity of W49 in the absence of denaturant, and urea has a greater effect on this dynamic behavior for rBABP than for hBABP. As such, the folding behavior of highly sequence related proteins in this family can be quite different. These differences imply that moderately sized proteins with high sequence and structural similarity can still populate quite different structures during folding. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Metastable, partially folded states in the productive folding and in the misfolding and amyloid aggregation of proteins

Understanding the energetic and structural basis of protein folding in a physiological context may represent an important step toward the elucidation of protein misfolding and aggregation events that take place in several pathological states. In particular, investigation of the structure and thermodynamic properties of partially folded intermediate states involved in productive folding or in misfolding/aggregation may provide insight into these processes and suggest novel approaches to prevent misfolding in living organisms. This goal, however, has remained elusive, because such intermediates are often transient and correspond to metastable states that are little populated under physiological conditions. Characterization of these states requires their stabilization by means of manipulation of the experimental conditions, involving changes in temperature, pH, or addition of different types of denaturants. In the past few years, hydrostatic pressure has been increasingly used as a thermodynamic variable in the study of both protein folding and misfolding/aggregation transitions. Compared with other chemical or physical denaturing agents, a unique feature of pressure is its ability to induce subtle changes in protein conformation, allowing the stabilization of partially folded states that are usually not significantly populated under more drastic conditions. Much of the recent work in this field has focused on the characterization of folding intermediates, because they seem to be involved in a variety of disease-causing protein misfolding and aggregation reactions. Here, we review recent examples of the use of hydrostatic pressure as a tool to gain insight into the forces and energetics governing the productive folding or the misfolding and amyloid aggregation of proteions.     

Function of phosducin-like proteins in G protein signaling and chaperone-assisted protein folding

Members of the phosducin gene family were initially proposed to act as down-regulators of G protein signaling by binding G protein βγ dimers (Gβγ) and inhibiting their ability to interact with G protein subunits (G) and effectors. However, recent findings have over-turned this hypothesis by showing that most members of the phosducin family act as co-chaperones with the cytosolic chaperonin complex (CCT) to assist in the folding of a variety of proteins from their nascent polypeptides. In fact rather than inhibiting G protein pathways, phosducin-like protein 1 (PhLP1) has been shown to be essential for G protein signaling by catalyzing the folding and assembly of the Gβγ dimer. PhLP2 and PhLP3 have no role in G protein signaling, but they appear to assist in the folding of proteins essential in regulating cell cycle progression as well as actin and tubulin. Phosducin itself is the only family member that does not participate with CCT in protein folding, but it is believed to have a specific role in visual signal transduction to chaperone Gβγ subunits as they translocate to and from the outer and inner segments of photoreceptor cells during light-adaptation.     

Relationships between the folding rate constant and the topological parameters of small two-state proteins based on general random walk model

In this paper, we propose an analytically tractable model of protein folding based on one-dimensional general random walk. A second-order differential equation for the mean folding time of a single protein is constructed which can be used to derive the observed relationship between the folding rate constant and the number of native contacts. The parameters appearing in the model can be determined by fitting the theoretical prediction to the experimental result. In addition, taking into account the fact that the number of native contacts is almost proportional to the relative contact order, we can also explain the observed relationship between the folding rate constant and the relative contact order.     

The coordination of the isomerization of a conserved non-prolyl cis peptide bond with the rate-limiting steps in the folding of dihydrofolate reductase

The propensity for peptide bonds to adopt the trans configuration in native and unfolded proteins, and the relatively slow rates of cis-trans isomerization reactions, imply that the formation of cis peptide bonds in native conformations are likely to limit folding reactions. The role of the conserved cis Gly95-Gly96 peptide bond in dihydrofolate reductase (DHFR) from Escherichia coli was examined by replacing Gly95 with alanine. The introduction of a beta carbon at position 95 is expected to increase the propensity for the trans isomer and perturb the isomerization reaction required to reach the native conformation. Although G95A DHFR is 1.30 kcal mol(-1) less stable than the wild-type protein, it adopts a well-folded structure that can be chemically denatured in a cooperative fashion. The mutant protein also retains the complex refolding kinetic pattern attributed to a parallel-channel mechanism in wild-type DHFR. The spectroscopic response upon refolding monitored by Trp fluorescence and the absence of a Trp/Trp exciton coupling apparent in the far-UV CD spectrum of the wild-type protein, however, indicated that the tertiary structure of the folded state for G95A DHFR is altered. The addition of methotrexate (MTX), a tight-binding inhibitor, to folded G95A DHFR restored the exciton coupling and the fluorescence properties through five slow kinetic events whose relaxation times are independent of the ligand and the denaturant concentrations. The results were interpreted to mean that MTX-binding drives the formation of the cis isomer of the peptide bond between Ala95 and Gly96 in five compact and stable but not wild-type-like conformations that contain the trans isomer. Folding studies in the presence of MTX for both wild-type and G95A DHFR support the notion that the cis peptide bond between Gly95 and Gly96 in the wild-type protein forms during four parallel rate-limiting steps, which are primarily controlled by folding reactions, and lead directly to a set of native, or native-like, conformers. The isomerization of the cis peptide bond is not a source of the parallel channels that characterize the complex folding mechanism for DHFR.     

Quantitative analysis of the kinetics of denaturation and renaturation of barstar in the folding transition zone.

The fluorescence-monitored kinetics of folding and unfolding of barstar by guanidine hydrochloride (GdnHCl) in the folding transition zone, at pH 7, 25 degrees C, have been quantitatively analyzed using a 3-state mechanism: U(S)<-->UF<-->N. U(S) and UF are slow-refolding and fast-refolding unfolded forms of barstar, and N is the native protein. U(S) and UF probably differ in possessing trans and cis conformations, respectively, of the Tyr 47-Pro 48 bond. The 3-state model could be used because the kinetics of folding and unfolding of barstar show 2 phases, a fast phase and a slow phase, and because the relative amplitudes of the 2 phases depend only on the final refolding conditions and not on the initial conditions. Analysis of the observed kinetics according to the 3-state model yields the values of the 4 microscopic rate constants that describe the transitions between the 3 states at different concentrations of GdnHCl. The value of the equilibrium unfolded ratio U(S):UF (K21) and the values of the rate constants of the U(S)-->UF and UF-->U(S) reactions, k12 and k21, respectively, are shown to be independent of the concentration of GdnHCl. K21 has a value of 2.1 +/- 0.1, and k12 and k21 have values of 5.3 x 10(-3) s-1 and 11.2 x 10(-3) s-1, respectively. Double-jump experiments that monitor reactions that are silent to fluorescence monitoring were used to confirm the values of K21, k12, and k21 obtained from the 3-state analysis and thereby the validity of the 3-state model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Characterization of the unfolded state of bovine alpha-lactalbumin and comparison with unfolded states of homologous proteins

The unfolded states of three homologous proteins with a very similar fold have been investigated by heteronuclear NMR spectroscopy. Secondary structure propensities as derived from interpretation of chemical shifts and motional restrictions as evidenced by heteronuclear (15)N relaxation rates have been analyzed in the reduced unfolded states of hen lysozyme and the calcium-binding proteins bovine alpha-lactalbumin and human alpha-lactalbumin. For all three proteins, significant deviations from random-coil predictions can be identified; in addition, the unfolded states also differ from each other, despite the fact that they possess very similar structures in their native states. Deviations from random-coil motional properties are observed in the alpha- and the beta-domain in bovine alpha-lactalbumin and lysozyme, while only regions within the alpha-domain deviate in human alpha-lactalbumin. The motional restrictions and residual secondary structure are determined both by the amino acid sequence of the protein and by residual long-range interactions. Even a conservative single point mutation from I to L in a highly conserved region between the two alpha-lactalbumins results in considerable differences in the motional properties. Given the differences in oxidative folding between hen lysozyme and alpha-lactalbumin, the results obtained on the unfolded states suggest that residual long-range interactions, i.e., those between the alpha- and the beta-domain of lysozyme, may act as nucleation sites for protein folding, while this property of residual structure is replaced by the calcium-binding site between the domains in alpha-lactalbumin.     

Structural analysis of the rate-limiting transition states in the folding of Im7 and Im9: similarities and differences in the folding of homologous proteins

The bacterial immunity proteins Im7 and Im9 fold with mechanisms of different kinetic complexity. Whilst Im9 folds in a two-state transition at pH 7.0 and 10 degrees C, Im7 populates an on-pathway intermediate under these conditions. In order to assess the role of sequence versus topology in the folding of these proteins, and to analyse the effect of populating an intermediate on the landscape for folding, we have determined the conformational properties of the rate-limiting transition state for Im9 folding/unfolding using Phi(F)-value analysis and have compared the results with similar data obtained previously for Im7. The data show that the rate-limiting transition states for Im9 and Im7 folding/unfolding are similar: both are compact (beta(T)=0.94 and 0.89, respectively) and contain three of the four native helices docked around a specific hydrophobic core. Significant differences are observed, however, in the magnitude of the Phi(F)-values obtained for the two proteins. Of the 20 residues studied in both proteins, ten have Phi(F)-values in Im7 that exceed those in Im9 by more than 0.2, and of these five differ by more than 0.4. The data suggest that the population of an intermediate in Im7 results in folding via a transition state ensemble that is conformationally restricted relative to that of Im9. The data are consistent with the view that topology is an important determinant of folding. Importantly, however, they also demonstrate that while the folding transition state may be conserved in homologous proteins that fold with two and three-state kinetics, the population of an intermediate can have a significant effect on the breadth of the transition state ensemble.     

Replacement of proline with valine does not remove an apparent proline isomerization-dependent folding event in CRABP I

Site-directed mutagenesis has frequently been used to replace proline with other amino acids in order to determine if proline isomerization is responsible for a slow phase during refolding. Replacement of Pro 85 with alanine in cellular retinoic acid binding protein I (CRABP-I) abolished the slowest refolding phase, suggesting that this phase is due to proline isomerization in the unfolded state. To further test this assumption, we mutated Pro 85 to valine, which is the conservative replacement in the two most closely related proteins in the family (cellular retinoic acid binding protein II and cellular retinol binding protein I). The mutant protein was about 1 kcal/mole more stable than wild type. Retinoic acid bound equally well to wild type and P85V-CRABP I, confirming the functional integrity of this mutation. The refolding and unfolding kinetics of the wild-type and mutant proteins were characterized by stopped flow fluorescence and circular dichroism. The mutant P85V protein refolded with three kinetic transitions, the same number as wild-type protein. This result conflicts with the P85A mutant, which lost the slowest refolding rate. The P85V mutation also lacked a kinetic unfolding intermediate found for wild-type protein. These data suggest that proline isomerization may not be responsible for the slowest folding phase of CRABP I. As such, the loss of a slow refolding phase upon mutation of a proline residue may not be diagnostic for proline isomerization effects on protein folding.     

The rate-limiting step in the folding of the cis-Pro167Thr mutant of TEM-1 β-lactamase is the trans to cis isomerization of a non-proline peptide bond

The stability and kinetics of unfolding and refolding of the P167T mutant of the TEM-1 β-lactamase have been investigated as a function of guanidine hydrochloride concentration. The activity of the mutant enzyme was not significantly modified, which strongly suggests that the Glu166–Thr167 peptide bond, like the Glu166–Pro167, is cis. The mutation, however, led to a significant decrease in the stability of the native state relative to both the thermodynamically stable intermediate and the fully unfolded state of the protein. In contrast to the two slower phases seen in the refolding of the wild-type enzyme, only one phase was detected in the refolding of the mutant, indicating a determining role of proline 167 in the kinetics of folding of the wild-type enzyme. The former phases are replaced by rapid refolding when the enzyme is unfolded for short periods of time, but the latter is independent of the time of unfolding. The monophasic refolding reaction of the mutant is proposed to reflect mainly the trans→cis isomerization of the Glu166–Thr167 peptide bond. © 1996 John Wiley & Sons, Inc.     

Role of the Cys 2-Cys 10 disulfide bond for the structure, stability, and folding kinetics of ribonuclease T1.

The Cys 2-Cys 10 disulfide bond in ribonuclease T1 was broken by substituting Cys 2 and Cys 10 by Ser and Asn, respectively, as present in ribonuclease F1. This C2S/C10N variant resembles the wild-type protein in structure and in catalytic activity. Minor structural changes were observed by 2-dimensional NMR in the local environment of the substituted amino acids only. The thermodynamic stability of ribonuclease T1 is strongly reduced by breaking the Cys 2-Cys 10 bond, and the free energy of denaturation is decreased by about 10 kJ/mol. The folding mechanism is not affected, and the trans to cis isomerizations of Pro 39 and Pro 55 are still the rate-limiting steps of the folding process. The differences in the time courses of unfolding and refolding are correlated with the decrease in stability: the folding kinetics of the wild-type protein and the C2S/C10N variant become indistinguishable when they are compared under conditions of identical stability. Apparently, the Cys 2-Cys 10 disulfide bond is important for the stability but not for the folding mechanism of ribonuclease T1. The breaking of this bond has the same effect on stability and folding kinetics as adding 1 M guanidinium chloride to the wild-type protein.     

Analysis of the differences in the folding mechanisms of c-type lysozymes based on contact maps constructed with interresidue average distances

A method for analyzing differences in the folding mechanisms of proteins in the same family is presented. Using only information from the amino acid sequences, contact maps derived from the interresidue average distances are employed. These maps, referred to as average distance maps (ADM), are applied to the folding of c-type lysozymes. The results reveal that the ADMs of these lysozymes reflect the differences in the detailed folding mechanisms. Further possible applications of the present method are also discussed.     

Conformational analysis of polypeptides and proteins for the study of protein folding, molecular recognition, and molecular design

Conformational energy calculations provide an understanding as to how interatomic interactions lead to the three-dimensional structures of polypeptides and proteins, and how these molecules interact with other molecules. Illustrative results of such calculations pertain to model systems (-helices and -sheets, and interactions between them), to various open-chain and cyclic peptides, to fibrous proteins, to globular proteins, and to enzyme-substrate complexes. In most cases, the validity of the computations is established by experimental tests of the predicted structures.This article was presented during the proceedings of the International Conference on Macromolecular Structure and Function, held at the National Defence Medical College, Tokorozawa, Japan, December 1985. This paper first appeared in the Israel Journal of Chemistry, Vol. 27, 1986.     

Hidden intermediates and levinthal paradox in the folding of small proteins

It has long been suggested that existence of partially folded intermediates may be essential for proteins to fold in a biologically meaningful time scale. Although partially folded intermediates have been commonly observed in larger proteins, they are generally not detectable in the kinetic folding of smaller proteins (approximately 100 amino acids or less). Recent native-state hydrogen exchange studies suggest that partially folded intermediates may exist behind the rate-limiting transition state in small proteins and evade detection by conventional kinetic methods.     

Parallel channels and rate-limiting steps in complex protein folding reactions: prolyl isomerization and the alpha subunit of Trp synthase,a TIM barrel protein

A kinetic folding mechanism for the alpha subunit of tryptophan synthase (alphaTS) from Escherichia coli, involving four parallel channels with multiple native, intermediate and unfolded forms, has recently been proposed. The hypothesis that cis/trans isomerization of several Xaa-Pro peptide bonds is the source of the multiple folding channels was tested by measuring the sensitivity of the three rate-limiting phases (tau(1), tau(2), tau(3)) to catalysis by cyclophilin, a peptidyl-prolyl isomerase. Although the absence of catalysis for the tau(1) (fast) phase leaves its assignment ambiguous, our previous mutational analysis demonstrated its connection to the unique cis peptide bond preceding proline 28. The acceleration of the tau(2) (medium) and tau(3) (slow) refolding phases by cyclophilin demonstrated that cis/trans prolyl isomerization is also the source of these phases. A collection of proline mutants, which covered all of the remaining 18 trans proline residues of alphaTS, was constructed to obtain specific assignments for these phases. Almost all of the mutant proteins retained the complex equilibrium and kinetic folding properties of wild-type alphaTS; only the P217A, P217G and P261A mutations caused significant changes in the equilibrium free energy surface. Both the P78A and P96A mutations selectively eliminated the tau(1) folding phase, while the P217M and P261A mutations eliminated the tau(2) and tau(3) folding phases, respectively. The redundant assignment of the tau(1) phase to Pro28, Pro78 and Pro96 may reflect their mutual interactions in non-random structure in the unfolded state. The non-native cis isomers for Pro217 and Pro261 may destabilize an autonomous C-terminal folding unit, thereby giving rise to kinetically distinct unfolded forms. The nature of the preceding amino acid, the solvent exposure, or the participation in specific elements of secondary structure in the native state, in general, are not determinative of the proline residues whose isomerization reactions can limit folding.     

Analysis of the differences in the folding kinetics of structurally homologous proteins based on predictions of the gross features of residue contacts

It is a general notion that proteins with very similar three-dimensional structures would show very similar folding kinetics. However, recent studies reveal that the folding kinetic properties of some proteins contradict this thought (i.e., the members in a same protein family fold through different pathways). For example, it has been reported that some beta-proteins in the intracellular lipid-binding protein family fold through quite different pathways (Burns et al., Proteins 1998;33:107-118). Similar differences in folding kinetics are also observed in the members of the globin family (Nishimura et al., Nat Struct Biol 2000;7:679-686). In our study, we examine the possibility of predicting qualitative differences in folding kinetics of the intracellular lipid-binding proteins and two globin proteins (i.e., myoglobin and leghemoglobin). The problem is tackled by means of a contact map based on the average distance statistics between residues, the Average Distance Map (ADM), as constructed from sequence. The ADMs for the three proteins show overall similarity, but some local differences among maps are also observed. Our results demonstrate that some properties of the protein folding kinetics are consistent with local differences in the ADMs. We also discuss the general possibility of predicting folding kinetics from sequence information.