Folding Nuclei in Proteins

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed in the vicinity of the equilibrium point. Here the two-state transition proceeds without any accumulation of metastable intermediates, and only the transition state (folding nucleus) is outlined by its key influence on the folding/unfolding kinetics. This review covers recent experimental and theoretical studies of folding nuclei.     

Kinetics of folding nuclei formation in proteins

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed in the vicinity of the equilibrium point. Here the "two-state" transition proceeds without any accumulation of metastable intermediates, and only the transition state ("folding nucleus") is outlined by its key influence on the folding/unfolding kinetics. This review covers recent experimental and theoretical studies of folding nuclei.     

Differential stabilization of two hydrophobic cores in the transition state of the villin 14T folding reaction

We report the distribution of hydrophobic core contacts during the folding reaction transition state for villin 14T, a small 126-residue protein domain. The solution structure of villin 14T contains a central beta-sheet with two flanking hydrophobic cores; transition states for this protein topology have not been previously studied. Villin 14T has no disulfide bonds or cis-proline residues in its native state; it folds reversibly, and in an apparently two-state manner under some conditions. To map the hydrophobic core contacts in the transition state, 27 point mutations were generated at positions spread throughout the two hydrophobic cores. After each point mutation, comparison of the change in folding kinetics with the equilibrium destabilization indicates whether the site of mutation is stabilized in the transition state. The results show that the folding nucleus, or the sub-region with the strongest transition state contacts, is located in one of the two hydrophobic cores (the predominantly aliphatic core). The other hydrophobic core, which is mostly aromatic, makes much weaker contacts in the transition state. This work is the first transition state mapping for a protein with multiple major hydrophobic cores in a single folding unit; the hydrophobic cores cannot be separated into individual folding subdomains. The stabilization of only one hydrophobic core in the transition state illustrates that hydrophobic core formation is not intrinsically capable of nucleating folding, but must also involve the right specific interactions or topological factors in order to be kinetically important.     

Noninteracting local-structure model of folding and unfolding transition in globular proteins. I. Formulation

A statistical-mechanical model (a noninteracting local structure model) of folding and unfolding transition in globular proteins is described and a formulation is given to calculate the partition function. The process of transition is discussed in this model within the framework of equilibrium statistical mechanics. In order to clarify the range of applicability of such an approach, the characteristics of the folding and unfolding transition in globular proteins are analyzed from the statistical-physical point of view. A theoretical advantage is pointed out in studying folding and unfolding processes taking place as conformational fluctuations in individual protein molecules under macroscopic equilibrium at the melting temperature. In this case, paths of folding and unfolding are shown to be identical in the statistical sense. A key to the noninteracting local structure model lies in the concept of local structures and the assumption of the absence of interactions between local structures. A local structure is defined as a continuous section of the chain which takes the same or similar local conformation as in the native conformation. The assumption of the absence of inter-actions between local structures endows the model with the remarkable character that its partition function can be calculated exactly; thereby the equilibrium population of various conformations along the folding and unfolding paths can be discussed only by a knowledge of the folded native conformation.     

Nucleation‐based prediction of the protein folding rate and its correlation with the folding nucleus size

The problem of protein self‐organization is in the focus of current molecular biology studies. Although the general principles are understood, many details remain unclear. Specifically, protein folding rates are of interest because they dictate the rate of protein aggregation which underlies many human diseases. Here we offer predictions of protein folding rates and their correlation with folding nucleus sizes. We calculated free energies of the transition state and sizes of folding nuclei for 84 proteins and peptides whose other parameters were measured at the point of thermodynamic equilibrium between their unfolded and native states. We used the dynamic programming method where each residue was considered to be either as folded as in its native state or completely disordered. The calculated and measured folding rates showed a good correlation at the temperature mid‐transition point (the correlation coefficient was 0.75). Also, we pioneered in demonstrating a moderate (‐0.57) correlation coefficient between the calculated sizes of folding nuclei and the folding rates. Predictions made by different methods were compared. The established good correlation between the estimated free energy barrier and the experimentally found folding rate of each studied protein/peptide indicates that our model gives reliable results for the considered data set. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Folding of Escherichia coli DsbC: characterization of a monomeric folding intermediate

The homodimeric protein DsbC is a disulfide isomerase and a chaperone located in the periplasm of Escherichia coli. We have studied the guanidine hydrochloride (GdnHCl)-induced unfolding and refolding of DsbC using mutagenesis, intrinsic fluorescence, circular dichroism spectra, size-exclusion chromatography, and sedimentation velocity analysis. The equilibrium refolding and unfolding of DsbC was thermodynamically reversible. The equilibrium folding profile measured by fluorescence excited at 280 nm exhibited a three-state transition profile with a stable folding intermediate formed at 0-2.0 M GdnHCl followed by a second transition at higher GdnHCl concentrations. Sedimentation velocity data revealed dissociation of the dimer to the monomer over the concentration range of the first transition (0-2.0 M). In contrast, fluorescence emission data for DsbC excited at 295 nm showed a single two-state transition. Fluorescence emission data for the equilibrium unfolding of the monomeric G49R mutant, excited at either 295 or 280 nm, indicated a single two-state transition. Data obtained for the dimeric Y52W mutant indicated a strong protein concentration dependence of the first transition but no dependence of the second transition in equilibrium unfolding. This suggests that the fluorescence of Y52W sensitively reports conformational changes caused by dissociation of the dimer. Thus, the folding of DsbC follows a three-state transition model with a monomeric folding intermediate formed in 0-2.0 M GdnHCl. The folding of DsbC in the presence of DTT indicates an important role for the non-active site disulfide bond in stabilizing the conformation of the molecule. Dimerization ensures the performance of chaperone and isomerase functions of DsbC.     

Folding thermodynamics and kinetics of the leucine-rich repeat domain of the virulence factor Internalin B

Although the folding of alpha-helical repeat proteins has been well characterized, much less is known about the folding of repeat proteins containing beta-sheets. Here we investigate the folding thermodynamics and kinetics of the leucine-rich repeat (LRR) domain of Internalin B (InlB), an extracellular virulence factor from the bacterium Lysteria monocytogenes. This domain contains seven tandem leucine-rich repeats, of which each contribute a single beta-strand that forms a continuous beta-sheet with neighboring repeats, and an N-terminal alpha-helical capping motif. Despite its modular structure, InlB folds in an equilibrium two-state manner, as reflected by the identical thermodynamic parameters obtained by monitoring its sigmoidal urea-induced unfolding transition by different spectroscopic probes. Although equilibrium two-state folding is common in alpha-helical repeat proteins, to date, InlB is the only beta-sheet-containing repeat protein for which this behavior is observed. Surprisingly, unlike other repeat proteins exhibiting equilibrium two-state folding, InlB also folds by a simple two-state kinetic mechanism lacking intermediates, aside from the effects of prolyl isomerization on the denatured state. However, like other repeat proteins, InlB also folds significantly more slowly than expected from contact order. When plotted against urea, the rate constants for the fast refolding and single unfolding phases constitute a linear chevron that, when fitted with a kinetic two-state model, yields thermodynamic parameters matching those observed for equilibrium folding. Based on these kinetic parameters, the transition state is estimated to comprise 40% of the total surface area buried upon folding, indicating that a large fraction of the native contacts are formed in the rate-limiting step to folding.     

On the role of some conserved and nonconserved amino acid residues in the transitional state and intermediate of apomyoglobin folding

The contributions of some amino acid residues in the A, B, G, and H helices to the formation of the folding nucleus and folding intermediate of apomyoglobin were estimated. The effects of point substitutions of Ala for hydrophobic amino acid residues on the structural stability of the native (N) protein and its folding intermediate (I), as well as on the folding/unfolding rates for four mutant apomyoglobin forms, were studied. The equilibrium and kinetic studies of the folding/unfolding rates of these mutant proteins in a wide range of urea concentrations demonstrated that their native state was considerably destabilized as compared with the wild-type protein, whereas the stability of the intermediate state changed moderately. It was shown that the amino acid residues in the A, G, and H helices contributed insignificantly to the stabilization of the apomyoglobin folding nucleus in the rate-limiting I ? N transition, taking place after the formation of the intermediate, whereas the residue of the B helix was of great importance in the formation of the folding nucleus in this transition.     

Revisiting the folding kinetics of bacteriorhodopsin

The elucidation of the physical principles that govern the folding and stability of membrane proteins is one of the greatest challenges in protein science. Several insights into the folding of α-helical membrane proteins have come from the investigation of the conformational equilibrium of H. halobium bacteriorhodopsin (bR) in mixed micelles using SDS as a denaturant. In an effort to confirm that folded bR and SDS-denatured bR reach the same conformational equilibrium, we found that bR folding is significantly slower than has been previously known. Interrogation of the effect of the experimental variables on folding kinetics reveals that the rate of folding is dependent not only on the mole fraction of SDS but also on the molar concentrations of mixed micelle components, a variable that was not controlled in the previous study of bR folding kinetics. Moreover, when the molar concentrations of mixed micelle components are fixed at the concentrations commonly employed for bR equilibrium studies, conformational relaxation in the transition zone is slower than hydrolysis of the retinal Schiff base. As a result, the conformational equilibrium between folded bR and SDS-denatured bR cannot be achieved under the conventional condition. Our finding suggests that the molar concentrations of mixed micelle components are important experimental variables in the investigation of the kinetics and thermodynamics of bR folding and should be accounted for to ensure the accurate assessment of the conformational equilibrium of bR without the interference of retinal hydrolysis.     

Altering the intermediate in the equilibrium folding of unmodified yeast tRNAPhe with monovalent and divalent cations

The isothermal equilibrium folding of the unmodified yeast tRNA(Phe) is studied as a function of Na(+), Mg(2+), and urea concentration with hydroxyl radical protection, circular dichroism, and diethyl pyrocarbonate (DEPC) modification. These assays indicate that this tRNA folds in Na(+) alone. Similar to folding in Mg(2+), folding in Na(+) can be described by two transitions, unfolded-to-intermediate-to-native. The I-to-N transition has a Na(+) midpoint of approximately 0.5 M and a Hill constant of approximately 4. Unexpectedly, the urea m-value, the dependence of free energy on urea concentration, for the I-to-N transition is significantly smaller in Na(+) than in Mg(2+), 0.4 versus 1.7 kcal mol(-1) M(-1), indicating that more structure is formed in the Mg(2+)-induced transition. DEPC modification indicates that the I state in Na(+)-induced folding contains all four helices of tRNA and the I-to-N transition primarily corresponds to the formation of the tertiary structure. In contrast, the intermediate in Mg(2+)-induced folding contains only three helices, and the I-to-N transition corresponds to the formation of the acceptor stem plus tertiary structure. The cation dependence of the intermediates arises from the differences in the stability of the acceptor stem and the tertiary structure. The acceptor stem is stable at a lower Na(+) concentration than required for the tertiary structure formation. The relative stability is reversed in Mg(2+) so that the acceptor stem and the tertiary structure form simultaneously in the I-to-N transition. These results demonstrate that formation of the RNA secondary structure can be independent or coupled to the formation of the tertiary structure depending on their relative stability in monovalent and divalent ions.     

Kinetic pathways of beta-hairpin (un)folding in explicit solvent

We examine the dynamical (un)folding pathways of the C-terminal beta-hairpin of protein G-B1 at room temperature in explicit solvent, by employing transition path sampling algorithms. The path ensembles contain information on the folding kinetics, including solvent motion. We determine the transition state ensembles for the two main transitions: 1), the hydrophobic collapse; and 2), the backbone hydrogen bond formation. In both cases the transition state ensembles are characterized by a layer (1) or a strip (2) of water molecules in between the two hairpin strands, supporting the hypothesis of the solvent as lubricant in the folding process. The transition state ensembles do not correspond with saddle points in the equilibrium free-energy landscapes. The kinetic pathways are thus not completely determined by the free-energy landscape. This phenomenon can occur if the order parameters obey different timescales. Using the transition interface sampling technique, we calculate the rate constants for (un)folding and find them in reasonable agreement with experiments, thus supporting the validation of using all-atom force fields to study protein folding.     

Rapid folding and unfolding of Apaf-1 CARD

Caspase recruitment domains (CARDs) are members of the death domain superfamily and contain six antiparallel helices in an alpha-helical Greek key topology. We have examined the equilibrium and kinetic folding of the CARD of Apaf-1 (apoptotic protease activating factor 1), which consists of 97 amino acid residues, at pH 6 and pH 8. The results showed that an apparent two state equilibrium mechanism is not adequate to describe the folding of Apaf-1 CARD at either pH, suggesting the presence of intermediates in equilibrium unfolding. Interestingly, the results showed that the secondary structure is less stable than the tertiary structure, based on the transition mid-points for unfolding. Single mixing and sequential mixing stopped-flow studies showed that Apaf-1 CARD folds and unfolds rapidly and suggest a folding mechanism that contains parallel channels with two unfolded conformations folding to the native conformation. Kinetic simulations show that a slow folding phase is described by a third conformation in the unfolded ensemble that interconverts with one or both unfolded species. Overall, the native ensemble is formed rapidly upon refolding. This is in contrast to other CARDs in which folding appears to be dominated by formation of kinetic traps.     

Characterization of the hydrodynamic properties of the folding transition state of an SH3 domain by magnetization transfer NMR spectroscopy

Protein folding kinetic data have been obtained for the marginally stable N-terminal Src homology 3 domain of the Drosophila protein drk (drkN SH3) in an investigation of the hydrodynamic properties of its folding transition state. Due to the presence of NMR resonances of both folded and unfolded states at equilibrium, kinetic data can be derived from NMR magnetization transfer techniques under equilibrium conditions. Kinetic analysis as a function of urea (less than approximately 1 M) and glycerol enables determination of alpha values, measures of the energetic sensitivity of the transition state to the perturbation relative to the end states of the protein folding reaction (the folded and unfolded states). Both end states have previously been studied experimentally by NMR spectroscopic and other biophysical methods in great detail and under nondenaturing conditions. Combining these results with the kinetic folding data obtained here, we can characterize the folding transition state without requiring empirical models for the unfolded state structure. We are thus able to give a reliable measure of the solvent-accessible surface area of the transition state of the drkN SH3 domain (4730 +/- 360 A(2)) based on urea titration data. Glycerol titration data give similar results and additionally demonstrate that folding of this SH3 domain is dependent on solvent viscosity, which is indicative of at least partial hydration of the transition state. Because SH3 domains appear to fold by a common folding mechanism, the data presented here provide valuable insight into the transition states of the drkN and other SH3 domains.     

Identification of equilibrium and kinetic intermediates involved in folding of urea-denatured creatine kinase

The unfolding transition and kinetic refolding of dimeric creatine kinase after urea denaturation were monitored by intrinsic fluorescence and far ultraviolet circular dichroism. An equilibrium intermediate and a kinetic folding intermediate were identified and characterized. The fluorescence intensity of the equilibrium intermediate is close to that of the unfolded state, whereas its ellipticity at 222 nm is about 50% of the native state. The transition curves measured by these two methods are therefore non-coincident. The kinetic folding intermediate, formed during the burst phase of refolding under native-like conditions, possesses 75% of the native secondary structure, but is mostly lacking in native tertiary structure. In moderate concentrations of urea, only the initial, rapid change in fluorescence intensity or negative ellipticity is observed, and the final state values do not reach the equivalent unfolding values. The unfolding and refolding transition curves measured under identical conditions are non-coincident within the transition from intermediate to fully unfolded state. It is observed by SDS-PAGE that disulfide bond-linked dimeric or oligomeric intermediates are formed in moderate urea concentrations, especially in the refolding reaction. These rapidly formed, soluble intermediates represent an off-pathway event that leads to the hysteresis in the refolding transition curves.     

Influence of Trp mutation on native, intermediate, and transition states of goat alpha-lactalbumin: an equilibrium and kinetic study

Equilibrium circular dichroism and kinetic stopped-flow fluorescence studies on the stability and the folding kinetics of a set of Trp to Phe mutants of goat alpha-lactalbumin (GLA) were used to characterize the native, intermediate, and transition states of these constructs. GLA contains four tryptophan residues, three of which, Trp26, Trp104, and Trp118, are located in the alpha-domain, while the fourth, Trp60, is located in the beta-domain. Trp26, Trp60, and Trp104 are part of a hydrophobic cluster, whereas Trp118 is situated in a more flexible region near the C-terminal end of the protein. In each case, the mutation leads to a reduction in the overall stability, but only for W26F and W60F is an equilibrium intermediate observed in guanidine hydrochloride-induced unfolding experiments. In kinetic refolding experiments, however, for all samples a burst phase is observed, the amplitude of which depends on the specific mutation. Refolding and unfolding kinetics can adequately be described by a sequential three-state mechanism. phi value analysis showed that the local structure around Trp26, Trp60, and Trp104 is formed in the intermediate and in the transition state of the folding reaction, while around Trp118 no persistent native contacts are observed. From these findings, we conclude that, although hydrophobicity is a major driving force for folding, minor steric changes induced by point mutation can considerably influence the overall stability and the folding process of the protein.     

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.     

Multifrequency calorimetry of the folding/unfolding transition of cytochrome c.

The folding-unfolding transition of Fe(III) cytochrome c has been studied with the new technique of multifrequency calorimetry. Multifrequency calorimetry is aimed at measuring directly the dynamics of the energetic events that take place during a thermally induced transition by measuring the frequency dispersion of the heat capacity. This is done by modulating the folding/unfolding equilibrium using a variable frequency, small oscillatory temperature perturbation (approximately 0.05-0.1 degrees C) centered at the equilibrium temperature of the system. Fe(III) cytochrome c at pH 4 undergoes a fully reversible folding/unfolding transition centered at 67.7 degrees C and characterized by an enthalpy change of 81 kcal/mol and heat capacity difference between unfolded and folded states of 0.9 kcal/K*mol. By measuring the temperature dependence of the frequency dispersion of the heat capacity in the frequency range of 0.1-1 Hz it has been possible to examine the time regime of the enthalpic events associated with the transition. The multifrequency calorimetry results indicate that approximately 85% of the excess heat capacity associated with the folding/unfolding transition relaxes with a single relaxation time of 326 +/- 68 ms at the midpoint of the transition region. This is the first time that the time regime in which heat is absorbed and released during protein folding/unfolding has been measured.     

D/H amide kinetic isotope effects reveal when hydrogen bonds form during protein folding

We have exploited a procedure to identify when hydrogen bonds (H-bonds) form under two-state folding conditions using equilibrium and kinetic deuterium/hydrogen amide isotope effects. Deuteration decreases the stability of equine cytochrome c and the dimeric and crosslinked versions of the GCN4-p1 coiled coil by approximately 0. 5 kcal mol-1. For all three systems, the decrease in equilibrium stability is reflected by a decrease in refolding rates and a near equivalent increase in unfolding rates. This apportionment indicates that approximately 50% of the native H-bonds are formed in the transition state of these helical proteins. In contrast, an alpha/beta protein, mammalian ubiquitin, exhibits a small isotope effect only on unfolding rates, suggesting its folding pathway may be different. These four proteins recapitulate the general trend that approximately 50% of the surface buried in the native state is buried in the transition state, leading to the hypothesis that H-bond formation in the transition state is cooperative, with alpha-helical proteins forming a number of H-bonds proportional to the amount of surface buried in the transition state.     

Folding mechanism of an ankyrin repeat protein: scaffold and active site formation of human CDK inhibitor p19(INK4d)

The p19(INK4d) protein consists of five ankyrin repeats (ANK) and controls the human cell cycle by inhibiting the cyclin D-dependent kinases (CDK) 4 and 6. We investigated the folding of p19(INK4d) by urea-induced unfolding transitions, kinetic analyses of unfolding and refolding, including double-mixing experiments and a special assay for folding intermediates. Folding is a sequential two-step reaction via a hyperfluorescent on-pathway intermediate. This intermediate is present under all conditions, during unfolding, refolding and at equilibrium. The folding mechanism was confirmed by a quantitative global fit of a consistent set of equilibrium and kinetic data revealing the thermodynamics and intrinsic folding rates of the different states. Surprisingly, the N<-->I transition is much faster compared to the I<-->U transition. The urea-dependence of the intrinsic folding rates causes population of the intermediate at equilibrium close to the transition midpoint. NMR detected hydrogen/deuterium exchange and the analysis of truncated variants showed that the C-terminal repeats ANK3-5 are already folded in the on-pathway intermediate, whereas the N-terminal repeats 1 and 2 are not folded. We suggest that during refolding, repeats ANK3-ANK5 first form the scaffold for the subsequent assembly of repeats ANK1 and ANK2. The binding function of p19(INK4d) resides in the latter repeats. We propose that the graded stability and the facile unfolding of repeats 1 and 2 is a prerequisite for the down-regulation of the inhibitory activity of p19(INK4d) during the cell-cycle.