Non-linear rate-equilibrium free energy relationships and Hammond behavior in protein folding

Non-linear rate-equilibrium relationships upon mutation or changes in solvent conditions are frequently observed in protein folding reactions and are usually interpreted in terms of Hammond behavior. Here we first give a general overview over the concept of transition state movements in chemical reactions and discuss its application to protein folding. We then show examples for genuine Hammond behavior and for apparent transition state movements caused by other effects like changes in the rate-limiting step of the folding reaction or ground state effects, i.e. structural changes in either the native state or the unfolded state. These examples show that apparent transition state movements can easily be mistaken for Hammond behavior. We describe experimental tests using self- and cross-interaction parameters to distinguish between structural changes in a single transition state following Hammond behavior and apparent transition state movements caused by other effects.     

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.     

Parallel protein-unfolding pathways revealed and mapped

Theoretical studies of protein folding suggest that multiple folding pathways should exist, but there is little experimental evidence to support this. Here we demonstrate changes in the flux between different transition states on parallel folding pathways, resulting in unprecedented upward curvature in the denaturant-dependent unfolding kinetics of a beta-sandwich protein. As denaturant concentration increases, the highly compact transition state of one pathway becomes destabilized and the dominant flux of protein molecules shifts toward another pathway with a less structured transition state. Furthermore, point mutations alter the relative accessibility of the pathways, allowing the structure of two transition states on separate, direct folding pathways to be mapped by systematic Phi-value analysis. It has been suggested that pathways with diffuse rather than localized transition states are evolutionarily selected to prevent misfolding, and indeed we find that the transition state favored at high concentrations of denaturant is more polarized than the physiologically relevant one.     

Protein folding transition states probed by loop extension

We propose a new way to characterize protein folding transition states by (1) insertion of one or more residues into an unstructured protein loop, (2) measurement of the effect on protein folding kinetics and thermodynamics, and (3) analysis of the results in terms of a rate-equilibrium free energy relationship, alpha(Loop). alpha(Loop) reports on the fraction of molecules that form the perturbed loop in the transition state. Interpretation of the changes in equilibrium free energy using standard polymer theory can help detect residual structure in the unfolded state. We illustrate our approach with data for the model proteins CI2 and the alpha spectrin SH3 domain.     

An error analysis for two-state protein-folding kinetic parameters and phi-values: progress toward precision by exploring pH dependencies on Leffler plots

The interpretation of φ-values has led to an understanding of the folding transition state ensemble of a variety of proteins. Although the main guidelines and equations for calculating φ are well established, there remains some controversy about the quality of the numerical values obtained. By analyzing a complete set of results from kinetic experiments with the SH3 domain of α-spectrin (Spc-SH3) and applying classical error methods and error-propagation formulas, we evaluated the uncertainties involved in two-state-folding kinetic experimental parameters and the corresponding calculated φ-values. We show that kinetic constants in water and m values can be properly estimated from a judicious weighting of fitting errors and describe some procedures to calculate the errors in Gibbs energies and φ-values from a traditional two-point Leffler analysis. Furthermore, on the basis of general assumptions made with the protein engineering method, we show how to generate multipoint Leffler plots via the analysis of pH dependencies of kinetic parameters. We calculated the definitive φ-values for a collection of single mutations previously designed to characterize the folding transition state of the α-spectrin SH3 domain. The effectiveness of the pH-scanning procedure is also discussed in the context of error analysis. Judging from the magnitudes of the error bars obtained from two-point and multipoint Leffler plots, we conclude that the precision obtained for φ-values should be ∼25%, a reasonable limit that takes into account the propagation of experimental errors.     

Engineering diverse changes in beta-turn propensities in the N-terminal beta-hairpin of ubiquitin reveals significant effects on stability and kinetics but a robust folding transition state

Using the N-terminal 17-residue beta-hairpin of ubiquitin as a "host" for mutational studies, we have investigated the influence of the beta-turn sequence on protein stability and folding kinetics by replacing the native G-bulged turn (TLTGK) with more flexible analogues (TG3K and TG5K) and a series of four-residue type I' beta-turn sequences, commonly found in beta-hairpins. Although a statistical analysis of type I' turns demonstrates residue preferences at specific sites, the frequency of occurrence appears to only broadly correlate with experimentally determined protein stabilities. The subsequent engineering of context-dependent non-native tertiary contacts involving turn residues is shown to produce large changes in stability. Relatively few point mutations have been described that probe secondary structure formation in ubiquitin in a manner that is independent of tertiary contacts. To this end, we have used the more rigorous rate-equilibrium free energy relationship (Leffler analysis), rather than the two-point phi value analysis, to show for a family of engineered beta-turn mutants that stability (range of approximately 20 kJ/mol) and folding kinetics (190-fold variation in refolding rate) are linearly correlated (alpha(f) = 0.74 +/- 0.08). The data are consistent with a transition state that is robust with regard to a wide range of statistically favored and disfavored beta-turn mutations and implicate a loosely assembled beta-hairpin as a key template in transition state stabilization with the beta-turn playing a central role.     

Cofactor effects on the protein folding reaction: acceleration of alpha-lactalbumin refolding by metal ions

About 30% of proteins require cofactors for their proper folding. The effects of cofactors on the folding reaction have been investigated with alpha-lactalbumin as a model protein and metal ions as cofactors. Metal ions accelerate the refolding of alpha-lactalbumin by lessening the energy barrier between the molten globule state and the transition state, mainly by decreasing the difference of entropy between the two states. These effects are linked to metal ion binding to the protein in the native state. Hence, relationships between the metal affinities for the intermediate states and those for the native state are observed. Some residual specificity for the calcium ion is still observed in the molten globule state, this specificity getting closer in the transition state to that of the native state. The comparison between kinetic and steady-state data in association with the Phi value method indicates the binding of the metal ions on the unfolded state of alpha-lactalbumin. Altogether, these results provide insight into cofactor effects on protein folding. They also suggest new possibilities to investigate the presence of residual native structures in the unfolded state of protein and the effects of such structures on the protein folding reaction and on protein stability.     

Electrostatic interactions in the denatured state and in the transition state for protein folding: effects of denatured state interactions on the analysis of transition state structure

The development of electrostatic interactions during the folding of the N-terminal domain of the ribosomal protein L9 (NTL9) is investigated by pH-dependent rate equilibrium free energy relationships. We show that Asp8, among six acidic residues, is involved in non-native, electrostatic interactions with K12 in the transition state for folding as well as in the denatured state. The perturbed native state pK(a) of D8 (pK(a) = 3.0) appears to be maintained through non-native interactions in both the transition state and the denatured state. Mutational effects on the stability of the transition state for protein (un)folding are often analyzed in respect to change in ground states. Thus, the interpretation of transition state analysis critically depends on an understanding of mutational effects on both the native and denatured state. Increasing evidence for structurally biased denatured states under physiological conditions raises concerns about possible denatured state effects on folding studies. We show that the structural interpretation of transition state analysis can be altered dramatically by denatured state effects.     

Temperature-dependent Hammond behavior in a protein-folding reaction: analysis of transition-state movement and ground-state effects

Characterization of the transition-state ensemble and the nature of the free-energy barrier for protein folding are areas of intense activity and some controversy. A key issue that has emerged in recent years is the width of the free-energy barrier and the susceptibility of the transition state to movement. Here we report denaturant-induced and temperature-dependent folding studies of a small mixed α-β protein, the N-terminal domain of L9 (NTL9). The folding of NTL9 was determined using fluorescence-detected stopped-flow fluorescence measurements conducted at seven different temperatures between 11 and 40 °C. Plots of the log of the observed first-order rate constant versus denaturant concentration, “chevron plots,” displayed the characteristic V shape expected for two-state folding. There was no hint of deviation from linearity even at the lowest denaturant concentrations. The relative position of the transition state, as judged by the Tanford β parameter, β_T, shifts towards the native state as the temperature is increased. Analysis of the temperature dependence of the kinetic and equilibrium m values indicates that the effect is due to significant movement of the transition state and also includes a contribution from temperature-dependent ground-state effects. Analysis of the Leffler plots, plots of ΔG^‡versus ΔG°, and their cross-interaction parameters confirms the transition-state movement. Since the protein is destabilized at high temperature, the shift represents a temperature-dependent Hammond effect. This provides independent confirmation of a recent theoretical prediction. The magnitude of the temperature-denaturant cross-interaction parameter is larger for NTL9 than has been reported for the few other cases studied. The implications for temperature-dependent studies of protein folding are discussed.     

Differences in the unfolding of procerain induced by pH, guanidine hydrochloride, urea, and temperature

The structural and functional aspects along with equilibrium unfolding of procerain, a cysteine protease from Calotropis procera, were studied in solution. The energetic parameters and conformational stability of procerain in different states were also estimated and interpreted. Procerain belongs to the alpha + beta class of proteins. At pH 2.0, procerain exists in a partially unfolded state with characteristics of a molten globule-like state, and the protein is predominantly a beta-sheet conformation and exhibits strong ANS binding. GuHCl and temperature denaturation of procerain in the molten globule-like state is noncooperative, contrary to the cooperativity seen with the native protein, suggesting the presence of two parts in the molecular structure of procerain, possibly domains, with different stability that unfolds in steps. Moreover, tryptophan quenching studies suggested the exposure of aromatic residues to solvent in this state. At lower pH, procerain unfolds to the acid-unfolded state, and a further decrease in the pH drives the protein to the A state. The presence of 0.5 M salt in the solvent composition directs the transition to the A state while bypassing the acid-unfolded state. GuHCl-induced unfolding of procerain at pH 3.0 seen by various methods is cooperative, but the transitions are noncoincidental. Besides, a strong ANS binding to the protein is observed at low concentrations of GuHCl, indicating the presence of an intermediate in the unfolding pathway. On the other hand, even in the presence of urea (8 M), procerain retains all the activity as well as structural parameters at neutral pH. However, the protein is susceptible to unfolding by urea at lower pH, and the transitions are cooperative and coincidental. Further, the properties of the molten globule-like state and the intermediate state are different, but both states have the same conformational stability. This indicates that these intermediates may be located on parallel folding routes of procerain.     

The final stages of folding of the membrane protein bacteriorhodopsin occur by kinetically indistinguishable parallel folding paths that are mediated by pH

The folding of the transmembrane protein bacteriorhodopsin that occurs during the binding of its retinal cofactor is investigated in a membrane-like environment. Changes in the retinal absorption band reveal two transient retinal-protein intermediate states, with apparent absorption maxima at 380 nm and 440 nm, respectively. Studies on a bacteriorhodopsin mutant of Lys216, which cannot bind retinal covalently, add to evidence that retinal is non-covalently bound in these intermediate states. The two retinal-protein intermediates are genuine intermediate states that form in parallel, each with an observed rate constant of 1.1 s-1. Meanwhile no formation of the folded state is detected. Folded bacteriorhodopsin, with all trans retinal covalently bound, forms from both retinal-bound intermediates with the same apparent rate constant of 0.0070 s-1 that is independent of retinal concentration. Retinal isomerisation then occurs with a rate constant of 0.00033 s-1 to give bacteriorhodopsin containing all trans and 13 cis-retinal. These results provide experimental evidence for multiple folding routes for a membrane protein that are pH dependent, with pH conditions determining the apparent folding route. These observed parallel folding paths are kinetically indistinguishable, which contrasts with most other observations of parallel folding pathways where only pathways with different kinetics have been reported. Furthermore, together with previous work, this study shows that bacteriorhodopsin has to populate at least two folding intermediates, during folding in the mixed lipid micelles investigated here, before the final fold is attained.     

Geometrical Frustration in Interleukin-33 Decouples the Dynamics of the Functional Element from the Folding Transition State Ensemble

Interleukin-33 (IL-33) is currently the focus of multiple investigations into targeting pernicious inflammatory disorders. This mediator of inflammation plays a prevalent role in chronic disorders such as asthma, rheumatoid arthritis, and progressive heart disease. In order to better understand the possible link between the folding free energy landscape and functional regions in IL-33, a combined experimental and theoretical approach was applied. IL-33 is a pseudo- symmetrical protein composed of three distinct structural elements that complicate the folding mechanism due to competition for nucleation on the dominant folding route. Trefoil 1 constitutes the majority of the binding interface with the receptor whereas Trefoils 2 and 3 provide the stable scaffold to anchor Trefoil 1. We identified that IL-33 folds with a three-state mechanism, leading to a rollover in the refolding arm of its chevron plots in strongly native conditions. In addition, there is a second slower refolding phase that exhibits the same rollover suggesting similar limitations in folding along parallel routes. Characterization of the intermediate state and the rate limiting steps required for folding suggests that the rollover is attributable to a moving transition state, shifting from a post- to pre-intermediate transition state as you move from strongly native conditions to the midpoint of the transition. On a structural level, we found that initially, all independent Trefoil units fold equally well until a Q_CA of 0.35 when Trefoil 1 will backtrack in order to allow Trefoils 2 and 3 to fold in the intermediate state, creating a stable scaffold for Trefoil 1 to fold onto during the final folding transition. The formation of this intermediate state and subsequent moving transition state is a result of balancing the difficulty in folding the functionally important Trefoil 1 onto the remainder of the protein. Taken together our results indicate that the functional element of the protein is geometrically frustrated, requiring the more stable elements to fold first, acting as a scaffold for docking of the functional element to allow productive folding to the native state.     

A residue in helical conformation in the native state adopts a β-strand conformation in the folding transition state despite its high and canonical Φ-value

Delineating structures of the transition states in protein folding reactions has provided great insight into the mechanisms by which proteins fold. The most common method for obtaining this information is Φ-value analysis, which is carried out by measuring the changes in the folding and unfolding rates caused by single amino acid substitutions at various positions within a given protein. Canonical Φ-values range between 0 and 1, and residues displaying high values within this range are interpreted to be important in stabilizing the transition state structure, and to elicit this stabilization through native-like interactions. Although very successful in defining the general features of transition state structures, Φ-value analysis can be confounded when non-native interactions stabilize this state. In addition, direct information on backbone conformation within the transition state is not provided. In the work described here, we have investigated structure formation at a conserved β-bulge (with helical conformation) in the Fyn SH3 domain by characterizing the effects of substituting all natural amino acids at one position within this structural motif. By comparing the effects on folding rates of these substitutions with database-derived local structure propensity values, we have determined that this position adopts a non-native backbone conformation in the folding transition state. This result is surprising because this position displays a high and canonical Φ-value of 0.7. This work emphasizes the potential role of non-native conformations in folding pathways and demonstrates that even positions displaying high and canonical Φ-values may, nevertheless, adopt a non-native conformation in the transition state.     

The analysis of protein folding kinetic data produced in protein engineering experiments

Over the past decade, the "protein engineering method" has been used to investigate the folding pathways of more than 20 different proteins. This method involves measuring the folding and unfolding rates of mutant proteins with single amino acid substitutions spread across the sequence. Comparison of folding rates of the mutant proteins to that of the wild-type protein allows the calculation of the phi value, which can be used to evaluate the stabilizing contribution of an amino acid side chain to the structure of the folding transition state. Here, we review the methodology for analysing data collected in protein engineering folding kinetics studies. We discuss the calculation of folding rates and kinetic m values, the estimation of errors in folding kinetics experiments, phi value calculation including potential pitfalls of the analysis, Br?nsted plots, detecting Hammond behaviour, and the analysis of curved chevron plots.     

Non-linear effects of temperature and urea on the thermodynamics and kinetics of folding and unfolding of hisactophilin

Extensive measurements and analysis of thermodynamic stability and kinetics of urea-induced unfolding and folding of hisactophilin are reported for 5-50 degrees C, at pH 6.7. Under these conditions hisactophilin has moderate thermodynamic stability, and equilibrium and kinetic data are well fit by a two-state transition between the native and the denatured states. Equilibrium and kinetic m values decrease with increasing temperature, and decrease with increasing denaturant concentration. The betaF values at different temperatures and urea concentrations are quite constant, however, at about 0.7. This suggests that the transition state for hisactophilin unfolding is native-like and changes little with changing solution conditions, consistent with a narrow free energy profile for the transition state. The activation enthalpy and entropy of unfolding are unusually low for hisactophilin, as is also the case for the corresponding equilibrium parameters. Conventional Arrhenius and Eyring plots for both folding and unfolding are markedly non-linear, but these plots become linear for constant DeltaG/T contours. The Gibbs free energy changes for structural changes in hisactophilin have a non-linear denaturant dependence that is comparable to non-linearities observed for many other proteins. These non-linearities can be fit for many proteins using a variation of the Tanford model, incorporating empirical quadratic denaturant dependencies for Gibbs free energies of transfer of amino acid constituents from water to urea, and changes in fractional solvent accessible surface area of protein constituents based on the known protein structures. Noteworthy exceptions that are not well fit include amyloidogenic proteins and large proteins, which may form intermediates. The model is easily implemented and should be widely applicable to analysis of urea-induced structural transitions in proteins.     

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.     

The family feud: do proteins with similar structures fold via the same pathway?

Theoretical and experimental studies of protein folding have suggested that the topology of the native state may be the most important factor determining the folding pathway of a protein, independent of its specific amino acid sequence. To test this concept, many experimental studies have been carried out with the aim of comparing the folding pathways of proteins that possess similar tertiary structures, but divergent sequences. Many of these studies focus on quantitative comparisons of folding transition state structures, as determined by Phi(f) value analysis of folding kinetic data. In some of these studies, folding transition state structures are found to be highly conserved, whereas in others they are not. We conclude that folds displaying more conserved transition state structures may have the most restricted number of possible folding pathways and that folds displaying low transition state structural conservation possess many potential pathways for reaching the native state.     

pH-dependent stability and folding kinetics of a protein with an unusual alpha-beta topology: the C-terminal domain of the ribosomal protein L9

The folding kinetics and thermodynamics of the isolated C-terminal domain of the ribosomal protein L9 (CTL9) have been studied as a function of pH. CTL9 is an alpha-beta protein that contains a single beta-sheet with an unusual mixed parallel, anti-parallel topology. The folding is fully reversible and two-state over the entire pH range. Stopped-flow fluorescence and CD experiments yield the same folding rate, and the chevron plots have the characteristic V-shape expected for two-state folding. The values of DeltaG*(H2O) and the m value calculated from the kinetic experiments are in excellent agreement with the equilibrium measurements. The extrapolated initial amplitudes of both the stopped-flow fluorescence and CD measurements show that there is no detectable burst phase intermediate. The domain contains three histidine residues, two of which are largely buried in the native state. They do not participate in salt-bridges or take part in a hydrogen bonded network. NMR measurements reveal that the buried histidine residues have significantly perturbed pK(a) values in the native state. The equilibrium stability and the folding rate are found to be strongly dependent upon their ionization state. There is a linear relationship between the log of the folding rate and DeltaG* (H2O) . The protein is much more stable and folds noticeably faster at pH values above the native state pK(a) values. DeltaG*(H2O) of unfolding increases from 2.90 kcal mol(-1) at pH 5.0 to 6.40 kcal mol(-1) at pH 8.0 while the folding rate increases from 0.60 to 18.7 s(-1). Tanford linkage analysis revealed that the interactions involving the two histidine residues are largely developed in the transition state. The results are compared to other studies of the pH-dependence of folding.     

Evidence for sequential barriers and obligatory intermediates in apparent two-state protein folding

Many small proteins fold fast and without detectable intermediates. This is frequently taken as evidence against the importance of partially folded states, which often transiently accumulate during folding of larger proteins. To get insight into the properties of free energy barriers in protein folding we analyzed experimental data from 23 proteins that were reported to show non-linear activation free-energy relationships. These non-linearities are generally interpreted in terms of broad transition barrier regions with a large number of energetically similar states. Our results argue against the presence of a single broad barrier region. They rather indicate that the non-linearities are caused by sequential folding pathways with consecutive distinct barriers and a few obligatory high-energy intermediates. In contrast to a broad barrier model the sequential model gives a consistent picture of the folding barriers for different variants of the same protein and when folding of a single protein is analyzed under different solvent conditions. The sequential model is also able to explain changes from linear to non-linear free energy relationships and from apparent two-state folding to folding through populated intermediates upon single point mutations or changes in the experimental conditions. These results suggest that the apparent discrepancy between two-state and multi-state folding originates in the relative stability of the intermediates, which argues for the importance of partially folded states in protein folding.     

Direct Observation of Parallel Folding Pathways Revealed Using a Symmetric Repeat Protein System

Although progress has been made to determine the native fold of a polypeptide from its primary structure, the diversity of pathways that connect the unfolded and folded states has not been adequately explored. Theoretical and computational studies predict that proteins fold through parallel pathways on funneled energy landscapes, although experimental detection of pathway diversity has been challenging. Here, we exploit the high translational symmetry and the direct length variation afforded by linear repeat proteins to directly detect folding through parallel pathways. By comparing folding rates of consensus ankyrin repeat proteins (CARPs), we find a clear increase in folding rates with increasing size and repeat number, although the size of the transition states (estimated from denaturant sensitivity) remains unchanged. The increase in folding rate with chain length, as opposed to a decrease expected from typical models for globular proteins, is a clear demonstration of parallel pathways. This conclusion is not dependent on extensive curve-fitting or structural perturbation of protein structure. By globally fitting a simple parallel-Ising pathway model, we have directly measured nucleation and propagation rates in protein folding, and have quantified the fluxes along each path, providing a detailed energy landscape for folding. This finding of parallel pathways differs from results from kinetic studies of repeat-proteins composed of sequence-variable repeats, where modest repeat-to-repeat energy variation coalesces folding into a single, dominant channel. Thus, for globular proteins, which have much higher variation in local structure and topology, parallel pathways are expected to be the exception rather than the rule.