Effects of the difference in the unfolded-state ensemble on the folding of Escherichia coli dihydrofolate reductase

The unfolded state of a protein is an ensemble of a large number of conformations ranging from fully extended to compact structures. To investigate the effects of the difference in the unfolded-state ensemble on protein folding, we have studied the structure, stability, and folding of "circular" dihydrofolate reductase (DHFR) from Escherichia coli in which the N and C-terminal regions are cross-linked by a disulfide bond, and compared the results with those of disulfide-reduced "linear" DHFR. Equilibrium studies by circular dichroism, difference absorption spectra, solution X-ray scattering, and size-exclusion chromatography show that whereas the native structures of both proteins are essentially the same, the unfolded state of circular DHFR adopts more compact conformations than the unfolded state of the linear form, even with the absence of secondary structure. Circular DHFR is more stable than linear DHFR, which may be due to the decrease in the conformational entropy of the unfolded state as a result of circularization. Kinetic refolding measurements by stopped-flow circular dichroism and fluorescence show that under the native conditions both proteins accumulate a burst-phase intermediate having the same structures and both fold by the same complex folding mechanism with the same folding rates. Thus, the effects of the difference in the unfolded state of circular and linear DHFRs on the refolding reaction are not observed after the formation of the intermediate. This suggests that for the proteins with close termini in the native structure, early compaction of a protein molecule to form a specific folding intermediate with the N and C-terminal regions in close proximity is a crucial event in folding. If there is an enhancement in the folding reflecting the reduction in the breadth of the unfolded-state ensemble for circular DHFR, this acceleration must occur in the sub-millisecond time-range.     

Conservation of folding pathways in evolutionarily distant globin sequences

To test the hypothesis that the folding pathways of evolutionarily related proteins with similar three-dimensional structures but widely different sequences should be similar, the folding pathway of apoleghemoglobin has been characterized using stopped-flow circular dichroism, heteronuclear NMR pulse labeling techniques and mass spectrometry. The pathway of folding was found to differ significantly from that of a protein of the same family, apomyoglobin, although both proteins appear to fold through helical burst phase intermediates. For leghemoglobin, the burst phase intermediate exhibits stable helical structure in the G and H helices, together with a small region in the center of the E helix. The A and B helices are not stabilized until later stages of the folding process. The structure of the burst phase folding intermediate thus differs from that of apomyoglobin, in which stable helical structure is formed in the A, B, G and H helix regions.     

Acceleration of the folding of acylphosphatase by stabilization of local secondary structure

The addition of trifluoroethanol or hexafluoroisopropanol converts the apparent two-state folding of acylphosphatase, a small alpha/beta protein, into a multistate mechanism where secondary structure accumulates significantly in the denatured state before folding to the native state. This results in a marked acceleration of folding as revealed by following the intrinsic fluorescence and circular dichroism changes upon folding. The folding rate is at a maximum when the secondary-structure content of the denatured state corresponds to that of the native state, while further stabilization of secondary structure decreases the folding rate. These findings indicate that stabilization of intermediate structure can either enhance or retard folding depending on its nature and content of native-like interactions.     

Stabilization of the ribosomal protein S6 by trehalose is counterbalanced by the formation of a putative off-pathway species

The effect of trehalose on folding and stability of the small ribosomal protein S6 was studied. Non-disruptive point mutations distributed along the protein structure were analyzed to characterize the stabilizing effect of trehalose and map the folding pathway of S6. On average, the stability of the wild-type and S6 mutants increases by 3 kcal/mol M trehalose. Despite the non-specific thermodynamic stabilization mechanism, trehalose particularly stabilizes the less destabilized mutants. Folding/unfolding kinetics shows clearly that trehalose induces the collapse of the unfolded state to an off-pathway intermediate with non-native diffuse contacts. This state is similar to the collapsed state induced by high concentrations of stabilizing salts, as previously reported. Although it leads to the accumulation of this off-pathway intermediate, trehalose does not change the compactness of the transition state ensemble. Furthermore, the productive folding pathway of S6 is not affected by trehalose as shown by a Phi-value analysis. The unfolded state ensemble of S6 should be more compact in the presence of trehalose and therefore destabilized due to decreased conformational entropy. Increased compaction of the unfolded state ensemble might also occur for more stable mutants of S6, thus explaining the synergistic effect of trehalose and point mutations on protein stabilization.     

Structurally homologous all beta-barrel proteins adopt different mechanisms of folding

Acidic fibroblast growth factors from human (hFGF-1) and newt (nFGF-1) (Notopthalamus viridescens) are 16-kDa, all beta-sheet proteins with nearly identical three-dimensional structures. Guanidine hydrochloride (GdnHCl)-induced unfolding of hFGF-1 and nFGF-1 monitored by fluorescence and far-UV circular dichroism (CD) shows that the FGF-1 isoforms differ significantly in their thermodynamic stabilities. GdnHCl-induced unfolding of nFGF-1 follows a two-state (Native state to Denatured state(s)) mechanism without detectable intermediate(s). By contrast, unfolding of hFGF-1 monitored by fluorescence, far-UV circular dichroism, size-exclusion chromatography, and NMR spectroscopy shows that the unfolding process is noncooperative and proceeds with the accumulation of stable intermediate(s) at 0.96 M GdnHCl. The intermediate (in hFGF-1) populated maximally at 0.96 M GdnHCl has molten globule-like properties and shows strong binding affinity to the hydrophobic dye, 1-Anilino-8-naphthalene sulfonate (ANS). Refolding kinetics of hFGF-1 and nFGF-1 monitored by stopped-flow fluorescence reveal that hFGF-1 and nFGF-1 adopts different folding mechanisms. The observed differences in the folding/unfolding mechanisms of nFGF-1 and hFGF-1 are proposed to be either due to differential stabilizing effects of the charged denaturant (Gdn(+) Cl(-)) on the intermediate state(s) and/or due to differences in the structural interactions stabilizing the native conformation(s) of the FGF-1 isoforms.     

Equilibrium unfolding of mutant apomyoglobins with substitutions of conserved nonfunctional residues by alanine

The problems of protein aggregation and protein misfolding in the cell are connected with the appearance of many genetic diseases. Both processes can be a consequence of substitutions of certain amino acid residues in proteins. The substitutions can influence the protein stability and protein folding rates in both the intermediate and the native states. We have studied equilibrium urea unfolding of mutant forms of apomyoglobin with substitutions of conserved nonfunctional residues by Ala to estimate their influence on protein stability. These residues include Val10, Trp14, Ilel11, Leu115, Met131 and Leu135. Conformational transitions were monitored by intrinsic Trp fluorescence and by circular dichroism spectra in the far UV region. Free energy changes upon the transition from the native to intermediate state and from the intermediate to unfolded state were determined. It was shown that all substitutions used lead to an appreciable decrease of the apomyoglobin native state stability, whereas the stability of the intermediate state is affected substantially smaller.     

Nanosecond dynamics of the single tryptophan reveals multi-state equilibrium unfolding of protein GB1

Unfolding of the immunoglobulin binding domain B1 of streptococcal protein G (GB1) was induced by guanidine hydrochloride (GdnHCl) and studied by circular dichroism, steady-state, and time-resolved fluorescence spectroscopy. The fluorescence methods employed the single tryptophan residue of GB1 as an intrinsic reporter. While the transitions monitored by circular dichroism and steady-state fluorescence coincided with each other, the transitions followed by dynamic fluorescence were markedly different. Specifically, fluorescence anisotropy data showed that a relaxation spectrum of tryptophan contained a slow motion with relaxation times of 9 ns in the native state and 4 ns in the unfolded state in 6 M GdnHCl. At intermediate GdnHCl concentrations of 3.8-4.2 M, however, the slow relaxation time increased to 18 ns. The fast nanosecond motion had an average time of 0.8 ns and showed no dependence on the formation of native structure. Overall, dynamic fluorescence revealed two preliminary stages in GB1 folding, which are equated with the formation of local structure in the beta(3)-strand hairpin and the initial collapse. Both stages exist without alpha-helix formation, i. e., before the appearance of any ordered secondary structure detectable by circular dichroism. Another stage in GB1 folding might exist at very low ( approximately 1 M) GdnHCl concentrations.     

Equilibrium unfolding of mutant apomyoglobins carrying substitutions of conserved nonfunctional residues with alanine

Protein aggregation or misfolding in the cell is connected with many genetic diseases and can result from substitutions in proteins. Substitutions can influence the protein stability and folding rates in both intermediate and native states. The equilibrium urea-induced unfolding was studied for mutant apomyoglobins carrying substitutions of the conserved nonfunctional residues Val10, Trp14, Ile111, Leu115, Met131, and Leu135 with Ala. Conformational transitions were monitored by intrinsic Trp fluorescence and far-UV circular dichroism. Free energy changes upon transition from the native to the intermediate state and from the intermediate to the unfolded state were determined. All substitutions considerably decreased the stability of native apomyoglobin, whereas the effect on the stability of the intermediate state was essentially smaller.     

Structural characterization of partially folded intermediates of apomyoglobin H64F

We present a detailed investigation of unfolded and partially folded states of a mutant apomyoglobin (apoMb) where the distal histidine has been replaced by phenylalanine (H64F). Previous studies have shown that substitution of His64, located in the E helix of the native protein, stabilizes the equilibrium molten globule and native states and leads to an increase in folding rate and a change in the folding pathway. Analysis of changes in chemical shift and in backbone flexibility, detected via [1H]-15N heteronuclear nuclear Overhauser effect measurements, indicates that the phenylalanine substitution has only minor effects on the conformational ensemble in the acid- and urea-unfolded states, but has a substantial effect on the structure, dynamics, and stability of the equilibrium molten globule intermediate formed near pH 4. In H64F apomyoglobin, additional regions of the polypeptide chain are recruited into the compact core of the molten globule. Since the phenylalanine substitution has negligible effect on the unfolded ensemble, its influence on folding rate and stability comes entirely from interactions within the compact folded or partly folded states. Replacement of His64 with Phe leads to favorable hydrophobic packing between the helix E region and the molten globule core and leads to stabilization of helix E secondary structure and overall thermodynamic stabilization of the molten globule. The secondary structure of the equilibrium molten globule parallels that of the burst phase kinetic intermediate; both intermediates contain significant helical structure in regions of the polypeptide that comprise the A, B, E, G, and H helices of the fully folded protein.     

A folding model of α-lactalbumin deduced from the three-state denaturation mechanism

It has been shown that α-lactalbumin undergoes a three-state denaturation, involving a helical intermediate state, on treatment with guanidine hydrochloride. The unfolding of the protein and the characteristics of the intermediate state are examined by means of circular dichroism, difference spectra and pH-jump measurements to investigate the temperature dependence and kinetic properties of the unfolding and refolding, the pH dependence of the transition between the intermediate and the fully unfolded states, and the effect of disulphide bond reduction on the stabilization of the intermediate.The results show that the long-range specific interactions such as specific electrostatic interactions and disulphide linkages are not important for stabilizing the intermediate, and that the transition between the intermediate and the fully unfolded states is extremely rapid (a relaxation time of less than one millisecond) and may correspond to the helix-coil transition of a polypeptide backbone. On the other hand, the activation parameters of the transition between the native and the intermediate states have suggested that the final stabilization by charge-pair interactions is preceded by hydrophobic interactions in the process of going from the intermediate to the native state.The mechanism of folding of the protein is discussed, and the folding process from the fully unfolded to the native state is apparently divided into at least three main steps: (1) the formation of incipient helical structures dictated by local interactions; (2) the packing of the helical segments accompanied with hydrophobic interactions; (3) the final stabilization by the electrostatic interactions. The relevance to the current theoretical results on protein folding is also discussed.     

Comparison of the folding processes of T. thermophilus and E. coli ribonucleases H

In order to examine how the stabilization of thermophilic proteins affects their folding, we have characterized the folding process of Thermus thermophilus ribonuclease H using circular dichroism, fluorescence, and pulse-labeling hydrogen exchange. Like its homolog from Escherichia coli, this thermophilic protein populates a partially folded kinetic intermediate within the first few milliseconds of folding. The structure of this intermediate is similar to that of E.coli RNase H and corresponds remarkably well to a partially folded form that is populated at low levels in the native state of the protein. Proline isomerization appears to partly limit the folding of the thermophilic but not the mesophilic protein. Lastly, unlike other thermophilic proteins, which unfold much more slowly than their mesophilic counterparts, T.thermophilus RNase H folds and unfolds with overall rates similar to those of E.coli RNase H.     

Differential salt-induced stabilization of structure in the initial folding intermediate ensemble of barstar

The effects of two salts, KCl and MgCl(2), on the stability and folding kinetics of barstar have been studied at pH 8. Equilibrium urea unfolding curves were used to show that the free energy of unfolding, deltaG(UN), of barstar increased from a value of 4.7 kcalmol(-1) in the absence of salt to a value of 6.9 kcalmol(-1) in the presence of 1M KCl or 1M MgCl(2). For both salts, deltaG(UN) increases linearly with an increase in concentration of salt from 0M to 1M, suggesting that stabilization of the native state occurs primarily through a Hofmeister effect. Refolding kinetics were studied in detail in the presence of 1M KCl as well as in the presence of 1M MgCl(2), and it is shown that the basic folding mechanism is not altered upon addition of salt. The major effects on the refolding kinetics can be attributed to the stabilization of the initial burst phase ensemble, I(E), by salt. Stabilization of structure in I(E) by KCl causes the fluorescence properties of I(E) to change, so that there is an initial burst phase change in fluorescence at 320 nm, during refolding. The structure in I(E) is stabilized by MgCl(2), but no burst phase change in fluorescence at 320 nm is observed during refolding. The fluorescence emission spectra of I(E) show that when refolding is initiated in 1M KCl, the three tryptophan residues in I(E) are less solvent exposed than when folding is initiated in 1M MgCl(2). Stabilization of I(E) leads to an acceleration in the rate of the fast observable phase of folding by both salts, suggesting that structure of the transition state resembles that of I(E). The stabilization of I(E) by salts can be accounted for largely by the same mechanism that accounts for the stabilization of the native state of the protein, namely through the Hofmeister effect. The salts do not affect the rates of the slower phases of folding, indicating that the late intermediate ensemble, I(L), is not stabilized by salts. Stabilization of the native state results in deceleration of the fast unfolding rate, which has virtually no dependence on the concentration of KCl or MgCl(2) at high concentrations. The observation that the salt-induced stabilization of structure in I(E) is accompanied by an acceleration in the fast folding rate, suggests that I(E) is likely to be a productive on-pathway intermediate.     

SecA folds via a dimeric intermediate

Though many proteins in the cell are large and multimeric, their folding has not been extensively studied. We have chosen SecA as a folding model because it is a large, homodimeric protein (monomer molecular mass of 102 kDa) with multiple folding domains. SecA is the ATPase for the Sec-dependent preprotein translocase of many bacteria. SecA is a soluble protein that can penetrate into the membrane during preprotein translocation. Because SecA may partially unfold prior to its insertion into the membrane, studies of its stability and folding pathway are important for understanding how it functions in vivo. Kinetic folding transitions in the presence of urea were monitored using circular dichroism and tryptophan fluorescence, while equilibrium folding transitions were monitored using the same techniques as well as a fluorescent ATP analogue. The reversible equilibrium folding transition exhibited a plateau, indicating the presence of an intermediate. Based on the data presented here, we propose a three-state model, N(2) if I(2) if 2U, where the native protein unfolds to a dimeric intermediate which then dissociates into two unfolded monomers. The SecA dimer was determined to have an overall stability (DeltaG) of -22.5 kcal/mol. We also investigated the stability of SecA using analytical ultracentrifugation equilibrium and velocity sedimentation, which again indicated that native or refolded SecA was a stable dimer. The rate-limiting step in the folding pathway was conversion of the dimeric intermediate to the native dimer. Unfolding of native, dimeric SecA was slow with a relaxation time in H(2)O of 3.3 x 10(4) s. Since SecA is a stable dimer, dissociation to monomeric subunits during translocation is unlikely.     

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.     

An alpha-helical burst in the src SH3 folding pathway

Src SH3 is a small all-beta-sheet protein composed of a single domain. We studied the folding behavior of src SH3 at various conditions by circular dichroism (CD), fluorescence, and X-ray solution scattering methods. On the src SH3 folding pathway, an alpha-helix-rich intermediate appeared not only at subzero temperatures but also above 0 degrees C. The fraction of alpha-helix in the kinetically observed intermediate is ca. 26% based on the kinetic CD experiment. X-ray solution scattering revealed that the intermediate was compact but not fully packed. The analysis of CD implies that the amplitude of the burst phase is proportional to the helical fraction calculated according to the helix-coil transition theory. This strongly suggests that the initial folding core is formed by the collapse of much less stably existing alpha-helices.     

Glycine to alanine substitutions in helices of glyceraldehyde-3-phosphate dehydrogenase: effects on stability

Glyceraldehyde-3-phosphate dehydrogenase (GAPDH) from chicken was expressed in and purified from Escherichia coli. To investigate the physical basis of possible protein stabilization strategies, the effect of substitutions of glycine residues by alanine in helical regions was determined. One Gly to Ala substitution (G316A) located in the central core of the subunit was found to strongly stabilize the protein, while the other mutations are neutral or destabilize the protein. The effect seen for the stabilizing mutant in irreversible heat denaturation correlates with the first transition in folding equilibrium experiments that is observable by fluorescence, but not with the one detected by circular dichroism measurements or in dilution-induced dissociation experiments. The stabilizing effect of a Gly to Ala substitution therefore does not seem to be caused by an entropic effect on the unfolded state. Rather, an internal cavity is filled by the substitution G316A, probably stabilizing the native state. In large oligomeric proteins, imperfect packing may be a frequent cause of limited stability.     

Equilibrium and kinetic studies on folding of the authentic and recombinant forms of human alpha-lactalbumin by circular dichroism spectroscopy

The equilibrium and kinetics of the unfolding and refolding of authentic and recombinant human alpha-lactalbumin, the latter of which had an extra methionine residue at the N-terminus, were studied by circular dichroism spectroscopy, and the results were compared with the results for bovine and goat alpha-lactalbumins obtained in our previous studies. As observed in the bovine and goat proteins, the presence of the extra methionine residue in the recombinant protein remarkably destabilized the native state, and the destabilization was entirely ascribed to an increase in the rate of unfolding. The thermodynamic stability of the native state against the unfolded state was lower, and the thermodynamic stability of the molten globule state against the unfolded state was higher for the human protein than for the other alpha-lactalbumins previously studied. Thus, the population of the molten globule intermediate was higher during the equilibrium unfolding of human alpha-lactalbumin by guanidine hydrochloride. Unlike the molten globule states of the bovine and goat proteins, the human alpha-lactalbumin molten globule showed remarkably more intense circular dichroism ellipticity than the native state in the far-ultraviolet region below 225 nm. During refolding from the unfolded state, human alpha-lactalbumin thus exhibited overshoot kinetics, in which the alpha-helical peptide ellipticity exceeded the native value when the molten globule folding intermediate was formed in the burst phase. The subsequent folding involved reorganization of nonnative secondary structures. It should be noted that the rate constant of the major refolding phase was approximately the same among the three types of alpha-lactalbumin and that the rate constant of unfolding was accelerated 18-600 times in the human protein, and these results interpreted the lower thermodynamic stability of this protein.     

Revealing a Concealed Intermediate that Forms after the Rate-limiting Step of Refolding of the SH3 Domain of PI3 Kinase

Kinetic and equilibrium studies of the folding and unfolding of the SH3 domain of the PI3 kinase, have been used to identify a folding intermediate that forms after the rate-limiting step on the folding pathway. Folding and unfolding, in urea as well as in guanidine hydrochloride (GdnHCl), were studied by monitoring changes in the intrinsic fluorescence or in the far-UV circular dichroism (CD) of the protein. The two probes yield non-coincident equilibrium transitions for unfolding in urea, indicating that an intermediate, I, exists in equilibrium with native (N) and unfolded (U) protein, during unfolding. Hence, the equilibrium unfolding data were analyzed according to a three-state N ↔ I ↔ U mechanism. An intermediate is observed also in kinetic unfolding studies, and its presence leads to the unfolding reaction in urea as well as in GdnHCl, occurring in two steps. The fast step is complete within the initial 11 ms of unfolding and manifests itself in a burst phase change in fluorescence. At high concentrations of GdnHCl, the entire change in fluorescence during unfolding occurs during the 11 ms burst phase. CD measurements indicate, however, that I retains N-like secondary structure. An analysis of the kinetic and thermodynamic data, according to a minimal three-state N ↔ I ↔ U mechanism, positions I after the rate-limiting transition state, TS1, of folding, on the reaction coordinate of folding in GdnHCl. Hence, I is not revealed when folding is commenced from U, regardless of the nature of the probe used to follow the folding reaction. Interrupted unfolding experiments, in which the protein is unfolded transiently in GdnHCl for various lengths of time before being refolded, showed that I refolds to N much faster than does U, confirms the analysis of the direct folding and unfolding experiments, that I is formed after the rate-limiting step of refolding in GdnHCl.     

Osmolyte‐induced conformational changes in the Hsp90 molecular chaperone

Osmolytes are small molecules that play a central role in cellular homeostasis and the stress response by maintaining protein thermodynamic stability at controlled levels. The underlying physical chemistry that describes how different osmolytes impact folding free energy is well understood, however little is known about their influence on other crucial aspects of protein behavior, such as native‐state conformational changes. Here we investigate this issue with the Hsp90 molecular chaperone, a large dimeric protein that populates a complex conformational equilibrium. Using small angle X‐ray scattering we observe dramatic osmolyte‐dependent structural changes within the native ensemble. The degree to which different osmolytes affect the Hsp90 conformation strongly correlates with thermodynamic metrics of their influence on stability. This observation suggests that the well‐established osmolyte principles that govern stability also apply to large‐scale conformational changes, a proposition that is corroborated by structure‐based fitting of the scattering data, surface area comparisons and m‐value analysis. This approach shows how osmolytes affect a highly cooperative open/closed structural transition between two conformations that differ by a domain‐domain interaction. Hsp90 adopts an additional ligand‐specific conformation in the presence of ATP and we find that osmolytes do not significantly affect this conformational change. Together, these results extend the scope of osmolytes by suggesting that they can maintain protein conformational heterogeneity at controlled levels using similar underlying principles that allow them to maintain protein stability; however the relative impact of osmolytes on different structural states can vary significantly.     

Topology and sequence in the folding of a TIM barrel protein: global analysis highlights partitioning between transient off-pathway and stable on-pathway folding intermediates in the complex folding mechanism of a (betaalpha)8 barrel of unknown function from B. subtilis

The relative contributions of chain topology and amino acid sequence in directing the folding of a (betaalpha)(8) TIM barrel protein of unknown function encoded by the Bacillus subtilis iolI gene (IOLI) were assessed by reversible urea denaturation and a combination of circular dichroism, fluorescence and time-resolved fluorescence anisotropy spectroscopy. The equilibrium reaction for IOLI involves, in addition to the native and unfolded species, a stable intermediate with significant secondary structure and stability and self-associated forms of both the native and intermediate states. Global kinetic analysis revealed that the unfolded state partitions between an off-pathway refolding intermediate and the on-pathway equilibrium intermediate early in folding. Comparisons with the folding mechanisms of two other TIM barrel proteins, indole-3-glycerol phosphate synthase from the thermophile Sulfolobus solfataricus (sIGPS) and the alpha subunit of Escherichia coli tryptophan synthase (alphaTS), reveal striking similarities that argue for a dominant role of the topology in both early and late events in folding. Sequence-specific effects are apparent in the magnitudes of the relaxation times and relative stabilities, in the presence of additional monomeric folding intermediates for alphaTS and sIGPS and in rate-limiting proline isomerization reactions for alphaTS.