Unfolded Ensemble Research Articles

Unfolded state of polyalanine is a segmented polyproline II helix.

Definition of the unfolded state of proteins is essential for understanding their stability and folding on biological timescales. Here, we find that under near physiological conditions the configurational ensemble of the unfolded state of the simplest protein structure, polyalanine alpha-helix, cannot be described by the commonly used Flory random coil model, in which configurational probabilities are derived from conformational preferences of individual residues. We utilize novel effectively ergodic sampling algorithms in the presence of explicit aqueous solvation, and observe water-mediated formation of polyproline II helical (P(II)) structure in the natively unfolded state of polyalanine, and its facilitation of alpha-helix formation in longer peptides. The segmented P(II) helical coil preorganizes the unfolded state ensemble for folding pathway entry by reducing the conformational space available to the diffusive search. Thus, as much as half of the folding search in polyalanine is accomplished by preorganization of the unfolded state.

The side chain of aspartic acid 69 dictates the folding mechanism of Bacillus subtilis HPr.

Many small, single-domain proteins show equilibrium and kinetic folding mechanisms that appear to be adequately described as two state. The two-state model makes several predictions that can be tested experimentally. First, the conformational stability determined at or extrapolated to a set of reference conditions should be independent of the measurement method (thermal or solvent denaturation or hydrogen exchange). Second, model-independent measures of the cardinal thermodynamic parameters (T(m), DeltaH) as determined from direct calorimetric means should be identical to those determined from the two-state analysis of thermal unfolding data. Third, the ratio of the kinetic folding and unfolding rate constants should be equal to K(eq) determined from an equilibrium measurement under the same conditions. Here, we show that the wild-type HPr protein from Bacillus subtilis does not meet all of these criteria under our standard conditions. However, if we replace the side chain of Asp69, or add moderate concentrations of salt, we find excellent two-state behavior in both equilibrium and kinetic folding. Thus, for this protein and possibly others, very subtle changes in the primary structure or in the solution conditions can dramatically alter the relative stabilities of the native intermediate, and unfolded ensembles can cause an observable change in the nature of the folding mechanism.

Cooperativity Principles in Protein Folding

Knowledge of the physical driving forces in proteins is essential for understanding their structures and functions. As polymers, proteins have remarkable thermodynamic and kinetic properties. A well-known observation is that the folding and unfolding of many small single-domain proteins, of which chymotrypsin inhibitor 2 is a prime example, appear to involve only two main states—N (native) and D (denatured). These proteins’ folding/unfolding transitions are often referred to as ‘‘cooperative’’ because of their phenomenological similarity to ‘‘all-or-none’’ processes. Traditionally, only N, D, and a small number of postulated intermediate states were invoked to account for experimental protein folding data. Under such an interpretative framework, two-state folding is described by the reaction N Ð D, and different properties are ascribed to N and D to account for different proteins. Although useful, this approach does not address the microscopic origins of experimentally observed two-state–like behavior. Traditional analyses simply assume that there are a small number of conformational states. But proteins are chain molecules. Physically, it is obvious that a polymer chain can adopt many conformations, ranging from the most open to maximally compact, and all intermediate compactness in between. Thus, whether and how the multitude of conformations available to a protein may be grouped into two or more ‘‘states’’—as traditionally assumed— should be ascertained through a fundamental understanding of the effective intrachain interactions involved. In the protein literature, however, folding energetics are often discussed in terms of the sum of contactlike energies of a fully folded native structure versus that of a random-coil–like state or a certain other prespecified unfolded conformational ensemble. Such analyses have yielded important insight. But they obscure the remarkable nature of protein cooperativities. This is because cooperativity has already been presumed in these discourses by their preclusion of many a priori possible conformations—notably compact nonnative conformations—from the energetic equation. To gain a consistent understanding

Characterization of non-alpha helical conformations in Ala peptides

The folded (alpha helical) and unfolded (non-alpha helical) ensembles of the 21 amino acid peptide Ace-A21-Nme are characterized structurally. The replica exchange molecular dynamics approach is used to generate these ensembles at 46 different temperatures ranging from 278 to 487 K. Each replica system is simulated in explicit solvent for a period of 10 ns/replica, for a total of 460 ns. In addition to alpha helices, poly proline II (PPII) structures were identified to occur significantly. At low T the alpha helical content is larger than the PPII content, but near 300 K the PPII population is larger. Below 300 K, the PPII population increases with T, but it decreases above 300 K. The alpha helical content decreases with temperature. At temperatures below 300 K, there is a PPII propagation free energy that enhances the formation of long segments of PPII structure. This propagation term is smaller than for alpha helices. PPII segments of length 8 or less are more likely to form than alpha helices of the same length. The obtained low propensity for the formation of PPII segments of length shorter than five suggest that the interactions are responsible for the formation of PPII structures require a PPII segment of at least four amino acids. Stretches of four consecutive amino acids in the PPII conformations are needed for the formation of a groove around the peptide backbone that is strongly hydrated. Water in this groove is delocalized along a channel formed by the peptide in the PPII conformation.

Effect of gatekeepers on the early folding kinetics of a model β-barrel protein

Recent exciting experimental observations have suggested the existence of gatekeeper residues in protein folding. These residues may influence only slightly the stabilization of a protein’s final folded state, but have an important kinetic function in the early stages of folding—to avoid nonproductive folding routes. We explore the physical mechanism for the action of such gatekeepers, in the form of salt-bridgelike charged residues, on the early folding behavior of a model 46-mer β-barrel protein. Computer simulations employing Langevin dynamics show that the gatekeepers enhance the kinetics of folding on time scales that are about three orders of magnitude shorter than previously reported folding times for this model system. Analysis of the unfolded ensembles of the wild type (WT) β-barrel and several good and poor salt bridge designs indicates that the proteins with well designed salt-bridge gatekeepers favor productive folding routes when compared to the WT system. The conclusions of our theoretical observations are in agreement with experimental studies of the ribosomal protein S6 and its mutants.

Fast protein folding on downhill energy landscape.

Proteins fold in a time range of microseconds to minutes despite the large amount of possible conformers. Molecular dynamics simulations of a three-stranded antiparallel beta-sheet peptide (for a total of 12.6 microsec and 72 folding events) show that at the melting temperature the unfolded state ensemble contains many more conformers than those sampled during a folding event.

Equilibrium and kinetic folding of an alpha-helical Greek key protein domain: caspase recruitment domain (CARD) of RICK.

We have characterized the equilibrium and kinetic folding of a unique protein domain, caspase recruitment domain (CARD), of the RIP-like interacting CLARP kinase (RICK) (RICK-CARD), which adopts a alpha-helical Greek key fold. At equilibrium, the folding of RICK-CARD is well described by a two-state mechanism representing the native and unfolded ensembles. The protein is marginally stable, with a DeltaG(H)()2(O) of 3.0 +/- 0.15 kcal/mol and an m-value of 1.27 +/- 0.06 kcal mol(-1) M(-1) (30 mM Tris-HCl, pH 8, 1 mM DTT, 25 degrees C). While the m-value is constant, the protein stability decreases in the presence of moderate salt concentrations (below 200 mM) and then increases at higher salt concentrations. The results suggest that electrostatic interactions are stabilizing in the native protein, and the favorable Coulombic interactions are reduced at low ionic strength. Above 200 mM salt, the results are consistent with Hofmeister effects. The unfolding pathway of RICK-CARD is complex and contains at least three non-native conformations. The refolding pathway of RICK-CARD also is complex, and the data suggest that the unfolded protein folds via two intermediate conformations prior to reaching the native state. Overall, the data suggest the presence of kinetically trapped, or misfolded, species that are on-pathway both in refolding and in unfolding.

Interleukin-1 beta folding between pH 5 and 7: experimental evidence for three-state folding behavior and robust transition state positions late in folding.

The thermodynamic stability and folding kinetics of the all beta-sheet protein interleukin-1beta were measured between 0 and 4 M GdmCl concentrations and pH 5-7. Native interleukin-1beta undergoes a 3.5 kcal/mol decrease in thermodynamic stability, Delta, as pH is increased from 5 to 7. The native state parameter m(NU), measuring protein destabilization/[GdmCl], remains constant between pH 5 and 7, indicating that the solvent-exposed surface area difference between the native state and unfolded ensemble is unchanged across this pH range. Similarly, pH changes between 5 and 7 decrease only the thermodynamic stability, DeltaG(H)2(O), and not the m-values, of the kinetic intermediate and transition states. This finding is shown to be consistent with transition state configurations which continue to be the high-energy configurations of the transition state in the face of changing stability conditions. A three-state folding mechanism U right arrow over left arrow I right arrow over left arrow N is shown to be sufficient in characterizing IL-1beta folding under all conditions studied. The m-values of refolding transitions are much larger than the m-values of unfolding transitions, indicating that that the fast, T(2) (U right arrow over left arrow I), and slow, T(1) (I right arrow over left arrow N), transition states are highly similar to the intermediate I and native state N, respectively. Many of the folding properties of interleukin-1beta are shared among other members of the beta-trefoil protein family, although clear differences can exist.

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations.

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.

Glutamine 53 is a gatekeeper residue in the FK506 binding protein.

The effect of non-random conformational averaging in the urea-unfolded state on the folding pathway has been investigated in a variant of the FK506 binding protein with three additional residues at the amino terminus (FKBP(*)). Three mutations (asparagine, aspartate, and threonine) were introduced into position Q53 to enhance formation of non-native helix observed in this part of the protein in the urea-unfolded state. NMR analysis showed minor structural changes in the native state of each mutant, but additional medium-range alphaN(i,i+2) of each mutant nuclear Overhauser enhancements were observed in the urea-unfolded state that were not in FKBP(*), indicating that the mutations had a more substantial effect on the unfolded state ensemble than on the native state ensemble. Isothermal equilibrium denaturation measurements showed that the Q53T and Q53D mutants were destabilized, whereas the Q53N mutant was stabilized relative to FKBP(*) with little change in the equilibrium m values. The unfolding rates of Q53N and Q53T were similar to that of FKBP(*), but Q53D unfolded twice as fast as FKBP(*). In contrast, the mutations had a more pronounced effect on the refolding kinetics. Q53N refolded slightly faster and exhibited a kinetic folding intermediate similar to that of FKBP(*). The Q53D and Q53T mutants also refolded faster than FKBP(*) but lacked the folding intermediate, indicating that these mutants experienced a different folding trajectory and transition state than FKBP(*) and Q53N. The refolding kinetic Phi values were 0.74, 1.4 and 7.9 for Q53N, Q53T, and Q53D, respectively. The data point to Q53 functioning as a gatekeeper residue in the folding of FKBP(*). This study shows that perturbing the unfolded state ensemble via mutagenesis can provide insights into residues that play important roles in the folding pathway, and represents an attractive strategy for mapping the high-energy portions of the folding energy landscape.

Native-like mean structure in the unfolded ensemble of small proteins.

The nature of the unfolded state plays a great role in our understanding of proteins. However, accurately studying the unfolded state with computer simulation is difficult, due to its complexity and the great deal of sampling required. Using a supercluster of over 10,000 processors we have performed close to 800 micros of molecular dynamics simulation in atomistic detail of the folded and unfolded states of three polypeptides from a range of structural classes: the all-alpha villin headpiece molecule, the beta hairpin tryptophan zipper, and a designed alpha-beta zinc finger mimic. A comparison between the folded and the unfolded ensembles reveals that, even though virtually none of the individual members of the unfolded ensemble exhibits native-like features, the mean unfolded structure (averaged over the entire unfolded ensemble) has a native-like geometry. This suggests several novel implications for protein folding and structure prediction as well as new interpretations for experiments which find structure in ensemble-averaged measurements.

Protein Unfolding Transitions in an Intrinsically Unstable Annexin Domain: Molecular Dynamics Simulation and Comparison with Nuclear Magnetic Resonance Data

Unfolding transitions of an intrinsically unstable annexin domain and the unfolded state structure have been examined using multiple ∼10-ns molecular dynamics simulations. Three main basins are observed in the configurational space: native-like state, compact partially unfolded or intermediate compact state, and the unfolded state. In the native-like state fluctuations are observed that are nonproductive for unfolding. During these fluctuations, after an initial loss of ∼20% of the core residue native contacts, the core of the protein transiently completely refolds to the native state. The transition from the native-like basin to the partially unfolded compact state involves ∼75% loss of native contacts but little change in the radius of gyration or core hydration properties. The intermediate state adopts for part of the time in one of the trajectories a novel highly compact salt-bridge stabilized structure that can be identified as a conformational trap. The intermediate-to-unfolded state transition is characterized by a large increase in the radius of gyration. After an initial relaxation the unfolded state recovers a native-like topology of the domain. The simulated unfolded state ensemble reproduces in detail experimental nuclear magnetic resonance data and leads to a convincing complete picture of the unfolded domain.

Distribution of molecular size within an unfolded state ensemble using small-angle X-ray scattering and pulse field gradient NMR techniques

The size distribution of molecules within an unfolded state of the N-terminal SH3 domain of drk (drkN SH3) has been studied by small-angle X-ray scattering (SAXS) and pulsed-field-gradient NMR (PFG-NMR) methods. An empirical model to describe this distribution in the unfolded state ensemble has been proposed based on (i) the ensemble-averaged radius of gyration and hydrodynamic radius derived from the SAXS and PFG-NMR data, respectively, and (ii) a histogram of the size distribution of structures obtained from preliminary analyses of structural parameters recorded on the unfolded state. Results show that this unfolded state, U exch, which exists in equilibrium with the folded state, F exch, under non-denaturing conditions, is relatively compact, with the average size of conformers within the unfolded state ensemble only 30–40 % larger than the folded state structure. In addition, the model predicts a significant overlap in the size range of structures comprising the U exch state with those in a denatured state obtained by addition of 2 M guanidinium chloride.

Determinants of the polyproline II helix from modeling studies

Despite the fact that Tiffany and Krimm (1968a,b) formulated their hypothesis more than thirty years ago, it is only now that we are beginning to truly appreciate the importance of the PPII helical conformation. Recent experimental work has demonstrated that the polypeptide backbone possesses a significant propensity to adopt the PPII helical conformation (Kelly et al., 2001; Rucker and Creamer, 2002; Shi et al., 2002). The major determinant of this backbone propensity would appear to be backbone solvation, as was originally hinted at by Krimm and Tiffany (1974) and later suggested by a number of groups (Adzhubei and Sternberg, 1993; Sreerama and Woody, 1999; Kelly et al., 2001; Rucker and Creamer, 2002; Shi et al., 2002). The calculations and modeling described above provide data in support of this hypothesis. Each residue has its own propensity to adopt the PPII conformation, with the backbone propensity being modulated by the side chain (Kelly et al., 2001). Short, bulky side chains occlude backbone from solvent and thus disfavor the PPII conformation, while the lack of a side chain or long, flexible side chains tend to favor the conformation (Kelly et al., 2001). Again, the described calculations support this. Steric interactions (Pappu et al., 2000) and side chain conformational entropy alos contribute to the observed propensities. Furthermore, as suggested from surveys of PPII helices in proteins of known structure (Stapley and Creamer, 1999), side chain-to-backbone hydrogen bonds may well play a role in stabilizing PPII helices. The survey data, plus supporting calculations, also suggest that some polar residues may play a PPII helic-capping role analogous to that observed in alpha-helices (Presta and Rose, 1988; Aurora and Rose, 1998). Taken in sum, an atomic-level picture of the stabilization of PPII helices is beginning to emerge. Once the determinants of PPII helix formation are known in more detail, it will become possible to apply them, along with the known determinants of the alpha-helical conformation, to the understanding of protein unfolded states. If, as suggested at the beginning of this article, protein unfolded states are dominated by residues in the PPII and alpha-conformations, these data will allow for modeling of the unfolded state ensembles of specific proteins with a level of realism that has not been previously anticipated.

GroEL channels the folding of thioredoxin along one kinetic route

Many proteins display complex folding kinetics, which represent multiple parallel folding pathways emanating from multiple unfolded forms and converging to the unique native form. The small protein thioredoxin from Escherichia coli is one such protein. The effect of the chaperonin GroEL on modulating the complex energy landscape that separates the unfolded ensemble from the native state of thioredoxin has been studied. It is shown that while the fluorescence change accompanying folding occurs in five kinetic phases in the absence of GroEL, only the two slowest kinetic phases are discernible in the presence of saturating concentrations of GroEL. This result is shown to be consistent with only one out of several available folding routes being operational in the presence of GroEL. It is shown that native protein, which forms via fast as well as slow routes in the absence of GroEL, forms only via a slow route in its presence. The effect of GroEL on the folding of thioredoxin is shown to be the consequence of it binding differentially to the many folding-competent forms. While some of these forms can continue folding when bound to GroEL, others cannot. All molecules are then drawn into the operational folding route by the law of mass action. This observation indicates a new role for GroEL, which is to bias the energy landscape of a folding polypeptide towards fewer available pathways. It is suggested that such channeling might be a mechanism to avoid possible aggregation-prone routes available to a refolding polypeptide in vivo.

Structure is lost incrementally during the unfolding of barstar.

Coincidental equilibrium unfolding transitions observed by multiple structural probes are taken to justify the modeling of protein unfolding as a two-state, N <==> U, cooperative process. However, for many of the large number of proteins that undergo apparently two-state equilibrium unfolding reactions, folding intermediates are detected in kinetic experiments. The small protein barstar is one such protein. Here the two-state model for equilibrium unfolding has been critically evaluated in barstar by estimating the intramolecular distance distribution by time-resolved fluorescence resonance energy transfer (TR-FRET) methods, in which fluorescence decay kinetics are analyzed by the maximum entropy method (MEM). Using a mutant form of barstar containing only Trp 53 as the fluorescence donor and a thionitrobenzoic acid moiety attached to Cys 82 as the fluorescence acceptor, the distance between the donor and acceptor has been shown to increase incrementally with increasing denaturant concentration. Although other probes, such as circular dichroism and fluorescence intensity, suggest that the labeled protein undergoes two-state equilibrium unfolding, the TR-FRET probe clearly indicates multistate equilibrium unfolding. Native protein expands progressively through a continuum of native-like forms that achieve the dimensions of a molten globule, whose heterogeneity increases with increasing denaturant concentration and which appears to be separated from the unfolded ensemble by a free energy barrier.

A change in the apparent m value reveals a populated intermediate under equilibrium conditions in Escherichia coli ribonuclease HI.

Experimental studies of protein stability often rely on the determination of an "m value", which describes the denaturant dependence of the free energy change between two states (DeltaG = DeltaG(H2O) - m[denaturant]). Changes in the m value accompanying site specific mutations are usually attributed to structural alterations in the native or unfolded ensemble. Here, we provide an example of significant reduction in the m value resulting from a subtle deviation in two-state behavior not detected by traditional methods. The protein that is studied is a variant of Escherchia coli RNase H in which three residues predicted to be involved in a partially buried salt bridge network were mutated to alanine (R46A, D102A, and D148A). Equilibrium denaturant profiles monitored by both fluorescence and circular dichroism appeared to be cooperative, and a two-state analysis yielded a DeltaG(UN) of approximately -3 kcal/mol with an m value of 1.4 kcal mol(-1) M(-1) (vs 2.3 for RNase H). Analysis of kinetic refolding experiments suggests that the system is actually three-state at equilibrium with an appreciable concentration of an intermediate state under low denaturant concentrations. The stability of the native state determined from a fit of these kinetic data is -6.7 kcal/mol, suggesting that the stability determined by traditional two-state equilibrium analysis is a gross underestimate. The only hint to this loss of two-state behavior was a decrease in the apparent m value, and the presence of the equilibrium intermediate was only identified by a kinetic analysis. Our work serves as a cautionary note; the possibility of a three-state system should be closely addressed before interpreting a change in the m value as a change in the native or unfolded state.

Hydrogen-exchange stabilities of RNase T1 and variants with buried and solvent-exposed Ala --> Gly mutations in the helix.

Hydrogen-exchange rates were measured for RNase T1 and three variants with Ala --> Gly substitutions at a solvent-exposed (residue 21) and a buried (residue 23) position in the helix: A21G, G23A, and A21G + G23A. These results were used to measure the stabilities of the proteins. The hydrogen-exchange stabilities (DeltaG(HX)) for the most stable residues in each variant agree with the equilibrium conformational stability measured by urea denaturation (DeltaG(U)), if the effects of D(2)O and proline isomerization are included [Huyghues-Despointes, B. M. P., Scholtz, J. M., and Pace, C. N. (1999) Nat. Struct. Biol. 6, 210-212]. These residues also show similar changes in DeltaG(HX) upon Ala --> Gly mutations (DeltaDeltaG(HX)) as compared to equilibrium measurements (DeltaDeltaG(U)), indicating that the most stable residues are exchanging from the globally unfolded ensemble. Alanine is stabilizing compared to glycine by 1 kcal/mol at a solvent-exposed site 21 as seen by other methods for the RNase T1 protein and peptide helix [Myers, J. K., Pace, C. N., and Scholtz, J. M. (1997) Proc. Natl. Acad. Sci. U.S.A. 94, 3833-2837], while it is destabilizing at the buried site 23 by the same amount. For the A21G variant, only local NMR chemical shift perturbations are observed compared to RNase T1. For the G23A variant, large chemical shift changes are seen throughout the sequence, although X-ray crystal structures of the variant and RNase T1 are nearly superimposable. Ala --> Gly mutations in the helix of RNase T1 at both helical positions alter the native-state hydrogen-exchange stabilities of residues throughout the sequence.

Structural transitions in the protein L denatured state ensemble.

We use a broad array of biophysical methods to probe the extent of structure and time scale of structural transitions in the protein L denatured state ensemble. Measurement of amide proton exchange protection during the first several milliseconds following initiation of refolding in 0.4 M sodium sulfate revealed weak protection in the first beta-hairpin and helix. A tryptophan residue was introduced into the first beta-hairpin to probe the extent of structure formation in this part of the protein; the intrinsic fluorescence of this tryptophan was found to deviate from that expected given its local sequence context in 2-3 M guanidine, suggesting some partial ordering of this region in the unfolded state ensemble. To further probe this partial ordering, dansyl groups were introduced via cysteine residues at three sites in the protein. It was found that fluorescence energy transfer from the introduced tryptophan to the dansyl groups decreased dramatically upon unfolding. Stopped-flow fluorescence studies showed that the recovery of dansyl fluorescence upon refolding occurred on a submillisecond time scale. To probe the interactions responsible for the residual structure observed in the denatured state ensemble, the conformation of a peptide corresponding to the first beta-hairpin and helix of protein L was studied using circular dichroism spectroscopy and compared to that of full-length protein L and previously characterized peptides corresponding to the isolated helix and second beta-hairpin.

Phase transitions in open quantum systems.

We consider the behavior of open quantum systems through the dependence of the coupling to one decay channel by introducing the coupling parameter alpha, which is proportional to the average degree of overlapping. Under critical conditions, a reorganization of the spectrum takes place that creates a bifurcation of the time scales with respect to the lifetimes of the resonance states. We derive analytically the conditions under which the reorganization process can be understood as a second-order phase transition and illustrate our results by numerical investigations. The conditions are fulfilled, e.g., for a uniform picket-fence level distribution with equal coupling of the states to the continuum. Energy dependencies within the system are included. We consider also the case of an unfolded Gaussian orthogonal ensemble and of a spectrum bounded from below. In all these cases, the reorganization of the spectrum occurs at the critical value alpha(crit) of the control parameter globally over the whole energy range of the spectrum. All states act cooperatively.