Molecular basis of cooperativity in protein folding IV. Core: A general cooperative folding model

The cooperative nature of the protein folding process is independent of the characteristic fold and the specific secondary structure attributes of a globular protein. A general folding/unfolding model should, therefore, be based upon structural features that transcend the peculiarities of α-helices, β-sheets, and other structural motifs found in proteins. The studies presented in this paper suggest that a single structural characteristic common to all globular proteins is essential for cooperative folding. The formation of a partly folded state from the native state results in the exposure to solvent of two distinct regions: (1) the portions of the protein that are unfolded; and (2) the “complementary surfaces,” located in the regions of the protein that remain folded. The cooperative character of the folding/unfolding transition is determined largely by the energetics of exposing complementary surface regions to the solvent. By definition, complementary regions are present only in partly folded states; they are absent from the native and unfolded states. An unfavorable free energy lowers the probability of partly folded states and increases the cooperativity of the transition. In this paper we present a mathematical formulation of this behavior and develop a general cooperative folding/unfolding model, termed the “complementary region” (CORE) model. This model successfully reproduces the main properties of folding/unfolding transitions without limiting the number of partly folded states accessible to the protein, thereby permitting a systematic examination of the structural and solvent conditions under which intermediates become populated. It is shown that the CORE model predicts two-state folding/unfolding behavior, even though the two-state character is not assumed in the model. © 1993 Wiley-Liss, Inc.     

Amino acid substitutions affecting protein dynamics in eglin C do not affect heat capacity change upon unfolding

The heat capacity change upon unfolding (deltaC(p)) is a thermodynamic parameter that defines the temperature dependence of the thermodynamic stability of proteins; however, physical basis of the heat capacity change is not completely understood. Although empirical surface area-based calculations can predict heat capacity changes reasonably well, accumulating evidence suggests that changes in hydration of those surfaces is not the only parameter contributing to the observed heat capacity changes upon unfolding. Because packing density in the protein interior is similar to that observed in organic crystals, we hypothesized that changes in protein dynamics resulting in increased rigidity of the protein structure might contribute to the observed heat capacity change upon unfolding. Using differential scanning calorimetry we characterized the thermodynamic behavior of a serine protease inhibitor eglin C and two eglin C variants with altered native state dynamics, as determined by NMR. We found no evidence of changes in deltaC(p) in either of the variants, suggesting that changes in rigidity do not contribute to the heat capacity change upon unfolding in this model system.     

Thermodynamic characterization of an equilibrium folding intermediate of staphylococcal nuclease.

High-sensitivity differential scanning calorimetry and CD spectroscopy have been used to probe the structural stability and measure the folding/unfolding thermodynamics of a Pro117-->Gly variant of staphylococcal nuclease. It is shown that at neutral pH the thermal denaturation of this protein is well accounted for by a 2-state mechanism and that the thermally denatured state is a fully hydrated unfolded polypeptide. At pH 3.5, thermal denaturation results in a compact denatured state in which most, if not all, of the helical structure is missing and the beta subdomain apparently remains largely intact. At pH 3.0, no thermal transition is observed and the molecule exists in the compact denatured state within the 0-100 degrees C temperature interval. At high salt concentration and pH 3.5, the thermal unfolding transition exhibits 2 cooperative peaks in the heat capacity function, the first one corresponding to the transition from the native to the intermediate state and the second one to the transition from the intermediate to the unfolded state. As is the case with other proteins, the enthalpy of the intermediate is higher than that of the unfolded state at low temperatures, indicating that, under those conditions, its stabilization must be of an entropic origin. The folding intermediate has been modeled by structural thermodynamic calculations. Structure-based thermodynamic calculations also predict that the most probable intermediate is one in which the beta subdomain is essentially intact and the rest of the molecule unfolded, in agreement with the experimental data. The structural features of the equilibrium intermediate are similar to those of a kinetic intermediate previously characterized by hydrogen exchange and NMR spectroscopy.     

Pressure-jump studies of the folding/unfolding of trp repressor.

The dimeric protein, trp apo-repressor of Escherichia coli has been subjected to high hydrostatic pressure under a variety of conditions, and the effects have been monitored by fluorescence spectroscopic and infra-red absorption techniques. Under conditions of micromolar protein concentration and low, non-denaturing concentrations of guanidinium hydrochloride (GuHCl), tryptophan and 8-anilino-1-naphthalene sulfonate (ANS) fluorescence detected high pressure profiles demonstrate that pressures below 3 kbar result in dissociation of the dimer to a monomeric species that presents no hydrophobic binding sites for ANS. The FTIR-detected high pressure profile obtained under significantly different solution conditions (30 mM trp repressor in absence of denaturant) exhibits a much smaller pressure dependence than the fluorescence detected profiles. The pressure-denatured form obtained under the FTIR conditions retains about 50 % alpha-helical structure. From this we conclude that the secondary structure present in the high pressure state achieved under the conditions of the fluorescence experiments is at least as disrupted as that achieved under FTIR conditions. Fluorescence-detected pressure-jump relaxation studies in the presence of non-denaturing concentrations of GuHCl reveal a positive activation volume for the association/folding reaction and a negative activation volume for dissociation/unfolding reaction, implicating dehydration as the rate-limiting step for association/folding and hydration as the rate-limiting step for unfolding. The GuHCl concentration dependence of the kinetic parameters place the transition state at least half-way along the reaction coordinate between the unfolded and folded states. The temperature dependence of the pressure-jump fluorescence-detected dissociation/unfolding reaction in the presence of non-denaturing GuHCl suggests that the curvature in the temperature dependence of the stability arises from non-Arrhenius behavior of the folding rate constant, consistent with a large decrease in heat capacity upon formation of the transition state from the unfolded state. The decrease in the equilibrium volume change for folding with increasing temperature (due to differences in thermal expansivity of the folded and unfolded states) arises from a decrease in the absolute value for the activation volume for unfolding, thus indicating that the thermal expansivity of the transition state is similar to that of the unfolded state.     

Energetic basis of structural stability in the molten globule state: alpha-lactalbumin

The denatured states of alpha-lactalbumin, which have features of a molten globule state, have been studied to elucidate the energetics of the molten globule state and its contribution to the stability of the native conformation. Analysis of calorimetric and CD data shows that the heat capacity increment of alpha-lactalbumin denaturation highly correlates with the degree of disorder of the residual structure of the state. As a result, the denaturational transition of alpha-lactalbumin from the native to a highly ordered compact denatured state, and from the native to the disordered unfolded state are described by different thermodynamic functions. The enthalpy and entropy of the denaturation of alpha-lactalbumin to compact denatured state are always greater than the enthalpy and entropy of its unfolding. This difference represents the unfolding of the molten globule state. Calorimetric measurements of the heat effect associated with the unfolding of the molten globule state reveal that it is negative in sign over the temperature range of molten globule stability. This observation demonstrates the energetic specificity of the molten globule state, which, in contrast to a protein with unique tertiary structure, is stabilized by the dominance of negative entropy and enthalpy of hydration over the positive conformational entropy and enthalpy of internal interactions. It is concluded that at physiological temperatures the entropy of dehydration is the dominant factor providing stability for the compact intermediate state on the folding pathway, while for the stability of the native state, the conformational enthalpy is the dominant factor.     

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This “unfolding‐up‐on‐squeezing” is counter‐intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results—that pressure denatured states are water‐swollen, and theoretical results—that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states—their water‐swollen nature, retention of secondary structure, and overall compactness—mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure‐dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately ?60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500–2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water‐swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Direct observation of microscopic reversibility in single-molecule protein folding

Both folded and unfolded conformations should be observed for a protein at its melting temperature (T(m)), where DeltaG between these states is zero. In an all-atom molecular dynamics simulation of chymotrypsin inhibitor 2 (CI2) at its experimental T(m), the protein rapidly loses its low-temperature native structure; it then unfolds before refolding to a stable, native-like conformation. The initial unfolding follows the unfolding pathway described previously for higher-temperature simulations: the hydrophobic core is disrupted, the beta-sheet pulls apart and the alpha-helix unravels. The unfolded state reached under these conditions maintains a kernel of structure in the form of a non-native hydrophobic cluster. Refolding simply reverses this path, the side-chain interactions shift, the helix refolds, and the native packing and hydrogen bonds are recovered. The end result of this refolding is not the initial crystal structure; it contains the proper topology and the majority of the native contacts, but the structure is expanded and the contacts are long. We believe this to be the native state at elevated temperature, and the change in volume and contact lengths is consistent with experimental studies of other native proteins at elevated temperature and the chemical denaturant equivalent of T(m).     

Non-native hydrophobic interactions detected in unfolded apoflavodoxin by paramagnetic relaxation enhancement

Transient structures in unfolded proteins are important in elucidating the molecular details of initiation of protein folding. Recently, native and non-native secondary structure have been discovered in unfolded A. vinelandii flavodoxin. These structured elements transiently interact and subsequently form the ordered core of an off-pathway folding intermediate, which is extensively formed during folding of this α–β parallel protein. Here, site-directed spin-labelling and paramagnetic relaxation enhancement are used to investigate long-range interactions in unfolded apoflavodoxin. For this purpose, glutamine-48, which resides in a non-native α-helix of unfolded apoflavodoxin, is replaced by cysteine. This replacement enables covalent attachment of nitroxide spin-labels MTSL and CMTSL. Substitution of Gln-48 by Cys-48 destabilises native apoflavodoxin and reduces flexibility of the ordered regions in unfolded apoflavodoxin in 3.4 M GuHCl, because of increased hydrophobic interactions in the unfolded protein. Here, we report that in the study of the conformational and dynamic properties of unfolded proteins interpretation of spin-label data can be complicated. The covalently attached spin-label to Cys-48 (or Cys-69 of wild-type apoflavodoxin) perturbs the unfolded protein, because hydrophobic interactions occur between the label and hydrophobic patches of unfolded apoflavodoxin. Concomitant hydrophobic free energy changes of the unfolded protein (and possibly of the off-pathway intermediate) reduce the stability of native spin-labelled protein against unfolding. In addition, attachment of MTSL or CMTSL to Cys-48 induces the presence of distinct states in unfolded apoflavodoxin. Despite these difficulties, the spin-label data obtained here show that non-native contacts exist between transiently ordered structured elements in unfolded apoflavodoxin.     

Folding/Unfolding Kinetics of Apomyoglobin

The equilibrium and kinetic folding/unfolding of apomyoglobin (ApoMb) were studied at pH 6.2, 11 °C by recording tryptophan fluorescence. The equilibrium unfolding of ApoMb in the presence of urea was shown to involve accumulation of an intermediate state, which had a higher fluorescence intensity as compared with the native and unfolded states. The folding proceeded through two kinetic phases, a rapid transition from the unfolded to the intermediate state and a slow transition from the intermediate to the native state. The accumulation of the kinetic intermediate state was observed in a wide range of urea concentrations. The intermediate was detected even in the region corresponding to the unfolding limb of the chevron plot. Urea concentration dependence was obtained for the observed folding/unfolding rate. The shape of the dependence was compared with that of two-state proteins characterized by a direct transition from the unfolded to the native state.     

Differential stability of beta-sheets and alpha-helices in beta-lactamase: a high temperature molecular dynamics study of unfolding intermediates.

beta-Lactamase, which catalyzes beta-lactam antibiotics, is prototypical of large alpha/beta proteins with a scaffolding formed by strong noncovalent interactions. Experimentally, the enzyme is well characterized, and intermediates that are slightly less compact and having nearly the same content of secondary structure have been identified in the folding pathway. In the present study, high temperature molecular dynamics simulations have been carried out on the native enzyme in solution. Analysis of these results in terms of root mean square fluctuations in cartesian and [phi, psi] space, backbone dihedral angles and secondary structural hydrogen bonds forms the basis for an investigation of the topology of partially unfolded states of beta-lactamase. A differential stability has been observed for alpha-helices and beta-sheets upon thermal denaturation to putative unfolding intermediates. These observations contribute to an understanding of the folding/unfolding processes of beta-lactamases in particular, and other alpha/beta proteins in general.     

Toward resolution of ambiguity for the unfolded state

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is proposed to quantify the molar degree of folding and the unfolded state. The model takes a global view of protein structure and can be applied to a number of analytic methods and to simulations. Three examples are given of application to small-angle scattering from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between extent of folding and chain size during folding for charge-driven folding in RNA.     

Mutational analysis of the BPTI folding pathway: II. Effects of aromatic-->leucine substitutions on folding kinetics and thermodynamics.

The rates of the individual steps in the disulfide-coupled folding and unfolding of eight BPTI variants, each containing a single aromatic to leucine amino acid replacement, were measured. From this analysis, the contributions of the four phenylalanine and four tyrosine residues to the stabilities of the native protein and the disulfide-bonded folding intermediates were determined. While the substitutions were found to destabilize the native protein by 2 to 7 kcal/mol, they had significantly smaller effects on the intermediates that represent the earlier stages of folding, even when the site of the substitution was located within the ordered regions of the intermediates. These results suggest that stabilizing interactions contribute less to conformational stability in the context of a partially folded intermediate than in a fully folded native protein, perhaps because of decreased cooperativity among the individual interactions. The kinetic analysis also provides new information about the transition states associated with the slowest steps in folding and unfolding, supporting previous suggestions that these transition states are extensively unfolded. Although the substitutions caused large changes in the distribution of folding intermediates and in the rates of some steps in the folding pathway, the kinetically-preferred pathway for all of the variants involved intramolecular disulfide rearrangements, as observed previously for the wild-type protein. These results suggest that the predominance of the rearrangement mechanism reflects conformational constraints present relatively early in the folding pathway.     

Molecular basis of cooperativity in protein folding. V. Thermodynamic and structural conditions for the stabilization of compact denatured states

The heat-denatured state of proteins has been usually assumed to be a fully hydrated random coil. It is now evident that under certain solvent conditions or after chemical or genetic modifications, the protein molecule may exhibit a hydrophobic core and residual secondary structure after thermal denaturation. This state of the protein has been called the “compact denatured” or “molten globule” state. Recently is has been shown that α-lactalbumin at pH < 5 denatures into a molten globule state upon increasing the temperature (Griko, Y., Freire, E., Privalov, P. L. Biochemistry 33:1889–1899, 1994). This state has a lower heat capacity and a higher enthalpy at low temperatures than the unfolded state. At those temperatures the stabilization of the molten globule state is of an entropic origin since the enthalpy contributes unfavorably to the Gibbs free energy. Since the molten globule is more structured than the unfolded state and, therefore, is expected to have a lower configurational entropy, the net entropic gain must originate primarily from solvent related entropy arising from the hydrophobic effect, and to a lesser extent from protonation or electrostatic effects. In this work, we have examined a large ensemble of partly folded states derived from the native structure of α-lactalbumin in order to identify those states that satisfy the energetic criteria of the molten globule. It was found that only few states satisfied the experimental constraints and that, furthermore, those states were part of the same structural family. In particular, the regions corresponding to the A, B, and C helices were found to be folded, while the β sheet and the D helix were found to be unfolded. At temperatures below 45°C the states exhibiting those structural characteristics are enthalpically higher than the unfolded state in agreement with the experimental data. Interestingly, those states have a heat capacity close to that observed for the acid pH compact denatured state of α-lactalbumin [980 cal (mol.K)^?l]. In addition, the folded regions of these states include those residues found to be highly protected by NMR hydrogen exchange experiments. This work represents an initial attempt to model the structural origin of the thermodynamic properties of partly folded states. The results suggest a number of structural features that are consistent with experimental data. © 1994 Wiley-Liss, Inc.     

Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds

A principal component analysis has been applied on equilibrium simulations of a beta-heptapeptide that shows reversible folding in a methanol solution. The analysis shows that the configurational space contains only three dense sub-states. These states of relatively low free energy correspond to the "native" left-handed helix, a partly helical intermediate, and a hairpin-like structure. The collection of unfolded conformations form a relatively diffuse cloud with little substructure. Internal hydrogen-bonding energies were found to correlate well with the degree of folding. The native helical structure folds from the N terminus; the transition from the major folding intermediate to the native helical structure involves the formation of the two most C-terminal backbone hydrogen bonds. A four-state Markov model was found to describe transition frequencies between the conformational states within error limits, indicating that memory-effects are negligible beyond the nanosecond time-scale. The dominant native state fluctuations were found to be very similar to unfolding motions, suggesting that unfolding pathways can be inferred from fluctuations in the native state. The low-dimensional essential subspace, describing 69% of the collective atomic fluctuations, was found to converge at time-scales of the order of one nanosecond at all temperatures investigated, whereas folding/unfolding takes place at significantly longer time-scales, even above the melting temperature.     

Comparative Fourier transform infrared spectroscopy study of cold-, pressure-, and heat-induced unfolding and aggregation of myoglobin

We studied the cold unfolding of myoglobin with Fourier transform infrared spectroscopy and compared it with pressure and heat unfolding. Because protein aggregation is a phenomenon with medical as well as biotechnological implications, we were interested in both the structural changes as well as the aggregation behavior of the respective unfolded states. The cold- and pressure-induced unfolding both yield a partially unfolded state characterized by a persistent amount of secondary structure, in which a stable core of G and H helices is preserved. In this respect the cold- and pressure-unfolded states show a resemblance with an early folding intermediate of myoglobin. In contrast, the heat unfolding results in the formation of the infrared bands typical of intermolecular antiparallel beta-sheet aggregation. This implies a transformation of alpha-helix into intermolecular beta-sheet. H/2H-exchange data suggest that the helices are first unfolded and then form intermolecular beta-sheets. The pressure and cold unfolded states do not give rise to the intermolecular aggregation bands that are typical for the infrared spectra of many heat-unfolded proteins. This suggests that the pathways of the cold and pressure unfolding are substantially different from that of the heat unfolding. After return to ambient conditions the cold- or pressure-treated proteins adopt a partially refolded conformation. This aggregates at a lower temperature (32 degrees C) than the native state (74 degrees C).     

Combined NMR-observation of cold denaturation in supercooled water and heat denaturation enables accurate measurement of ΔC p of protein unfolding

Cold and heat denaturation of the double mutant Arg 3→Glu/Leu 66→Glu of cold shock protein Csp of Bacillus caldolyticus was monitored using 1D ¹H NMR spectroscopy in the temperature range from −12°C in supercooled water up to +70°C. The fraction of unfolded protein, f _u, was determined as a function of the temperature. The data characterizing the unfolding transitions could be consistently interpreted in the framework of two-state models: cold and heat denaturation temperatures were determined to be −11°C and 39°C, respectively. A joint fit to both cold and heat transition data enabled the accurate spectroscopic determination of the heat capacity difference between native and denatured state, ΔC _p of unfolding. The approach described in this letter, or a variant thereof, is generally applicable and promises to be of value for routine studies of protein folding.     

Water as a conformational editor in protein folding

As molecules approach one another in aqueous solution, desolvation free energy barriers to association are encountered. Experiments suggest these (de)solvation effects contribute to the free energy barriers separating the folded and unfolded states of protein molecules. To explore their influence on the energy landscapes of protein folding reactions, we have incorporated desolvation barriers into a semi-realistic, off-lattice protein model that uses a simplified physico-chemical force-field determined solely by the sequence of amino acids. Monte Carlo sampling techniques were used to study the effects on the thermodynamics and kinetics of folding of a number of systems, diverse in structure and sequence. In each case, desolvation barriers increase the stability of the native conformation and the cooperativity of the major folding/unfolding transition. The folding times of these systems are reduced significantly upon inclusion of desolvation barriers, demonstrating that the particulate nature of the solvent engenders a more defined route to the native fold.     

Refolding of the hyperthermophilic protein Ssh10b involves a kinetic dimeric intermediate

The α/β-mixed dimeric protein Ssh10b from the hyperthermophile Sulfolobus shibatae is a member of the Sac10b family that is thought to be involved in chromosomal organization or DNA repair/recombination. The equilibrium unfolding/refolding of Ssh10b induced by denaturants and heat was fully reversible, suggesting that Ssh10b could serve as a good model for folding/unfolding studies of protein dimers. Here, we investigate the folding/unfolding kinetics of Ssh10b in detail by stopped-flow circular dichroism (SF-CD) and using GdnHCl as denaturant. In unfolding reactions, the native Ssh10b turned rapidly into fully unfolded monomers within the stopped-flow dead time with no detectable kinetic intermediate, agreeing well with the results of equilibrium unfolding experiments. In refolding reactions, two unfolded monomers associate in the burst phase to form a dimeric intermediate that undergoes a further, slower, first-order folding process to form the native dimer. Our results demonstrate that the dimerization is essential for maintaining the native tertiary interactions of the protein Ssh10b. In addition, folding mechanisms of Ssh10b and several other α/β-mixed or pure β-sheet proteins are compared.