Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.     

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.     

Predicting the equilibrium protein folding pathway: Structure-based analysis of staphylococcal nuclease

The equilibrium folding pathway of staphylococcal nucleas (SNase) has been approximated using a statistical thermodynamic formalism that utilizes the high-resolution structure of the native state as a template to generate a large ensemble of partially folded states. Close to 400,000 different states ranging from the native to the completely unfolded states were included in the analysis. The probability of each state was estimated using an empirical structural parametrization of the folding energetics. It is shown that this formalism predicts accurately the stability of the protein, the cooperativity of the folding/unfolding transition observed by differential scanning calorimetry (DSC) or urea denaturation and the thermodynamic parameters for unfolding. More importantly, this formalism provides a quantitative account of the experimental hydrogen exchange protection factors measured under native conditions for SNase. These results suggest that the computer-generated distribution of states approximates well the ensemble of conformations existing in solution. Furthermore, this formalism represents the first model capable of quantitatively predicting within a unified framework the probability distribution of states seen under native conditions and its change upon unfolding. © 1997 Wiley-Liss, Inc.     

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

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

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.     

Trehalose favors a cutinase compact intermediate off-folding pathway

The folding of cutinase, an enzyme displaying lipolytic activity, has been studied in the presence of trehalose. Equilibrium unfolding data show that trehalose increases the free energy change between folded and unfolded states. Unfolding kinetics reveal the presence of an intermediate which is ca. 60% folded in terms of solvent exposure. Trehalose stabilizes this intermediate relative to the folded state. In contrast, the intermediate revealed by folding kinetics is more compact than the transition state, as shown by the positive slope observed at low denaturant concentration in the chevron plot, as well as the decrease in the observable rate constant for folding with the increase in trehalose concentration. This intermediate displays more than 50% of area buried from the solvent (relative to the native state) compared to around 40% for the transition state for folding and therefore appears to be off the folding pathway. Trehalose stabilizes and guanidine hydrochloride destabilizes this compact intermediate. Both unfolding and folding kinetics show that compact conformational states are stabilized by trehalose, in agreement with current models on the effect of compatible solutes. This effect occurs even for compact states that decelerate the folding as in the case of the intermediate revealed by folding kinetics.     

The molecular basis of cooperativity in protein folding. Thermodynamic dissection of interdomain interactions in phosphoglycerate kinase.

In the presence of guanidine hydrochloride, phosphoglycerate kinase from yeast can be reversibly denatured by either heating or cooling the protein solution above or below room temperature [Griko, Y. V., Venyaminov, S. Y., & Privalov, P. L. (1989) FEBS Lett. 244, 276-278]. The heat denaturation of PGK is characterized by the presence of a single peak in the excess heat capacity function obtained by differential scanning calorimetry. The transition curve approaches the two-state mechanism, indicating that the two domains of the molecule display strong cooperative interactions and that partially folded intermediates are not largely populated during the transition. On the contrary, the cold denaturation is characterized by the presence of two peaks in the heat capacity function. Analysis of the data indicates that at low temperatures the two domains behave independently of each other. The crystallographic structure of PGK has been used to identify the nature of the interactions between the two domains. These interactions involve primarily the apposition of two hydrophobic surfaces of approximately 480 A2 and nine hydrogen bonds. This information, in conjunction with experimental thermodynamic values for hydrophobic, hydrogen bonding interactions and statistical thermodynamic analysis, has been used to quantitatively account for the folding/unfolding behavior of PGK. It is shown that this type of analysis accurately predicts the cooperative behavior of the folding/unfolding transition and its dependence on GuHCl concentration.     

Multiple interactions of a DNA-binding protein in vivo. II. Effects of host mutations on DNA replication of phage T4 gene 32 mutants.

A quantitative analysis has been made of the kinetics of disulphide bond formation, breakage, and rearrangement which occur during the folding and unfolding of the pancreatic trypsin inhibitor. The results have been used to infer the energetics of the protein conformational transitions which accompany each step.The folding transition is shown to be a co-operative process in which all intermediate states with one or two disulphide bonds are unstable relative to the unfolded, reduced protein and that in the fully folded conformation with three disulphide bonds. The approximate two-state nature of the transition at equilibrium was demonstrated experimentally. The folding transition of the inhibitor which has been determined kinetically is therefore analogous to that observed generally with other globular proteins.     

Folding intermediates of a model three-helix bundle protein. Pressure and cold denaturation studies

The stability and equilibrium unfolding of a model three-helix bundle protein, alpha(3)-1, by guanidine hydrochloride (GdnHCl), hydrostatic pressure, and temperature have been investigated. The combined use of these denaturing agents allowed detection of two partially folded states of alpha(3)-1, as monitored by circular dichroism, intrinsic fluorescence emission, and fluorescence of the hydrophobic probe bis-ANS (4,4'-dianilino-1,1'-binaphthyl-5,5'-disulfonic acid). The overall free-energy change for complete unfolding of alpha(3)-1, determined from GdnHCl unfolding data, is +4.6 kcal/mol. The native state is stabilized by -1.4 kcal/mol relative to a partially folded pressure-denatured intermediate (I(1)). Cold denaturation at high pressure gives rise to a second partially (un)folded conformation (I(2)), suggesting a significant contribution of hydrophobic interactions to the stability of alpha(3)-1. The free energy of stabilization of the native-like state relative to I(2) is evaluated to be -2.5 kcal/mol. Bis-ANS binding to the pressure- and cold-denatured states indicates the existence of significant residual hydrophobic structure in the partially (un)folded states of alpha(3)-1. The demonstration of folding intermediates of alpha(3)-1 lends experimental support to a number of recent protein folding simulation studies of other three-helix bundle proteins that predicted the existence of such intermediates. The results are discussed in terms of the significance of de novo designed proteins for protein folding studies.     

Folding kinetic pathway of phosphofructokinase-2 from Escherichia coli: a homodimeric enzyme with a complex domain organization

Phosphofructokinase-2 is a 66 kD homodimer whose subunits are associated by means of a bimolecular domain, the β-clasp, which is linked to the larger portion of each subunit by a reentrant chain topology. To investigate how this structural organization determines the folding pathway of Pfk-2, unfolding and folding kinetic experiments were performed. The folding pathway shows an unstructured monomeric intermediate and that most part of the dimer structure is reached as a slow concerted folding/association step with a quite folded transition state in terms of solvent exposure. Unfolding kinetics show a transient intermediate, probably a partially unfolded dimer. We propose that these characteristics arise by a mutual constrain between the large domain and the β-clasp domain imposed by their interrupted chain connectivity.     

Long-range electrostatic effects on peptide folding.

The reversible folding/unfolding of a short peptide in solution is studied by molecular dynamics simulations. The effects of long-range electrostatic interactions are examined and found to be important both for the equilibrium between folded and unfolded states and the dynamics of the folding process. The neglect of long-range electrostatics leads to an increased population of unfolded states and increased structural fluctuations. When such interactions are taken into account, the peptide unfolds and folds to the experimentally determined structure several times during a 25 ns trajectory, with approximately equal populations of folded and unfolded states in the neighborhood of its proposed melting temperature. The effect of using spherical boundary conditions rather than periodic ones does not appear to have any major effect on the folding dynamics.     

Temperature-dependent downhill unfolding of ubiquitin. II. Modeling the free energy surface

To provide evidence for the interpretation of temperature‐dependent unfolding kinetics and the downhill unfolding scenario presented in the accompanying experimental article (Part I), the free energy surface of ubiquitin unfolding is calculated using statistical mechanical models of the Muñoz‐Eaton (ME) form. The models allow only two states for each amino acid residue, folded or unfolded, and permutations of these states generate an ensemble of microstates. One‐dimensional free energy curves are calculated using the number of folded residues as a reaction coordinate. The proposed sequential unfolding of ubiquitin's β‐sheet is tested by mapping the free energy onto two reaction coordinates inspired by the experiment as follows: the number of folded residues in ubiquitin's stable β‐strands I and II and those of the less stable strands III–V. Although the original ME model successfully captures folding features of zipper‐like one‐dimensional folders, it misses important tertiary interactions between residues that are far from each other in primary sequence. To take tertiary contacts into account, partially folded microstates based on a spherical growth model are included in the calculation and compared with the original model. By calculating the folding probability of each residue for a given point on the free energy surface, the unfolding pathway of ubiquitin is visualized. At low temperature, thermal unfolding occurs along a sequential unfolding pathway as follows: disruption of the β‐strands III–V followed by unfolding of the strands I and II. At high temperature, multiple unfolding routes are formed. The heterogeneity of the transition state explains the global nonexponential unfolding observed in the T‐jump experiment at high temperature. The calculation also reports a high stability for the α‐helix of ubiquitin. Proteins 2008. © 2008 Wiley‐Liss, Inc.     

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.     

Relationship between chain collapse and secondary structure formation in a partially folded protein

Chain collapse and secondary structure formation are frequently observed during the early stages of protein folding. Is the chain collapse brought about by interactions between secondary structure units or is it due to polymer behavior in a poor solvent (coil‐globule transition)? To answer this question, we measured small‐angle X‐ray scattering for a series of β‐lactoglobulin mutants under conditions in which they assume a partially folded state analogous to the folding intermediates. Mutants that were designed to disrupt the secondary structure units showed the gyration radii similar to that of the wild type protein, indicating that chain collapse is due to coil‐globule transitions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 651–658, 2014.     

Wild type, mutant protein unfolding and phase transition detected by single-nanopore recording

Understanding protein folding remains a challenge. A difficulty is to investigate experimentally all the conformations in the energy landscape. Only single molecule methods, fluorescence and force spectroscopy, allow observing individual molecules along their folding pathway. Here we observe that single-nanopore recording can be used as a new single molecule method to explore the unfolding transition and to examine the conformational space of native or variant proteins. We show that we can distinguish unfolded states from partially folded ones with the aerolysin pore. The unfolding transition curves of the destabilized variant are shifted toward the lower values of the denaturant agent compared to the wild type protein. The dynamics of the partially unfolded wild type protein follows a first-order transition. The denaturation curve obtained with the aerolysin pore is similar to that obtained with the α-hemolysin pore. The nanopore geometry or net charge does not influence the folding transition but changes the dynamics.     

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

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

Destabilization of the Escherichia coli RNase H kinetic intermediate: switching between a two-state and three-state folding mechanism

Escherichia coli RNase H folds through a partially folded kinetic intermediate that mirrors a rarely populated, partially unfolded form detectable by native-state hydrogen exchange under equilibrium conditions. Residue 53 is at the interface of two helices known to be structured in this intermediate. Kinetic refolding studies on mutant proteins varying in size and hydrophobicity at residue 53 support a contribution of hydrophobicity to the stabilities of the kinetic intermediate and the transition state. Packing interactions also play a significant role in the stability of these two states, though they play a much larger role in the native-state stability. One dramatic mutation, I53D, results in the conversion from a three-state to a two-state folding mechanism, which is explained most easily through a simple destabilization of the kinetic intermediate such that it is no longer stable with respect to the unfolded state. These results demonstrate that interactions that stabilize an intermediate can accelerate folding if these same interactions are present in the transition state. Our results are consistent with a hierarchical model of folding, where the intermediate consists of native-like interactions, is on-pathway, and is productive for folding.     

Native-like partially folded conformations and folding process revealed in the N-terminal large fragments of staphylococcal nuclease: a study by NMR spectroscopy

The N-terminal large fragments of staphylococcal nuclease (SNase), SNase110 (1-110 residues), SNase121 (1-121 residues), and SNase135 (1-135 residues), and the fragment mutants G88W110, G88W121, V66W110 and V66W121 were studied by heteronuclear multidimensional NMR spectroscopy. Ensembles of co-existent native-like partially folded and unfolded states were observed for fragments. The persistent native-like tertiary interaction drives fragments to be in partially folded states, which reveal native-like beta-barrel conformations. G88W and V66W mutations modulate the extent of inherent native-like tertiary interaction in fragment molecules, and in consequence, fragment mutants fold into native-like beta-subdomain conformations. In cooperation with the inherent tertiary interaction, 2 M TMAO (trimethylamine N-oxide) can promote the folding reaction of fragments through the changes of unfolding free energy, and a native-like beta-subdomain conformation is observed when the chain length contains 135 residues. Heterogeneous partially folded conformations of 1-121 and 1-135 fragments due to cis and trans X-prolyl bond of Lys116-Pro117 make a non-unique folding pathway of fragments. The folding reaction of fragments can be characterized as a hierarchical process.     

Pressure-Temperature Analysis of the Stability of the CTL9 Domain Reveals Hidden Intermediates

The observation of two-state unfolding for many small single-domain proteins by denaturants has led to speculation that protein sequences may have evolved to limit the population of partially folded states that could be detrimental to fitness. How such strong cooperativity arises from a multitude of individual interactions is not well understood. Here, we investigate the stability and folding cooperativity of the C-terminal domain of the ribosomal protein L9 in the pressure-temperature plane using site-specific NMR. In contrast to apparent cooperative unfolding detected with denaturant-induced and thermal-induced unfolding experiments and stopped-flow refolding studies at ambient pressure, NMR-detected pressure unfolding revealed significant deviation from two-state behavior, with a core region that was selectively destabilized by increasing temperature. Comparison of pressure-dependent NMR signals from both the folded and unfolded states revealed the population of at least one invisible excited state at atmospheric pressure. The core destabilizing cavity-creating I98A mutation apparently increased the cooperativity of the loss of folded-state peak intensity while also increasing the population of this invisible excited state present at atmospheric pressure. These observations highlight how local stability is subtly modulated by sequence to tune protein conformational landscapes and illustrate the ability of pressure- and temperature-dependent studies to reveal otherwise hidden states.     

Free energy landscape and folding mechanism of a beta-hairpin in explicit water: a replica exchange molecular dynamics study

The free energy landscape and the folding mechanism of the C-terminal beta-hairpin of protein G is studied by extensive replica exchange molecular dynamics simulations (40 replicas and 340 ns total simulation time), using the GROMOS96 force field and the SPC explicit water solvent. The study reveals that the system preferentially adopts a beta-hairpin structure at biologically important temperatures, and that the helix content is low at all temperatures studied. Representing the free energy landscape as a function of several types of reaction coordinates, four local minima corresponding to the folded, partially folded, molten globule, and unfolded states are identified. The findings suggest that the folding of the beta-hairpin occurs as the sequence: collapse of hydrophobic core --> formation of H-bond --> formation of the turn. Identifying the folded and molten globule states as the main conformations, the free energy landscape of the beta-hairpin is consistent with a two-state behavior with a broad transition state. The temperature dependence of the folding-unfolding transition is investigated in some detail. The enthalpy and entropy jumps at the folding transition temperature are found to be about three times lower than the experimental estimates, indicating that the folding-unfolding transition in silico is less cooperative than its in vitro counterpart.