How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding.     

Frustrated folding of guanine quadruplexes in telomeric DNA

Human chromosomes terminate in long, single-stranded, DNA overhangs of the repetitive sequence (TTAGGG)n. Sets of four adjacent TTAGGG repeats can fold into guanine quadruplexes (GQ), four-stranded structures that are implicated in telomere maintenance and cell immortalization and are targets in cancer therapy. Isolated GQs have been studied in detail, however much less is known about folding in long repeat sequences. Such chains adopt an enormous number of configurations containing various arrangements of GQs and unfolded gaps, leading to a highly frustrated energy landscape. To better understand this phenomenon, we used mutagenesis, thermal melting, and global analysis to determine stability, kinetic, and cooperativity parameters for GQ folding within chains containing 8–12 TTAGGG repeats. We then used these parameters to simulate the folding of 32-repeat chains, more representative of intact telomeres. We found that a combination of folding frustration and negative cooperativity between adjacent GQs increases TTAGGG unfolding by up to 40-fold, providing an abundance of unfolded gaps that are potential binding sites for telomeric proteins. This effect was most pronounced at the chain termini, which could promote telomere extension by telomerase. We conclude that folding frustration is an important and largely overlooked factor controlling the structure of telomeric DNA.     

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.     

Kinetic analysis of folding and unfolding the 56 amino acid IgG-binding domain of streptococcal protein G.

The 56 amino acid B domain of protein G (GB) is a stable globular folding unit with no disulfide cross-links. The physical properties of GB offer extraordinary flexibility for evaluating the energetics of the folding reaction. The protein is monomeric and very soluble in both folded and unfolded forms. The folding reaction has been previously examined by differential scanning calorimetry (Alexander et al., 1992) and found to exhibit two-state unfolding behavior over a wide pH range with an unfolding transition near 90 degrees C (GB1) at neutral pH. Here, the kinetics of folding and unfolding two naturally occurring versions of GB have been measured using stopped-flow mixing methods and analyzed according to transition-state theory. GB contains no prolines, and the kinetics of folding and unfolding can be fit to a single, first-order rate constant over the temperature range of 5-35 degrees C. The major thermodynamic changes going from the unfolded state to the transition state are (1) a large decrease in heat capacity (delta Cp), indicating that the transition state is compact and solvent inaccessible relative to the unfolded state; (2) a large loss of entropy; and (3) a small increase in enthalpy. The most surprising feature of the folding of GB compared to that of previously studied proteins is that its folding approximates a rapid diffusion controlled process with little increase in enthalpy going from the unfolded to the transition state.     

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.     

Stability and folding properties of a model beta-sheet protein, Escherichia coli CspA.

Although beta-sheets represent a sizable fraction of the secondary structure found in proteins, the forces guiding the formation of beta-sheets are still not well understood. Here we examine the folding of a small, all beta-sheet protein, the E. coli major cold shock protein CspA, using both equilibrium and kinetic methods. The equilibrium denaturation of CspA is reversible and displays a single transition between folded and unfolded states. The kinetic traces of the unfolding and refolding of CspA studied by stopped-flow fluorescence spectroscopy are monoexponential and thus also consistent with a two-state model. In the absence of denaturant, CspA refolds very fast with a time constant of 5 ms. The unfolding of CspA is also rapid, and at urea concentrations above the denaturation midpoint, the rate of unfolding is largely independent of urea concentration. This suggests that the transition state ensemble more closely resembles the native state in terms of solvent accessibility than the denatured state. Based on the model of a compact transition state and on an unusual structural feature of CspA, a solvent-exposed cluster of aromatic side chains, we propose a novel folding mechanism for CspA. We have also investigated the possible complications that may arise from attaching polyhistidine affinity tags to the carboxy and amino termini of CspA.     

DNA-RNA hybrid G-quadruplex tends to form near the 3′ end of telomere overhang

Telomeric repeat-containing RNA (TERRA) has been suggested to participate in telomere maintenance. TERRA consisting of UUAGGG repeats is capable of forming an intermolecular G-quadruplex (GQ) with single-stranded TTAGGG-repeat DNA in the telomere 3′ overhang. To explore the structural features and potential functions of this DNA-RNA hybrid GQ (HGQ), we used single-molecule FRET to study the folding patterns of DNA with four to seven telomeric tandem repeats annealed with a short RNA consisting of two or five telomeric repeats. Our data highlight that RNA prefers to form DNA-RNA HGQ near the 3′ end of telomeric DNA. Furthermore, the unfolding of secondary structures by a complementary C-rich sequence was observed for DNA GQ but not for DNA-RNA HGQ, which demonstrated the enhanced stability of the telomere 3′ end via hybridization with RNA. These conformational and physical properties of telomeric DNA-RNA HGQ suggest that TERRA might limit access to the 3′ end of the telomeric DNA overhang, which is known to be critical for the interaction with telomerase and other telomere-associated proteins.     

Folding and stability of trp aporepressor from Escherichia coli

Equilibrium and kinetic studies of the urea-induced unfolding of trp aporepressor from Escherichia coli were performed to probe the folding mechanism of this intertwined, dimeric protein. The equilibrium unfolding transitions at pH 7.6 and 25 degrees C monitored by difference absorbance, fluorescence, and circular dichroism spectroscopy are coincident within experimental error. All three transitions are well described by a two-state model involving the native dimer and the unfolded monomer; the free energy of folding in the absence of denaturant and under standard-state conditions is estimated to be 23.3 +/- 0.9 kcal/mol of dimer. The midpoint of the equilibrium unfolding transition increases with increasing protein concentration in the manner expected from the law of mass action for the two-state model. We find no evidence for stable folding intermediates. Kinetic studies reveal that unfolding is governed by a single first-order reaction whose relaxation time decreases exponentially with increasing urea concentration and also decreases with increasing protein concentration in the transition zone. Refolding involves at least three phases that depend on both the protein concentration and the final urea concentration in a complex manner. The relaxation time of the slowest of these refolding phases is identical with that for the single phase in unfolding in the transition zone, consistent with the results expected for a reaction that is kinetically reversible. The two faster refolding phases are presumed to arise from slow isomerization reactions in the unfolded form and reflect parallel folding channels.     

Test for cooperativity in the early kinetic intermediate in lysozyme folding

During the folding of many proteins, collapsed globular states are formed prior to the native structure. The role of these states for the folding process has been widely discussed. Comparison with properties of synthetic homo and heteropolymers had suggested that the initial collapse represented a shift of the ensemble of unfolded conformations to more compact states without major energy barriers. We investigated the folding/unfolding transition of a collapsed state, which transiently populates early in lysozyme folding. This state forms within the dead-time of stopped-flow mixing and it has been shown to be significantly more compact and globular than the denaturant-induced unfolded state. We used the GdmCl-dependence of the dead-time signal change to characterize the unfolding transition of the burst phase intermediate. Fluorescence and far-UV CD give identical unfolding curves, arguing for a cooperative two-state folding/unfolding transition between unfolded and collapsed lysozyme. These results show that collapse leads to a distinct state in the folding process, which is separated from the ensemble of unfolded molecules by a significant energy barrier. NMR, fluorescence and small angle X-ray scattering data further show that some local interactions in unfolded lysozyme exist at denaturant concentrations above the coil-collapse transition. These interactions might play a crucial role in the kinetic partitioning between fast and slow folding pathways.     

Force-induced unfolding of human telomeric G-quadruplex: A steered molecular dynamics simulation study

We study the unfolding of a parallel G-quadruplex from human telomeric DNA by mechanical stretching using steered molecular dynamics (MD) simulation. We find that the force curves and unfolding processes strongly depend on the pulling sites. With pulling sites located on the sugar-phosphate backbone, the force-extension curve shows a single peak and the unfolding proceeds sequentially. Pulling sites located on the terminal nucleobases lead to a force-extension curve with two peaks and the unfolding is more cooperative. Simulations of the refolding of partially unfolded quadruplexes show very different behavior for the two different pulling modalities. In particular, starting from an unfolded state prepared by nucleobase pulling leads to a long-lived intermediate state whose existence is also corroborated by the free energy profile computed with the Jarzynski equation. Based on this observation, we propose a novel folding pathway for parallel G-quadruplexes with the human telomere sequence.     

Energetics of protein structure and folding

The available experimental date on the kinetics of unfolding and refolding of small proteins are reviewed. Excluding slow transitions in the unfolded protein due to cis–trans isomerization of peptide bonds, the rate-limiting transition state in both unfolding and refolding is concluded to be a high-energy distortion of the fully folded state. Partially folded intermediates are undoubtedly important for folding, but their formation is normally not rate limiting. A simple model is used to illustrate some of the aspects of protein-folding energetics.     

Low folding cooperativity of HP35 revealed by single-molecule force spectroscopy and molecular dynamics simulation

Some small proteins, such as HP35, fold at submicrosecond timescale with low folding cooperativity. Although these proteins have been extensively investigated, still relatively little is known about their folding mechanism. Here, using single-molecule force spectroscopy and steered molecule dynamics simulation, we study the unfolding of HP35 under external force. Our results show that HP35 unfolds at extremely low forces without a well-defined unfolding transition state. Subsequently, we probe the structure of unfolded HP35 using the persistence length obtained in the force spectroscopy. We found that the persistence length of unfolded HP35 is around 0.72 nm, >40% longer than typical unstructured proteins, suggesting that there are a significant amount of residual secondary structures in the unfolded HP35. Molecular dynamics simulation further confirmed this finding and revealed that many native contacts are preserved in HP35, even its two ends have been extended up to 8 nm. Our results therefore suggest that retaining a significant amount of secondary structures in the unfolded state of HP35 may be an efficient way to reduce the entropic cost for the formation of tertiary structure and increase the folding speed, although the folding cooperativity is compromised. Moreover, we anticipate that the methods we used in this work can be extended to the study of other proteins with complex folding behaviors and even intrinsically disordered ones.     

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.     

Molecular basis of co-operativity in protein folding.

The folding/unfolding transition of proteins is a highly co-operative process characterized by the presence of very few or no thermodynamically stable partially folded intermediate states. The purpose of this paper is to present a thermodynamic formalism aimed at describing quantitatively the co-operative folding behavior of proteins. In order to account for this behavior, a hierarchical algorithm aimed at evaluating the folding/unfolding partition function has been developed. This formalism defines the partition function in terms of multiple levels of interacting co-operative folding units. A co-operative folding unit is defined as a protein structural element that exhibits two-state folding/unfolding behavior. At the most fundamental level are those structural elements that behave co-operatively as a result of purely local interactions. Higher-order co-operative folding units are formed through interactions between different structural elements. The hierarchical formalism utilizes the crystallographic structure of the protein as a template to generate partially folded conformations defined in terms of co-operative folding units. The Gibbs free energy of those states and their corresponding statistical weights are then computed using experimental energetic parameters determined calorimetrically. This formalism has been applied to the case of myoglobin. It is shown that the hierarchical partition function correctly predicts the presence, energetics and co-operativity of the heat and cold denaturation transitions. The major contribution to the co-operative folding behavior arises from the solvent exposure of non-polar residues located in regions complementary to those that have undergone unfolding. This entropically uncompensated and energetically unfavorable solvent exposure characterizes all partially folded states but not the unfolded state, thus minimizing the population of partially folded intermediates throughout the folding/unfolding transition.     

Folding and stability of sweet protein single-chain monellin. An insight to protein engineering

Engineered single-chain monellin (SCM) proteins were constructed by recombinant technology without disrupting the topology and sweet activity of native protein. Data from 8-anilinonaphthalene-1-sulfonic acid fluorescence, size-exclusion chromatography, and heteronuclear NMR strongly suggest the presence of a folding intermediate at 1.5 m GdnHCl for SCM protein. The structural feature of the folding intermediate from NMR data reveals that the secondary structures became mostly unstable, and protein experiences a dynamic equilibrium between native and unfolded state. All backbone amide protons exchange within 10 min, which imply that no stable hydrogen bonds exist in the secondary structural regions in the folding intermediate. From equilibrium unfolding and mutagenesis studies, the unfolding transition midpoints of mutant proteins gradually shifted toward lower denaturant concentration, indicating stability reductions of mutant proteins. Our results suggest that stability and folding pathways of SCM proteins could be regulated by a combined study of spectroscopy and mutagenesis, and these studies will provide useful information for understanding the folding kinetics of novel engineered proteins.     

Kinetic Partitioning Modulates Human Telomere DNA G-Quadruplex Structural Polymorphism

Telomeres are specialized chromatin structures found at the end of chromosomes and are crucial to the maintenance of eukaryotic genome stability. Human telomere DNA is comprised of the repeating sequence (T₂AG₃)_n, which is predominantly double-stranded but terminates with a 3’ single-stranded tail. The guanine-rich tail can fold into secondary structures known as a G-quadruplexes (GQs) that may exist as a polymorphic mixture of anti-parallel, parallel, and several hybrid topological isomers. Using single-molecule Förster resonance energy transfer (smFRET), we have reconstructed distributions of telomere DNA GQ conformations generated by an in situ refolding protocol commonly employed in single-molecule studies of GQ structure, or using a slow cooling DNA annealing protocol typically used in the preparation of GQ samples for ensemble biophysical analyses. We find the choice of GQ folding protocol has a marked impact on the observed distributions of DNA conformations under otherwise identical buffer conditions. A detailed analysis of the kinetics of GQ folding over timescales ranging from minutes to hours revealed the distribution of GQ structures generated by in situ refolding gradually equilibrates to resemble the distribution generated by the slow cooling DNA annealing protocol. Interestingly, conditions of low ionic strength, which promote transient GQ unfolding, permit the fraction of folded DNA molecules to partition into a distribution that more closely approximates the thermodynamic folding equilibrium. Our results are consistent with a model in which kinetic partitioning occurs during in situ folding at room temperature in the presence of K⁺ ions, producing a long-lived non-equilibrium distribution of GQ structures in which the parallel conformation predominates on the timescale of minutes. These results suggest that telomere DNA GQ folding kinetics, and not just thermodynamic stability, likely contributes to the physiological ensemble GQ structures.     

RPA-Mediated Unfolding of Systematically Varying G-Quadruplex Structures

G-quadruplex (GQ) is a noncanonical nucleic acid structure that is formed by guanine rich sequences. Unless it is destabilized by proteins such as replication protein A (RPA), GQ could interfere with DNA metabolic functions, such as replication or repair. We studied RPA-mediated GQ unfolding using single-molecule FRET on two groups of GQ structures that have different loop lengths and different numbers of G-tetrad layers. We observed a linear increase in the steady-state stability of the GQ against RPA-mediated unfolding with increasing number of layers or decreasing loop length. The stability demonstrated by different GQ structures varied by at least three orders of magnitude. Those with shorter loops (less than three nucleotides long) or a greater number of layers (more than three layers) maintained a significant folded population even at physiological RPA concentration (≈1 μM), raising the possibility of physiological viability of such GQ structures. Finally, we measured the transition time between the start and end of the RPA-mediated GQ unfolding process to be 0.35 ± 0.10 s for all GQ constructs we studied, despite significant differences in their steady-state stabilities. We propose a two-step RPA-mediated GQ unfolding mechanism that is consistent with our observations.     

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.     

How do chemical denaturants affect the mechanical folding and unfolding of proteins?

We present the first single-molecule atomic force microscopy study on the effect of chemical denaturants on the mechanical folding/unfolding kinetics of a small protein GB1 (the B1 immunoglobulin-binding domain of protein G from Streptococcus). Upon increasing the concentration of the chemical denaturant guanidinium chloride (GdmCl), we observed a systematic decrease in the mechanical stability of GB1, indicating the softening effect of the chemical denaturant on the mechanical stability of proteins. This mechanical softening effect originates from the reduced free-energy barrier between the folded state and the unfolding transition state, which decreases linearly as a function of the denaturant concentration. Chemical denaturants, however, do not alter the mechanical unfolding pathway or shift the position of the transition state for mechanical unfolding. We also found that the folding rate constant of GB1 is slowed down by GdmCl in mechanical folding experiments. By combining the mechanical folding/unfolding kinetics of GB1 in GdmCl solution, we developed the “mechanical chevron plot” as a general tool to understand how chemical denaturants influence the mechanical folding/unfolding kinetics and free-energy diagram in a quantitative fashion. This study demonstrates great potential in combining chemical denaturation with single-molecule atomic force microscopy techniques to reveal invaluable information on the energy landscape underlying protein folding/unfolding reactions.     

Selective stabilization of a partially unfolded protein by a metabolite

When proteins fold in vivo, the intermediates that exist transiently on their folding pathways are exposed to the potential interactions with a plethora of metabolites within the cell. However, these potential interactions are commonly ignored. Here, we report a case in which a ubiquitous metabolite interacts selectively with a nonnative conformation of a protein and facilitates protein folding and unfolding process. From our previous proteomics study, we have discovered that Escherichia coli glyceraldehyde-3-phosphate dehydrogenase (GAPDH), which is not known to bind ATP under native conditions, is apparently destabilized in the presence of a physiological concentration of ATP. To decipher the origin of this surprising effect, we investigated the thermodynamics and kinetics of folding and unfolding of GAPDH in the presence of ATP. Equilibrium unfolding of the protein in urea showed that a partially unfolded equilibrium intermediate accumulates in the presence of ATP. This intermediate has a quaternary structure distinct from the native protein. Also, ATP significantly accelerates the unfolding of GAPDH by selectively stabilizing a transition state that is distinct from the native state of the protein. Moreover, ATP also significantly accelerates the folding of GAPDH. These results demonstrate that ATP interacts specifically with a partially unfolded form of GAPDH and affects the kinetics of folding and unfolding of this protein. This unusual effect of ATP on the folding of GAPDH implies that endogenous metabolites may facilitate protein folding in vivo by interacting with partially unfolded intermediates.