Cooperativity in two-state protein folding kinetics

We present a solvable model that predicts the folding kinetics of two-state proteins from their native structures. The model is based on conditional chain entropies. It assumes that folding processes are dominated by small-loop closure events that can be inferred from native structures. For CI2, the src SH3 domain, TNfn3, and protein L, the model reproduces two-state kinetics, and it predicts well the average Phi-values for secondary structures. The barrier to folding is the formation of predominantly local structures such as helices and hairpins, which are needed to bring nonlocal pairs of amino acids into contact.     

Importance of hydrophobic cluster formation through long-range contacts in the folding transition state of two-state proteins

Understanding the folding pathways of proteins is a challenging task. The Phi value approach provides a detailed understanding of transition-state structures of folded proteins. In this work, we have computed the hydrophobicity associated with each residue in the folded state of 16 two-state proteins and compared the Phi values of each mutant residue. We found that most of the residues with high Phi value coincide with local maximum in surrounding hydrophobicity, or have nearby residues that show such maximum in hydrophobicity, indicating the importance of hydrophobic interactions in the transition state. We have tested our approach to different structural classes of proteins, such as alpha-helical, SH3 domains of all-beta proteins, beta-sandwich, and alpha/beta proteins, and we observed a good agreement with experimental results. Further, we have proposed a hydrophobic contact network pattern to relate the Phi values with long-range contacts, which will be helpful to understand the transition-state structures of folded proteins. The present approach could be used to identify potential hydrophobic clusters that may form through long-range contacts during the transition state.     

The folding transition state of the cold shock protein is strongly polarized

It has been shown recently that an 11-residue peptide fragment of transthyretin, TTR(105-115), can form amyloid fibrils in vitro by adopting an extended beta-strand conformation. We used molecular dynamics simulations on systems of TTR(105-115) peptides, for a total length of about 5 micros, to explore the process of self-assembly and the structures of the resulting aggregates. Our results suggest that an antiparallel association of the beta-strands is more probable than a parallel one and that the central residues (T106-L111) in a beta-strand have a high propensity to form inter-peptide hydrogen bonds. The study of the dynamics of self-association indicated that, for this peptide, trajectories leading to conformations with high alpha-helical content are off-pathway from those leading to aggregates with high beta-structure content. We also show that the diverse oligomeric structures that form spontaneously in the molecular dynamics simulations are, to a large extent, compatible with solid-state NMR experimental measurements, including chemical shifts, on fully formed fibrils. The strategy that we present may therefore be used in the design of new experiments to determine the structure of amyloid fibrils, such as those involving site-specific isotope labelling schemes to measure key inter-atomic distances.     

Three topologically equivalent core residues affect the transition state ensemble in a protein folding reaction

The single domain protein, interleukin-1beta, is representative of a distinct class of proteins characterized by their beta-trefoil topology. Each subdomain of this structural class is composed of a beta beta beta loop beta (betabetabetaLbeta) motif comprised of approximately 50 residues and gives the protein a pseudo- 3-fold axis of symmetry. A common feature of proteins in this topological family appears to be that they are slow folders, which reach the native state on the order of tens to 100s of seconds. Sequence analysis of interleukin-1beta indicates that three phenylalanine residues located at positions 42, 101, and 146 are well conserved, separated by approximately 50 residues in the primary sequence, located in similar positions in the pseudo-symmetric units of the trefoil, and are juxtaposed to one another in conformational space. These residues surround the hydrophobic cavity and "pin" the hairpin triplet cap to the core beta-barrel. To determine if cap-barrel interactions are involved in maintaining the structural stability and cooperativity or in controlling the slow formation of the native state, we performed a series of mutational studies. The results indicate that interleukin-1beta tolerates large increases in side-chain volume at these three topologically conserved sites with little effect on stability, while the kinetics show significant differences in both the unfolding and refolding rates. Taken together, our results indicate that these conserved core residues are essential contacts in the transition-state ensemble for folding.     

Non-native interactions play an effective role in protein folding dynamics

Systematic Monte Carlo simulations of simple lattice models show that the final stage of protein folding is an ordered process where native contacts get locked (i.e., the residues come into contact and remain in contact for the duration of the folding process) in a well‐defined order. The detailed study of the folding dynamics of protein‐like sequences designed as to exhibit different contact energy distributions, as well as different degrees of sequence optimization (i.e., participation of non‐native interactions in the folding process), reveals significant differences in the corresponding locking scenarios—the collection of native contacts and their average locking times, which are largely ascribable to the dynamics of non‐native contacts. Furthermore, strong evidence for a positive role played by non‐native contacts at an early folding stage was also found. Interestingly, for topologically simple target structures, a positive interplay between native and non‐native contacts is observed also toward the end of the folding process, suggesting that non‐native contacts may indeed affect the overall folding process. For target models exhibiting clear two‐state kinetics, the relation between the nucleation mechanism of folding and the locking scenario is investigated. Our results suggest that the stabilization of the folding transition state can be achieved through the establishment of a very small network of native contacts that are the first to lock during the folding process.     

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.     

Folding rates and low-entropy-loss routes of two-state proteins

We develop a simple model for computing the rates and routes of folding of two-state proteins from the contact maps of their native structures. The model is based on the graph-theoretical concept of effective contact order (ECO). The model predicts that proteins fold by "zipping up" in a sequence of small-loop-closure events, depending on the native chain fold. Using a simple equation, with a few physical rate parameters, we obtain a good correlation with the folding rates of 24 two-state folding proteins. The model rationalizes data from Phi-value analysis that have been interpreted in terms of delocalized or polarized transition states. This model indicates how much of protein folding may take place in parallel, not along a single reaction coordinate or with a single transition state.     

Charge centers and formation of the protein folding core

Electrostatic interactions are important for protein folding. At low resolution, the electrostatic field of the whole molecule can be described in terms of charge center(s). To study electrostatic effects, the centers of positive and negative charge were calculated for 20 small proteins of known structure, for which hydrogen exchange cores had been determined experimentally. Two observations seem to be important. First, in all 20 proteins studied 30-100% of the residues forming hydrogen exchange core(s) were clustered around the charge centers. Moreover, in each protein more than half of the core sequences are located near the centers of charge. Second, the general architecture of all-alpha proteins from the set seems to be stabilized by interactions of residues surrounding the charge centers. In most of the alpha-beta proteins, either or both of the centers are located near a pair of consecutive strands, and this is even more characteristic for alpha/Beta and all-beta structures. Consecutive strands are very probable sites of early folding events. These two points lead to the conclusion that charge centers, defined solely from the structure of the folded protein may indicate the location of a protein's hydrogen exchange/folding core. In addition, almost all the proteins contain well-conserved continuous hydrophobic sequences of three or more residues located in the vicinity of the charge centers. These hydrophobic sequences may be primary nucleation sites for protein folding. The results suggest the following scheme for the order of events in folding: local hydrophobic nucleation, electrostatic collapse of the core, global hydrophobic collapse, and slow annealing to the native state. This analysis emphasizes the importance of treating electrostatics during protein-folding simulations.     

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.     

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.     

Rapid collapse precedes the fast two-state folding of the cold shock protein

The cold shock protein Bc-Csp folds very rapidly in a reaction that is well described by a kinetic two-state mechanism without intermediates. We measured the shortening of six intra-protein distances during folding by F?rster resonance energy transfer (FRET) in combination with stopped-flow experiments. Single tryptophan residues were engineered into the protein as the donors, and single 5-(((acetylamino)ethyl)amino)naphthalene-1-sulfonate (AEDANS) residues were placed as the acceptors at solvent-exposed sites of Bc-Csp. Their R0 value of about 22 A was well suited for following distance changes during the folding of this protein with a high sensitivity. The mutagenesis and the labeling did not alter the refolding kinetics. The changes in energy transfer during folding were monitored by both donor and acceptor emission and reciprocal effects were found. In two cases the donor-acceptor distances were similar in the unfolded and the folded state and, as a consequence, the kinetic changes in energy transfer upon folding were very small. For four donor/acceptor pairs we found that > or =50% of the increase in energy transfer upon folding occurred prior to the rate-limiting step of folding. This reveals that about half of the shortening of the intra-molecular distances upon folding has occurred already before the rate-limiting step and suggests that the fast two-state folding reaction of Bc-Csp is preceded by a very rapid collapse.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

Sequence-based study of two related proteins with different folding behaviors

Z(SPA-1) is an engineered protein that binds to its parent, the three-helix-bundle Z domain of staphylococcal protein A. Uncomplexed Z(SPA-1) shows a reduced helix content and a melting behavior that is less cooperative, compared with the wild-type Z domain. Here we show that the difference in folding behavior between these two sequences can be partly understood in terms of an off-lattice model with 5-6 atoms per amino acid and a minimalistic potential, in which folding is driven by backbone hydrogen bonding and effective hydrophobic attraction.     

Domains in folding of model proteins.

By means of Monte Carlo simulation, we investigated the equilibrium between folded and unfolded states of lattice model proteins. The amino acid sequences were designed to have pronounced energy minimum target conformations of different length and shape. For short fully compact (36-mer) proteins, the all-or-none transition from the unfolded state to the native state was observed. This was not always the case for longer proteins. Among 12 designed sequences with the native structure of a fully compact 48-mer, a simple all-or-none transition was observed in only three cases. For the other nine sequences, three states of behavior-the native, denatured, and intermediate states-were found. The contiguous part of the native structure (domain) was conserved in the intermediate state, whereas the remaining part was completely unfolded and structureless. These parts melted separately from each other.     

Critical nucleation size in the folding of small apparently two-state proteins

For apparently two-state proteins, we found that the size (number of folded residues) of a transition state is mostly encoded by the topology, defined by total contact distance (TCD) of the native state, and correlates with its folding rate. This is demonstrated by using a simple procedure to reduce the native structures of the 41 two-state proteins with native TCD as a constraint, and is further supported by analyzing the results of eight proteins from protein engineering studies. These results support the hypothesis that the major rate-limiting process in the folding of small apparently two-state proteins is the search for a critical number of residues with the topology close to that of the native state.     

Outlining folding nuclei in globular proteins

Our theoretical approach for prediction of folding/unfolding nuclei in three-dimensional protein structures is based on a search for free energy saddle points on networks of protein unfolding pathways. Under some approximations, this search is performed rapidly by dynamic programming and results in prediction of Phi values, which can be compared with those found experimentally. In this study, we optimize some details of the model (specifically, hydrogen atoms are taken into account in addition to heavy atoms), and compare the theoretically obtained and experimental Phi values (which characterize involvement of residues in folding nuclei) for all 17 proteins, where Phi values are now known for many residues. We show that the model provides good Phi value predictions for proteins whose structures have been determined by X-ray analysis (the average correlation coefficient is 0.65), with a more limited success for proteins whose structures have been determined by NMR techniques only (the average correlation coefficient is 0.34), and that the transition state free energies computed from the same model are in a good anticorrelation with logarithms of experimentally measured folding rates at mid-transition (the correlation coefficient is -0.73).     

Rapid cooperative two-state folding of a miniature alpha-beta protein and design of a thermostable variant

There is a great deal of interest in developing small stably folded miniature proteins. A limited number of these molecules have been described, however they typically have not been characterized in depth. In particular, almost no detailed studies of the thermodynamics and folding kinetics of these proteins have been reported. Here we describe detailed studies of the thermodynamics and kinetics of folding of a 39 residue mixed alpha-beta protein (NTL9(1-39)) derived from the N-terminal domain of the ribosomal protein L9. The protein folds cooperatively and rapidly in a two-state fashion to a native state typical of those found for normal globular proteins. At pH 5.4 in 20mM sodium acetate, 100mM NaCl the temperature of maximum stability is 6 degrees C, the t(m) is 65.3 degrees C, deltaH degrees (t(m)) is between 24.6 kcalmol(-1) and 26.3 kcalmol(-1), and deltaC(p) degrees is 0.38 kcalmol(-1)deg(-1). The thermodynamic parameters are in the range expected on the basis of per residue values determined from databases of globular proteins. H/2H exchange measurements reveal a set of amides that exchange via global unfolding, exactly as expected for a normal cooperatively folded globular protein. Kinetic measurements show that folding is two-state folding. The folding rate is 640 s(-1) and the value of deltaG degrees calculated from the folding and unfolding rates is in excellent agreement with the equilibrium value. A designed thermostable variant, generated by mutating K12 to M, was characterized and found to have a t(m) of 82 degrees C. Equilibrium and kinetic measurements demonstrate that its folding is cooperative and two-state.