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.     

Weak cooperativity in the core causes a switch in folding mechanism between two proteins of the cks family

The human protein ckshs1 (cks1) is a 79 residue alpha/beta protein with low thermodynamic and kinetic stability. Its folding mechanism was probed by mutation at sites throughout the structure. Many of the mutations caused changes in the slope of the unfolding arm of the chevron plot. The effects can be rationalised in terms of either transition-state movement or native-state "breathing", and in either case, the magnitude of the effect enables the sequence of events in the folding reaction to be determined. Those sites that fold early exhibit a small perturbation, whilst those sites that fold late exhibit a large perturbation. The results show that cks1 folds sequential pairs of beta-strands first; beta1/beta2 and beta3/beta4. Subsequently, these pairs pack against each other and onto the alpha-helical region to form the core. The folding process of cks1 contrasts with that of the homologue, suc1. The 113 residue suc1 has the same beta-sheet core structure but, additionally, two large insertions that confer much greater thermodynamic and kinetic stability. The more extensive network of tertiary interactions in suc1 provides sufficient enthalpic gain to overcome the entropic cost of forming the core and thus tips the balance in favour of non-local interactions: the non-local, central beta-strand pair, beta2/beta4, forms first and the periphery strands pack on later. Moreover, the greater cooperativity of the core of suc1 protects its folding from perturbation and consequently the slope of the unfolding arm of the chevron plot is much less sensitive to mutation.     

Fine structure analysis of a protein folding transition state; distinguishing between hydrophobic stabilization and specific packing

Developing a detailed understanding of the structure and energetics of protein folding transition states is a key step in describing the folding process. The phi-value analysis approach allows the energetic contribution of side-chains to be mapped out by comparing wild-type with individual mutants where conservative changes are introduced. Studies where multiple substitutions are made at individual sites are much rarer but are potentially very useful for understanding the contribution of each element of a side-chain to transition state formation, and for distinguishing the relative importance of specific packing versus hydrophobic interactions. We have made a series of conservative mutations at multiple buried sites in the N-terminal domain of L9 in order to assess the relative importance of specific side-chain packing versus less specific hydrophobic stabilization of the transition state. A total of 28 variants were prepared using both naturally occurring and non-naturally occurring amino acids at six sites. Analysis of the mutants by NMR and CD showed no perturbation of the structure. There is no correlation between changes in hydrophobicity and changes in stability. In contrast, there is excellent linear correlation between the hydrophobicity of a side-chain and the log of the folding rate, ln(k(f)). The correlation between ln(k(f)) and the change in hydrophobicity holds even for substitutions that change the shape and/or size of a side-chain significantly. For most sites, the correlation with the logarithm of the unfolding rate, ln(k(u)), is much worse. Mutants with more hydrophobic amino acid substitutions fold faster, and those with less hydrophobic amino acid substitutions fold slower. The results show that hydrophobic interactions amongst core residues are an important driving force for forming the transition state, and are more important than specific tight packing interactions. Finally, a number of substitutions lead to negative phi-values and the origin of these effects are described.     

Equilibrium amide hydrogen exchange and protein folding kinetics

The classical Linderstrøm-Lang hydrogen exchange (HX) model is extended to describe the relationship between the HX behaviors (EX1 and EX2) and protein folding kinetics for the amide protons that can only exchange by global unfolding in a three-state system including native (N), intermediate (I), and unfolded (U) states. For these slowly exchanging amide protons, it is shown that the existence of an intermediate (I) has no effect on the HX behavior in an off-pathway three-state system (IUN). On the other hand, in an on-pathway three-state system (UIN), the existence of a stable folding intermediate has profound effect on the HX behavior. It is shown that fast refolding from the unfolded state to the stable intermediate state alone does not guarantee EX2 behavior. The rate of refolding from the intermediate state to the native state also plays a crucial role in determining whether EX1 or EX2 behavior should occur. This is mainly due to the fact that only amide protons in the native state are observed in the hydrogen exchange experiment. These new concepts suggest that caution needs to be taken if one tries to derive the kinetic events of protein folding from equilibrium hydrogen exchange experiments.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

The folding mechanism of a two-domain protein: folding kinetics and domain docking of the gene-3 protein of phage fd

The gene-3 protein (G3P) of filamentous phages is essential for the infection of Escherichia coli. The carboxy-terminal domain anchors this protein in the phage coat, whereas the two amino-terminal domains N1 and N2 protrude from the phage surface. We analyzed the folding mechanism of the two-domain fragment N1-N2 of G3P (G3P(*)) and the interplay between folding and domain assembly. For this analysis, a variant of G3P(*) was used that contained four stabilizing mutations (IIHY-G3P(*)). The observed refolding kinetics extend from 10 ms to several hours. Domain N1 refolds very rapidly (with a time constant of 9.4 ms at 0.5 M guanidinium chloride, 25 degrees C) both as a part of IIHY-G3P(*) and as an isolated protein fragment. The refolding of domain N2 is slower and involves two reactions with time constants of seven seconds and 42 seconds. These folding reactions of the individual domains are followed by a very slow, spectroscopically silent docking process, which shows a time constant of 6200 seconds. This reaction was detected by a kinetic unfolding assay for native molecules. Before docking, N1 and N2 unfold fast and independently, after docking they unfold slowly in a correlated fashion. A high energy barrier is thus created by domain docking, which protects G3P kinetically against unfolding. The slow domain docking is possibly important for the infection of E.coli by the phage. Upon binding to the F pilus, the N2 domain separates from N1 and the binding site for TolA on domain N1 is exposed. Since domain reassembly is so slow, this binding site remains accessible until pilus retraction has brought N1 close to TolA on the bacterial surface.     

Dynamics of hydrogen bond desolvation in protein folding

As proteins fold, a progressive structuring, immobilization and eventual exclusion of water surrounding backbone hydrogen bonds takes place. This process turns hydrogen bonds into major determinants of the folding pathway and compensates for the penalty of desolvation of the backbone polar groups. Taken as an average over all hydrogen bonds in a native fold, this extent of protection is found to be nearly ubiquitous. It is dynamically crucial, determining a constraint in the long-time limit behavior of coarse-grained ab initio simulations. Furthermore, an examination of one of the longest available (1micros) all-atom simulations with explicit solvent reveals that this average extent of protection is a constant of motion for the folding trajectory. We propose how such a stabilization is best achieved by clustering five hydrophobes around the backbone hydrogen bonds, an arrangement that yields the optimal stabilization. Our results support and clarify the view that hydrophobic surface burial should be commensurate with hydrogen-bond formation and enable us to define a basic desolvation motif inherent to structure and folding dynamics.     

Origin of unusual phi-values in protein folding: evidence against specific nucleation sites

phi(f)-value analysis is one of the most common methods to characterize the structure of protein folding transition states. It compares the effects of mutations on the folding kinetics with the respective effects on equilibrium stability. The interpretation of the results usually focuses on a few unusual phi(f)-values, which are either particularly high or which are larger than 1 or smaller than 0. These mutations are believed to affect the most important regions for the folding process. A major uncertainty in experimental phi(f)-values is introduced by the commonly used analysis of only a single mutant at various positions in a protein (two-point analysis). To test the reliability of two-point phi(f)-values we used reference data from three positions in two different proteins at which multiple mutations have been introduced. The results show that two-point phi(f)-values are highly inaccurate if the difference in stability between two variants is less than 7 kJ/mol, corresponding to a 20-fold difference in equilibrium constant. Comparison with reported phi(f)-values for 11 proteins shows that most unusual phi(f)-values are observed in mutants which show changes in protein stability that are too small to allow a reliable analysis. The results argue against specific nucleation sites in protein folding and give a picture of transition states as distorted native states for the major part of a protein or for large substructures.     

The protein folding network

The conformation space of a 20 residue antiparallel beta-sheet peptide, sampled by molecular dynamics simulations, is mapped to a network. Snapshots saved along the trajectory are grouped according to secondary structure into nodes of the network and the transitions between them are links. The conformation space network describes the significant free energy minima and their dynamic connectivity without requiring arbitrarily chosen reaction coordinates. As previously found for the Internet and the World-Wide Web as well as for social and biological networks, the conformation space network is scale-free and contains highly connected hubs like the native state which is the most populated free energy basin. Furthermore, the native basin exhibits a hierarchical organization, which is not found for a random heteropolymer lacking a predominant free-energy minimum. The network topology is used to identify conformations in the folding transition state (TS) ensemble, and provides a basis for understanding the heterogeneity of the TS and denatured state ensemble as well as the existence of multiple pathways.     

Simulation and experiment at high temperatures: ultrafast folding of a thermophilic protein by nucleation-condensation

We used Phi-value analysis to characterise the transition state for folding of a thermophilic protein at the relatively high temperature of 325 K. PhiF values for the folding of the three-helix bundle, peripheral subunit binding domain from Bacillus stearothermophilus (E3BD) were determined by temperature-jump experiments in the absence of chemical denaturants. E3BD folded in microseconds through a highly diffuse transition state. Excellent agreement was observed between experiment and the results from eight (independent) molecular dynamics simulations of unfolding at 373 K. We used a combination of heteronuclear NMR experiments and molecular dynamics simulations to characterise the denatured ensemble, and found that it contained very little persistent, residual structure. However, those regions that adopt helical structure in the native state were found by simulation to be poised for helix formation in the denatured state. These regions also had significant structure in the transition state for folding. The overall folding pathway appears to be nucleation-condensation.     

Thermodynamics and folding kinetics analysis of the SH3 domain form discrete molecular dynamics

We perform a detailed analysis of the thermodynamics and folding kinetics of the SH3 domain fold with discrete molecular dynamic simulations. We propose a protein model that reproduces some of the experimentally observed thermodynamic and folding kinetic properties of proteins. Specifically, we use our model to study the transition state ensemble of the SH3 fold family of proteins, a set of unstable conformations that fold to the protein native state with probability 1/2. We analyze the participation of each secondary structure element formed at the transition state ensemble. We also identify the folding nucleus of the SH3 fold and test extensively its importance for folding kinetics. We predict that a set of amino acid contacts between the RT-loop and the distal hairpin are the critical folding nucleus of the SH3 fold and propose a hypothesis that explains this result.     

Protein folding kinetics beyond the phi value: using multiple amino acid substitutions to investigate the structure of the SH3 domain folding transition state

The SH3 domain folding transition state structure contains two well-ordered turn regions, known as the diverging turn and the distal loop. In the Src SH3 domain transition state, these regions are stabilized by a hydrogen bond between Glu30 in the diverging turn and Ser47 in the distal loop. We have examined the effects on folding kinetics of amino acid substitutions at the homologous positions (Glu24 and Ser41) in the Fyn SH3 domain. In contrast to most other folding kinetics studies which have focused primarily on non-disruptive substitutions with Ala or Gly, here we have examined the effects of substitutions with diverse amino acid residues. Using this approach, we demonstrate that the transition state structure is generally tolerant to amino acid substitutions. We also uncover a unique role for Ser at position 41 in facilitating folding of the distal loop, which can only be replicated by Asp at the same position. Both these residues appear to accelerate folding through the formation of short-range side-chain to backbone hydrogen bonds. The folding of the diverging turn region is shown to be driven primarily by local interactions. The diverging turn and distal loop regions are found to interact in the transition state structure, but only in the context of particular mutant backgrounds. This work demonstrates that studying the effects of a variety of amino acid substitutions on protein folding kinetics can provide unique insights into folding mechanisms which cannot be obtained by standard Phi value analysis.     

Evidence for sequential barriers and obligatory intermediates in apparent two-state protein folding

Many small proteins fold fast and without detectable intermediates. This is frequently taken as evidence against the importance of partially folded states, which often transiently accumulate during folding of larger proteins. To get insight into the properties of free energy barriers in protein folding we analyzed experimental data from 23 proteins that were reported to show non-linear activation free-energy relationships. These non-linearities are generally interpreted in terms of broad transition barrier regions with a large number of energetically similar states. Our results argue against the presence of a single broad barrier region. They rather indicate that the non-linearities are caused by sequential folding pathways with consecutive distinct barriers and a few obligatory high-energy intermediates. In contrast to a broad barrier model the sequential model gives a consistent picture of the folding barriers for different variants of the same protein and when folding of a single protein is analyzed under different solvent conditions. The sequential model is also able to explain changes from linear to non-linear free energy relationships and from apparent two-state folding to folding through populated intermediates upon single point mutations or changes in the experimental conditions. These results suggest that the apparent discrepancy between two-state and multi-state folding originates in the relative stability of the intermediates, which argues for the importance of partially folded states in protein folding.     

Analysis of the pH-dependent folding and stability of histidine point mutants allows characterization of the denatured state and transition state for protein folding

pH-Dependent studies of the folding kinetics and stability of a set of His to Gln point mutants were used to characterize the denatured state and transition state ensembles for the C-terminal domain of the ribosomal protein L9 (CTL9). CTL9 contains three histidine residues, two of which, H106 and H134, are buried in the native state, while the third, H144, is more exposed. Comparison of the pH-dependent stability calculated using the Tanford-Wyman linkage relationship to the measured values demonstrates that the apparent pK(a) values of the three histidine residues are not significantly perturbed in the denatured state ensemble. Kinetic measurements show that mutation of H134 has a larger effect on the folding process than does mutation of H106 and H144. The Phi-value for H134 is significantly larger than the Phi-values for the other histidine residues, which are near zero at both pH 5.45 and pH 8.0. The Phi-value for H134 is higher, 0.55, at pH 8.0 than at pH 5.45, 0.39. At pH 5.45, H134 is protonated in the unfolded state but deprotonated in the native state, while at pH 8.0 it is deprotonated in both. There is an excellent linear relationship between stability (logK) and folding rates (logk(f)) over the range of pH 5-9 for all mutants. From these plots, the ratio of DeltaQ( not equal)/DeltaQ can be calculated for each mutant. DeltaQ( not equal) is the difference in the number of protons bound to the transition state and to the unfolded state, while DeltaQ represents the difference between folded and denatured state. The linear plots indicate that the relative position of the transition state ensemble as judged by DeltaQ( not equal)/DeltaQ is independent of pH. The linkage analysis is consistent with the Phi-value analysis, showing that H134 is the most critical contributor to the development of pH-dependent interactions, including desolvation effects in the transition state ensemble.     

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.     

Surprisingly high correlation between early and late stages in non-two-state protein folding

We collected quantitative kinetic data on early and late stages of folding in non-two-state proteins from the literature, and studied the relationship between the kinetics of the two stages. There was a surprisingly high correlation between the rate constants of these stages. The correlation coefficient of the logarithmic rate constants was as high as 0.97, which could not be caused by chance. We also studied relationships of the logarithmic rate constants of the two stages with native three-dimensional structures represented by the residue-residue contact map. There were again surprisingly high correlations between the logarithmic rate constants and the number of non-local contact clusters obtained from the contact maps. Because the number of non-local contact clusters represents overall arrangement of substructures in a native protein, the results strongly suggested the importance of the arrangement of the substructures for the kinetics of both early and late stages of protein folding.     

Interpretation of protein folding psi values

The structural characterization of transition states is essential for understanding the mechanism of protein folding. Analyzing the effect of mutations on protein stability and folding kinetics in phi-value analysis is commonly used to gain information about the presence of side-chain interactions in transition states. Recently, specific binding of ligands to engineered binding sites was applied to monitor the formation of local structures in transition states (psi analysis). A surprising result from psi analysis was the presence of parallel folding pathways in all reported studies and a major discrepancy between phi and psi values measured in the same protein. Here, we show that psi values cannot be analyzed in the same way as other rate-equilibrium free energy relationships due to the involvement of bimolecular reactions that may have different dissociation constants for the native, unfolded and transition state. As a consequence, psi values reflect the relative binding energy (kappa) of the transition state only for the extreme values of kappa=0 or kappa=1. In all other cases, non-linear rate-equilibrium free-energy relationships (Leffler plots) are observed. This apparently indicates the presence of parallel folding pathways even if folding occurs over a single homogeneous transition state. Consequently, the results from Leffler plots do not yield information about the structural properties of the transition state. This explains the lack of agreement between results from psi analysis and other methods used to characterize protein folding transition states. We further show that the same considerations apply for the analysis of the effect of pH on protein folding.     

Thermodynamic characterisation of two transition states along parallel protein folding pathways

Recent work has shown that a β-sandwich domain from the human muscle protein titin (TI I27) unfolds via more than one pathway, providing experimental evidence for a long-standing theoretical prediction in protein folding. Here we present a thermodynamic analysis of two transition states along different folding pathways for this protein. The unusual upwards curvature previously observed in the denaturant-dependent unfolding kinetics is increased at both high and low temperatures, indicating that the high denaturant pathway is becoming more accessible. The transition states in each pathway are structurally distinct and have very different heat capacities. Interestingly the nucleation-condensation pathway is dominant at all physiologically relevant temperatures, supporting the suggestion that pathways with diffuse rather than localised transition states have been selected for by evolution to prevent misfolding.