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.     

Contact order revisited: influence of protein size on the folding rate

Guided by the recent success of empirical model predicting the folding rates of small two-state folding proteins from the relative contact order (CO) of their native structures, by a theoretical model of protein folding that predicts that logarithm of the folding rate decreases with the protein chain length L as L(2/3), and by the finding that the folding rates of multistate folding proteins strongly correlate with their sizes and have very bad correlation with CO, we reexamined the dependence of folding rate on CO and L in attempt to find a structural parameter that determines folding rates for the totality of proteins. We show that the Abs_CO = CO x L, is able to predict rather accurately folding rates for both two-state and multistate folding proteins, as well as short peptides, and that this Abs_CO scales with the protein chain length as L(0.70 +/- 0.07) for the totality of studied single-domain proteins and peptides.     

Asymmetric effect of domain interactions on the kinetics of folding in yeast phosphoglycerate kinase

The aim of this work is to shed more light on the effect of domain-domain interactions on the kinetics and the pathway of protein folding. A model protein system consisting of several single-tryptophan variants of the two-domain yeast phosphoglycerate kinase (PGK) and its individual domains was studied. Refolding was initiated from the guanidine-unfolded state by stopped-flow or manual mixing and monitored by tryptophan fluorescence from 1 msec to 1000 sec. Denaturant titrations of both individual domains showed apparent two-state unfolding transitions. Refolding kinetics of the individual domains from different denaturant concentrations, however, revealed the presence of intermediate structures during titration for both domains. Refolding of the same domains within the complete protein showed that domain-domain interactions direct the folding of both domains, but in an asymmetric way. Folding of the N domain was already altered within 1 msec, while detectable changes in the folding of the C domain occurred only 60-100 msec after initiating refolding. All mutants showed a hyperfluorescent kinetic intermediate. Both the disappearance of this intermediate and the completion of the folding were significantly faster in the individual N domain than in the complete protein. On the contrary, folding of the individual C domain was slower than in the complete protein. The presence of the C domain directs the refolding of the N domain along a completely different pathway than that of the individual N domain, while folding of the individual C domain follows the same path as within the complete protein.     

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.     

Topological frustration and the folding of interleukin-1 beta

The cytokine, interleukin-1beta (IL-1beta), adopts a beta-trefoil fold. It is known to be much slower folding than similarly sized proteins, despite having a low contact order. Proteins are sufficiently well designed that their folding is not dominated by local energetic traps. Therefore, protein models that encode only the folded structure and are energetically unfrustrated (Gō-type), can capture the essentials of the folding routes. We investigate the folding thermodynamics of IL-1beta using such a model and molecular dynamics (MD) simulations. We develop an enhanced sampling technique (a modified multicanonical method) to overcome the sampling problem caused by the slow folding. We find that IL-1beta has a broad and high free energy barrier. In addition, the protein fold causes intermediate unfolding and refolding of some native contacts within the protein along the folding trajectory. This "backtracking" occurs around the barrier region. Complex folds like the beta-trefoil fold and functional loops like the beta-bulge of IL-1beta can make some of the configuration space unavailable to the protein and cause topological frustration.     

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.     

Predicting repeat protein folding kinetics from an experimentally determined folding energy landscape

The Notch ankyrin domain is a repeat protein whose folding has been characterized through equilibrium and kinetic measurements. In previous work, equilibrium folding free energies of truncated constructs were used to generate an experimentally determined folding energy landscape (Mello and Barrick, Proc Natl Acad Sci USA 2004;101:14102–14107). Here, this folding energy landscape is used to parameterize a kinetic model in which local transition probabilities between partly folded states are based on energy values from the landscape. The landscape‐based model correctly predicts highly diverse experimentally determined folding kinetics of the Notch ankyrin domain and sequence variants. These predictions include monophasic folding and biphasic unfolding, curvature in the unfolding limb of the chevron plot, population of a transient unfolding intermediate, relative folding rates of 19 variants spanning three orders of magnitude, and a change in the folding pathway that results from C‐terminal stabilization. These findings indicate that the folding pathway(s) of the Notch ankyrin domain are thermodynamically selected: the primary determinants of kinetic behavior can be simply deduced from the local stability of individual repeats.     

Revisiting the folding kinetics of bacteriorhodopsin

The elucidation of the physical principles that govern the folding and stability of membrane proteins is one of the greatest challenges in protein science. Several insights into the folding of α-helical membrane proteins have come from the investigation of the conformational equilibrium of H. halobium bacteriorhodopsin (bR) in mixed micelles using SDS as a denaturant. In an effort to confirm that folded bR and SDS-denatured bR reach the same conformational equilibrium, we found that bR folding is significantly slower than has been previously known. Interrogation of the effect of the experimental variables on folding kinetics reveals that the rate of folding is dependent not only on the mole fraction of SDS but also on the molar concentrations of mixed micelle components, a variable that was not controlled in the previous study of bR folding kinetics. Moreover, when the molar concentrations of mixed micelle components are fixed at the concentrations commonly employed for bR equilibrium studies, conformational relaxation in the transition zone is slower than hydrolysis of the retinal Schiff base. As a result, the conformational equilibrium between folded bR and SDS-denatured bR cannot be achieved under the conventional condition. Our finding suggests that the molar concentrations of mixed micelle components are important experimental variables in the investigation of the kinetics and thermodynamics of bR folding and should be accounted for to ensure the accurate assessment of the conformational equilibrium of bR without the interference of retinal hydrolysis.     

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.     

A comprehensive database of verified experimental data on protein folding kinetics

Insights into protein folding rely increasingly on the synergy between experimental and theoretical approaches. Developing successful computational models requires access to experimental data of sufficient quantity and high quality. We compiled folding rate constants for what initially appeared to be 184 proteins from 15 published collections/web databases. To generate the highest confidence in the dataset, we verified the reported lnk_f value and exact experimental construct and conditions from the original experimental report(s). The resulting comprehensive database of 126 verified entries, ACPro, will serve as a freely accessible resource ( https://www.ats.amherst.edu/protein/ ) for the protein folding community to enable confident testing of predictive models. In addition, we provide a streamlined submission form for researchers to add new folding kinetics results, requiring specification of all the relevant experimental information according to the standards proposed in 2005 by the protein folding consortium organized by Plaxco. As the number and diversity of proteins whose folding kinetics are studied expands, our curated database will enable efficient and confident incorporation of new experimental results into a standardized collection. This database will support a more robust symbiosis between experiment and theory, leading ultimately to more rapid and accurate insights into protein folding, stability, and dynamics.     

Chain length is the main determinant of the folding rate for proteins with three-state folding kinetics

We demonstrate that chain length is the main determinant of the folding rate for proteins with the three-state folding kinetics. The logarithm of their folding rate in water (k(f)) strongly anticorrelates with their chain length L (the correlation coefficient being -0.80). At the same time, the chain length has no correlation with the folding rate for two-state folding proteins (the correlation coefficient is -0.07). Another significant difference of these two groups of proteins is a strong anticorrelation between the folding rate and Baker's "relative contact order" for the two-state folders and the complete absence of such correlation for the three-state folders.     

Protein folding: defining a "standard" set of experimental conditions and a preliminary kinetic data set of two-state proteins

Recent years have seen the publication of both empirical and theoretical relationships predicting the rates with which proteins fold. Our ability to test and refine these relationships has been limited, however, by a variety of difficulties associated with the comparison of folding and unfolding rates, thermodynamics, and structure across diverse sets of proteins. These difficulties include the wide, potentially confounding range of experimental conditions and methods employed to date and the difficulty of obtaining correct and complete sequence and structural details for the characterized constructs. The lack of a single approach to data analysis and error estimation, or even of a common set of units and reporting standards, further hinders comparative studies of folding. In an effort to overcome these problems, we define here a "consensus" set of experimental conditions (25 degrees C at pH 7.0, 50 mM buffer), data analysis methods, and data reporting standards that we hope will provide a benchmark for experimental studies. We take the first step in this initiative by describing the folding kinetics of 30 apparently two-state proteins or protein domains under the consensus conditions. The goal of our efforts is to set uniform standards for the experimental community and to initiate an accumulating, self-consistent data set that will aid ongoing efforts to understand the folding process.     

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.     

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.     

Folding thermodynamics and kinetics of the leucine-rich repeat domain of the virulence factor Internalin B

Although the folding of alpha-helical repeat proteins has been well characterized, much less is known about the folding of repeat proteins containing beta-sheets. Here we investigate the folding thermodynamics and kinetics of the leucine-rich repeat (LRR) domain of Internalin B (InlB), an extracellular virulence factor from the bacterium Lysteria monocytogenes. This domain contains seven tandem leucine-rich repeats, of which each contribute a single beta-strand that forms a continuous beta-sheet with neighboring repeats, and an N-terminal alpha-helical capping motif. Despite its modular structure, InlB folds in an equilibrium two-state manner, as reflected by the identical thermodynamic parameters obtained by monitoring its sigmoidal urea-induced unfolding transition by different spectroscopic probes. Although equilibrium two-state folding is common in alpha-helical repeat proteins, to date, InlB is the only beta-sheet-containing repeat protein for which this behavior is observed. Surprisingly, unlike other repeat proteins exhibiting equilibrium two-state folding, InlB also folds by a simple two-state kinetic mechanism lacking intermediates, aside from the effects of prolyl isomerization on the denatured state. However, like other repeat proteins, InlB also folds significantly more slowly than expected from contact order. When plotted against urea, the rate constants for the fast refolding and single unfolding phases constitute a linear chevron that, when fitted with a kinetic two-state model, yields thermodynamic parameters matching those observed for equilibrium folding. Based on these kinetic parameters, the transition state is estimated to comprise 40% of the total surface area buried upon folding, indicating that a large fraction of the native contacts are formed in the rate-limiting step to folding.     

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.     

Kinetics of folding and unfolding of goat alpha-lactalbumin

The equilibrium unfolding and the kinetic folding and unfolding of goat alpha-lactalbumin (GLA) were studied by near- and far-ultraviolet circular dichroism (CD) and by stopped-flow fluorescence spectroscopy. Specifically, the influence of environmental conditions such as pH and Ca2+ binding was examined. Compared to the apo-form, the Ca2+-bound form was found to be strongly stabilized in equilibrium conditions at pH 7.5 and 25 degrees C. The kinetics of the refolding of apo-GLA show a major change of fluorescence intensity during the experimental dead-time, but this unresolved effect is strongly diminished in holo-GLA. In both cases, however, the chevron plots can adequately be fitted to a three-state model. Moreover, double-mix stopped-flow experiments showed that the native state (N) is reached through one major pathway without the occurrence of alternative tracks. In contrast to the homologous bovine alpha-lactalbumin (BLA), the compactness of GLA is strongly influenced by the presence of Ca2+ ions. Unlike the two-state transition observed in guanidine hydrochloride (GdnHCl)-induced equilibrium denaturation experiments at higher pH, an equilibrium intermediate state (I) is involved in denaturation at pH 4.5. In the latter case, analysis of the kinetic data makes clear that the intermediate and the unfolded states (U) show practically no Gibbs free energy difference and that they are in rapid equilibrium with each other. A possible explanation for these variations in stability and in folding characteristics with pH could be the degree of protonation of His107 that directly influences non-native interactions. Variation of environmental conditions and even small differences in sequence, therefore, can result in important effects on thermodynamic and folding parameters.     

Charge-charge interactions in the denatured state influence the folding kinetics of ribonuclease Sa

Gaining a better understanding of the denatured state ensemble of proteins is important for understanding protein stability and the mechanism of protein folding. We studied the folding kinetics of ribonuclease Sa (RNase Sa) and a charge-reversal variant (D17R). The refolding kinetics are similar, but the unfolding rate constant is 10-fold greater for the variant. This suggests that charge-charge interactions in the denatured state and the transition state ensembles are more favorable in the variant than in RNase Sa, and shows that charge-charge interactions can influence the kinetics and mechanism of protein folding.