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.     

Differentiation between two-state and multi-state folding proteins based on sequence

Prediction of protein-folding rates follows different rules in two-state and multi-state kinetics. The prerequisite for the prediction is to recognize the folding kinetic pathway of proteins. Here, we use the logistic regression and support vector machine to discriminate between two-state and multi-state folding proteins. We find that chain length is sufficient to accurately recognize multi-state proteins. There is a transition boundary between two kinetic models. Protein folds with multi-state kinetics, if its length is larger than 112 residues. The logistic prediction from amino acid composition shows that the kinetic pathway of folding is closely related to amino acid volume. Small amino acids make two-state folding easier, and vice versa. However, cysteine, alanine, arginine, lysine, histidine, and methionine do not conform to this rule.     

Pathways in two-state protein folding

Thermodynamic measurements of proteins indicate that the folding to the native state takes place either through stable intermediates or through a two-state process without intermediates. The rather short folding times of proteins indicate that folding is guided through some sequence of contact bindings. We discuss the possibility of reconciling a two-state folding event with a sequential folding process in a schematic model of protein folding. We propose a new dynamical transition temperature that is lower than the temperature at which proteins in equilibrium unfold. This is in qualitative agreement with observations of in vivo protein folding activity quantified by chaperone concentration in Escherichia coli. Finally, we discuss our framework in connection with the unfolding of proteins at low temperatures.     

Topology, stability, sequence, and length: defining the determinants of two-state protein folding kinetics

The fastest simple, single domain proteins fold a million times more rapidly than the slowest. Ultimately this broad kinetic spectrum is determined by the amino acid sequences that define these proteins, suggesting that the mechanisms that underlie folding may be almost as complex as the sequences that encode them. Here, however, we summarize recent experimental results which suggest that (1) despite a vast diversity of structures and functions, there are fundamental similarities in the folding mechanisms of single domain proteins and (2) rather than being highly sensitive to the finest details of sequence, their folding kinetics are determined primarily by the large-scale, redundant features of sequence that determine a protein's gross structural properties. That folding kinetics can be predicted using simple, empirical, structure-based rules suggests that the fundamental physics underlying folding may be quite straightforward and that a general and quantitative theory of protein folding rates and mechanisms (as opposed to unfolding rates and thus protein stability) may be near on the horizon.     

Diffusional barrier crossing in a two-state protein folding reaction.

There has been some debate as to whether protein folding involves diffusive chain motions and thus depends on solvent viscosity. The interpretation of folding kinetics in viscous solvents has remained difficult and controversial, in that viscogenic agents affect folding rates not only by increasing solvent viscosity but also by increasing protein stability. By carefully choosing experimental conditions, we can now eliminate the effect on stability and show that the folding dynamics of the cold shock protein CspB are viscosity dependent. Thus Kramers' theory of reaction rates rather than transition state theory should be used to describe this folding reaction.     

A fusion tag to fold on: the S-layer protein SgsE confers improved folding kinetics to translationally fused enhanced green fluorescent protein

Genetic fusion of two proteins frequently induces beneficial effects to the proteins, such as increased solubility, besides the combination of two protein functions. Here, we study the effects of the bacterial surface layer protein SgsE from Geobacillus stearothermophilus NRS 2004/3a on the folding of a C-terminally fused enhanced green fluorescent protein (EGFP) moiety. Although GFPs are generally unable to adopt a functional confirmation in the bacterial periplasm of Escherichia coli cells, we observed periplasmic fluorescence from a chimera of a 150-amino-acid N-terminal truncation of SgsE and EGFP. Based on this finding, unfolding and refolding kinetics of different S-layer-EGFP chimeras, a maltose binding protein-EGFP chimera, and sole EGFP were monitored using green fluorescence as indicator for the folded protein state. Calculated apparent rate constants for unfolding and refolding indicated different folding pathways for EGFP depending on the fusion partner used, and a clearly stabilizing effect was observed for the SgsE_C fusion moiety. Thermal stability, as determined by differential scanning calorimetry, and unfolding equilibria were found to be independent of the fused partner. We conclude that the stabilizing effect SgsE_C exerts on EGFP is due to a reduction of degrees of freedom for folding of EGFP in the fused state.     

Robustness of protein folding kinetics to surface hydrophobic substitutions

We use both combinatorial and site-directed mutagenesis to explore the consequences of surface hydrophobic substitutions for the folding of two small single domain proteins, the src SH3 domain, and the IgG binding domain of Peptostreptococcal protein L. We find that in almost every case, destabilizing surface hydrophobic substitutions have much larger effects on the rate of unfolding than on the rate of folding, suggesting that nonnative hydrophobic interactions do not significantly interfere with the rate of core assembly.     

Future directions in folding: The multi-state nature of protein structure

All possible protein folding intermediates exist in equilibrium with the native protein at native as well as non-native conditions, with occupation determined by their free energy level. The study of these forms can illuminate the fundamental principles of protein structure and folding. Hydrogen exchange methods can be used to detect and characterize these partially unfolded forms at native conditions and as a function of mild denaturant and temperature. This information illuminates the requirements that govern the ability of kinetic and equilibrium methods to study folding intermediates.     

Exploring the relationship between funneled energy landscapes and two-state protein folding

It should take an astronomical time span for unfolded protein chains to find their native state based on an unguided conformational random search. The experimental observation that folding is fast can be rationalized by assuming that protein energy landscapes are sloped towards the native state minimum, such that rapid folding can proceed from virtually any point in conformational space. Folding transitions often exhibit two-state behavior, involving extensively disordered and highly structured conformers as the only two observable kinetic species. This study employs a simple Brownian dynamics model of "protein particles" moving in a spherically symmetrical potential. As expected, the presence of an overall slope towards the native state minimum is an effective means to speed up folding. However, the two-state nature of the transition is eradicated if a significant energetic bias extends too far into the non-native conformational space. The breakdown of two-state cooperativity under these conditions is caused by a continuous conformational drift of the unfolded proteins. Ideal two-state behavior can only be maintained on surfaces exhibiting large regions that are energetically flat, a result that is supported by other recent data in the literature (Kaya and Chan, Proteins: Struct Funct Genet 2003;52:510-523). Rapid two-state folding requires energy landscapes exhibiting the following features: (i) A large region in conformational space that is energetically flat, thus allowing for a significant degree of random sampling, such that unfolded proteins can retain a random coil structure; (ii) a trapping area that is strongly sloped towards the native state minimum.     

Evolutionary conservation in protein folding kinetics

The sequence and structural conservation of folding transition states have been predicted on theoretical grounds. Using homologous sequence alignments of proteins previously characterized via coupled mutagenesis/kinetics studies, we tested these predictions experimentally. Only one of the six appropriately characterized proteins exhibits a statistically significant correlation between residues' roles in transition state structure and their evolutionary conservation. However, a significant correlation is observed between the contributions of individual sequence positions to the transition state structure across a set of homologous proteins. Thus the structure of the folding transition state ensemble appears to be more highly conserved than the specific interactions that stabilize it.     

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.     

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.     

Complex folding kinetics of a multidomain protein

Spectrin domains are three-helix bundles, commonly found in large tandem arrays. Equilibrium studies have shown that spectrin domains are significantly stabilized by their neighbors. In this work we show that domain:domain interactions can also have profound effects on their kinetic behavior. We have studied the folding of a tandem pair of spectrin domains (R1617) using a combination of single- and double-jump stopped flow experiments (monitoring folding by both circular dichroism and fluorescence). Mutant proteins were also used to investigate the complex folding kinetics. We find that, although the domains fold and unfold individually, there is a single rate-determining step for both folding and unfolding of the protein. This is consistent with the equilibrium observation of cooperative folding of the entire two-domain protein. The results may have important biological implications. Not only will the protein fold more efficiently during cotranslational folding, but the ability of the multidomain protein to withstand thermal unfolding in the cell will be dramatically increased. This study suggests that caution has to be exercised when extrapolating from single domains to larger proteins with a number of independently folding modules arranged in tandem. The multidomain protein spectrin is certainly more than "the sum of its parts".     

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.     

ALASKA: A Mathematica package for two-state kinetic analysis of protein folding reactions

A Mathematica package (ALASKA) has been developed to simplify the measurement of protein folding kinetics by analysis of ¹H NMR lineshape analysis. This package reads NMR data in ASCII format and can simulate an aromatic ¹ NMR spectrum with or without lineshape broadening from chemical exchange. We describe the analysis of a urea denaturation series of a fast-folding protein, the G46A/G48A variant of monomeric repressor.     

Formation of short-lived protein aggregates directly from the coil in two-state folding.

Recent results on the 102 residue protein U1A show that protein aggregation is not always slow and irreversible but may take place transiently in refolding studies on a millisecond time scale. In this study we observe a similar aggregation behavior with the classical two-state protein CI2. Since both U1A and CI2 appear to fold directly from the coil at low protein concentrations, it is likely that the aggregates also form directly from the coil. This is in contrast to the behavior of larger multistate proteins where aggregation occurs in connection to "sticky" intermediates.