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.     

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.     

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.     

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".     

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.     

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.     

Application of dynamic light scattering to studies of protein folding kinetics

The applicability of dynamic light scattering to studies of the kinetics of unfolding and refolding reactions of proteins is discussed and demonstrated experimentally. The experimental set-up and the data acquisition and data evaluation schemes that have been optimized for kinetic experiments are described. The relationship of the signal-to-noise ratio to the minimum data acquisition time that is needed to obtain results of sufficiently high precision is discussed. It turns out that the attainable time resolution is of the order of a few seconds for proteins with molar masses of about 50,000 g · mol^–1 and concentrations of 1 g · l^–1. Thus, DLS is too slow to follow conformational changes in the subsecond region, but it is useful for studies of unfolding-refolding reactions of proteins that proceed with time constants in the range of seconds or minutes. This is demonstrated by investigations of the kinetics of the cold denaturation of 3-phosphoglycerate kinase from yeast.Abbreviations DLS dynamic light scattering - PGK 3-phosphoglycerate kinase - EDTA ethylenediamine tetraacetic acid - GuHCl guanidine hydrochloride - DTT dithiothreitol     

The use of pressure-jump relaxation kinetics to study protein folding landscapes

Pressure-jump induced relaxation kinetics can be used to study both protein unfolding and refolding. These processes can be initiated by upward and downward pressure-jumps of amplitudes of a few 10 to 100 MPa, with a dead-time on the order of milliseconds. In many cases, the relaxation times can be easily determined when the pressure cell is connected to a spectroscopic detection device, such as a spectrofluorimeter. Adiabatic heating or cooling can be limited by small pressure-jump amplitudes and a special design of the sample cell. Here, we discuss the application of this method to four proteins: 33-kDa and 23-kDa proteins from photo-system II, a variant of the green fluorescent protein, and a fluorescent variant of ribonuclease A. The thermodynamically predicted equivalency of upward and downward pressure-jump induced protein relaxation kinetics for typical two-state folders was observed for the 33-kDa protein, only. In contrast, the three other proteins showed significantly different kinetics for pressure-jumps in opposite directions. These results cannot be explained by sequential reaction schemes. Instead, they are in line with a more complex free energy landscape involving multiple pathways.     

Probing the kinetics of single molecule protein folding

We propose an approach to integrate the theory, simulations, and experiments in protein-folding kinetics. This is realized by measuring the mean and high-order moments of the first-passage time and its associated distribution. The full kinetics is revealed in the current theoretical framework through these measurements. In the experiments, information about the statistical properties of first-passage times can be obtained from the kinetic folding trajectories of single molecule experiments (for example, fluorescence). Theoretical/simulation and experimental approaches can be directly related. We study in particular the temperature-varying kinetics to probe the underlying structure of the folding energy landscape. At high temperatures, exponential kinetics is observed; there are multiple parallel kinetic paths leading to the native state. At intermediate temperatures, nonexponential kinetics appears, revealing the nature of the distribution of local traps on the landscape and, as a result, discrete kinetic paths emerge. At very low temperatures, exponential kinetics is again observed; the dynamics on the underlying landscape is dominated by a single barrier. The ratio between first-passage-time moments is proposed to be a good variable to quantitatively probe these kinetic changes. The temperature-dependent kinetics is consistent with the strange kinetics found in folding dynamics experiments. The potential applications of the current results to single-molecule protein folding are discussed.     

The building block folding model and the kinetics of protein folding.

Here we show that qualitatively, the building blocks folding model accounts for three-state versus the two-state protein folding. Additionally, it is consistent with the faster versus slower folding rates of the two-state proteins. Specifically, we illustrate that the building blocks size, their mode of associations in the native structure, the number of ways they can combinatorially assemble, their population times and the way they are split in the iterative, step-by-step structural dissection which yields the anatomy trees, explain a broad range of folding rates. We further show that proteins with similar general topologies may have different folding pathways, and hence different folding rates. On the other hand, the effect of mutations resembles that of changes in conditions, shifting the population times and hence the energy landscapes. Hence, together with the secondary structure type and the extent of local versus non-local interactions, a coherent, consistent rationale for folding kinetics can be outlined, in agreement with experimental results. Given the native structure of a protein, these guidelines enable a qualitative prediction of the folding kinetics. We further describe these in the context of the protein folding energy landscape. Quantitatively, in principle, the diffusion-collision model for the building block association can be used. However, the folding rates of the building blocks and traps in their formation and association, need to be considered.     

GANDivAWeb: A web server for detecting early folding units ("foldons") from protein 3D structures

Background  

It has long been known that small regions of proteins tend to fold independently and are then stabilized by interactions between these distinct subunits or modules. Such units, also known as autonomous folding units (AFUs) or"foldons" play a key role in protein folding. A knowledge of such early folding units has diverse applications in protein engineering as well as in developing an understanding of the protein folding process. Such AFUs can also be used as model systems in order to study the structural organization of proteins.     

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.     

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.