What determines protein folding type? An investigation of intrinsic structural properties and its implications for understanding folding mechanisms

Protein folding experiments demonstrate that the folding behaviors of many proteins can be roughly classified into two types: two-state kinetics and multi-state kinetics. Although the two types of protein folding kinetics have been observed for a long time, what determines the folding type of a protein is still largely unclear. The present work performed a comparative study based on a dataset of 43 two-state and 42 multi-state folders at different levels of proteins' intrinsic properties from the simplest sequence length to native structure topology. The results show that protein's amino acids composition and the long-range interaction-based topological complexity rather than secondary structure contents are the major determinants of protein folding type. Furthermore, a sequence-based folding type prediction achieved an accuracy of more than 80%. These findings implicate that there is no clear boundary between secondary and tertiary structure formation during the protein folding process and support the existence of a continuum of folding mechanism between the two ends of hierarchic and nucleation folding scenarios.     

Toward minimalist models of larger proteins: a ubiquitin-like protein

Our recently developed off-lattice bead model capable of simulating protein structures with mixed alpha/beta content has been extended to model the folding of a ubiquitin-like protein and provides a means for examining the more complex kinetics involved in the folding of larger proteins. Using trajectories generated from constant-temperature Langevin dynamics simulations and sampling with the multiple multi-histogram method over five-order parameters, we are able to characterize the free energy landscape for folding and find evidence for folding through compact intermediates. Our model reproduces the observation that the C-terminus loop structure in ubiquitin is the last to fold in the folding process and most likely plays a spectator role in the folding kinetics. The possibility of a productive metastable intermediate along the folding pathway consisting of collapsed states with no secondary structure, and of intermediates or transition structures involving secondary structural elements occurring early in the sequence, is also supported by our model. The kinetics of folding remain multi-exponential below the folding temperature, with glass-like kinetics appearing at T/T(f) approximately 0.86. This new physicochemical model, designed to be predictive, helps validate the value of modeling protein folding at this level of detail for genomic-scale studies, and motivates further studies of other protein topologies and the impact of more complex energy functions, such as the addition of solvation forces.     

Probing the folding and unfolding dynamics of secondary and tertiary structures in a three-helix bundle protein

Fast relaxation kinetics studies of the B-domain of staphylococcal protein A were performed to characterize the folding and unfolding of this small three-helix bundle protein. The relaxation kinetics were initiated using a laser-induced temperature jump and probed using time-resolved infrared spectroscopy. The kinetics monitored within the amide I' absorbance of the polypeptide backbone exhibit two distinct kinetics phases with nanosecond and microsecond relaxation times. The fast kinetics relaxation time is close to the diffusion limits placed on protein folding reactions. The fast kinetics phase is dominated by the relaxation of the solvated helix (nu = 1632 cm(-1)), which reports on the fast relaxation of the individual helices. The slow kinetics phase follows the cooperative relaxation of the native helical bundle core that is monitored by both solvated (nu = 1632 cm(-1)) and buried helical IR bands (nu = 1652 cm(-1)). The folding rates of the slow kinetics phase calculated over an extended temperature range indicate that the core formation of this protein follows a pathway that is energetically downhill. The unfolding rates are much more strongly temperature-dependent indicating an activated process with a large energy barrier. These results provide significant insight into the primary process of protein folding and suggest that fast formation of helices can drive the folding of helical proteins.     

Multiple parallel-pathway folding of proline-free Staphylococcal nuclease

When a protein exhibits complex kinetics of refolding, we often ascribe the complexity to slow isomerization events in the denatured protein, such as cis/trans isomerization of peptidyl prolyl bonds. Does the complex folding kinetics arise only from this well-known reason? Here, we have investigated the refolding of a proline-free variant of staphylococcal nuclease by stopped-flow, double-jump techniques, to examine the folding reactions without the slow prolyl isomerizations. As a result, the protein folds into the native state along at least two accessible parallel pathways, starting from a macroscopically single denatured-state ensemble. The presence of intermediates on the individual folding pathways has revealed the existence of multiple parallel pathways, and is characterized by multi-exponential folding kinetics with a lag phase. Therefore, a "single" amino acid sequence can fold along the multiple parallel pathways. This observation in staphylococcal nuclease suggests that the multiple folding may be more general than we have expected, because the multiple parallel-pathway folding cannot be excluded from proteins that show simpler kinetics.     

Mechanism of induced folding: Both folding before binding and binding before folding can be realized in staphylococcal nuclease mutants

A considerable number of functional proteins are unstructured under physiological condition. These "intrinsically disordered" proteins exhibit induced folding when they bind their targets. The induced folding comprises two elementary processes: folding and binding. Two mechanisms are possible for the induced folding: either folding before binding or binding before folding. We found that these two mechanisms can be distinguished by the target-concentration dependence of folding kinetics. We also created two types of mutants of staphylococcal nuclease showing the different inhibitor-concentration dependence of induced folding kinetics. One mutant obeys the scheme of binding before folding, while the other the folding before binding. This is the first experimental evidence demonstrating that both mechanisms are realized for a single protein. Binding before folding is possible, when the protein lacks essential nonlocal interaction to stabilize the native conformation. The results cast light on the protein folding mechanism involved in the intrinsically disordered proteins.     

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.     

Recombination of S-peptide with S-protein during folding of ribonuclease S. I. Folding pathways of the slow-folding and fast-folding classes of unfolded S-protein.

The refolding kinetics of ribonuclease S have been measured by tyrosine absorbance, by tyrosine fluorescence emission, and by rapid binding of the specific inhibitor 2′CMP ² to folded RNAase S. The S-protein is first unfolded at pH 1.7 and then either mixed with S-peptide as refolding is initiated by a stopped-flow pH jump to pH 6.8, or the same results are obtained if S-protein and S-peptide are present together before refolding is initiated. The refolding kinetics of RNAase S have been measured as a function of temperature (10 to 40 °C) and of protein concentration (10 to 120 μm). The results are compared to the folding kinetics of S-protein alone and to earlier studies of RNAase A. A thermal folding transition of S-protein has been found below 30 °C at pH 1.7; its effects on the refolding kinetics are described in the following paper (Labhardt &; Baldwin, 1979).In this paper we characterize the refolding kinetics of unfolded S-protein, as it is found above 30 °C at pH 1.7, together with the kinetics of combination between S-peptide and S-protein during folding at pH 6.8. Two classes of unfolded S-protein molecules are found, fast-folding and slow-folding molecules, in a 20: 80 ratio. This is the same result as that found earlier for RNAase A; it is expected if the slow-folding molecules are produced by the slow cis-trans isomerization of proline residues after unfolding, since S-protein contains all four proline residues of RNAase A.The refolding kinetics of the fast-folding molecules show clearly that combination between S-peptide and S-protein occurs before folding of S-protein is complete. If combination occurred only after complete folding, then the kinetics of formation of RNAase S should be rather slow (5 s and 100 s at 30 °C) and nearly independent of protein concentration, as shown by separate measurements of the folding kinetics of S-protein, and of the combination between S-peptide and folded S-protein. The observed folding kinetics are faster than predicted by this model and also the folding rate increases strongly with protein concentration (apparent 1.6 order kinetics). The fact that RNAase S is formed more rapidly than S-protein alone is sufficient by itself to show that combination with S-peptide precedes complete folding of S-protein. Computer simulation of a simple, parallel-pathway scheme is able to reproduce the folding kinetics of the fast-folding molecules. All three probes give the same folding kinetics.These results exclude the model for protein folding in which the rate-limiting step is an initial diffusion of the polypeptide chain into a restricted range of three-dimensional configurations (“nueleation”) followed by rapid folding (“propagation”). If this model were valid, one would expect comparable rates of folding for RNAase A and for S-protein and one would also expect to find no populated folding intermediates, so that combination between S-peptide and S-protein should occur after folding is complete. Instead, RNAase A folds 60 times more rapidly than S-protein and also combination with S-peptide occurs before folding of S-protein is complete. The results demonstrate that the folding rate of S-protein increases after the formation, or stabilization, of an intermediate which results from combination with S-peptide. They support a sequential model for protein folding in which the rates of successive steps in folding depend on the stabilities of preceding intermediates.The refolding kinetics of the slow-folding molecules are complex. Two results demonstrate the presence of folding intermediates: (1) the three probes show different kinetic progress curves, and (2) the folding kinetics are concentration-dependent, in contrast to the results expected if complete folding of S-protein precedes combination with S-peptide. A faster phase of the slow-refolding reaction is detected both by tyrosine absorbance and fluorescence emission but not by 2′CMP binding, indicating that native RNAase S is not formed in this phase. Comparison of the kinetic progress curves measured by different probes is made with the use of the kinetic ratio test, which is defined here.     

Analysis of the differences in the folding kinetics of structurally homologous proteins based on predictions of the gross features of residue contacts

It is a general notion that proteins with very similar three-dimensional structures would show very similar folding kinetics. However, recent studies reveal that the folding kinetic properties of some proteins contradict this thought (i.e., the members in a same protein family fold through different pathways). For example, it has been reported that some beta-proteins in the intracellular lipid-binding protein family fold through quite different pathways (Burns et al., Proteins 1998;33:107-118). Similar differences in folding kinetics are also observed in the members of the globin family (Nishimura et al., Nat Struct Biol 2000;7:679-686). In our study, we examine the possibility of predicting qualitative differences in folding kinetics of the intracellular lipid-binding proteins and two globin proteins (i.e., myoglobin and leghemoglobin). The problem is tackled by means of a contact map based on the average distance statistics between residues, the Average Distance Map (ADM), as constructed from sequence. The ADMs for the three proteins show overall similarity, but some local differences among maps are also observed. Our results demonstrate that some properties of the protein folding kinetics are consistent with local differences in the ADMs. We also discuss the general possibility of predicting folding kinetics from sequence information.     

Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures.

We investigate a novel approach for studying the kinetics of protein folding. Our framework has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMs) that have been applied in many diverse fields with great success. In our previous work, we presented our PRM-based technique and obtained encouraging results studying protein folding pathways for several small proteins. In this paper, we describe how our motion planning framework can be used to study protein folding kinetics. In particular, we present a refined version of our PRM-based framework and describe how it can be used to produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap which is computed in a few hours on a desktop PC. Results are presented for 14 proteins. Our ability to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics, such as proteins that exhibit both two-state and three-state kinetics that are not captured by other theoretical techniques.     

Protein folding: then and now

Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.     

The kinetics of bovine growth hormone folding are consistent with a framework model

The framework model of protein folding requires the hydrogen-bonded secondary structure to be formed early in folding (i.e. the formation of secondary structure precedes the tertiary structure) (Kim, P. S., and Baldwin, R. L. (1982) Annu. Rev. Biochem. 51, 459-489). To test the framework model directly the kinetics of bovine growth hormone (bGH) folding were compared utilizing two methods of detection, one that measures the secondary structure (far ultraviolet circular dichroism) and another that measures the tertiary structure (near ultraviolet absorbance). The results demonstrate that, under identical folding conditions, the kinetics observed by far ultraviolet circular dichroism are faster than those observed by ultraviolet absorption. The faster kinetics observed by circular dichroism indicate the existence of a helix-containing intermediate which is consistent with the framework model. The effect of protein concentration and denaturant concentration on the kinetics of refolding were studied. The rate of refolding measured by absorbance and circular dichroism was dependent on protein concentration. The protein concentration dependence on refolding is due to the transient formation of an associated intermediate. The concentration dependence of folding is taken as evidence that folding is a sequential process with partially folded monomers responsible for the observed association effect. At dilute protein concentrations the refolding can be studied independent of the association phenomena. The growth hormones utilized in this study were derived from Escherichia coli through recombinant DNA technology and from bovine pituitaries. The pituitary-derived bGH has been shown to be heterogeneous at the NH2 terminus (Lorenson, M. F., and Ellis, S. (1975) Endocrinology 96, 833-838), whereas the recombinant DNA-derived bGH contains a single NH2 terminus. No differences in the folding kinetics between the recombinant DNA and pituitary derived-bGH were observed. It is concluded that the heterogeneity of the NH2 terminus of growth hormone obtained from bovine pituitaries does not affect the observed in vitro folding kinetics.     

Native geometry and the dynamics of protein folding

In this paper, we investigate the role of native geometry on the kinetics of protein folding based on simple lattice models and Monte Carlo simulations. Results obtained within the scope of the Miyazawa-Jernigan indicate the existence of two dynamical folding regimes depending on the protein chain length. For chains larger than 80 amino acids, the folding performance is sensitive to the native state's conformation. Smaller chains, with less than 80 amino acids, fold via two-state kinetics and exhibit a significant correlation between the contact order parameter and the logarithmic folding times. In particular, chains with N=48 amino acids were found to belong to two broad classes of folding, characterized by different cooperativity, depending on the contact order parameter. Preliminary results based on the Go model show that the effect of long-range contact interaction strength in the folding kinetics is largely dependent on the native state's geometry.     

Simulation and experiment conspire to reveal cryptic intermediates and a slide from the nucleation-condensation to framework mechanism of folding

There is a change from three-state to two-state kinetics of folding across the homeodomain superfamily of proteins as the mechanism slides from framework to nucleation-condensation. The tendency for framework folding in this family correlates with inherent helical propensity. The cellular myeloblastis protein (c-Myb) falls in the mechanistic transition region. An earlier, preliminary report of protein engineering experiments and molecular dynamics simulations (MD) showed that the folding mechanism for this protein has aspects of both the nucleation-condensation and framework models. In the more in-depth analysis of the MD trajectories presented here, we find that folding may be attributed to both of these mechanisms in different regions of the protein. The folding of the loop, middle helix, and turn is best described by nucleation-condensation, whereas folding of the N and C-terminal helices may be described by the framework model. Experimentally, c-Myb folds by apparent two-state kinetics, but the MD simulations predict that the kinetics hide a high-energy intermediate. We stabilized this hypothetical folding intermediate by deleting a residue (P174) in the loop between its second and third helices, and the mutant intermediate is long-lived in the simulations. Equilibrium and kinetic experiments demonstrate that folding of the DeltaP174 mutant is indeed three-state. The presence and shape of the intermediate observed in the simulations were confirmed by small angle X-ray scattering experiments.     

Squeezed exponential kinetics to describe a nonglassy downhill folding as observed in a lattice protein model

We previously studied the so-called strange kinetics in the two-dimensional lattice HP model. To further study the strange kinetics, folding processes of a 27-mer cubic lattice protein model with Gō potential were investigated by simulating how the bundle of folding trajectories, consisting of a number of independent Monte Carlo simulations, evolves as the folding reaction proceeds, covering a wide range of temperature. Three realms of folding kinetics were observed depending on temperature. Although at temperatures where folding was two-state-like, the kinetics was conventional single exponential, we found that the time course data were well represented by a squeezed (or "shrunken") exponential function, exp [-(t/tau)beta] with beta > 1, at temperatures lower than the folding temperature, where folding was fastest and of a nonglassy downhill type. The squeezed exponential kinetics was found to pertain to the subdiffusion on the nonglassy downhill free energy surface and presents a marked contrast both to the single exponential kinetics and to the stretched exponential kinetics that was observed at lower temperatures where folding was also downhill but topological frustration came into effect. The observed temperature dependence of the folding kinetics suggests that some small single-domain proteins may follow the squeezed exponential kinetics at about the room temperature.     

Slow and Bimolecular Folding of a De Novo Designed Monomeric Protein DS119

De novo protein design offers a unique means to test and advance our understanding of how proteins fold. However, most current design methods are native structure eccentric and folding kinetics has rarely been considered in the design process. Here, we show that a de novo designed mini-protein DS119, which folds into a βαβ structure, exhibits unusually slow and concentration-dependent folding kinetics. For example, the folding time for 50 μM of DS119 was estimated to be ∼2 s. Stopped-flow fluorescence resonance energy transfer experiments further suggested that its folding was likely facilitated by a transient dimerization process. Taken together, these results highlight the need for consideration of the entire folding energy landscape in de novo protein design and provide evidence suggesting nonnative interactions can play a key role in protein folding.     

Kinetics analysis methods for approximate folding landscapes

MOTIVATION: Protein motions play an essential role in many biochemical processes. Lab studies often quantify these motions in terms of their kinetics such as the speed at which a protein folds or the population of certain interesting states like the native state. Kinetic metrics give quantifiable measurements of the folding process that can be compared across a group of proteins such as a wild-type protein and its mutants. RESULTS: We present two new techniques, map-based master equation solution and map-based Monte Carlo simulation, to study protein kinetics through folding rates and population kinetics from approximate folding landscapes, models called maps. From these two new techniques, interesting metrics that describe the folding process, such as reaction coordinates, can also be studied. In this article we focus on two metrics, formation of helices and structure formation around tryptophan residues. These two metrics are often studied in the lab through circular dichroism (CD) spectra analysis and tryptophan fluorescence experiments, respectively. The approximated landscape models we use here are the maps of protein conformations and their associated transitions that we have presented and validated previously. In contrast to other methods such as the traditional master equation and Monte Carlo simulation, our techniques are both fast and can easily be computed for full-length detailed protein models. We validate our map-based kinetics techniques by comparing folding rates to known experimental results. We also look in depth at the population kinetics, helix formation and structure near tryptophan residues for a variety of proteins. AVAILABILITY: We invite the community to help us enrich our publicly available database of motions and kinetics analysis by submitting to our server: http://parasol.tamu.edu/foldingserver/.     

Matching simulation and experiment: a new simplified model for simulating protein folding.

Simulations of simplified protein folding models have provided much insight into solving the protein folding problem. We propose here a new off-lattice bead model, capable of simulating several different fold classes of small proteins. We present the sequence for an alpha/beta protein resembling the IgG-binding proteins L and G. The thermodynamics of the folding process for this model are characterized using the multiple multihistogram method combined with constant-temperature Langevin simulations. The folding is shown to be highly cooperative, with chain collapse nearly accompanying folding. Two parallel folding pathways are shown to exist on the folding free energy landscape. One pathway contains an intermediate--similar to experiments on protein G, and one pathway contains no intermediates-similar to experiments on protein L. The folding kinetics are characterized by tabulating mean-first passage times, and we show that the onset of glasslike kinetics occurs at much lower temperatures than the folding temperature. This model is expected to be useful in many future contexts: investigating questions of the role of local versus nonlocal interactions in various fold classes, addressing the effect of sequence mutations affecting secondary structure propensities, and providing a computationally feasible model for studying the role of solvation forces in protein folding.     

Temperature-dependent folding pathways of Pin1 WW domain: an all-atom molecular dynamics simulation of a Gō model

We study the folding thermodynamics and kinetics of the Pin1 WW domain, a three-stranded beta-sheet protein, by using all-atom (except nonpolar hydrogens) discontinuous molecular dynamics simulations at various temperatures with a Gō model. The protein exhibits a two-state folding kinetics near the folding transition temperature. A good agreement between our simulations and the experimental measurements by the Gruebele group has been found, and the simulation sheds new insights into the structure of transition state, which is hard to be straightforwardly captured in experiments. The simulation also reveals that the folding pathways at approximately the transition temperature and at low temperatures are much different, and an intermediate state at a low temperature is predicted. The transition state of this small beta-protein at its folding transition temperature has a well-established hairpin 1 made of beta1 and beta2 strands while its low-temperature kinetic intermediate has a formed hairpin 2 composed of beta2 and beta3 strands. Theoretical results are compared with other simulation results as well as available experimental data. This study confirms that specific side-chain packing in an all-atom Gō model can yield a reasonable prediction of specific folding kinetics for a given protein. Different folding behaviors at different temperatures are interpreted in terms of the interplay of entropy and enthalpy in folding process.     

Effects of mutation, truncation, and temperature on the folding kinetics of a WW domain

The purpose of this work is to show how mutation, truncation, and change of temperature can influence the folding kinetics of a protein. This is accomplished by principal component analysis of molecular-dynamics-generated folding trajectories of the triple β-strand WW domain from formin binding protein 28 (FBP28) (Protein Data Bank ID: 1E0L) and its full-size, and singly- and doubly-truncated mutants at temperatures below and very close to the melting point. The reasons for biphasic folding kinetics [i.e., coexistence of slow (three-state) and fast (two-state) phases], including the involvement of a solvent-exposed hydrophobic cluster and another delocalized hydrophobic core in the folding kinetics, are discussed. New folding pathways are identified in free-energy landscapes determined in terms of principal components for full-size mutants. Three-state folding is found to be a main mechanism for folding the FBP28 WW domain and most of the full-size and truncated mutants. The results from the theoretical analysis are compared to those from experiment. Agreements and discrepancies between the theoretical and experimental results are discussed. Because of its importance in understanding protein kinetics and function, the diffusive mechanism by which the FBP28 WW domain and its full-size and truncated mutants explore their conformational space is examined in terms of the mean-square displacement and principal component analysis eigenvalue spectrum analyses. Subdiffusive behavior is observed for all studied systems.     

Bacterial proteins fold faster than eukaryotic proteins with simple folding kinetics

Protein domain frequency and distribution among kingdoms was statistically analyzed using the SCOP structural database. It appeared that among chosen protein domains with the best resolution, eukaryotic proteins more often belong to α-helical and β-structural proteins, while proteins of bacterial origin belong to α/β structural class. Statistical analysis of folding rates of 73 proteins with known experimental data revealed that bacterial proteins with simple kinetics (23 proteins) exhibit a higher folding rate compared to eukaryotic proteins with simple folding kinetics (27 proteins). Analysis of protein domain amino acid composition showed that the frequency of amino acid residues in proteins of eukaryotic and bacterial origin is different for proteins with simple and complex folding kinetics.