Two-State Folding of Lysozyme Versus Multiple-State Folding of α-Lactalbumin Illustrated by the Technique of Disulfide Scrambling

The folding of lysozyme and of alpha-lactalbumin exhibits vastly different kinetics and pathways. Existing evidence indicates that folding intermediates of alphaLA form a well-populated equilibrium molten globule state that is absent in the case of hen lysozyme. We demonstrate here such divergent folding mechanisms of lysozyme and alphaLA using the technique of disulfide scrambling. Two extensively unfolded homologous isomers (beads-form) of lysozyme (Cys6-Cys30, Cys64-Cys76, Cys80-Cys94, Cys115-Cys127) and alphaLA (Cys6-Cys28, Cys61-Cys73, Cys77-Cys91, Cys111-Cys120) were allowed to refold in parallel to form the native protein. Folding kinetics was measured by the recovery of the native structure. Folding intermediates, which illustrate the folding pathway, were trapped by quenching disulfide shuffling and were analyzed by reversed-phase high-pressure liquid chromatography. The results revealed that under identical folding conditions, the folding rate of lysozyme is about 30-fold faster than that of alphaLA. Folding intermediates of lysozyme are far less heterogeneous and sparsely populated than those of alphaLA. Numerous predominant on-pathway and off-pathway intermediates observed along the folding pathway of alphaLA are conspicuously absent in the case of lysozyme. The difference is most striking under fast folding conditions performed in the presence of protein disulfide isomerase. Under these conditions, folding of lysozyme undergoes a near two-state mechanism without accumulation of stable folding intermediates.     

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.     

Is protein folding rate dependent on number of folding stages? Modeling of protein folding with ferredoxin-like fold

Statistical analysis of protein folding rates has been done for 84 proteins with available experimental data. A surprising result is that the proteins with multi-state kinetics from the size range of 50–100 amino acid residues (a.a.) fold as fast as proteins with two-state kinetics from the same size range. At the same time, the proteins with two-state kinetics from the size range 101–151 a.a. fold faster than those from the size range 50–100 a.a. Moreover, it turns out unexpectedly that usually in the group of structural homologs from the size range 50–100 a.a., proteins with multi-state kinetics fold faster than those with two-state kinetics. The protein folding for six proteins with a ferredoxin-like fold and with a similar size has been modeled using Monte Carlo simulations and dynamic programming. Good correlation between experimental folding rates, some structural parameters, and the number of Monte Carlo steps has been obtained. It is shown that a protein with multi-state kinetics actually folds three times faster than its structural homologs.     

Compactness determines protein folding type

We have demonstrated here that protein compactness, which we define as the ratio of the accessible surface area of a protein to that of the ideal sphere of the same volume, is one of the factors determining the mechanism of protein folding. Proteins with multi-state kinetics, on average, are more compact (compactness is 1.49 +/- 0.02 for proteins within the size range of 101-151 amino acid residues) than proteins with two-state kinetics (compactness is 1.59 +/- 0.03 for proteins within the same size range of 101-151 amino acid residues). We have shown that compactness for homologous proteins can explain both the difference in folding rates and the difference in folding mechanisms.     

Towards a consistent modeling of protein thermodynamic and kinetic cooperativity: how applicable is the transition state picture to folding and unfolding?

To what extent do general features of folding/unfolding kinetics of small globular proteins follow from their thermodynamic properties? To address this question, we investigate a new simplified protein chain model that embodies a cooperative interplay between local conformational preferences and hydrophobic burial. The present four-helix-bundle 55mer model exhibits protein-like calorimetric two-state cooperativity. It rationalizes native-state hydrogen exchange observations. Our analysis indicates that a coherent, self-consistent physical account of both the thermodynamic and kinetic properties of the model leads naturally to the concept of a native state ensemble that encompasses considerable conformational fluctuations. Such a multiple-conformation native state is seen to involve conformational states similar to those revealed by native-state hydrogen exchange. Many of these conformational states are predicted to lie below native baselines commonly used in interpreting calorimetric data. Folding and unfolding kinetics are studied under a range of intrachain interaction strengths as in experimental chevron plots. Kinetically determined transition midpoints match well with their thermodynamic counterparts. Kinetic relaxations are found to be essentially single-exponential over an extended range of model interaction strengths. This includes the entire unfolding regime and a significant part of a folding regime with a chevron rollover, as has been observed for real proteins that fold with non-two-state kinetics. The transition state picture of protein folding and unfolding is evaluated by comparing thermodynamic free energy profiles with actual kinetic rates. These analyses suggest that some chevron rollovers may arise from an internal frictional effect that increasingly impedes chain motions with more native conditions, rather than being caused by discrete deadtime folding intermediates or shifts of the transition state peak as previously posited.     

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.     

Secondary structure length as a determinant of folding rate of proteins with two- and three-state kinetics

We present a simple method for determining the folding rates of two- and three-state proteins from the number of residues in their secondary structures (secondary structure length). The method is based on the hypothesis that two- and three-state foldings share a common pattern. Three-state proteins first condense into metastable intermediates, subsequent forming of alpha-helices, turns, and beta-sheets at slow rate-limiting step. The folding rate of such proteins anticorrelate with the length of these beta-secondary structures. It is also assumed that in two-state folding, rapidly folded alpha-helices and turns may facilitate formation of fleeting unobservable intermediates and thus show two-state behavior. There is an inverse relationship between the folding rate and the length of beta-sheets and loops. Our study achieves 94.0 and 88.1% correlations with folding rates determined experimentally for 21 three- and 38 two-state proteins, respectively, suggesting that protein-folding rates are determined by the secondary structure length. The kinetic kinds are selected on the basis of a competitive formation of hydrophobic collapse and alpha-structure in early intermediates.     

How the folding rates of two‐ and multistate proteins depend on the amino acid properties

Proteins fold by either two‐state or multistate kinetic mechanism. We observe that amino acids play different roles in different mechanism. Many residues that are easy to form regular secondary structures (α helices, β sheets and turns) can promote the two‐state folding reactions of small proteins. Most of hydrophilic residues can speed up the multistate folding reactions of large proteins. Folding rates of large proteins are equally responsive to the flexibility of partial amino acids. Other properties of amino acids (including volume, polarity, accessible surface, exposure degree, isoelectric point, and phase transfer energy) have contributed little to folding kinetics of the proteins. Cysteine is a special residue, it triggers two‐state folding reaction and but inhibits multistate folding reaction. These findings not only provide a new insight into protein structure prediction, but also could be used to direct the point mutations that can change folding rate. Proteins 2014; 82:2375–2382. © 2014 Wiley Periodicals, Inc.     

Determination of protein folding kinetic types using sequence and predicted secondary structure and solvent accessibility

Proteins fold through a two-state (TS), with no visible intermediates, or a multi-state (MS), via at least one intermediate, process. We analyze sequence-derived factors that determine folding types by introducing a novel sequence-based folding type predictor called FOKIT. This method implements a logistic regression model with six input features which hybridize information concerning amino acid composition and predicted secondary structure and solvent accessibility. FOKIT provides predictions with average Matthews correlation coefficient (MCC) between 0.58 and 0.91 measured using out-of-sample tests on four benchmark datasets. These results are shown to be competitive or better than results of four modern predictors. We also show that FOKIT outperforms these methods when predicting chains that share low similarity with the chains used to build the model, which is an important advantage given the limited number of annotated chains. We demonstrate that inclusion of solvent accessibility helps in discrimination of the folding kinetic types and that three of the features constitute statistically significant markers that differentiate TS and MS folders. We found that the increased content of exposed Trp and buried Leu are indicative of the MS folding, which implies that the exposure/burial of certain hydrophobic residues may play important role in the formation of the folding intermediates. Our conclusions are supported by two case studies.     

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.     

Monte Carlo Simulations of Proteins in Cages: Influence of Confinement on the Stability of Intermediate States

We study the folding of small proteins inside confining potentials. Proteins are described using an effective potential model that contains the Ramachandran angles as degrees of freedom and does not need any a priori information about the native state. Hydrogen bonds, dipole-dipole-, and hydrophobic interactions are taken explicitly into account. An interesting feature displayed by this potential is the presence of metastable intermediates between the unfolded and native states. We consider different types of confining potentials to describe proteins folding inside cages with repulsive or attractive walls. Using the Wang-Landau algorithm, we determine the density of states and analyze in detail the thermodynamical properties of the confined proteins for different sizes of the cages. We show that confinement dramatically reduces the phase space available to the protein and that the presence of intermediate states can be controlled by varying the properties of the confining potential. Cages with strongly attractive walls destabilize the intermediate states and lead to a two-state folding into a configuration that is less stable than the native structure. However, cages with slightly attractive walls enhance the stability of native structure and induce a folding process, which occurs through intermediate configurations.     

Protein folding rates estimated from contact predictions

Folding rates of small single-domain proteins that fold through simple two-state kinetics can be estimated from details of the three-dimensional protein structure. Previously, predictions of secondary structure had been exploited to predict folding rates from sequence. Here, we estimate two-state folding rates from predictions of internal residue-residue contacts in proteins of unknown structure. Our estimate is based on the correlation between the folding rate and the number of predicted long-range contacts normalized by the square of the protein length. It is well known that long-range order derived from known structures correlates with folding rates. The surprise was that estimates based on very noisy contact predictions were almost as accurate as the estimates based on known contacts. On average, our estimates were similar to those previously published from secondary structure predictions. The combination of these methods that exploit different sources of information improved performance. It appeared that the combined method reliably distinguished fast from slow two-state folders.     

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.     

Folding Nuclei in Proteins

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed in the vicinity of the equilibrium point. Here the two-state transition proceeds without any accumulation of metastable intermediates, and only the transition state (folding nucleus) is outlined by its key influence on the folding/unfolding kinetics. This review covers recent experimental and theoretical studies of folding nuclei.     

Kinetics of folding nuclei formation in proteins

When a protein folds or unfolds, it passes through many half-folded microstates. Only a few of them can accumulate and be seen experimentally, and this happens only when the folding (or unfolding) occurs far from the point of thermodynamic equilibrium between the native and denatured states. The universal features of folding, though, are observed in the vicinity of the equilibrium point. Here the "two-state" transition proceeds without any accumulation of metastable intermediates, and only the transition state ("folding nucleus") is outlined by its key influence on the folding/unfolding kinetics. This review covers recent experimental and theoretical studies of folding nuclei.     

Disulfide formation and stability of a cysteine-rich repeat protein from Helicobacter pylori

Helicobacter pylori cysteine-rich proteins (Hcps) are disulfide-containing repeat proteins. The repeating unit is a 36-residue, disulfide-bridged, helix-loop-helix motif. We use the protein HcpB, which has four repeats and four disulfide bridges arrayed in tandem, as a model to determine the thermodynamic stability of a disulfide-rich repeat protein and to study the formation and the contribution to stability of the disulfide bonds. When the disulfide bonds are intact, the chemical unfolding of HcpB at pH 5 is cooperative and can be described by a two-state reaction. Thermal unfolding is reversible between pH 2 and 5 and irreversible at higher pH 5. Differential scanning calorimetry shows noncooperative structural changes preceding the main thermal unfolding transition. Unfolding of the oxidized protein is not an all-or-none two-state process, and the disulfide bonds prevent complete unfolding of the polypeptide chain. The reduced protein is significantly less stable and does not unfold in a cooperative way. During oxidative refolding of the fully reduced protein, all the possible disulfide intermediates with a correct disulfide bond are formed. Formation of "wrong" (non-native) disulfide bonds could not be demonstrated, indicating that the reduced protein already has some partial repeating structure. There is a major folding intermediate with disulfides in the second, third, and fourth repeat and reduced cysteines in the first repeat. Disulfide formation in the first repeat limits the overall rate of oxidative refolding and contributes about half of the thermodynamic stability to native HcpB, estimated as 27 kJ mol(-1) at 25 degrees C and pH 7. The high contribution to stability of the first repeat may be explained by the repeat acting as a cap to protect the hydrophobic interior of the molecule.     

Folding and unfolding mechanism of highly stable full-consensus ankyrin repeat proteins

Full-consensus designed ankyrin repeat proteins were designed with one to six identical repeats flanked by capping repeats. These proteins express well in Escherichia coli as soluble monomers. Compared to our previously described designed ankyrin repeat protein library, randomized positions have now been fixed according to sequence statistics and structural considerations. Their stability increases with length and is even higher than that of library members, and those with more than three internal repeats are resistant to denaturation by boiling or guanidine hydrochloride. Full denaturation requires their heating in 5 M guanidine hydrochloride. The folding and unfolding kinetics of the proteins with up to three internal repeats were analyzed, as the other proteins could not be denatured. Folding is monophasic, with a rate that is nearly identical for all proteins (∼ 400-800 s^− 1), indicating that essentially the same transition state must be crossed, possibly the folding of a single repeat. In contrast, the unfolding rate decreases by a factor of about 10⁴ with increasing repeat number, directly reflecting thermodynamic stability in these extraordinarily slow denaturation rates. The number of unfolding phases also increases with repeat number. We analyzed the folding thermodynamics and kinetics both by classical two-state and three-state cooperative models and by an Ising-like model, where repeats are considered as two-state folding units that can be stabilized by interacting with their folded nearest neighbors. This Ising model globally describes both equilibrium and kinetic data very well and allows for a detailed explanation of the ankyrin repeat protein folding mechanism.     

Cooperativity,smooth energy landscapes and the origins of topology-dependent protein folding rates

The relative folding rates of simple, single-domain proteins, proteins whose folding energy landscapes are smooth, are highly dispersed and strongly correlated with native-state topology. In contrast, the relative folding rates of small, Gō-potential lattice polymers, which also exhibit smooth energy landscapes, are poorly dispersed and insignificantly correlated with native-state topology. Here, we investigate this discrepancy in light of a recent, quantitative theory of two-state folding kinetics, the topomer search model. This model stipulates that the topology-dependence of two-state folding rates is a direct consequence of the extraordinarily cooperative equilibrium folding of simple proteins. We demonstrate that traditional Gō polymers lack the extreme cooperativity that characterizes the folding of naturally occurring, two-state proteins and confirm that the folding rates of a diverse set of Gō 27-mers are poorly dispersed and effectively uncorrelated with native state topology. Upon modestly increasing the cooperativity of the Gō-potential, however, significantly increased dispersion and strongly topology-dependent kinetics are observed. These results support previous arguments that the cooperative folding of simple, single-domain proteins gives rise to their topology-dependent folding rates. We speculate that this cooperativity, and thus, indirectly, the topology-rate relationship, may have arisen in order to generate the smooth energetic landscapes upon which rapid folding can occur.     

Oxidative folding of conotoxins sharing an identical disulfide bridging framework

Conotoxins are short, disulfide-rich peptide neurotoxins produced in the venom of predatory marine cone snails. It is generally accepted that an estimated 100,000 unique conotoxins fall into only a handful of structural groups, based on their disulfide bridging frameworks. This unique molecular diversity poses a protein folding problem of relationships between hypervariability of amino acid sequences and mechanism(s) of oxidative folding. In this study, we present a comparative analysis of the folding properties of four conotoxins sharing an identical pattern of cysteine residues forming three disulfide bridges, but otherwise differing significantly in their primary amino acid sequence. Oxidative folding properties of M-superfamily conotoxins GIIIA, PIIIA, SmIIIA and RIIIK varied with respect to kinetics and thermodynamics. Based on rates for establishing the steady-state distribution of the folding species, two distinct folding mechanisms could be distinguished: first, rapid-collapse folding characterized by very fast, but low-yield accumulation of the correctly folded form; and second, slow-rearrangement folding resulting in higher accumulation of the properly folded form via the reshuffling of disulfide bonds within folding intermediates. Effects of changing the folding conditions indicated that the rapid-collapse and the slow-rearrangement mechanisms were mainly determined by either repulsive electrostatic or productive noncovalent interactions, respectively. The differences in folding kinetics for these two mechanisms were minimized in the presence of protein disulfide isomerase. Taken together, folding properties of conotoxins from the M-superfamily presented in this work and from the O-superfamily published previously suggest that conotoxin sequence diversity is also reflected in their folding properties, and that sequence information rather than a cysteine pattern determines the in vitro folding mechanisms of conotoxins.     

The kinetic pathway of folding of barnase

To search for folding intermediates, we have examined the folding and unfolding kinetics of wild-type barnase and four representative mutants under a wide range of conditions that span two-state and multi-state kinetics. The choice of mutants and conditions provided in-built controls for artifacts that might distort the interpretation of kinetics, such as the non-linearity of kinetic and equilibrium data with concentration of denaturant. We measured unfolding rate constants over a complete range of denaturant concentration by using by 1H/2H-exchange kinetics under conditions that favour folding, conventional stopped-flow methods at higher denaturant concentrations and continuous flow. Under conditions that favour multi-state kinetics, plots of the rate constants for unfolding against denaturant concentration fitted quantitatively to the equation for three-state kinetics, with a sigmoid component for a change of rate determining step, as did the refolding kinetics. The position of the transition state on the reaction pathway, as measured by solvent exposure (the Tanford beta value) also moved with denaturant concentration, fitting quantitatively to the same equations with a change of rate determining step. The sigmoid behaviour disappeared under conditions that favoured two-state kinetics. Those data combined with direct structural observations and simulation support a minimal reaction pathway for the folding of barnase that involves two detectable folding intermediates. The first intermediate, I(1), is the denatured state under physiological conditions, D(Phys), which has native-like topology, is lower in energy than the random-flight denatured state U and is suggested by molecular dynamics simulation of unfolding to be on-pathway. The second intermediate, I(2), is high energy, and is proven by the change in rate determining step in the unfolding kinetics to be on-pathway. The change in rate determining step in unfolding with structure or environment reflects the change in partitioning of this intermediate to products or starting materials.