Molecular dynamics simulations of folding processes of a beta-hairpin in an implicit solvent

Computer simulations of beta-hairpin folding are relatively difficult, especially those based on the explicit water model. This greatly limits the complete analysis and understanding of their folding mechanisms. In this paper, we use the generalized Born/solvent accessible implicit solvent model to simulate the folding processes of a nine-residue beta-hairpin. We find that the beta-hairpin can fold into its native structure very easily, even using the traditional molecular dynamics method. This allows us to extract 21 complete folding events and investigate the folding process sufficiently. Our results show that there exist four most stable states on the free energy landscape of the short peptide, one native state and three intermediates. We find that two of the non-native stable states have almost the same potential energy as the native state but with lower entropy. This suggests that the native state can be stabilized entropically. Furthermore, we find that the folding processes of this peptide have common features: to fold into its native state, the peptide undergoes a continuous collapsing-extending-recollapsing process to adjust the positions of the side chains in order to form the native middle inter-strand hydrogen bonds. The formations of these bonds are the key step of the folding process. Once these bonds are formed, the peptide can fold into the native state quickly.     

Folding and unfolding of gammaTIM monomers and dimers

Kinetic simulations of the folding and unfolding of triosephosphate isomerase (TIM) from yeast were conducted using a single monomer gammaTIM polypeptide chain that folds as a monomer and two gammaTIM chains that fold to the native dimer structure. The basic protein model used was a minimalist Gō model using the native structure to determine attractive energies in the protein chain. For each simulation type--monomer unfolding, monomer refolding, dimer unfolding, and dimer refolding--thirty simulations were conducted, successfully capturing each reaction in full. Analysis of the simulations demonstrates four main conclusions. First, all four simulation types have a similar "folding order", i.e., they have similar structures in intermediate stages of folding between the unfolded and folded state. Second, despite this similarity, different intermediate stages are more or less populated in the four different simulations, with 1), no intermediates populated in monomer unfolding; 2), two intermediates populated with beta(2)-beta(4) and beta(1)-beta(5) regions folded in monomer refolding; 3), two intermediates populated with beta(2)-beta(3) and beta(2)-beta(4) regions folded in dimer unfolding; and 4), two intermediates populated with beta(1)-beta(5) and beta(1)-beta(5) + beta(6) + beta(7) + beta(8) regions folded in dimer refolding. Third, simulations demonstrate that dimer binding and unbinding can occur early in the folding process before complete monomer-chain folding. Fourth, excellent agreement is found between the simulations and MPAX (misincorporation proton alkyl exchange) experiments. In total, this agreement demonstrates that the computational Gō model is accurate for gammaTIM and that the energy landscape of gammaTIM appears funneled to the native state.     

Conformation and thermodynamic stability of pre-molten and molten globule states of mammalian cytochromes-c

Proteins in cells fold via a number of intermediates. These intermediates are quite important as they guide the protein to attain its unique native conformation. To solve the immensely difficult problem of protein folding, it is necessary to characterize intermediates which will unravel the mystery of the steps involved in the proper folding of proteins. Cytochromes-c (cyts-c) have played an important role in studies of the earliest events and intermediates in protein folding. They have always been considered as model proteins for protein folding studies due to their intrinsic properties that can be measured by multiple probes. A large number of different solvent conditions have been employed to obtain equilibrium intermediates of cyts-c. These intermediates show structural heterogeneity which is mainly due to the different solvent conditions used to induce them. In this review we present results of conformational and thermodynamic characterization of equilibrium intermediates (molten globules and pre-molten globules) of the mammalian cyts-c under different solvent conditions.     

Structure of a rapidly formed intermediate in ribonuclease T1 folding.

Kinetic intermediates in protein folding are short-lived and therefore difficult to detect and to characterize. In the folding of polypeptide chains with incorrect isomers of Xaa-Pro peptide bonds the final rate-limiting transition to the native state is slow, since it is coupled to prolyl isomerization. Incorrect prolyl isomers thus act as effective traps for folding intermediates and allow their properties to be studied more easily. We employed this strategy to investigate the mechanism of slow folding of ribonuclease T1. In our experiments we use a mutant form of this protein with a single cis peptide bond at proline 39. During refolding, protein chains with an incorrect trans proline 39 can rapidly form extensive secondary structure. The CD signal in the amide region is regained within the dead-time of stopped-flow mixing (15 ms), indicating a fast formation of the single alpha-helix of ribonuclease T1. This step is correlated with partial formation of a hydrophobic core, because the fluorescence emission maximum of tryptophan 59 is shifted from 349 nm to 325 nm within less than a second. After about 20 s of refolding an intermediate is present that shows about 40% enzymatic activity compared to the completely refolded protein. In addition, the solvent accessibility of tryptophan 59 is drastically reduced in this intermediate and comparable to that of the native state as determined by acrylamide quenching of the tryptophan fluorescence. Activity and quenching measurements have long dead-times and therefore we do not know whether enzymatic activity and solvent accessibility also change in the time range of milliseconds. At this stage of folding at least part of the beta-sheet structure is already present, since it hosts the active site of the enzyme. The trans to cis isomerization of the tyrosine 38-proline 39 peptide bond in the intermediate and consequently the formation of native protein is very slow (tau = 6,500 s at pH 5.0 and 10 degrees C). It is accompanied by an additional increase in tryptophan fluorescence, by the development of the fine structure of the tryptophan emission spectrum, and by the regain of the full enzymatic activity. This indicates that the packing of the hydrophobic core, which involves both tryptophan 59 and proline 39, is optimized in this step. Apparently, refolding polypeptide chains with an incorrect prolyl isomer can very rapidly form partially folded intermediates with native-like properties.     

Thermodynamics and kinetics of protein folding: an evolutionary perspective

This article appeals to an evolutionary model which postulates that primordial proteins were described by small polypeptide chains which (i) lack disulfide bridges, and (ii) display slow folding rates with multi-state kinetics, to determine relations between structural properties of proteins and their folding kinetics. We parameterize the energy landscape of proteins in terms of thermodynamic activation variables. The model studies evolutionary changes in these thermodynamic parameters, and we invoke relations between these activation variables and structural properties of the protein to predict the following correspondence between protein structure and folding kinetics. 1. Proteins with inter- and intra-chain disulfide bridges: large variability in both folding rates and stability of intermediates, multi-state kinetics. 2. Proteins which lack inter and intra-chain disulfide bridges. 2.1 Single-domain chains: fast folding rates; unstable intermediates; two-state kinetics. 2.2 Multi-domain monomers: intermediate rates; metastable intermediates; multi-state kinetics. 2.3 Multi-domain oligomers: slow rates; metastable intermediates; multi-state kinetics. The evolutionary model thus provides a kinetic characterization of one important subfamily of proteins which we describe by the following properties: Folding dynamics of single-domain proteins which lack disulfide bridges are described by two-state kinetics. Folding rate of this class of proteins is positively correlated with the thermodynamic stability of the folded state.     

The folding pathway of barnase: the rate-limiting transition state and a hidden intermediate under native conditions

The nature of the rate-limiting transition state at zero denaturant (TS(1)) and whether there are hidden intermediates are the two major unsolved problems in defining the folding pathway of barnase. In earlier studies, it was shown that TS(1) has small phi values throughout the structure of the protein, suggesting that the transition state has either a defined partially folded secondary structure with all side chains significantly exposed or numerous different partially unfolded structures with similar stability. To distinguish the two possibilities, we studied the effect of Gly mutations on the folding rate of barnase to investigate the secondary structure formation in the transition state. Two mutations in the same region of a beta-strand decreased the folding rate by 20- and 50-fold, respectively, suggesting that the secondary structures in this region are dominantly formed in the rate-limiting transition state. We also performed native-state hydrogen exchange experiments on barnase at pD 5.0 and 25 degrees C and identified a partially unfolded state. The structure of the intermediate was investigated using protein engineering and NMR. The results suggest that the intermediate has an omega loop unfolded. This intermediate is more folded than the rate-limiting transition state previously characterized at high denaturant concentrations (TS(2)). Therefore, it exists after TS(2) in folding. Consistent with this conclusion, the intermediate folds with the same rate and denaturant dependence as the wild-type protein, but unfolds faster with less dependence on the denaturant concentration. These and other results in the literature suggest that barnase folds through partially unfolded intermediates that exist after the rate-limiting step. Such folding behavior is similar to those of cytochrome c and Rd-apocyt b(562). Together, we suggest that other small apparently two-state proteins may also fold through hidden intermediates.     

Protein surface mapping by chemical oxidation: structural analysis by mass spectrometry

The solvent-accessible surface area of proteins is important in biological function for many reasons, including protein-protein interactions, protein folding, and catalytic sites. Here we present a chemical technique to oxidize amino acid side chains in a model protein, apomyoglobin, and subsequent elucidation of the effect of solvent accessibility on the sites of oxidation. Under conditions of low protein oxidation (zero to three oxygen atoms added per apomyoglobin molecule), we have positively identified five oxidation sites by liquid chromatography-tandem mass spectrometry and high-resolution Fourier transform mass spectrometry. Our results indicate that all oxidized amino acids, with the exception of methionine, have highly solvent-accessible side chains, but the rate of oxidation may not be dictated solely by solvent accessibility and amino acid identity.     

Solvent entropy-driven searching for protein modeling examined and tested in simplified models.

Solvent entropy is a force to consider in protein folding and protein design but is difficult to model. It is investigated here in the context of the hp model: Two types of residues, hydrophobic and hydrophilic, are modeled on a lattice. Nine chains and two- and three-dimensional simulations are compared. We show that considering solvent entropy alone, efficient folding of lattice chains (identification of the native fold) can be achieved by an entropy-driven simulation on its own. Moreover, in a detailed comparison over a wide range of parameters, entropy-guided searching outperforms an energy-driven search in the model. The combination of energy- and entropy-driven search yields the most efficient searching. It is compared in detail with the above results, indicating also how this solvent shell model may advantageously be implemented in more complex protein modeling simulations.     

Smoothing of the GB1 Hairpin Folding Landscape by Interfacial Confinement

We study the effects of confinement between planar walls on the folding thermodynamics of a β-hairpin, using large-scale replica-exchange molecular-dynamics simulations with an all-atom model and explicit solvent. We find that the folding free-energy landscape of this peptide observed in bulk is significantly modified when the peptide is confined between the walls. Most notably, the propensity of the peptide to form a misfolded state observed in the bulk solution becomes negligible under confinement. The absence of the misfolded state under confinement can be explained by an increased tendency of hydrophobic aromatic side chains to stay near the walls, because the misfolded state is characterized by a nonnative arrangement of aromatic side chains. These results from a simple confinement model may provide clues about the role of chaperonin confinement in smoothing folding landscapes by avoiding trapped intermediates.     

Cooperativity of hydrophobic anchor interactions: evidence for epitope selection by MHC class II as a folding process

Peptide binding to MHC class II (MHCII) molecules is stabilized by hydrophobic anchoring and hydrogen bond formation. We view peptide binding as a process in which the peptide folds into the binding groove and to some extent the groove folds around the peptide. Our previous observation of cooperativity when analyzing binding properties of peptides modified at side chains with medium to high solvent accessibility is compatible with such a view. However, a large component of peptide binding is mediated by residues with strong hydrophobic interactions that bind to their respective pockets. If these reflect initial nucleation events they may be upstream of the folding process and not show cooperativity. To test whether the folding hypothesis extends to these anchor interactions, we measured dissociation and affinity to HLA-DR1 of an influenza hemagglutinin-derived peptide with multiple substitutions at major anchor residues. Our results show both negative and positive cooperative effects between hydrophobic pocket interactions. Cooperativity was also observed between hydrophobic pockets and positions with intermediate solvent accessibility, indicating that hydrophobic interactions participate in the overall folding process. These findings point out that predicting the binding potential of epitopes cannot assume additive and independent contributions of the interactions between major MHCII pockets and corresponding peptide side chains.     

Accurate prediction of protein folding rates from sequence and sequence‐derived residue flexibility and solvent accessibility

Protein folding rates vary by several orders of magnitude and they depend on the topology of the fold and the size and composition of the sequence. Although recent works show that the rates can be predicted from the sequence, allowing for high‐throughput annotations, they consider only the sequence and its predicted secondary structure. We propose a novel sequence‐based predictor, PFR‐AF, which utilizes solvent accessibility and residue flexibility predicted from the sequence, to improve predictions and provide insights into the folding process. The predictor includes three linear regressions for proteins with two‐state, multistate, and unknown (mixed‐state) folding kinetics. PFR‐AF on average outperforms current methods when tested on three datasets. The proposed approach provides high‐quality predictions in the absence of similarity between the predicted and the training sequences. The PFR‐AF's predictions are characterized by high (between 0.71 and 0.95, depending on the dataset) correlation and the lowest (between 0.75 and 0.9) mean absolute errors with respect to the experimental rates, as measured using out‐of‐sample tests. Our models reveal that for the two‐state chains inclusion of solvent‐exposed Ala may accelerate the folding, while increased content of Ile may reduce the folding speed. We also demonstrate that increased flexibility of coils facilitates faster folding and that proteins with larger content of solvent‐exposed strands may fold at a slower pace. The increased flexibility of the solvent‐exposed residues is shown to elongate folding, which also holds, with a lower correlation, for buried residues. Two case studies are included to support our findings. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Characterization of a quaternary-structured folding intermediate of an antibody Fab-fragment.

Antibody folding is a complex process comprising folding and association reactions. Although it is usually difficult to characterize kinetic folding intermediates, in the case of the antibody Fab fragment, domain-domain interactions lead to a rate-limiting step of folding, thus accumulating folding intermediates at a late step of folding. Here, we analyzed a late folding intermediate of the Fab fragment of the monoclonal antibody MAK 33 from mouse (kappa/IgG1). As a strategy for accumulation of this intermediate we used partial denaturation of the native Fab by guanidinium chloride. This denaturation intermediate, which can be populated to about 90%, is indistinguishable from a late-folding intermediate with respect to denaturation and renaturation kinetics. The spectroscopic analysis reveals a native-like secondary structure of this intermediate with aromatic side chains only slightly more solvent exposed than in the native state. The respective partner domains are weekly associated. From these data we conclude that the intramolecular association of the two chains during folding, with all domains in a native-like structure, follows a two-step mechanism. In this mechanism, presumably hydrophobic interactions are followed by rearrangements leading to the exact complementarity of the contact sites of the respective domains.     

Simulating RNA folding kinetics on approximated energy landscapes

We present a general computational approach to simulate RNA folding kinetics that can be used to extract population kinetics, folding rates and the formation of particular substructures that might be intermediates in the folding process. Simulating RNA folding kinetics can provide unique insight into RNA whose functions are dictated by folding kinetics and not always by nucleotide sequence or the structure of the lowest free-energy state. The method first builds an approximate map (or model) of the folding energy landscape from which the population kinetics are analyzed by solving the master equation on the map. We present results obtained using an analysis technique, map-based Monte Carlo simulation, which stochastically extracts folding pathways from the map. Our method compares favorably with other computational methods that begin with a comprehensive free-energy landscape, illustrating that the smaller, approximate map captures the major features of the complete energy landscape. As a result, our method scales to larger RNAs. For example, here we validate kinetics of RNA of more than 200 nucleotides. Our method accurately computes the kinetics-based functional rates of wild-type and mutant ColE1 RNAII and MS2 phage RNAs showing excellent agreement with experiment.     

Molecular basis of co-operativity in protein folding. III. Structural identification of cooperative folding units and folding intermediates.

The hierarchical partition function formalism for protein folding developed earlier has been extended through the use of three-dimensional polar and apolar contact plots. For each amino acid residue in the protein, these plots indicate the apolar and polar surfaces that are buried from the solvent, the identity of all amino acid residues that contribute to this shielding, and the magnitude of their contributions. These contact plots are then used to examine the distribution of the free energy of stabilization throughout the protein molecule. Analysis of these data allows identification of co-operative folding units and their hierarchical levels, and the identification of partially folded intermediates with a significant probability of being populated. The overall folding/unfolding thermodynamics of 12 globular proteins, for which crystallographic and experimental thermodynamics are available, is predicted within error. An energetic classification of partially folded intermediates is presented and the results compared to those cases for which structural and thermodynamic experimental information is available. Four different types of partially folded states and their structural energies are considered. (1) Local intermediates, in which only a local region of the protein loses secondary and tertiary interactions, while the rest of the protein remains intact. (2) Global intermediates, corresponding to the standard molten globule definition, in which significant secondary structure is maintained but native-like tertiary structure contacts are disrupted. (3) Extended intermediates characterized by the existence of secondary structure elements (e.g. alpha-helices) exposed to solvent. (4) Folding intermediates in proteins with two structural domains. The structure and energetics of folding intermediates of apo-myoglobin, alpha-lactalbumin, phosphoglycerate kinase and arabinose-binding protein are considered in detail.     

A newly synthesized, ribosome-bound polypeptide chain adopts conformations dissimilar from early in vitro refolding intermediates

Little is known about the conformations of newly synthesized polypeptide chains as they emerge from the large ribosomal subunit, or how these conformations compare with those populated immediately after dilution of polypeptide chains out of denaturant in vitro. Both in vivo and in vitro, partially folded intermediates of the tailspike protein from Salmonella typhimurium phage P22 can be trapped in the cold. A subset of monoclonal antibodies raised against tailspike recognize partially folded intermediates, whereas other antibodies recognize only later intermediates and/or the native state. We have used a pair of monoclonal antibodies to probe the conformational features of full-length, newly synthesized tailspike chains recovered on ribosomes from phage-infected cells. The antibody that recognizes early intermediates in vitro also recognizes the ribosome-bound intermediates. Surprisingly, the antibody that did not recognize early in vitro intermediates did recognize ribosome-bound tailspike chains translated in vivo. Thus, the newly synthesized, ribosome-bound tailspike chains display structured epitopes not detected upon dilution of tailspike chains from denaturant. As opposed to the random ensemble first populated when polypeptide chains are diluted out of denaturant, folding in vivo from the ribosome may begin with polypeptide conformations already directed toward the productive folding and assembly pathway.     

Structural insights into the two sequential folding transition states of the PB1 domain of NBR1 from Φ value analysis and biased molecular dynamics simulations

The PB1 domain of NBR1 folds via a single pathway mechanism involving two sequential energy barriers separated by a high-energy intermediate. The structural ensemble representing each of the two transition states (TS1 and TS2) has been calculated using experimental Φ values and biased molecular dynamics simulations. Both TS1 and TS2 represent compact states (β(TS1) = 0.71, and β(TS2) = 0.93) but are defined by quite different distributions of Φ values, degrees of structural heterogeneity, and nativelike secondary structure. TS1 forms a heterogeneous ensemble of dynamic structures, representing a global collapse of the polypeptide chain around a set of weak nativelike contacts. In contrast, TS2 has a high proportion of nativelike secondary structure, which is reflected in an extensive distribution of high Φ values. Two snapshots along the folding pathway of the PB1 domain reveal insights into the malleability, the solvent accessibility, and the timing of nativelike core packing that stabilizes the folded state.     

Solvent accessibility, protein surfaces, and protein folding.

Studies of the native structures of proteins, together with measurements of the thermodynamic properties of the transition between unfolded and native states, have defined the major components of the forces that stabilize native protein structures. However, the nature of the intermediates in the folding process remains largely hypothetical. It is a fairly widespread and not implausible assumption that the intermediates in the folding of a monomeric protein contain the same kinds of secondary and tertiary structures that appear in the native conformation, and that, although unstable, their lifetimes are prolonged by forces similar to those that stabilize the native structure. We wished to examine what happens if, during the folding of a monomeric protein, regions of secondary structure come together to form an intermediate of reduced instability. We applied calculations of accessible surface area (a measure of hydrophobic stabilization) and parameterized nonbonded energy calculations (measuring the strengths of van der Waals forces) to identify the kinds of stabilizing interactions that might be available to such an intermediate. First, we analyzed the total buried surface area of two types of proteins into contributions from formation of secondary structure alone, interaction of pairs of secondary-structural elements, the formation of the structure alone, interaction of pairs of secondary-structural elements, the formation of the complete secondary structure without the turns, and the complete native structure. The formation of secondary structure alone, without tertiary-structural interactions, buries roughly half the surface that the complete structure does. We then analyzed in more detail the approach of two alpha-helices to form a complex, as an illustrative example of the nature of the interaction between compact structural units which remain fairly rigid during their interaction. Many features of the results are not limited to the interaction of alpha-helices. (The results therefore neither confirm nor refute the hypothesis that alpha-helices are intermediates in the folding proteins). We find that the first forces to be felt upon approach arise from solvent conditions on the relative position and orientation of the two helices as does the close packing which optimizes the van der Waals interactions at shorter distances apart. Therefore there appears to be a range of distances in which hydrophobic interactions could create a nonspecific complex between two helices in which the side chains might have sufficient time to seek the proper interdigitation observed in the native structure, where the two helices are in intimate contact. Indeed, we find that only in the final stages of approach is the native geometry the most stable; in the region in which solvent-exclusion forces predominate, the conformation with helix axes parallel is more stable than the native conformation, in the cases we examined...     

Solvent accessibility and purifying selection within proteins of Escherichia coli and Salmonella enterica

The neutral theory of molecular evolution predicts that variation within species is inversely related to the strength of purifying selection, but the strength of purifying selection itself must be related to physical constraints imposed by protein folding and function. In this paper, we analyzed five enzymes for which polymorphic sequence variation within Escherichia coli and/or Salmonella enterica was available, along with a protein structure. Single and multivariate logistic regression models are presented that evaluate amino acid size, physicochemical properties, solvent accessibility, and secondary structure as predictors of polymorphism. A model that contains a positive coefficient of association between polymorphism and solvent accessibility and separate intercepts for each secondary-structure element is sufficient to explain the observed variation in polymorphism between sites. The model predicts an increase in the probability of amino acid polymorphism with increasing solvent accessibility for each protein regardless of physicochemical properties, secondary-structure element, or size of the amino acid. This result, when compared with the distribution of synonymous polymorphism, which shows no association with solvent accessibility, suggests a strong decrease in purifying selection with increasing solvent accessibility.     

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.     

The mechanism of folding of pancreatic ribonucleases is independent of the presence of covalently linked carbohydrate

The role of asparagine-linked oligosaccharides for the mechanism of protein folding was investigated. We compared the stability and folding kinetics for two sets of pancreatic ribonucleases (RNases) with identical amino acid sequences and differences in glycosylation. First the folding of RNases A (carbohydrate free) and B (a single N-linked oligosaccharide) from bovine pancreas was investigated. The kinetics of refolding were identical under a wide range of conditions. The rate of unfolding by guanidinium chloride was decreased in RNase B. In further experiments the folding of porcine RNase (three carbohydrate chains at Asn-21, -34, and -76) was compared with the corresponding data for the deglycosylated protein. Even for this RNase with almost 40% carbohydrate content the mechanism of refolding is independent of glycosylation. Although the folding mechanism is conserved, the rates of individual steps in folding are decreased about 2-fold upon deglycosylation. We interpret this to originate from a slight destabilization of folding intermediates by carbohydrate depletion. In control experiments with nonglycosylated bovine RNase A it was ascertained that treatment with HF (as used for deglycosylation) did not affect the folding kinetics. The in vitro folding mechanism of glycosylated RNases apparently does not depend on the presence of N-linked oligosaccharide chains. The information for the folding of glycoproteins is contained exclusively in the protein moiety, i.e. in the amino acid sequence. Carbohydrate chains are attached at chain positions which remain solvent exposed. This ensures that the presence of oligosaccharides does not interfere with correct folding of the polypeptide chain.