Cunning simplicity of a hierarchical folding

A hierarchic scheme of protein folding does not solve the Levinthal paradox since it cannot provide a simultaneous explanation for major features observed for protein folding: (i) folding within non-astronomical time, (ii) independence of the native structure on large variations in the folding rates of given protein under different conditions, and (iii) co-existence, in a visible quantity, of only the native and the unfolded molecules during folding of moderate size (single-domain) proteins. On the contrary, a nucleation mechanism can account for all these major features simultaneously and resolves the Levinthal paradox.     

Cunning Simplicity of a Hierarchical Folding

Abstract

A hierarchic scheme of protein folding does not solve the Levinthal paradox since it cannot provide a simultaneous explanation for major features observed for protein folding: (i) folding within non-astronomical time, (ii) independence of the native structure on large variations in the folding rates of given protein under different conditions, and (iii) co-existence, in a visible quantity, of only the native and the unfolded molecules during folding of moderate size (single-domain) proteins. On the contrary, a nucleation mechanism can account for all these major features simultaneously and resolves the Levinthal paradox.     

Rate of beta-structure formation in polypeptides

An explanation is suggested for why a marginally stable beta-structure folds extremely slowly; it is predicted that even a small increase in stability drastically accelerates beta-folding. According to the theory, this folding is a first-order phase transition, and the rate-limiting step is nucleation. The rate-determining "nucleus" (transition state) is the smallest beta-sheet that is sufficiently large to provide an overall free energy reduction during subsequent folding. If the stability of the beta-structure is low, the nucleus is large and possesses a high free energy due to having a large perimeter. When the net stability of the final beta-structure increases (due to either an increase of the beta-sheet stability or a decrease in stability of the competing structures, e.g., alpha-helices), the size and energy of a nucleus decrease and the rate of folding increases exponentially. This must result in a fast folding of polypeptides enriched by beta-forming residues (e.g., protein chains). The theory is developed for intramolecular beta-structure, but it can also explain the overall features of intermolecular beta-folding; it is applicable both to antiparallel and parallel beta-sheets. The difference in folding of beta-sheets, alpha-helices, and proteins is discussed.     

Alternate pathways for folding in the flavodoxin fold family revealed by a nucleation-growth model

A recent study of experimental results for flavodoxin-like folds suggests that proteins from this family may exhibit a similar, signature pattern of folding intermediates. We study the folding landscapes of three proteins from the flavodoxin family (CheY, apoflavodoxin, and cutinase) using a simple nucleation and growth model that accurately describes both experimental and simulation results for the transition state structure, and the structure of on-pathway and misfolded intermediates for CheY. Although the landscape features of these proteins agree in basic ways with the results of the study, the simulations exhibit a range of folding behaviours consistent with two alternate folding routes corresponding to nucleation and growth from either side of the central beta-strand.     

Non-native interactions play an effective role in protein folding dynamics

Systematic Monte Carlo simulations of simple lattice models show that the final stage of protein folding is an ordered process where native contacts get locked (i.e., the residues come into contact and remain in contact for the duration of the folding process) in a well‐defined order. The detailed study of the folding dynamics of protein‐like sequences designed as to exhibit different contact energy distributions, as well as different degrees of sequence optimization (i.e., participation of non‐native interactions in the folding process), reveals significant differences in the corresponding locking scenarios—the collection of native contacts and their average locking times, which are largely ascribable to the dynamics of non‐native contacts. Furthermore, strong evidence for a positive role played by non‐native contacts at an early folding stage was also found. Interestingly, for topologically simple target structures, a positive interplay between native and non‐native contacts is observed also toward the end of the folding process, suggesting that non‐native contacts may indeed affect the overall folding process. For target models exhibiting clear two‐state kinetics, the relation between the nucleation mechanism of folding and the locking scenario is investigated. Our results suggest that the stabilization of the folding transition state can be achieved through the establishment of a very small network of native contacts that are the first to lock during the folding process.     

Helix folding simulations with various initial conformations.

Using a solvent-referenced energy calculation, a 16-residue peptide with alanine side chains folded into predominantly alpha-helical conformations during constant temperature (274 K) simulations. From different initial conformations, helical conformations were reached and the multiple energy minima did not become a serious problem. Under the same conditions, the simulation did not indiscriminately fold a sequence such as polyglycine into stable helices. Interesting observations from the simulations relate to the folding mechanism. The electrostatic interactions between the successive amides favored extended conformations (or beta strands) and caused energy barriers to helix folding. beta-bends were observed as intermediates during helix nucleation. The helix propagation toward the C-terminus seemed faster than that toward the N-terminus. In helical conformations, hydrogen bond oscillation between the i,i+ 4 and the i,i+3 patterns was observed. The i,i+3 hydrogen bonds occurred more frequently during helix propagation and deformation near both ends of the helical segment.     

Exploring structures in protein folding funnels with free energy functionals: the transition state ensemble

We use free energy functionals that account for the partial ordering of residues in the transition state ensemble to characterize the free energy surfaces for fast folding proteins. We concentrate on chymotrypsin inhibitor and lambda-repressor. We show how the explicit cooperativity that can arise from many body forces, such as side-chain ordering or hydrophobic surface burial, determines the crossover from folding with a large delocalized nucleus and the specific small classical nucleus of the type envisioned in nucleation growth scenarios. We compare the structural correlations present in the transition state ensemble obtained from free energy functionals with those inferred from experiment using extrathermodynamic free energy relations for folding time obtained via protein engineering kinetics experiments. We also use the free energy functionals to examine both the size of barriers and multidimensional representations of the free energy profiles in order to address the question of appropriate reaction coordinates for folding.     

The SH3-fold family: experimental evidence and prediction of variations in the folding pathways

To investigate the relationships between protein topology, amino acid sequence and folding mechanisms, the folding transition state of the Sso7d protein has been characterised both experimentally and theoretically. Although Sso7d protein has a similar topology to that of the SH3 domains, the structure of its transition state is different from that of alpha-spectrin and src SH3 domains previously studied. The folding algorithm, Fold-X, including an energy function with specific sequence features, accounts for these differences and reproduces with a good agreement the set of experimental phi(double dagger-U) values obtained for the three proteins. Our analysis shows that taking into account sequence features underlying protein topology is critical for an accurate prediction of the folding process.     

An analysis of protein folding pathways

We have developed a model of the protein folding process based on three primary assumptions: that burying of hydrophobic area is the dominant contribution to the relative free energy of a conformation, that a record of the folding process is largely preserved in the final structure, and that the denatured state is a random coil. Detailed folding pathways are identified for 19 protein structures. The picture of the folding process that emerges from this analysis is one of nucleation by regions of 8-16 residues. Nucleation sites then lead to larger structures by two mechanisms: propagation and diffusion/collision. A Monte Carlo simulation is used to follow the folding pathway when propagation is the dominant mechanism. Because detailed pathways are derived for each protein, the models are susceptible to experimental verification.     

The Plastic Energy Landscape of Protein Folding: A TRIANGULAR FOLDING MECHANISM WITH AN EQUILIBRIUM INTERMEDIATE FOR A SMALL PROTEIN DOMAIN*

Protein domains usually fold without or with only transiently populated intermediates, possibly to avoid misfolding, which could result in amyloidogenic disease. Whether observed intermediates are productive and obligatory species on the folding reaction pathway or dispensable by-products is a matter of debate. Here, we solved the crystal structure of a small protein domain, SAP97 PDZ2 I342W C378A, and determined its folding pathway. The presence of a folding intermediate was demonstrated both by single and double-mixing kinetic experiments using urea-induced (un)folding as well as ligand-induced folding. This protein domain was found to fold via a triangular scheme, where the folding intermediate could be either on- or off-pathway, depending on the experimental conditions. Furthermore, we found that the intermediate was present at equilibrium, which is rarely seen in folding reactions of small protein domains. The folding mechanism observed here illustrates the roughness and plasticity of the protein folding energy landscape, where several routes may be employed to reach the native state. The results also reconcile the folding mechanisms of topological variants within the PDZ domain family.     

Exploring the folding energy landscapes of heme proteins using a hybrid AWSEM-heme model

Heme is an active center in many proteins. Here we explore computationally the role of heme in protein folding and protein structure. We model heme proteins using a hybrid model employing the AWSEM Hamiltonian, a coarse-grained forcefield for the protein chain along with AMBER, an all-atom forcefield for the heme. We carefully designed transferable force fields that model the interactions between the protein and the heme. The types of protein–ligand interactions in the hybrid model include thioester covalent bonds, coordinated covalent bonds, hydrogen bonds, and electrostatics. We explore the influence of different types of hemes (heme b and heme c) on folding and structure prediction. Including both types of heme improves the quality of protein structure predictions. The free energy landscape shows that both types of heme can act as nucleation sites for protein folding and stabilize the protein folded state. In binding the heme, coordinated covalent bonds and thioester covalent bonds for heme c drive the heme toward the native pocket. The electrostatics also facilitates the search for the binding site.

     

Folding Steps in the Fibrillation of Functional Amyloid: Denaturant Sensitivity Reveals Common Features in Nucleation and Elongation

Functional bacterial amyloids (FuBA) are intrinsically disordered proteins (IDPs) which rapidly and efficiently aggregate, forming extremely stable fibrils. The conversion from IDP to amyloid is evolutionarily optimized and likely couples folding to association. Many FuBA contain several imperfect repeat sequences which contribute to the stability of mature FuBA fibrils. Aggregation can be considered an intermolecular extension of the process of intramolecular protein folding which has traditionally been studied using chemical denaturants. Here we employ denaturants to investigate folding steps during fibrillation of CsgA and FapC. We quantify protein compactification (i.e. the extent of burial of otherwise exposed surface area upon association of proteins) during different stages of fibrillation based on the dependence of fibrillation rate constants on the denaturant concentration (m-values) determined from fibrillation curves. For both proteins, urea mainly affects nucleation and elongation (not fragmentation), consistent with the fact that these steps involve both intra- and intermolecular association. The two steps have similar m-values, indicating that activation steps in nucleation and elongation involve the same level of folding. Surprisingly, deletion of two or three repeats from FapC leads to larger m-values (i.e. higher compactification) during the activation step of fibril growth. This observation is extended by SAXS analysis of the fibrils which indicates that weakening of the amyloidogenic core caused by repeat deletions causes a larger portion of normally unstructured regions of the protein to be included into the amyloid backbone. We conclude that the sensitivity of fibrillation to denaturants can provide useful insight into molecular mechanisms of aggregation.     

Unveiling a hidden folding intermediate in c-type cytochromes by protein engineering

Several investigators have highlighted a correlation between the basic features of the folding process of a protein and its topology, which dictates the folding pathway. Within this conceptual framework we proposed that different members of the cytochrome c (cyt c) family share the same folding mechanism, involving a consensus partially structured state. Pseudomonas aeruginosa cyt c(551) (Pa cyt c(551)) folds via an apparent two-state mechanism through a high energy intermediate. Here we present kinetic evidence demonstrating that it is possible to switch its folding mechanism from two to three state, stabilizing the high energy intermediate by rational mutagenesis. Characterization of the folding kinetics of one single-site mutant of the Pa cyt c(551) (Phe(7) to Ala) indeed reveals an additional refolding phase and a fast unfolding process which are explained by the accumulation of a partially folded species. Further kinetic analysis highlights the presence of two parallel processes both leading to the native state, suggesting that the above mentioned species is a non obligatory on-pathway intermediate. Determination of the crystallographic structure of F7A shows the presence of an extended internal cavity, which hosts three "bound" water molecules and a H-bond in the N-terminal helix, which is shorter than in the wild type protein. These two features allow us to propose a detailed structural interpretation for the stabilization of the native and especially the intermediate states induced by a single crucial mutation. These results show how protein engineering, x-ray crystallography and state-of-the-art kinetics concur to unveil a folding intermediate and the structural determinants of its stability.     

Origin of unusual phi-values in protein folding: evidence against specific nucleation sites

phi(f)-value analysis is one of the most common methods to characterize the structure of protein folding transition states. It compares the effects of mutations on the folding kinetics with the respective effects on equilibrium stability. The interpretation of the results usually focuses on a few unusual phi(f)-values, which are either particularly high or which are larger than 1 or smaller than 0. These mutations are believed to affect the most important regions for the folding process. A major uncertainty in experimental phi(f)-values is introduced by the commonly used analysis of only a single mutant at various positions in a protein (two-point analysis). To test the reliability of two-point phi(f)-values we used reference data from three positions in two different proteins at which multiple mutations have been introduced. The results show that two-point phi(f)-values are highly inaccurate if the difference in stability between two variants is less than 7 kJ/mol, corresponding to a 20-fold difference in equilibrium constant. Comparison with reported phi(f)-values for 11 proteins shows that most unusual phi(f)-values are observed in mutants which show changes in protein stability that are too small to allow a reliable analysis. The results argue against specific nucleation sites in protein folding and give a picture of transition states as distorted native states for the major part of a protein or for large substructures.     

Kinetics and Reaction Coordinates of the Reassembly of Protein Fragments Via Forward Flux Sampling

We studied the mechanism of the reassembly and folding process of two fragments of a split lattice protein by using forward flux sampling (FFS). Our results confirmed previous thermodynamics and kinetics analyses that suggested that the disruption of the critical core (of an unsplit protein that folds by a nucleation mechanism) plays a key role in the reassembly mechanism of the split system. For several split systems derived from a parent 48-mer model, we estimated the reaction coordinates in terms of collective variables by using the FFS least-square estimation method and found that the reassembly transition is best described by a combination of the total number of native contacts, the number of interchain native contacts, and the total conformational energy of the split system. We also analyzed the transition path ensemble obtained from FFS simulations using the estimated reaction coordinates as order parameters to identify the microscopic features that differentiate the reassembly of the different split systems studied. We found that in the fastest folding split system, a balanced distribution of the original-core amino acids (of the unsplit system) between protein fragments propitiates interchain interactions at early stages of the folding process. Only this system exhibits a different reassembly mechanism from that of the unsplit protein, involving the formation of a different folding nucleus. In the slowest folding system, the concentration of the folding nucleus in one fragment causes its early prefolding, whereas the second fragment tends to remain as a detached random coil. We also show that the reassembly rate can be either increased or decreased by tuning interchain cooperativeness via the introduction of a single point mutation that either strengthens or weakens one of the native interchain contacts (prevalent in the transition state ensemble).     

Some recommendations for the practitioner to improve the precision of experimentally determined protein folding rates and phi values

The mechanism by which proteins fold from an initially random conformation into a functional, native structure remains a major unsolved question in molecular biology. Of particular interest to the protein folding community is the structure that the protein adopts in the folding transition state (the highest free energy state on the pathway from unfolded to folded), as that state forms the barrier that defines the folding pathway. Unfortunately, however, unlike those of the initial, unfolded state and the final, folded state of the protein, the structure in the transition state cannot be directly assessed via experiment. Instead, experimentalists infer the structure of the transition state, often by estimating changes in its free energy by measuring the effects of amino acid substitutions on folding and unfolding rates (Phi-value analysis). In this article we show how to obtain more efficient estimates of these important quantities via improved experimental designs, and how to avoid common pitfalls in the analysis of kinetic data during the extraction of these parameters.     

Protein β-Sheet Nucleation Is Driven by Local Modular Formation

Despite its central role in the protein folding process, the specific mechanism(s) behind β-sheet formation has yet to be determined. For example, whether the nucleation of β-sheets, often containing strands separated in sequence by many residues, is local or not remains hotly debated. Here, we investigate the initial nucleation step of β-sheet formation by performing an analysis of the smallest β-sheets in a non-redundant dataset on the grounds that the smallest sheets, having undergone little growth after nucleation, will be enriched for nucleating characteristics. We find that the residue propensities are similar for small and large β-sheets as are their interstrand pairing preferences, suggesting that nucleation is not primarily driven by specific residues or interacting pairs. Instead, an examination of the structural environments of the two-stranded sheets shows that virtually all of them are contained in single, compact structural modules, or when multiple modules are present, one or both of the chain termini are involved. We, therefore, find that β-nucleation is a local phenomenon resulting either from sequential or topological proximity. We propose that β-nucleation is a result of two opposite factors; that is, the relative rigidity of an associated folding module that holds two stretches of coil close together in topology coupled with sufficient chain flexibility that enables the stretches of coil to bring their backbones in close proximity. Our findings lend support to the hydrophobic zipper model of protein folding (Dill, K. A., Fiebig, K. M., and Chan, H. S. (1993) Proc. Natl. Acad. Sci. U.S.A. 90, 1942–1946). Implications for protein folding are discussed.     

Changing Folding and Binding Stability in a Viral Coat Protein: A Comparison between Substitutions Accessible through Mutation and Those Fixed by Natural Selection

Previous studies have shown that most random amino acid substitutions destabilize protein folding (i.e. increase the folding free energy). No analogous studies have been carried out for protein-protein binding. Here we use a structure-based model of the major coat protein in a simple virus, bacteriophage φX174, to estimate the free energy of folding of a single coat protein and binding of five coat proteins within a pentameric unit. We confirm and extend previous work in finding that most accessible substitutions destabilize both protein folding and protein-protein binding. We compare the pool of accessible substitutions with those observed among the φX174-like wild phage and in experimental evolution with φX174. We find that observed substitutions have smaller effects on stability than expected by chance. An analysis of adaptations at high temperatures suggests that selection favors either substitutions with no effect on stability or those that simultaneously stabilize protein folding and slightly destabilize protein binding. We speculate that these mutations might involve adjusting the rate of capsid assembly. At normal laboratory temperature there is little evidence of directional selection. Finally, we show that cumulative changes in stability are highly variable; sometimes they are well beyond the bounds of single substitution changes and sometimes they are not. The variation leads us to conclude that phenotype selection acts on more than just stability. Instances of larger cumulative stability change (never via a single substitution despite their availability) lead us to conclude that selection views stability at a local, not a global, level.     

RNA and protein folding: common themes and variations

Visualizing the navigation of an ensemble of unfolded molecules through the bumpy energy landscape in search of the native state gives a pictorial view of biomolecular folding. This picture, when combined with concepts in polymer theory, provides a unified theory of RNA and protein folding. Just as for proteins, the major folding free energy barrier for RNA scales sublinearly with the number of nucleotides, which allows us to extract the elusive prefactor for RNA folding. Several folding scenarios can be anticipated by considering variations in the energy landscape that depend on sequence, native topology, and external conditions. RNA and protein folding mechanism can be described by the kinetic partitioning mechanism (KPM) according to which a fraction (Phi) of molecules reaches the native state directly, whereas the remaining fraction gets kinetically trapped in metastable conformations. For two-state folders Phi approximately 1. Molecular chaperones are recruited to assist protein folding whenever Phi is small. We show that the iterative annealing mechanism, introduced to describe chaperonin-mediated folding, can be generalized to understand protein-assisted RNA folding. The major differences between the folding of proteins and RNA arise in the early stages of folding. For RNA, folding can only begin after the polyelectrolyte problem is solved, whereas protein collapse requires burial of hydrophobic residues. Cross-fertilization of ideas between the two fields should lead to an understanding of how RNA and proteins solve their folding problems.     

Transferable Coarse-Grained Potential for De Novo Protein Folding and Design

Protein folding and design are major biophysical problems, the solution of which would lead to important applications especially in medicine. Here we provide evidence of how a novel parametrization of the Caterpillar model may be used for both quantitative protein design and folding. With computer simulations it is shown that, for a large set of real protein structures, the model produces designed sequences with similar physical properties to the corresponding natural occurring sequences. The designed sequences require further experimental testing. For an independent set of proteins, previously used as benchmark, the correct folded structure of both the designed and the natural sequences is also demonstrated. The equilibrium folding properties are characterized by free energy calculations. The resulting free energy profiles not only are consistent among natural and designed proteins, but also show a remarkable precision when the folded structures are compared to the experimentally determined ones. Ultimately, the updated Caterpillar model is unique in the combination of its fundamental three features: its simplicity, its ability to produce natural foldable designed sequences, and its structure prediction precision. It is also remarkable that low frustration sequences can be obtained with such a simple and universal design procedure, and that the folding of natural proteins shows funnelled free energy landscapes without the need of any potentials based on the native structure.