The nature of protein folding pathways

How do proteins fold, and why do they fold in that way? This Perspective integrates earlier and more recent advances over the 50-y history of the protein folding problem, emphasizing unambiguously clear structural information. Experimental results show that, contrary to prior belief, proteins are multistate rather than two-state objects. They are composed of separately cooperative foldon building blocks that can be seen to repeatedly unfold and refold as units even under native conditions. Similarly, foldons are lost as units when proteins are destabilized to produce partially unfolded equilibrium molten globules. In kinetic folding, the inherently cooperative nature of foldons predisposes the thermally driven amino acid-level search to form an initial foldon and subsequent foldons in later assisted searches. The small size of foldon units, ∼20 residues, resolves the Levinthal time-scale search problem. These microscopic-level search processes can be identified with the disordered multitrack search envisioned in the “new view” model for protein folding. Emergent macroscopic foldon–foldon interactions then collectively provide the structural guidance and free energy bias for the ordered addition of foldons in a stepwise pathway that sequentially builds the native protein. These conclusions reconcile the seemingly opposed new view and defined pathway models; the two models account for different stages of the protein folding process. Additionally, these observations answer the “how” and the “why” questions. The protein folding pathway depends on the same foldon units and foldon–foldon interactions that construct the native structure.     

Investigation of routes and funnels in protein folding by free energy functional methods

We use a free energy functional theory to elucidate general properties of heterogeneously ordering, fast folding proteins, and we test our conclusions with lattice simulations. We find that both structural and energetic heterogeneity can lower the free energy barrier to folding. Correlating stronger contact energies with entropically likely contacts of a given native structure lowers the barrier, and anticorrelating the energies has the reverse effect. Designing in relatively mild energetic heterogeneity can eliminate the barrier completely at the transition temperature. Sequences with native energies tuned to fold uniformly, as well as sequences tuned to fold reliably by a single or a few routes, are rare. Sequences with weak native energetic heterogeneity are more common; their folding kinetics is more strongly determined by properties of the native structure. Sequences with different distributions of stability throughout the protein may still be good folders to the same structure. A measure of folding route narrowness is introduced that correlates with rate and that can give information about the intrinsic biases in ordering arising from native topology. This theoretical framework allows us to investigate systematically the coupled effects of energy and topology in protein folding and to interpret recent experiments that investigate these effects.     

Theory for protein mutability and biogenesis.

Using an elementary physical model for protein folding, of self-avoiding short copolymer chains on two-dimensional square lattices, we address two questions regarding the evolution and origins of globular proteins. (i) How will protein native structures and stabilities be affected by single-and double-site mutations? (ii) What is the probability that a randomly chosen sequence of amino acids will be compact and globular under folding conditions? For a large number of different sequences, we search the conformational space exhaustively to find unequivocally the "native" conformation(s), of global minimum free energy, for each sequence. We find that replacing nonpolar residues in the core by polar residues is generally destabilizing, that surface sites are less sensitive than core sites, that some mutations increase the degeneracy of native states, and that overall it is most probable that a mutation will be neutral, having no effect on the native structure. These results support a "Continuity Principle," that small changes in sequence seldom have large effects on structure or stability of the native state. The simulations also show that (i) the number of "convergent" sequences (different sequences coding for the same native structure) is extremely large and (ii) most sequences become quite dense under folding conditions. This implies that the probability of formation of a globular protein from a random sequence of amino acids by prebiotic or mutational methods is significantly greater than zero.     

Protein folding by zipping and assembly

How do proteins fold so quickly? Some denatured proteins fold to their native structures in only microseconds, on average, implying that there is a folding "mechanism," i.e., a particular set of events by which the protein short-circuits a broader conformational search. Predicting protein structures using atomically detailed physical models is currently challenging. The most definitive proof of a putative folding mechanism would be whether it speeds up protein structure prediction in physical models. In the zipping and assembly (ZA) mechanism, local structuring happens first at independent sites along the chain, then those structures either grow (zip) or coalescence (assemble) with other structures. Here, we apply the ZA search mechanism to protein native structure prediction by using the AMBER96 force field with a generalized Born/surface area implicit solvent model and sampling by replica exchange molecular dynamics. Starting from open denatured conformations, our algorithm, called the ZA method, converges to an average of 2.2 A from the Protein Data Bank native structures of eight of nine proteins that we tested, which ranged from 25 to 73 aa in length. In addition, experimental Phi values, where available on these proteins, are consistent with the predicted routes. We conclude that ZA is a viable model for how proteins physically fold. The present work also shows that physics-based force fields are quite good and that physics-based protein structure prediction may be practical, at least for some small proteins.     

Optimization of rates of protein folding: the nucleation-condensation mechanism and its implications.

Small, single-module proteins that fold in a single cooperative step may be paradigms for understanding early events in protein-folding pathways generally. Recent experimental studies of the 64-residue chymotrypsin inhibitor 2 (CI2) support a nucleation mechanism for folding, as do some computer stimulations. CI2 has a nucleation site that develops only in the transition state for folding. The nucleus is composed of a set of adjacent residues (an alpha-helix), stabilized by long-range interactions that are formed as the rest of the protein collapses around it. A simple analysis of the optimization of the rate of protein folding predicts that rates are highest when the denatured state has little residual structure under physiological conditions and no intermediates accumulate. This implies that any potential nucleation site that is composed mainly of adjacent residues should be just weakly populated in the denatured state and become structured only in a high-energy intermediate or transition state when it is stabilized by interactions elsewhere in the protein. Hierarchical mechanisms of folding in which stable elements of structure accrete are unfavorable. The nucleation-condensation mechanism of CI2 fulfills the criteria for fast folding. On the other hand, stable intermediates do form in the folding of more complex proteins, and this may be an unavoidable consequence of increasing size and nucleation at more than one site.     

Effects of surface tethering on protein folding mechanisms

The folding mechanisms of proteins are increasingly being probed through single-molecule experiments in which the protein is immobilized on a surface. Nevertheless, a clear understanding of how the surface might affect folding, and whether or not it changes folding from its bulk behavior, is lacking. In this work, we use molecular dynamics simulations of a model beta-barrel protein tethered to a surface to systematically investigate how the surface impacts folding. In the bulk, this protein folds in a three-state manner through a compact intermediate state, and its transition state (TS) has a well formed hydrophobic core. Upon tethering, we find that folding rates and stability are impacted differently by the surface, with dependencies on both the length and location of the tether. Significant changes in folding times are observed for tether points that do not alter the folding temperature. Tethering also locally enhances the formation of structure for residues proximal to the tether point. We find that neither the folding mechanism nor the TS of this protein are altered if the tether is in a fully structured or completely unstructured region of the TS. By contrast, tethering in a partially structured region of the TS leads to dramatic changes. For one such tether point, the intermediate present in bulk folding is eliminated, leading to a two-state folding process with a heterogeneous, highly unstructured TS ensemble. These results have implications for both the design of single-molecule experiments and biotechnological applications of tethered proteins.     

An elongated spine of buried core residues necessary for in vivo folding of the parallel beta-helix of P22 tailspike adhesin

The parallel beta-helix is an elongated beta-sheet protein domain associated with microbial virulence factors, toxins, viral adhesins, and allergens. Long stacks of similar, buried residues are a prominent feature of this fold, as well as the polypeptide chain fold of an amyloid structure. The 13-rung, right-handed, parallel beta-helix of the homotrimeric P22 tailspike adhesin exhibits predominantly hydrophobic stacks. The role of these stacked residues in the folding and stabilization of the protein is unclear. Through scanning alanine mutagenesis we have identified a folding spine of stacked residues in continuous contact along the length of P22 tailspike's beta-helix domain that is necessary for folding within cells. Nearly all chains carrying alanine substitutions of the 103 buried nonalanines were defective in folding in vivo at 37 degrees C. However, the majority of these chains successfully reached a native state, stable to >80 degrees C, when folded inside cells at low temperatures. Thus, nearly the entire buried core was critical for in vivo beta-helix folding but negligible for stability. Folding at 18 degrees C revealed the minimal folding spine of 29 nonglycine stack positions that were intolerant to alanine substitution. These results indicate that a processive folding mechanism, dependent on stacking contacts, controls beta-helix formation. Such a stepwise folding pathway offers a new target for drug design against this class of microbial virulence factors.     

Protein folding funnels: a kinetic approach to the sequence-structure relationship.

A lattice model of protein folding is developed to distinguish between amino acid sequences that do and do not fold into unique conformations. Although Monte Carlo simulations provide insights into the long-time processes involved in protein folding, these simulations cannot systematically chart the conformational energy surface that enables folding. By assuming that protein folding occurs after chain collapse, a kinetic map of important pathways on this surface is constructed through the use of an analytical theory of probability flow. Convergent kinetic pathways, or "folding funnels," guide folding to a unique, stable, native conformation. Solution of the probability flow equations is facilitated by limiting treatment to diffusion between geometrically similar collapsed conformers. Similarity is measured in terms of a reconfigurational distance. Two specific amino acid sequences are deemed foldable and nonfoldable because one gives rise to a single, large folding funnel leading to a native conformation and the other has multiple pathways leading to several stable conformers. Monte Carlo simulations demonstrate that folding funnel calculations accurately predict the fact of and the pathways involved in folding-specific sequences. The existence of folding funnels for specific sequences suggests that geometrically related families of stable, collapsed conformers fulfill kinetic and thermodynamic requirements of protein folding.     

TOUCHSTONE: an ab initio protein structure prediction method that uses threading-based tertiary restraints

The successful prediction of protein structure from amino acid sequence requires two features: an efficient conformational search algorithm and an energy function with a global minimum in the native state. As a step toward addressing both issues, a threading-based method of secondary and tertiary restraint prediction has been developed and applied to ab initio folding. Such restraints are derived by extracting consensus contacts and local secondary structure from at least weakly scoring structures that, in some cases, can lack any global similarity to the sequence of interest. Furthermore, to generate representative protein structures, a reduced lattice-based protein model is used with replica exchange Monte Carlo to explore conformational space. We report results on the application of this methodology, termed TOUCHSTONE, to 65 proteins whose lengths range from 39 to 146 residues. For 47 (40) proteins, a cluster centroid whose rms deviation from native is below 6.5 (5) A is found in one of the five lowest energy centroids. The number of correctly predicted proteins increases to 50 when atomic detail is added and a knowledge-based atomic potential is combined with clustered and nonclustered structures for candidate selection. The combination of the ratio of the relative number of contacts to the protein length and the number of clusters generated by the folding algorithm is a reliable indicator of the likelihood of successful fold prediction, thereby opening the way for genome-scale ab initio folding.     

Structure of the transition state for the folding/unfolding of the barley chymotrypsin inhibitor 2 and its implications for mechanisms of protein folding.

The equilibrium and kinetics of folding of the single-domain protein chymotrypsin inhibitor 2 conform to the simple two-state model. The structure of the rate-determining transition state has been mapped out at the resolution of individual side chains by using the protein engineering method on 74 mutants that have been constructed at 37 of the 64 residues. The structure contains no elements of secondary structure that are fully formed. The majority of interactions are weakened by > 50% in the transition state, although most regions do have some very weak structure. The structure of the transition state appears to be an expanded form of the native state in which secondary and tertiary elements have been partly formed concurrently. This is consistent with a "global collapse" model of folding rather than a framework model in which folding is initiated from fully preformed local secondary structural elements. This may be a general feature for the folding of proteins lacking a folding intermediate and is perhaps representative of the early stages of folding for multidomain or multimodule proteins. The major transition state for the folding of barnase, for example, has some fully formed secondary and tertiary structural elements in the major transition state, and barnase appears to form by a framework process. However, the fully formed framework may be preceded by a global collapse, and a unified folding scheme is presented.     

Inverse protein folding problem: designing polymer sequences.

We consider the question of how to design proteins. How can we find "good" amino acid sequences (i) that fold to a desired "target" structure as a native conformation of lowest accessible free energy and (ii) that will not simultaneously fold to many other conformations of the same free energy? Current protein designs often focus on helix propensities and turns. We focus here on designing the hydrophobicity. For a model of self-avoiding hydrophobic/polar chains on two-dimensional square lattices, geometric proofs and exhaustive enumerations show the following results. (i) The strategy hydrophobic residues inside/polar residues outside is not optimal. Placement of additional hydrophobic residues on the surface is often necessary. (ii) To avoid unwanted conformations, the designed sequence must have neither too many nor too few hydrophobic residues. (iii) The computational complexity of inverse folding appears to be in a different class than folding: unlike the folding problem, the design problem does not scale exponentially with chain length. Some design strategies, described here for the lattice model, produce good sequences and scale only linearly with chain length.     

Structural insights into an equilibrium folding intermediate of an archaeal ankyrin repeat protein

Repeat proteins are widespread in nature, with many of them functioning as binding molecules in protein-protein recognition. Their simple structural architecture is used in biotechnology for generating proteins with high affinities to target proteins. Recent folding studies of ankyrin repeat (AR) proteins revealed a new mechanism of protein folding. The formation of an intermediate state is rate limiting in the folding reaction, suggesting a scaffold function of this transient state for intrinsically less stable ARs. To investigate a possible common mechanism of AR folding, we studied the structure and folding of a new thermophilic AR protein (tANK) identified in the archaeon Thermoplasma volcanium. The x-ray structure of the evolutionary much older tANK revealed high homology to the human CDK inhibitor p19(INK4d), whose sequence was used for homology search. As for p19(INK4d), equilibrium and kinetic folding analyses classify tANK to the family of sequential three-state folding proteins, with an unusual fast equilibrium between native and intermediate state. Under equilibrium conditions, the intermediate can be populated to >90%, allowing characterization on a residue-by-residue level using NMR spectroscopy. These data clearly show that the three C-terminal ARs are natively folded in the intermediate state, whereas native cross-peaks for the rest of the molecule are missing. Therefore, the formation of a stable folding unit consisting of three ARs is the necessary rate-limiting step before AR 1 and 2 can assemble to form the native state.     

Prediction of protein-folding mechanisms from free-energy landscapes derived from native structures

Guided by recent experimental results suggesting that protein-folding rates and mechanisms are determined largely by native-state topology, we develop a simple model for protein folding free-energy landscapes based on native-state structures. The configurations considered by the model contain one or two contiguous stretches of residues ordered as in the native structure with all other residues completely disordered; the free energy of each configuration is the difference between the entropic cost of ordering the residues, which depends on the total number of residues ordered and the length of the loop between the two ordered segments, and the favorable attractive interactions, which are taken to be proportional to the total surface area buried by the ordered residues in the native structure. Folding kinetics are modeled by allowing only one residue to become ordered/disordered at a time, and a rigorous and exact method is used to identify free-energy maxima on the lowest free-energy paths connecting the fully disordered and fully ordered configurations. The distribution of structure in these free-energy maxima, which comprise the transition-state ensemble in the model, are reasonably consistent with experimental data on the folding transition state for five of seven proteins studied. Thus, the model appears to capture, at least in part, the basic physics underlying protein folding and the aspects of native-state topology that determine protein-folding mechanisms.     

High-resolution protein folding with a transferable potential

A generalized computational method for folding proteins with a fully transferable potential and geometrically realistic all-atom model is presented and tested on seven helix bundle proteins. The protocol, which includes graph-theoretical analysis of the ensemble of resulting folded conformations, was systematically applied and consistently produced structure predictions of approximately 3 A without any knowledge of the native state. To measure and understand the significance of the results, extensive control simulations were conducted. Graph theoretic analysis provides a means for systematically identifying the native fold and provides physical insight, conceptually linking the results to modern theoretical views of protein folding. In addition to presenting a method for prediction of structure and folding mechanism, our model suggests that an accurate all-atom amino acid representation coupled with a physically reasonable atomic interaction potential and hydrogen bonding are essential features for a realistic protein model.     

Folding funnels and frustration in off-lattice minimalist protein landscapes

A full quantitative understanding of the protein folding problem is now becoming possible with the help of the energy landscape theory and the protein folding funnel concept. Good folding sequences have a landscape that resembles a rough funnel where the energy bias towards the native state is larger than its ruggedness. Such a landscape leads not only to fast folding and stable native conformations but, more importantly, to sequences that are robust to variations in the protein environment and to sequence mutations. In this paper, an off-lattice model of sequences that fold into a β-barrel native structure is used to describe a framework that can quantitatively distinguish good and bad folders. The two sequences analyzed have the same native structure, but one of them is minimally frustrated whereas the other one exhibits a high degree of frustration.     

Hierarchical folding mechanism of apomyoglobin revealed by ultra-fast H/D exchange coupled with 2D NMR

The earliest steps in the folding of proteins are complete on an extremely rapid time scale that is difficult to access experimentally. We have used rapid-mixing quench-flow methods to extend the time resolution of folding studies on apomyoglobin and elucidate the structural and dynamic features of members of the ensemble of intermediate states that are populated on a submillisecond time scale during this process. The picture that emerges is of a continuum of rapidly interconverting states. Even after only 0.4 ms of refolding time a compact state is formed that contains major parts of the A, G, and H helices, which are sufficiently well folded to protect amides from exchange. The B, C, and E helix regions fold more slowly and fluctuate rapidly between open and closed states as they search docking sites on this core; the secondary structure in these regions becomes stabilized as the refolding time is increased from 0.4 to 6 ms. No further stabilization occurs in the A, G, H core at 6 ms of folding time. These studies begin to time-resolve a progression of compact states between the fully unfolded and native folded states and confirm the presence an ensemble of intermediates that interconvert in a hierarchical sequence as the protein searches conformational space on its folding trajectory.     

A theoretical search for folding/unfolding nuclei in three-dimensional protein structures

When a protein folds or unfolds, it has to pass through many half-folded microstates. Only a few of them can be seen experimentally. In a two-state transition proceeding with no accumulation of metastable intermediates [Fersht, A. R. (1995) Curr. Opin. Struct. Biol. 5, 79-84], only the semifolded microstates corresponding to the transition state can be outlined; they influence the folding/unfolding kinetics. Our aim is to calculate them, provided the three-dimensional protein structure is given. The presented approach follows from the capillarity theory of protein folding and unfolding [Wolynes, P. G. (1997) Proc. Natl. Acad. Sci. USA 94, 6170-6175]. The approach is based on a search for free-energy saddle point(s) on a network of protein unfolding pathways. Under some approximations, this search is rapidly performed by dynamic programming and, despite its relative simplicity, gives a good correlation with experiment. The computed folding nuclei look like ensembles of those compact and closely packed parts of the three-dimensional native folds that contain a small number of disordered protruding loops. Their estimated free energy is consistent with the rapid (within seconds) folding and unfolding of small proteins at the point of thermodynamic equilibrium between the native fold and the coil.     

Shaping up the protein folding funnel by local interaction: lesson from a structure prediction study

Predicting protein tertiary structure by folding-like simulations is one of the most stringent tests of how much we understand the principle of protein folding. Currently, the most successful method for folding-based structure prediction is the fragment assembly (FA) method. Here, we address why the FA method is so successful and its lesson for the folding problem. To do so, using the FA method, we designed a structure prediction test of "chimera proteins." In the chimera proteins, local structural preference is specific to the target sequences, whereas nonlocal interactions are only sequence-independent compaction forces. We find that these chimera proteins can find the native folds of the intact sequences with high probability indicating dominant roles of the local interactions. We further explore roles of local structural preference by exact calculation of the HP lattice model of proteins. From these results, we suggest principles of protein folding: For small proteins, compact structures that are fully compatible with local structural preference are few, one of which is the native fold. These local biases shape up the funnel-like energy landscape.     

Associative memory Hamiltonians for structure prediction without homology: alpha/beta proteins

We describe a method for predicting the structure of alpha beta class proteins in the absence of information from homologous structures. The method is based on an associative memory model for short to intermediate range in sequence contacts and a contact potential for long range in sequence contacts. The coefficients in the energy function are chosen to maximize the ratio of the folding temperature to the glass transition temperature. We use the resulting optimized model to predict the structure of three alpha beta protein domains ranging in length from 81 to 115 residues. The resulting predictions align with low rms deviations to large portions of the native state. We have also calculated the free energy as a function of similarity to the native state for one of these three domains, and we show that, as expected from the optimization criteria, the free energy surface resembles a rough funnel to the native state. Finally, we briefly demonstrate the effect of roughness in the energy landscape on the dynamics.