Probing the folding free energy landscape of the Src-SH3 protein domain

The mechanism and thermodynamics of folding of the Src homology 3 (SH3) protein domain are characterized at an atomic level through molecular dynamics with importance sampling. This methodology enables the construction of the folding free energy landscape of the protein as a function of representative reaction coordinates. We observe that folding proceeds in a downhill manner under native conditions, with early compaction and structure formation in the hydrophobic sheet consisting of the three central beta strands of the protein. This state bears considerable resemblance to the experimentally determined transition state for folding. Folding proceeds further with the formation of the second hydrophobic sheet consisting of the terminal strands and the RT loop. The final stages of folding appear to involve the formation of the hydrophobic core through the expulsion of water molecules bridging the two hydrophobic sheets. This work sheds new light on the complementary roles of sequence and topology in governing the folding mechanism of small proteins and provides further support for the role of water in facilitating the late stages in folding.     

Quantitative criteria for native energetic heterogeneity influences in the prediction of protein folding kinetics

Energy landscape theory requires that the protein-folding mechanism is generally globally directed or funneled toward the native state. The collective nature of transition state ensembles further suggests that sufficient averaging of the native interactions can occur so that the knowledge of the native topology may suffice for predicting the mechanism. Nevertheless, while simple homogeneously weighted native topology-based models predict the folding mechanisms for many proteins, for other proteins knowledge of the native topology, by itself, seems not to suffice in determining the folding mechanism. Simulations of proteins with differing topologies reveal that the failure of homogeneously weighted topology-based models can, however, be completely understood within the framework of a funneled energy landscape and can be quantified by comparing the fluctuation of entropy cost for forming contacts to the expected fluctuations in contact energy. To be precise, we find the transition state ensembles of proteins with all-α topologies, which are more uniform in the specific entropy cost of contact formation, have transition state ensembles that are more readily perturbed by differences in energetic weights than are the transition state ensembles of proteins with significant amounts of β-structure, where the specific entropy costs of contact formation are more widely distributed. This behavior is consistent with a random-field Ising model analogy that follows from the free energy functional approach to folding.     

Kinetics and thermodynamics of folding in model proteins.

Monte Carlo simulations on a class of lattice models are used to probe the thermodynamics and kinetics of protein folding. We find two transition temperatures: one at T theta, when chains collapse from a coil to a compact phase, and the other at Tf (< T theta), when chains adopt a conformation corresponding to their native state. The kinetics are probed by several correlation functions and are interpreted in terms of the underlying energy landscape. The transition from the coil to the native state occurs in three distinct stages. The initial stage corresponds to a random collapse of the protein chain. At intermediate times tau c, during which much of the native structure is acquired, there are multiple pathways. For longer times tau r (>> tau c) the decay is exponential, suggestive of a late transition state. The folding time scale (approximately tau r) varies greatly depending on the model. Implications of our results for in vitro folding of proteins are discussed.     

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.     

Nonglassy kinetics in the folding of a simple single-domain protein

Theory suggests that the otherwise rapid folding of simple heteropolymer models becomes "glassy"-dominated by multiple kinetically trapped misfolded states-at low temperatures or when the overall bias toward the native state is reduced relative to the depth of local minima. Experimental observations of nonsingle-exponential protein-folding kinetics have been taken as evidence that the protein-folding free energy landscape is similarly rough. No equivalent analysis, however, has been reported for a simple single-domain protein lacking prolines, disulfide bonds, prosthetic groups, or other gross structural features that might complicate folding. In an effort to characterize the glassiness of a folding free energy landscape in the absence of these potentially complicating factors, we have monitored the folding of a kinetically simple protein, peptostreptococcal protein L (protein L). We observe no statistically significant deviation from homogeneous single-exponential relaxation kinetics across temperatures ranging from near the protein's melting temperature to as low as -15 degrees C. On the basis of these observations, we estimate that, if there is a glass transition in the folding of protein L, it occurs at least 45 degrees C and possibly more than 145 degrees C below the freezing point of water. Apparently the folding free energy landscape of protein L is extremely smooth, which may be indicative of a rate-limiting step in folding that is, effectively, a nonglassy process.     

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.     

A PDZ domain recapitulates a unifying mechanism for protein folding

A unifying view has been recently proposed according to which the classical diffusion-collision and nucleation-condensation models may represent two extreme manifestations of an underlying common mechanism for the folding of small globular proteins. We report here the characterization of the folding process of the PDZ domain, a protein that recapitulates the three canonical steps involved in this unifying mechanism, namely: (i) the early formation of a weak nucleus that determines the native-like topology of a large portion of the structure, (ii) a global collapse of the entire polypeptide chain, and (iii) the consolidation of the remaining partially structured regions to achieve the native state conformation. These steps, which are clearly detectable in the PDZ domain investigated here, may be difficult to distinguish experimentally in other proteins, which would thus appear to follow one of the two limiting mechanisms. The analysis of the (un)folding kinetics for other three-state proteins (when available) appears consistent with the predictions ensuing from this unifying mechanism, thus providing a powerful validation of its general nature.     

Single-molecule transition-state analysis of RNA folding

How RNA molecules fold into functional structures is a problem of great significance given the expanding list of essential cellular RNA enzymes and the increasing number of applications of RNA in biotechnology and medicine. A critical step toward solving the RNA folding problem is the characterization of the associated transition states. This is a challenging task in part because the rugged energy landscape of RNA often leads to the coexistence of multiple distinct structural transitions. Here, we exploit single-molecule fluorescence spectroscopy to follow in real time the equilibrium transitions between conformational states of a model RNA enzyme, the hairpin ribozyme. We clearly distinguish structural transitions between effectively noninterchanging sets of unfolded and folded states and characterize key factors defining the transition state of an elementary folding reaction where the hairpin ribozyme's two helical domains dock to make several tertiary contacts. Our single-molecule experiments in conjunction with site-specific mutations and metal ion titrations show that the two RNA domains are in a contact or close-to-contact configuration in the transition state even though the native tertiary contacts are at most partially formed. Such a compact transition state without well formed tertiary contacts may be a general property of elementary RNA folding reactions.     

Excluded volume, local structural cooperativity, and the polymer physics of protein folding rates

A coarse-grained variational model is used to investigate the polymer dynamics of barrier crossing for a diverse set of two-state folding proteins. The model gives reliable folding rate predictions provided excluded volume terms that induce minor structural cooperativity are included in the interaction potential. In general, the cooperative folding routes have sharper interfaces between folded and unfolded regions of the folding nucleus and higher free energy barriers. The calculated free energy barriers are strongly correlated with native topology as characterized by contact order. Increasing the rigidity of the folding nucleus changes the local structure of the transition state ensemble nonuniformly across the set of proteins studied. Nevertheless, the calculated prefactors k(0) are found to be relatively uniform across the protein set, with variation in 1/k(0) less than a factor of 5. This direct calculation justifies the common assumption that the prefactor is roughly the same for all small two-state folding proteins. Using the barrier heights obtained from the model and the best-fit monomer relaxation time 30 ns, we find that 1/k(0) approximately 1-5 mus (with average 1/k(0) approximately 4 micros). This model can be extended to study subtle aspects of folding such as the variation of the folding rate with stability or solvent viscosity and the onset of downhill folding.     

Topography of funneled landscapes determines the thermodynamics and kinetics of protein folding

The energy landscape approach has played a fundamental role in advancing our understanding of protein folding. Here, we quantify protein folding energy landscapes by exploring the underlying density of states. We identify three quantities essential for characterizing landscape topography: the stabilizing energy gap between the native and nonnative ensembles δE, the energetic roughness ΔE, and the scale of landscape measured by the entropy S. We show that the dimensionless ratio between the gap, roughness, and entropy of the system accurately predicts the thermodynamics, as well as the kinetics of folding. Large Λ implies that the energy gap (or landscape slope towards the native state) is dominant, leading to more funneled landscapes. We investigate the role of topological and energetic roughness for proteins of different sizes and for proteins of the same size, but with different structural topologies. The landscape topography ratio Λ is shown to be monotonically correlated with the thermodynamic stability against trapping, as characterized by the ratio of folding temperature versus trapping temperature. Furthermore, Λ also monotonically correlates with the folding kinetic rates. These results provide the quantitative bridge between the landscape topography and experimental folding measurements.     

Simple model of protein folding kinetics.

A simple model of the kinetics of protein folding is presented. The reaction coordinate is the "correctness" of a configuration compared with the native state. The model has a gap in the energy spectrum, a large configurational entropy, a free energy barrier between folded and partially folded states, and a good thermodynamic folding transition. Folding kinetics is described by a master equation. The folding time is estimated by means of a local thermodynamic equilibrium assumption and then is calculated both numerically and analytically by solving the master equation. The folding time has a maximum near the folding transition temperature and can have a minimum at a lower temperature.     

Exploring the folding landscape of a structured RNA

Structured RNAs achieve their active states by traversing complex, multidimensional energetic landscapes. Here we probe the folding landscape of the Tetrahymena ribozyme by using a powerful approach: the folding of single ribozyme molecules is followed beginning from distinct regions of the folding landscape. The experiments, combined with small-angle x-ray scattering results, show that the landscape contains discrete folding pathways. These pathways are separated by large free-energy barriers that prevent interconversion between them, indicating that the pathways lie in deep channels in the folding landscape. Chemical protection and mutagenesis experiments are then used to elucidate the structural features that determine which folding pathway is followed. Strikingly, a specific long-range tertiary contact can either help folding or hinder folding, depending on when it is formed during the process. Together these results provide an unprecedented view of the topology of an RNA folding landscape and the RNA structural features that underlie this multidimensional landscape.     

Full distance-resolved folding energy landscape of one single protein molecule

Kinetic bulk and single molecule folding experiments characterize barrier properties but the shape of folding landscapes between barrier top and native state is difficult to access. Here, we directly extract the full free energy landscape of a single molecule of the GCN4 leucine zipper using dual beam optical tweezers. To this end, we use deconvolution force spectroscopy to follow an individual molecule’s trajectory with high temporal and spatial resolution. We find a heterogeneous energy landscape of the GCN4 leucine zipper domain. The energy profile is divided into two stable C-terminal heptad repeats and two less stable repeats at the N-terminus. Energies and transition barrier positions were confirmed by single molecule kinetic analysis. We anticipate that deconvolution sampling is a powerful tool for the model-free investigation of protein energy landscapes.     

Salt-induced detour through compact regions of the protein folding landscape.

In several cases, inorganic salts have been used to induce partly structured states in protein folding. But what is the nature of these states: Do they represent key stepping stones in the folding process, or are they circumstantial pitfalls in the energy landscape? Here we report that, in the case of the two-state protein S6, the salt-induced collapsed state is off the usual folding routes in the sense that it is prematurely collapsed and slows down folding by several orders of magnitude. Although this species is over-compact, it is not a dead-end trap but may fold by alternative channels to the native state.     

A minimalist model protein with multiple folding funnels

Kinetic and structural studies of wild-type proteins such as prions and amyloidogenic proteins provide suggestive evidence that proteins may adopt multiple long-lived states in addition to the native state. All of these states differ structurally because they lie far apart in configuration space, but their stability is not necessarily caused by cooperative (nucleation) effects. In this study, a minimalist model protein is designed to exhibit multiple long-lived states to explore the dynamics of the corresponding wild-type proteins. The minimalist protein is modeled as a 27-monomer sequence confined to a cubic lattice with three different monomer types. An order parameter-the winding index-is introduced to characterize the extent of folding. The winding index has several advantages over other commonly used order parameters like the number of native contacts. It can distinguish between enantiomers, its calculation requires less computational time than the number of native contacts, and reduced-dimensional landscapes can be developed when the native state structure is not known a priori. The results for the designed model protein prove by existence that the rugged energy landscape picture of protein folding can be generalized to include protein "misfolding" into long-lived states.     

Unspecific hydrophobic stabilization of folding transition states

Here we present a method for determining the inference of non-native conformations in the folding of a small domain, alpha-spectrin Src homology 3 domain. This method relies on the preservation of all native interactions after Tyr/Phe exchanges in solvent-exposed, contact-free positions. Minor changes in solvent exposure and free energy of the denatured ensemble are in agreement with the reverse hydrophobic effect, as the Tyr/Phe mutations slightly change the polypeptide hydrophilic/hydrophobic balance. Interestingly, more important Gibbs energy variations are observed in the transition state ensemble (TSE). Considering the small changes induced by the H/OH replacements, the observed energy variations in the TSE are rather notable, but of a magnitude that would remain undetected under regular mutations that alter the folded structure free energy. Hydrophobic residues outside of the folding nucleus contribute to the stability of the TSE in an unspecific nonlinear manner, producing a significant acceleration of both unfolding and refolding rates, with little effect on stability. These results suggest that sectors of the protein transiently reside in non-native areas of the landscape during folding, with implications in the reading of phi values from protein engineering experiments. Contrary to previous proposals, the principle that emerges is that non-native contacts, or conformations, could be beneficial in evolution and design of some fast folding proteins.     

Toward a better understanding of protein folding pathways.

Experimental observations of how unfolded proteins refold to their native three-dimensional structures contrast with many popular theories of protein folding mechanisms. The available experimental evidence (ignoring slow cis-trans peptide bond isomerization) is largely consistent with the following general scheme: under folding conditions, unfolded protein molecules rapidly equilibrate between different conformations prior to complete refolding. This rapid prefolding equilibrium favors certain compact conformations that have somewhat lower free energies than the other unfolded conformations. Some of the favored conformations are important for productive folding. The rate-limiting step occurs late in the pathway and involves a high-energy, distorted form of the native conformation; there appears to be a single transition state through which essentially all molecules refold. Consequently, proteins are not assembled via a large number of independent pathways, nor is folding initiated by a nucleation event in the unfolded protein followed by rapid growth of the folded structure. The known folding pathways involving disulfide bond formation follow the same general principles. An exceptional folding mechanism for reduced ribonuclease A proposed by Scheraga et al. (Scheraga, H.A., Konishi, Y., Rothwarf, D.M. & Mui, P.W. (1987) Proc. Natl. Acad. Sci. USA 84, 5740-5744) is shown to result from experimental shortcomings, an incorrect kinetic analysis, and a failure to consider the kinetics of unfolding.     

Exploring the folding energy landscape of a series of designed consensus tetratricopeptide repeat proteins

Repeat proteins contain short, tandem arrays of simple structural motifs (20−40 aa). These stack together to form nonglobular structures that are stabilized by short-range interactions from residues close in primary sequence. Unlike globular proteins, they have few, if any, long-range nonlocal stabilizing interactions. One ubiquitous repeat is the tetratricopeptide motif (TPR), a 34-aa helix-turn-helix motif. In this article we describe the folding kinetics of a series of 7 designed TPR proteins that are assembled from arraying identical designed consensus repeats (CTPRan). These range from the smallest 2-repeat protein to a large 10-repeat protein (≈350 aa). In particular, we describe how the energy landscape changes with the addition of repeat units. The data reveal that although the CTPRa proteins have low local frustration, their highly symmetric, modular native structure is reflected in their multistate kinetics of unfolding and folding. Moreover, although the initial folding of all CTPRan proteins involves a nucleus with similar solvent accessibility, their subsequent folding to the native structure depends directly on repeat number. This corresponds to an increasingly complex landscape that culminates in CTPRa10 populating a misfolded, off-pathway intermediate. These results extend our current understanding of the malleable folding pathways of repeat proteins and highlight the consequences of adding identical repeats to the energy landscape.     

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.