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Native mass spectrometry (MS) is a powerful means for studying macromolecular protein assemblies, including accessing activated states. However, much remains to be understood about what governs which regions of the protein (un)folding funnel, which can be explored by activation of protein ions in a vacuum. Here, we examine the trajectory that Cu/Zn superoxide dismutase (SOD1) dimers take over the unfolding and dissociation free energy landscape in a vacuum. We examined wild-type SOD1 and six disease-related point mutants by using tandem MS and ion-mobility MS as a function of collisional activation. For six of the seven SOD1 variants, increasing activation prompted dimers to transition through two unfolding events and dissociate symmetrically into monomers with (as near as possible) equal charges. The exception was G37R, which proceeded only through the first unfolding transition and displayed a much higher abundance of asymmetric products. Supported by the observation that ejected asymmetric G37R monomers were more compact than symmetric G37R ones, we localized this effect to the formation of a gas-phase salt bridge in the first activated conformation. To examine the data quantitatively, we applied Arrhenius-type analysis to estimate the barriers on the corresponding free energy landscape. This reveals a heightening of the barrier to unfolding in G37R by >5 kJ/mol-1 over the other variants, consistent with expectations for the strength of a salt bridge. Our work demonstrates weaknesses in the simple general framework for understanding protein complex dissociation in a vacuum and highlights the importance of individual residues, their local environment, and specific interactions in governing product formation.

Transient excited states in proteins can be accurately probed from temperature dependence of amide proton (1HN) chemical shifts displaying significant curvatures. Characterizing these near-native alternative states is of high therapeutic relevance in conformational diseases wherein missense mutations promote structural instability that leads to conformational heterogeneity. Extending the structure-function paradigm from physiology to pathology, we recently reported the solution NMR structure and dynamics of a severe congenital cataract variant, G57W of human γS-crystallin (abbreviated as γS-G57W) which is resistant towards crystallization. In an endeavour to explore the functional consequences of this mutation, here we report for the first time, native state conformational ruggedness in human γS-G57W as compared to its wild-type counterpart from residue resolved nonlinear temperature dependence of backbone 1HN chemical shifts using solution NMR spectroscopy. Our calculations suggest that the simulated chemical shift curvatures are indicative of low energy excited states within 2–4 kcal mol−1 from the native state. Residues accessing alternative conformations populate the N-terminal domain of γS-G57W more than its C-terminal counterpart. Collectively, curvatures retaining native state ensemble on mild denaturation suggest that the free energy landscape in human γS-G57W at the bottom of the folding funnel is sufficiently robust and malleable against such perturbations. Overall, this critical study highlights the functional aspects of such structural malleability promoting infantile cataracts as a global health risk marker.

Practically proteins perform their functions exposed to various molecules (macro/micro) of different shapes, sizes, and high concentrations. In such conditions, proteins fold through various intermediate states to execute their type of functions. There are various in vitro studies that showed that proteins yield intermediate states (either pre-molten globule, PMG or molten globules, MG) in changing environments (pH, temperature, and co-solute). Here, we investigate that myoglobin (Mb) yields two intermediate states in the presence of polyethylene glycol, PEG (4 kDa molecular weight) at two different concentrations. These intermediates were characterized by various spectroscopic techniques, further; we demonstrated that these changes in the structure of the protein were due to soft interactions which were confirmed by isothermal titration calorimetric and computational studies. Besides, in silico (molecular dynamic simulations) studies were exploited to know the atomic-level details of the protein which are useful to comprehend the functional characteristics of the bio-molecule with structural change and to study atomic motions and inter-atomic interactions in the bio-molecular systems. This is the first time that two intermediates (MG and PMG state) in the protein (Mb) at two different concentrations in the presence of solo size of PEG are yielded. This study shows folding of a protein does not follow a singular and specific pathway but occurs through routes down a folding funnel more like rain flowing down a funnel, hence foresees the energy landscape theory. Moreover, the study provides the significance of crowding concentrations in the cellular organism.

The N-terminal domain of L9 (NTL9) is a 56-residue mixed α-β protein that lacks disulfides, does not bind cofactors, and folds reversibly. NTL9 has been widely used as a model system for experimental and computational studies of protein folding and for investigations of the unfolded state. The role of side-chain interactions in the folding of NTL9 is probed by mutational analysis. ϕ-values, which represent the ratio of the change in the log of the folding rate upon mutation to the change in the log of the equilibrium constant for folding, are reported for 25 point mutations and 15 double mutants. All ϕ-values are small, with an average over all sites probed of only 0.19 and a largest value of 0.4. The effect of modulating unfolded-state interactions is studied by measuring ϕ-values in second- site mutants and under solvent conditions that perturb unfolded-state energetics in a defined way. Neither of these alterations significantly affects the distribution of ϕ-values. The results, combined with those of earlier studies that probe the role of hydrogen-bond formation in folding and the burial of surface area, reveal that the transition state for folding contains extensive backbone structure and buries a significant fraction of hydrophobic surface area, but lacks well developed side-chain-side-chain interactions. The folding transition state for NTL9 does not contain a specific “nucleus” consisting of a few key residues; rather, it involves extensive backbone hydrogen bonding and partially formed structure delocalized over almost the entire domain. The potential generality of these observations is discussed.

Native mass spectrometry (MS) is a powerful means for studying macromolecular protein assemblies, including accessing activated states. However, much remains to be understood about what governs which regions of the protein (un)folding funnel are explored by activation of protein ions in vacuum. Here we examine the trajectory that dimeric Cu/Zn superoxide dismutase (SOD1) dimers take over the unfolding and dissociation free energy landscape in vacuum. We examined wild-type SOD1 and six disease-related point-mutants by using tandem MS and ion-mobility MS (MS/MS-IMMS) coupled with increasing collisional activation potentials. For six of the seven SOD1 variants, increasing activation promoted dimers to transition through two unfolding events to access three gas-phase conformers before dissociating symmetrically into monomers with (as near as possible) equal charges. The exception was G37R, which proceeded only through the first unfolding transition, and displayed a much higher abundance of asymmetric products. We localise this effect to the formation of a new salt-bridge in the first activated conformation. To examine the data quantitatively, we generated a model of SOD1 gas phase unfolding and dissociation, and applied Arrhenius-type analysis to estimate the barriers on the corresponding free energy landscape. This reveals an increase in the barrier height to unfolding in G37R to be >5 kJ/mol-1 higher than for the other variants, consistent with expectations for the strength of a salt-bridge. Our work demonstrates the importance of bond formation during the unfolding of proteins in vacuum, and provides a framework for comparing quantitatively the free energy landscape they explore upon activation.

A complete description of the pathways and mechanisms of protein folding requires a detailed structural and energetic characterization of the conformational ensemble along the entire folding reaction coordinate. Simulations can provide this level of insight for small proteins. In contrast, with the exception of hydrogen exchange, which does not monitor folding directly, experimental studies of protein folding have not yielded such structural and energetic detail. NMR can provide residue specific atomic level structural information, but its implementation in protein folding studies using chemical or temperature perturbation is problematic. Here we present a highly detailed structural and energetic map of the entire folding landscape of the leucine-rich repeat protein, pp32 (Anp32), obtained by combining pressure-dependent site-specific 1H-15N HSQC data with coarse-grained molecular dynamics simulations. The results obtained using this equilibrium approach demonstrate that the main barrier to folding of pp32 is quite broad and lies near the unfolded state, with structure apparent only in the C-terminal region. Significant deviation from two-state unfolding under pressure reveals an intermediate on the folded side of the main barrier in which the N-terminal region is disordered. A nonlinear temperature dependence of the population of this intermediate suggests a large heat capacity change associated with its formation. The combination of pressure, which favors the population of folding intermediates relative to chemical denaturants; NMR, which allows their observation; and constrained structure-based simulations yield unparalleled insight into protein folding mechanisms.

Using hydrodynamic description of protein folding, the process of the first-passage folding of ubiquitin has been studied. Since a large number of folding trajectories were required to obtain converged folding flows, a coarse-grained representation of the protein in the form of a C-bead Gō-model was employed, and discrete molecular dynamics was used to perform simulations. It has been found that the free energy surface has a maximum width in the transition state region, so that the densities of folding flows (probability fluxes) decrease to minimum when the system passes through the transition state. There are indications that the increasing number of different protein conformations in the transition state region compared with those in the neighboring regions of semi-compact and native-like states is responsible for the present phenomena. It has also been shown that if the free energy is projected onto a single reaction coordinate, the low populations of the transition states can be compensated by the increasing number of states, which can lead to a considerable decrease or even disappearance of the free energy barrier in the transition state.

Intermediate states in protein folding may slow folding, and sometimes can provide a starting point for aggregation. Recently, the FBP28 WW domain of the formin-binding protein was used as a model for a computational study of the origin and prevention of intermediate-state formation, and local hydrophobic interactions of Leu26 were implicated. Here, we combine new simulations over a broad temperature range with experimental temperature-jump data to study this site in more detail. We replace Leu26 by Asp26 or Trp26 to alter the folding scenario from three-state folding toward two-state or downhill folding at temperatures below the melting point, whereas the wild type shows two-state behavior only near its melting temperature. We offer an explanation of this behavior mainly in terms of principles of hydrophobic interactions.

Protein folding is the process that a protein molecule transforms from the linear polymer of peptides to a three-dimensional native structure with specific biological function. By now, the protein folding problem has been studied for more than 50 years and already became a broad and active research field. To answer the 58th question raised by Science in 2005, in this article we briefly reviewed the background and research history of the protein folding problem, and introduced the progresses of protein folding prediction research from four aspects: the protein folding process prediction (protein folding simulation), the folding process related parameter prediction, the protein folding result prediction (protein structure prediction), and the folding result related parameter prediction. The studies on the protein folding problem began in the 60s of 20th century, with the efforts to seek a solution to the paradox that a protein can actually form a native 3D structure in only several seconds but the time scale estimated by a thermodynamic ergodic hypothesis would be longer than the age of universe. Computer simulation is an important approach for protein folding study. The protein models can be classified into 3 categories: lattice model, off-lattice model and all-atom model. The current knowledge about protein folding mechanism is based on the concept of folding funnel on a free-energy landscape, and the current opinion is that the protein folding mechanism is not unique for the whole protein universe and that there may exist a continuum between the two extreme ends of hierarchical folding and nucleation folding scenarios. The hardware for protein folding simulation was becoming more powerful; distributed systems (e.g, Folding@home), special-purpose machines (e.g, ANTON), and GPU-based platforms have been developed for protein folding simulation. Meanwhile, the folding simulation software was continuously enhanced. An important issue in protein folding simulation is to overcome the local energy barrier to find the global energy minimum; several approaches such as replica-exchange, multi-scale modeling and Modeling Employing Limited Data (MELD) were developed to tackle this issue; human intelligence involvement (e.g, “Foldit” Game) is another interesting effort. During the past two decades, the ability of protein folding simulation was continuously rising. For now, the folding simulation for the proteins with dozens of amino acids can reach a time scale of millisecond, while the protein size able to do effective folding simulation is around 100 amino acids. The targets of protein folding simulation have been largely expanded and now include both the in vitro and the in vivo folding such as co-translational folding, chaperone-assistant folding, small-molecule- induced folding and metal-coupled folding. Folding rate and folding type are two important parameters related with the protein folding process and now they can be predicted by statistical and machine-learning approaches based on different levels of structural features such as the topological properties of tertiary structure, the contents of secondary structure and the amino acid frequencies of primary structure. The result of a protein folding process is the formation of a protein structure. According to the hierarchy of structural organization, the protein structure prediction problem includes secondary structure prediction, tertiary structure prediction and quaternary structure prediction. By now, the secondary structure prediction algorithm has experienced five generations and the current accuracy is about 80% for 3-classes prediction. The tertiary structure prediction approaches mainly include two categories: template-based modeling and free modeling, with the former having higher accuracy and the latter having larger application scope. The quaternary structure prediction includes the prediction of complex structure and the prediction of the possibility of protein-protein interaction, and these predictions can be performed based on protein 3D structure or merely amino acid sequence. Structure related parameter prediction also attracted research interests, including the predictions of protein structural classes, secondary structure contents, disordered regions, solvent accessible surface region and the amino acid contacting pairs in the interface of protein-protein interaction. In the end, some possible development directions worth noticing in the future of protein folding research were suggested and they are: the coupling between protein folding and binding, the fusion of protein folding research with systems biology and the application of deep-learning techniques in the field of protein folding prediction.

This paper proposes a generalization of the well-known folding funnel concept of proteins. In the funnel model the polypeptide chain is treated as an individual object not interacting with other proteins. Since biological systems are considerably crowded, protein-protein interaction is a fundamental feature during the life cycle of proteins. The folding superfunnel proposed here describes the folding process of interacting proteins in various situations. The first example discussed is the folding of the freshly synthesized protein with the aid of chaperones. Another important aspect of protein-protein interactions is the folding of the recently characterized intrinsically disordered proteins, where binding to target proteins plays a crucial role in the completion of the folding process. The third scenario where the folding superfunnel is used is the formation of aggregates from destabilized proteins, which is an important factor in case of several conformational diseases. The folding superfunnel constructed here with the minimal assumption about the interaction potential explains all three cases mentioned above. Proteins 2016; 84:1009-1016. © 2016 Wiley Periodicals, Inc.

The relationship between folding cooperativity and downhill, or barrier-free, folding of proteins under highly stabilizing conditions remains an unresolved topic, especially for proteins such as λ-repressor that fold on the microsecond timescale. Under aqueous conditions where downhill folding is most likely to occur, we measure the stability of multiple H bonds, using hydrogen exchange (HX) in a λYA variant that is suggested to be an incipient downhill folder having an extrapolated folding rate constant of 2 × 10(5) s(-1) and a stability of 7.4 kcal·mol(-1) at 298 K. At least one H bond on each of the three largest helices (α1, α3, and α4) breaks during a common unfolding event that reflects global denaturation. The use of HX enables us to both examine folding under highly stabilizing, native-like conditions and probe the pretransition state region for stable species without the need to initiate the folding reaction. The equivalence of the stability determined at zero and high denaturant indicates that any residual denatured state structure minimally affects the stability even under native conditions. Using our ψ analysis method along with mutational ϕ analysis, we find that the three aforementioned helices are all present in the folding transition state. Hence, the free energy surface has a sufficiently high barrier separating the denatured and native states that folding appears cooperative even under extremely stable and fast folding conditions.

This chapter (The Amino Acid Sequences of Proteins Determine Folding and Non-folding) continues where Chap. 1 left off. Amino acid sequences determine the folded structure of proteins. The manner in which the protein folds is visualized by an energy landscape called a protein folding funnel. This chapter describes the funnel and how it relates to three-dimensional protein structure. This chapter describes the spin glass theory which also visualizes protein folding. Regions of amino acids called foldons are described. The 20 amino acid building blocks of proteins are enumerated in this chapter. The ice-like blanket that surrounds a protein and its effects on folding are described in this chapter. Other forces that stabilize the folded structure are described. This chapter defines and describes intrinsically disordered proteins (IDP) and intrinsically disordered protein regions (IDPR) and their functions. Effects of hypoxia on protein structure are discussed. Scaffolding and hubs are described.

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps., Comment: 9 pages, 5 figures

α-Helical hairpin (two-helix bundle) is a structure motif composed of two interacting helices connected by a turn or a short loop. It is an important model for protein folding studies, filling the gap between isolated α-helix and larger all-α domains. Here, we present, for the first time, successful folding simulations of an α-helical hairpin. Our RSFF1 and RSFF2 force fields give very similar predicted structures of this αtα peptide, which is in good agreement with its NMR structure. Our simulations also give site-specific stability of α-helix formation in good agreement with amide hydrogen exchange experiments. Combining the folding free energy landscapes and analyses of structures sampled in five different ranges of the fraction of native contacts (Q), a folding mechanism of αtα is proposed. The most stable sites of Q9-E15 in helix-1 and E24-A30 in helix-2 close to the loop region act as the folding initiation sites. The formation of interhelix side-chain contacts also initiates near the loop region, but some residues in the central parts of the two helices also form contacts quite early. The two termini fold at a final stage, and the loop region remains flexible during the whole folding process. This mechanism is similar to the "zipping out" pathway of β-hairpin folding.

Integrated-tempering-sampling molecular dynamics simulation is utilized to investigate the folding of a 67-residue three-α-helix bundle, α3W. Reversible folding and unfolding can be observed in individual trajectories and a total of 28 folding events are achieved within 7 μs simulation, giving sufficient sampling on the configuration space of protein folding. The native-like state with a left-handed topology constitutes the largest fraction of the conformational ensemble sampled by the simulation. In addition, a misfolded state with mirror-image (right-handed) topology is observed with smaller population. The free energy landscape analysis demonstrates that the folding of α3W is initiated by the formation of α-helical secondary structures and is followed by the assembling of folded α-helices to construct tertiary structure. The “correct” α-helix assembling which leads to the native structure is mainly dominated by inter-helical hydrophobic interactions whereas the “incorrect” assembling which leads to a misfolded mirror-image structure is highly affected by not only hydrophobic but also charge interactions. It is speculated on the basis of the present study on α3W and other studies on the B domain of protein A and α3D that the misfolding probability of α-helix bundle proteins is dependent on the strength of intra-protein hydrophobic and charge interactions: proteins containing stronger hydrophobic interactions but weaker charge interactions should have smaller misfolding probability. The importance of intra-protein hydrophobic interactions in preventing protein misfolding has been also seen in our previous studies on β-hairpins. Therefore, the present study along with our previous studies provide comprehensive, atomic-level picture of the folding/misfolding of α-helix bundle and β-hairpin proteins.

To characterize experimentally the ruggedness of the free energy landscape of protein folding is challenging, because the distributed small free energy barriers are usually dominated by one, or a few, large activation free energy barriers. This study delineates changes in the roughness of the free energy landscape by making use of the observation that a decrease in ruggedness is accompanied invariably by an increase in folding cooperativity. Hydrogen exchange (HX) coupled to mass spectrometry was used to detect transient sampling of local energy minima and the global unfolded state on the free energy landscape of the small protein single-chain monellin. Under native conditions, local noncooperative openings result in interconversions between Boltzmann-distributed intermediate states, populated on an extremely rugged "uphill" energy landscape. The cooperativity of these interconversions was increased by selectively destabilizing the native state via mutations, and further by the addition of a chemical denaturant. The perturbation of stability alone resulted in seven backbone amide sites exchanging cooperatively. The size of the cooperatively exchanging and/or unfolding unit did not depend on the extent of protein destabilization. Only upon the addition of a denaturant to a destabilized mutant variant did seven additional backbone amide sites exchange cooperatively. Segmentwise analysis of the HX kinetics of the mutant variants further confirmed that the observed increase in cooperativity was due to the smoothing of the ruggedness of the free energy landscape of folding of the protein by the chemical denaturant.

Water is known to play a critical role in protein folding and stability. Here we develop and employ a coarse-grained (CG) model to directly explore the role of water in shaping the conformational landscape explored during protein folding. For this purpose, we simulate a designed sequence with binary patterning of neutral and hydrophobic residues, which is capable of folding to a three-helix bundle in explicit water. We find two folded states of this sequence, with rotation of the helices occurring to trade between hydrophobic packing and water expulsion from the core. This work provides insight into the role of water and hydrophobicity in generating competing folded states for a protein.

According to the thermodynamic hypothesis, the native state of proteins is that in which the free energy of the system is at its lowest, so that at normal temperature and pressure, proteins evolve to that state. We selected four proteins representative of each of the four classes, and for each protein make four simulations, one starting from the native structure and the other three starting from the structure obtained by threading the sequence of one protein onto the native backbone fold of the other three proteins. Because of their large conformational distances with respect to the native structure, the three alternative initial structures cannot be considered as local minima within the native ensemble of the corresponding protein. As expected, the initial native states are preserved in the .5 μs simulations performed here and validate the simulations. On the other hand, when the initial state is not native, an analysis of the trajectories does not reveal any evolution towards the native state, during that time. These results indicate that the distribution of protein conformations is multipeak shaped, so that apart from the peak corresponding to the native state, there are other peaks associated with average structures that are very different from the native and that can last as long as the native state.

The protein folding (Levinthal’s) paradox states that it would not be possible in a physically meaningful time to a protein to reach the native (functional) conformation by a random search of the enormously large number of possible structures. This paradox has been solved: it was shown that small biases toward the native conformation result in realistic folding times of realistic-length sequences. This solution of the paradox is, however, not amenable to most chemistry or biology students due to the demanding mathematics. Here, a simplification of the study of the paradox and its solution is provided so that it is accessible to chemists and biologists at an undergraduate or graduate level. Despite its simplicity, the model captures some fundamental aspects of the protein folding mechanism and allows students to grasp the actual significance of the popular folding funnel representation of the protein energy landscape. The analysis of the folding model provides a rich basis for a discussion of the relations...

Three homologous spectrin domains have remarkably different folding characteristics. We have previously shown that the slow-folding R16 and R17 spectrin domains can be altered to resemble the fast folding R15, in terms of speed of folding (and unfolding), landscape roughness and folding mechanism, simply by substituting five residues in the core. Here we show that, by contrast, R15 cannot be engineered to resemble R16 and R17. It is possible to engineer a slow-folding version of R15, but our analysis shows that this protein neither has a rougher energy landscape nor does change its folding mechanism. Quite remarkably, R15 appears to be a rare example of a protein with a folding nucleus that does not change in position or in size when its folding nucleus is disrupted. Thus, while two members of this protein family are remarkably plastic, the third has apparently a restricted folding landscape., Graphical Abstract, Highlights • Homologous spectrin domains have very different folding kinetics and mechanisms. • R15 has been engineered to fold and unfold slowly similar to R16 and R17. • The folding pathway is entirely unchanged. • R15 is a rare example of a protein with an inflexible transition state.

Chain collapse and secondary structure formation are frequently observed during the early stages of protein folding. Is the chain collapse brought about by interactions between secondary structure units or is it due to polymer behavior in a poor solvent (coil-globule transition)? To answer this question, we measured small-angle X-ray scattering for a series of β-lactoglobulin mutants under conditions in which they assume a partially folded state analogous to the folding intermediates. Mutants that were designed to disrupt the secondary structure units showed the gyration radii similar to that of the wild type protein, indicating that chain collapse is due to coil-globule transitions. © 2013 Wiley Periodicals, Inc. Biopolymers 101: 651–658, 2014.

A hyperstable Pin1 WW domain has been circularly permuted via excision of the fold-nucleating turn; it still folds to form the native three-strand sheet and hydrophobic core features. Multiprobe folding dynamics studies of the normal and circularly permuted sequences, as well as their constituent hairpin fragments and comparable-length β-strand-loop-β-strand models, indicate 2-state folding for all topologies. N-terminal hairpin formation is the fold nucleating event for the wild-type sequence; the slower folding circular permutant has a more distributed folding transition state.

Recent experimental and computational results have suggested that attractive interactions between a chaperonin and an enclosed substrate can have an important effect on the protein folding rate: it appears that folding may even be slower inside the cavity than under unconfined conditions, in contrast to what we would expect from excluded volume effects on the unfolded state. Here we examine systematically the dependence of the protein stability and folding rate on the strength of such attractive interactions between the chaperonin and substrate, by using molecular simulations of model protein systems in an idealised attractive cavity. Interestingly, we find a maximum in stability, and a rate which indeed slows down at high attraction strengths. We have developed a simple phenomenological model which can explain the variations in folding rate and stability due to differing effects on the free energies of the unfolded state, folded state, and transition state; changes in the diffusion coefficient along the folding coordinate are relatively small, at least for our simplified model. In order to investigate a possible role for these attractive interactions in folding, we have studied a recently developed model for misfolding in multidomain proteins. We find that, while encapsulation in repulsive cavities greatly increases the fraction of misfolded protein, sufficiently strong attractive protein-cavity interactions can strongly reduce the fraction of proteins reaching misfolded traps.

Understanding protein folding and function is one of the most important problems in biological research. Energy landscape theory and the folding funnel concept have provided a framework to investigate the mechanisms associated to these processes. Since protein energy landscapes are in most cases minimally frustrated, structure based models (SMBs) have successfully determined the geometrical features associated with folding and functional transitions. However, structural information is limited, particularly with respect to different functional configurations. This is a major limitation for SBMs. Alternatively, statistical methods to study amino acid co-evolution provide information on residue-residue interactions useful for the study of structure and function. Here, we show how the combination of these two methods gives rise to a novel way to investigate the mechanisms associated with folding and function. We use this methodology to explore the mechanistic aspects of protein translocation in the integral membrane protease FtsH. Dual basin-SBM simulations using the open and closed state of this hexameric motor reveals a functionally important paddling motion in the catalytic cycle. We also find that Direct Coupling Analysis (DCA) predicts physical contacts between AAA and peptidase domains of the motor, which are crucial for the open to close transition. Our combined method, which uses structural information from the open state experimental structure and co-evolutionary couplings, suggests that this methodology can be used to explore the functional landscape of complex biological macromolecules previously inaccessible to methods dependent on experimental structural information. This efficient way to sample the conformational space of large systems creates a theoretical/computational framework capable of better characterizing the functional landscape in large biomolecular assemblies.

We have investigated effects of salt ions on folding events of a helical miniprotein chicken villin headpiece subdomain HP36. Low concentrations of ions alter electrostatic interactions between charged groups of a protein and can change the populations of conformers. Here, we compare two data sets of folding simulations of HP36 in explicit water solvent with or without ions. For efficient sampling of the conformational space of HP36, the multicanonical replica-exchange molecular dynamics method was employed. Our analyses suggest that salt alters salt-bridging nature of the protein at later stages of folding at room temperature. Especially, more nonnative, nonlocal salt bridges are formed at near-native conformations in pure water. Our analyses also show that such salt-bridge formation hinders the fully native hydrophobic-core packing at the final stages of folding. Proteins 2014; 82:933–943. © 2013 Wiley Periodicals, Inc.

The folding of larger proteins generally differs from the folding of similarly large nucleic acids in the number and stability of the intermediates involved. To date, however, no similar comparison has been made between the folding of smaller proteins, which typically fold without well-populated intermediates, and the folding of small, simple nucleic acids. In response, in this study, we compare the folding of a 38-base DNA aptamer with the folding of a set of equivalently simple proteins. We find that, as is true for the large majority of simple, single domain proteins, the aptamer folds through a concerted, millisecond-scale process lacking well-populated intermediates. Perhaps surprisingly, the observed folding rate falls within error of a previously described relationship between the folding kinetics of single-domain proteins and their native state topology. Likewise, similarly to single-domain proteins, the aptamer exhibits a relatively low urea-derived Tanford β, suggesting that its folding transition state is modestly ordered. In contrast to this, however, and in contrast to the behavior of proteins, ϕ-value analysis suggests that the aptamer's folding transition state is highly ordered, a discrepancy that presumably reflects the markedly more important role that secondary structure formation plays in the folding of nucleic acids. This difference notwithstanding, the similarities that we observe between the two-state folding of single-domain proteins and the two-state folding of this similarly simple DNA presumably reflect properties that are universal in the folding of all sufficiently cooperative heteropolymers irrespective of their chemical details.

It has been well accepted that the folding energy landscape may resemble a funnel according to the theory of protein folding. This theory of "folding funnel" has been extensively studied and thought to play an important role in guiding the sampling process of the protein folding and refinement in protein structure prediction. Here, we have investigated the relationship between the "funnel likeness" of protein folding and the size/structure of the proteins based on a set of non-homologous proteins we have recently evaluated using a statistical mechanics- based scoring function ITScorePro. It was found that larger proteins that consist of more helix/sheet structures tend to have a higher score-Root Mean Square Deviation (RMSD) correlation (or a more funnel like energy landscape). Another measurement in protein folding, Z-score, has also shown some correlation with the size of the proteins. As expected, proteins with a better "olding funnel likeness" (or score-RMSD correlation) tend to have a better- predicted conformation with a lower RMSD from their native structures. These findings can be extremely valuable for the development and improvement of sampling and scoring algorithms for protein structure prediction.

Trp-cage is a synthetic 20-residue miniprotein which folds rapidly and spontaneously to a well-defined globular structure more typical of larger proteins. Due to its small size and fast folding, it is an ideal model system for experimental and theoretical investigations of protein folding mechanisms. However, Trp-cage's exact folding mechanism is still a matter of debate.,Here we investigate Trp-cage's relaxation dynamics in the amide I' spectral region (1530- 1700 cm(-1)) using time-resolved infrared spectroscopy. Residue-specific information was obtained by incorporating an isotopic label (C-13=O-18) into the amide carbonyl group of residue Gly11, thereby spectrally isolating an individual 3(10)-helical residue. The folding unfolding equilibrium is perturbed using a nanosecond temperature jump (T jump), and the subsequent re-equilibration is probed by observing the time dependent vibrational response in the amide I' region. We observe bimodal relaxation kinetics with time constants of 100 +/- 10 and 770 +/- 40 ns at 322 K, suggesting that the folding involves an intermediate state, the character of which can be determined from the time and frequency resolved data We find that the relaxation dynamics close to the melting temperature involve fast fluctuations in the polyproline II region, whereas the slower process can be attributed to conformational rearrangements due to the global (un)folding transition of the protein. Combined analysis of our T-jump data and molecular dynamics simulations indicates that the formation of a well-defined alpha-helix precedes the rapid formation of the hydrophobic cage structure, implying a native like folding intermediate, that Mainly differs from the folded conformation in the orientation of the C-terminal polyproline II helix relative to the N-terminal part of the backbone., We find that the main free energy barrier is positioned between the folding intermediate and the unfolded state ensemble, and that it involves the formation of the alpha-helix, the 3(10)-helix, and the Asp9- Arg16 salt bridge. Our results suggest that at low temperature (T << T-m) a folding path via formation of alpha-helical contacts followed by hydrophobic clustering becomes more important.

Using action-derived molecular dynamics (ADMD), we study the dynamic folding pathway models of the Trp-cage protein by providing its sequential conformational changes from its initial disordered structure to the final native structure at atomic details. We find that the numbers of native contacts and native hydrogen bonds are highly correlated, implying that the native structure of Trp-cage is achieved through the concurrent formations of native contacts and native hydrogen bonds. In early stage, an unfolded state appears with partially formed native contacts (~40%) and native hydrogen bonds (~30%). Afterward, the folding is initiated by the contact of the side chain of Tyr3 with that of Trp6, together with the formation of the N-terminalα-helix. Then, the C-terminal polyproline structure docks onto the Trp6 and Tyr3 rings, resulting in the formations of the hydrophobic core of Trp-cage and its near-native state. Finally, the slow adjustment processes of the near-native states into the native structure are dominant in later stage. The ADMD results are in agreement with those of the experimental folding studies on Trp-cage and consistent with most of other computational studies.

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the "foldable" protein domains.

Understanding how proteins fold through a vast number of unfolded states is a major subject in the study of protein folding. Herein, we present itinerary profiling as a simple method to analyze molecular dynamics trajectories, and apply this method to Trp-cage. In itinerary profiling, structural clusters included in a trajectory are represented by a bit sequence, and a number of trajectories, as well as the structural clusters, can be compared and classified. As a consequence, the structural clusters that characterize the foldability of trajectories were able to be identified. The connections between the clusters were then illustrated as a network and the structural features of the clusters were examined. We found that in the true folding funnel, Trp-cage formed a left-handed main-chain topology and the Trp6 side-chain was located at the front of the main-chain ring, even in the initial unfolded states. In contrast, in the false folding funnel of the pseudo-native states, in which the Trp6 side-chain is upside down in the protein core, Trp-cage had a right-handed main-chain topology and the Trp side-chain was at the back. The initial topological partition, as determined by the main-chain handedness and the location of the Trp residue, predetermines Trp-cage foldability and the destination of the trajectory to the native state or the pseudo-native states.

We have studied the folding of ribonuclease A by mapping it onto coarse-grained lattice protein models. With replica exchange Wang-Landau sampling, we calculated the free energy vs end-to-end distance as a function of temperature. A mapping to the famous hydrophobic-polar (HP) model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, extending the HP model with an additional "neutral" monomer type (i.e., a mapping to the three-letter H0P model) has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.

Peptide cross-linking has been widely explored as a means of constraining short sequences into stable folded conformations, most commonly α-helices. The prevailing hypothesis for the origin of helix stabilization is an entropic effect resulting from backbone pre-organization; however, obtaining direct evidence bearing on this hypothesis is challenging. Here, we compare the folding thermodynamics of a small helix-rich protein domain and analogues containing one of three common cross-linking motifs. Analysis of the folding free energy landscapes of linear vs. cyclized species reveal consistent trends in the effect of cyclization on folding energetics, as well as subtle differences based on the chemistry of the cross link. Stabilization in all three systems arises entirely from a reduction in the entropic penalty of folding that more than compensates for an enthalpic destabilization of the folded state.

Determining how polypeptide chain collapse initiates structure formation during protein folding is a long standing goal. It has been challenging to characterize experimentally the dynamics of the polypeptide chain, which lead to the formation of a compact kinetic molten globule (MG) in about a millisecond. In this study, the sub-millisecond events that occur early during the folding of monellin from the guanidine hydrochloride-unfolded state have been characterized using multiple fluorescence and fluorescence resonance energy transfer probes. The kinetic MG is shown to form in a noncooperative manner from the unfolded (U) state as a result of at least three different processes happening during the first millisecond of folding. Initial chain compaction completes within the first 37 μs, and further compaction occurs only after structure formation commences at a few milliseconds of folding. The transient nonnative and native-like hydrophobic clusters with side chains of certain residues buried form during the initial chain collapse and the nonnative clusters quickly disassemble. Subsequently, partial chain desolvation occurs, leading to the formation of a kinetic MG. The initial chain compaction and subsequent chain rearrangement appear to be barrierless processes. The two structural rearrangements within the collapsed globule appear to prime the protein for the actual folding transition.

The B1 domain of protein G is a well-studied model system of protein folding that has a mixed secondary structure, high stability and relatively slow folding kinetics. However recent measurements on the sub-millisecond timescale show significant complexity before final folding step at ∼1ms which depends on how folding is observed. Since protein folding is still a poorly understood process, different denaturants have been put into experiment to better understand the folding process of various proteins. Applying force is one natural method for denaturing proteins in order to observe the process of refolding in detail, but the time resolution of standard instruments typically make investigation of fast folding proteins difficult. In this study, two alkyne-containing unnatural amino acid residues were added to both N and C termini of GB1 and connected via click chemistry to double stranded DNA handles. The protein-DNA chimeras were then suspended between a pair of polystyrene beads held in high-resolution dual optical traps and reversible folding/unfolding events were observed both during force-extension pulling/relaxation experiments as well as under constant force feedback conditions. Results presented here show that since GB1 structure undergoes rapid switching between intermediate states of varied extension, thus a two-state model is not appropriate for understanding full folding path of this domain.

Friction plays a critical role in protein folding. Frictional forces originating from random solvent and protein fluctuations both retard motion along the folding pathway and activate protein molecules to cross free energy barriers. Studies of friction thus may provide insights into the driving forces underlying protein conformational dynamics. However, the molecular origin of friction in protein folding remains poorly understood because, with the exception of the native conformer, there generally is little detailed structural information on the other states participating in the folding process. Here, we study the folding of the four-helix bundle FF domain that proceeds via a transiently formed, sparsely populated compact on-pathway folding intermediate whose structure was elucidated previously. Because the intermediate is stabilized by both native and nonnative interactions, friction in the folding transition between intermediate and folded states is expected to arise from intrachain reorganization in the protein. However, the viscosity dependencies of rates of folding from or unfolding to the intermediate, as established by relaxation dispersion NMR spectroscopy, clearly indicate that contributions from internal friction are small relative to those from solvent, so solvent frictional forces drive the folding process. Our results emphasize the importance of solvent dynamics in mediating the interconversion between protein configurations, even those that are highly compact, and in equilibrium folding/unfolding fluctuations in general.

Although protein folding is typically studied in dilute solution, folding in a cell will be affected by interactions with other biomolecules and excluded volume effects. Here, we examine the effect of hydrophobic confinement on folding of the Trp-cage miniprotein. We used replica exchange molecular dynamics simulations to probe the differences between folding in the bulk, on a hydrophobic surface, and confined between two hydrophobic walls. In addition to promotion of helix formation due to reduced conformational entropy of the unfolded state upon confinement, adsorption of Trp-cage to a hydrophobic surface stabilizes intermediate structures not present in the bulk. These new intermediate structures may alter the folding mechanism and kinetics and show the importance of including environmental effects when studying protein folding.

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.

The concept of a folding funnel with kinetic traps describes folding of individual proteins. Using in situ Atomic Force Microscopy to investigate S-layer assembly on mica, we show this concept is equally valid during self-assembly of proteins into extended matrices. We find the S-layer-on-mica system possesses a kinetic trap associated with conformational differences between a long-lived transient state and the final stable state. Both ordered tetrameric states emerge from clusters of the monomer phase, however, they then track along two different pathways. One leads directly to the final low-energy state and the other to the kinetic trap. Over time, the trapped state transforms into the stable state. By analyzing the time and temperature dependencies of formation and transformation we find that the energy barriers to formation of the two states differ by only 0.7 kT, but once the high-energy state forms, the barrier to transformation to the low-energy state is 25 kT. Thus the transient state exhibits the characteristics of a kinetic trap in a folding funnel.

The elongated three-helix bundle domains spectrin R16 and R17 fold some two to three orders of magnitude more slowly than their homologue R15. We have shown that this slow folding is due, at least in part, to roughness in the free-energy landscape of R16 and R17. We have proposed that this roughness is due to a frustrated search for the correct docking of partly preformed helices. However, this accounts for only a small part of the slowing of folding and unfolding. Five residues on the A helix of R15, when inserted together into R16 or R17, increase the folding rate constants, reduce landscape roughness, and alter the folding mechanism to one resembling R15. The effect of each of these mutations individually is investigated here. No one mutation causes the behavior seen for the five in combination. However, two mutations, E18F and K25V, significantly increase the folding and unfolding rates of both R16 and R17 but without a concomitant loss in landscape roughness. E18F has the greatest effect on the kinetics, and a Φ-value analysis of the C helix reveals that the folding mechanism is unchanged. For both E18F and K25V the removal of the charge and resultant transition state stabilization is the main origin of the faster folding. Consequently, the major cause of the unusually slow folding of R16 and R17 is the non-native burial of the two charged residues in the transition state. The slowing due to landscape roughness is only about fivefold.

Optimization of surface exposed charge–charge interactions in the native state has emerged as an effective means to enhance protein stability; but the effect of electrostatic interactions on the kinetics of protein folding is not well understood. To investigate the kinetic consequences of surface charge optimization, we characterized the folding kinetics of a Fyn SH3 domain variant containing five amino acid substitutions that was computationally designed to optimize surface charge–charge interactions. Our results demonstrate that this optimized Fyn SH3 domain is stabilized primarily through an eight-fold acceleration in the folding rate. Analyses of the constituent single amino acid substitutions indicate that the effects of optimization of charge–charge interactions on folding rate are additive. This is in contrast to the trend seen in folded state stability, and suggests that electrostatic interactions are less specific in the transition state compared to the folded state. Simulations of the transition state using a coarse-grained chain model show that native electrostatic contacts are weakly formed, thereby making the transition state conducive to nonspecific, or even nonnative, electrostatic interactions. Because folding from the unfolded state to the folding transition state for small proteins is accompanied by an increase in charge density, nonspecific electrostatic interactions, that is, generic charge density effects can have a significant contribution to the kinetics of protein folding. Thus, the interpretation of the effects of amino acid substitutions at surface charged positions may be complicated and consideration of only native-state interactions may fail to provide an adequate picture. Proteins 2011. © 2012 Wiley Periodicals, Inc.

Protein folding into tertiary structures is controlled by an interplay of attractive contact interactions and steric effects. We investigate the balance between these contributions using structure-based models using an all-atom representation of the structure combined with a coarse-grained contact potential. Tertiary contact interactions between atoms are collected into a single broad attractive well between the C(β) atoms between each residue pair in a native contact. Through the width of these contact potentials we control their tolerance for deviations from the ideal structure and the spatial range of attractive interactions. In the compact native state dominant packing constraints limit the effects of a coarse-grained contact potential. During folding, however, the broad attractive potentials allow an early collapse that starts before the native local structure is completely adopted. As a consequence the folding transition is broadened and the free energy barrier is decreased. Eventually two-state folding behavior is lost completely for systems with very broad attractive potentials. The stabilization of native-like residue interactions in non-perfect geometries early in the folding process frequently leads to structural traps. Global mirror images are a notable example. These traps are penalized by the details of the repulsive interactions only after further collapse. Successful folding to the native state requires simultaneous guidance from both attractive and repulsive interactions.

Statistical mechanics and molecular dynamics simulations proposed that the folding of proteins can follow multiple parallel pathways on a rugged energy landscape from unfolded state en route to their folded native states. Kinetic partitioning mechanism is one of the possible mechanisms underlying such complex folding dynamics. Here, we use single-molecule atomic force microscopy technique to directly probe the multiplicity of the folding pathways of the third fibronectin type III domain from the extracellular matrix protein tenascin-C (TNfn3). By stretching individual (TNfn3) 8 molecules, we forced TNfn3 domains to undergo mechanical unfolding and refolding cycles, allowing us to directly observe the folding pathways of TNfn3. We found that, after being mechanically unraveled and then relaxed to zero force, TNfn3 follows multiple parallel pathways to fold into their native states. The majority of TNfn3 fold into the native state in a simple two-state fashion, while a small percentage of TNfn3 were found to be trapped into kinetically stable folding intermediate states with well-defined three-dimensional structures. Furthermore, the folding of TNfn3 was also influenced by its neighboring TNfn3 domains. Complex misfolded states of TNfn3 were observed, possibly due to the formation of domain-swapped dimeric structures. Our studies revealed the ruggedness of the folding energy landscape of TNfn3 and provided direct experimental evidence that the folding dynamics of TNfn3 are governed by the kinetic partitioning mechanism. Our results demonstrated the unique capability of single-molecule AFM to probe the folding dynamics of proteins at the single-molecule level.

Folding experiments have suggested that some proteins have kinetic intermediates with a non-native structure. A simple G ̅o model does not explain such non-native intermediates. Therefore, the folding energy landscape of proteins with non-native intermediates should have characteristic properties. To identify such properties, we investigated the folding of bovine β-lactoglobulin (βLG). This protein has an intermediate with a non-native α-helical structure, although its native form is predominantly composed of β-structure. In this study, we prepared mutants whose α-helical and β-sheet propensities are modified and observed their folding using a stopped-flow circular dichroism apparatus. One interesting finding was that E44L, whose β-sheet propensity was increased, showed a folding intermediate with an amount of β-structure similar to that of the wild type, though its folding took longer. Thus, the intermediate seems to be a trapped intermediate. The high α-helical propensity of the wild-type sequence likely causes the folding pathway to circumvent such time-consuming intermediates. We propose that the role of the non-native intermediate is to control the pathway at the beginning of the folding reaction.

Coarse-grained, self-contained polymer models are powerful tools in the study of protein folding. They are also essential to assess predictions from less rigorous theoretical approaches that lack an explicit-chain representation. Here we review advances in coarse-grained modeling of cooperative protein folding, noting in particular that the Levinthal paradox was raised in response to the experimental discovery of two-state-like folding in the late 1960s, rather than to the problem of conformational search per se. Comparisons between theory and experiment indicate a prominent role of desolvation barriers in cooperative folding, which likely emerges generally from a coupling between local conformational preferences and nonlocal packing interactions. Many of these principles have been elucidated by native-centric models, wherein nonnative interactions may be treated perturbatively. We discuss these developments as well as recent applications of coarse-grained chain modeling to knotted proteins and to intrinsically disordered proteins.

We investigate the phase transition properties of isolated and aggregated protein by exhaustive numerical study in the confined conformation space with maximally compact lattice model. The study within the confined conformation space shows some general folding properties. Various sequences show different folding properties: two-state folding, three-state folding and prion-like folding behavior. We find that the aggregated protein holds a more evident transition than isolated one and the transition temperature is generally lower than that in isolated case.

We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.

Formation of beta-hairpins is considered the initial step of folding of many proteins and, consequently, peptides constituting the beta-hairpin sequence of proteins (the beta-hairpin-forming peptides) are considered as models of early stages of protein folding. In this article, we discuss the results of experimental studies (circular-dichroism, infrared and nuclear magnetic resonance spectroscopy, and differential scanning calorimetry) of the structure of beta-hairpin-forming peptides excised from the B1 domain of protein G, which are known to fold on their own. We demonstrate that local interactions at the turn sequence and hydrophobic interactions between nonpolar residues are the dominant structure-determining factors, while there is no convincing evidence that stable backbone hydrogen bonds are formed in these peptides in aqueous solution. Consequently, the most plausible mechanism for folding of the beta-hairpin sequence appears to be the broken-zipper mechanism consisting of the following three steps: (i) bending the chain at the turn sequence owing to favorable local interactions, (ii) formation of loose hydrophobic contacts between nonpolar residues, which occur close to the contacts in the native structure of the protein but not exactly in the same position and, finally, (iii) formation of backbone hydrogen bonds and locking the hydrophobic contacts in the native positions as a hydrophobic core develops, sufficient to dehydrate the backbone peptide groups. This mechanism provides sufficient uniqueness (contacts form between residues that become close together because the chain is bent at the turn position) and robustness (contacts need not occur at once in the native positions) for folding a beta-hairpin sequence.

Key elements of β-structure folding include hydrophobic core collapse, turn formation, and assembly of backbone hydrogen bonds. In the present folding simulations of several β-hairpins and β-sheets (peptide 1, protein G B1 domain peptide, TRPZIP2, TRPZIP4, 20mer, and 20mer D P6D), the folding free-energy landscape as a function of several reaction coordinates corresponding to the three key elements indicates apparent dependence on turn stability and side-chain hydrophobicity, which demonstrates different folding mechanisms of similar β-structures of varied sequences. Turn stability is found to be the key factor in determining the formation order of the three structural elements in the folding of β-structures. Moreover, turn stability and side-chain hydrophobicity both affect the stability of backbone hydrogen bonds. The three-stranded β-sheets fold through a three-state transition in which the formation of one hairpin always takes precedence over the other. The different stabilities of two anti-parallel hairpins in each three-stranded β-sheet are shown to correlate well with the different levels of their hydrophobic interactions.

Despite its small size, chicken villin headpiece subdomain HP36 folds into the native structure with a stable hydrophobic core within several microseconds. How such a small protein keeps up its conformational stability and fast folding in solution is an important issue for understanding molecular mechanisms of protein folding. In this study, we performed multicanonical replica-exchange simulations of HP36 in explicit water, starting from a fully extended conformation. We observed at least five events of HP36 folding into nativelike conformations. The smallest backbone root mean-square deviation from the crystal structure was 1.1 Å. In the nativelike conformations, the stably formed hydrophobic core was fully dehydrated. Statistical analyses of the simulation trajectories show the following sequential events in folding of HP36: 1), Helix 3 is formed at the earliest stage; 2), the backbone and the side chains near the loop between Helices 2 and 3 take nativelike conformations; and 3), the side-chain packing at the hydrophobic core and the dehydration of the core side chains take place simultaneously at the later stage of folding. This sequence suggests that the initial folding nucleus is not necessarily the same as the hydrophobic core, consistent with a recent experimental ϕ-value analysis.