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The structure of proteins as well as their folding/unfolding equilibrium are commonly attributed to H-bonding and hydrophobic interactions. We have used the molecular dynamic simulations in an explicit water environment based on the standard empirical potential as well as more accurately (and thus also more reliably) on the QM/MM potential. The simulations where the dispersion term was suppressed have led to a substantial change of the tryptophan-cage protein structure (unfolded structure). This structure cannot fold without the dispersion energy term, whereas, if it is covered fully, the system finds its native structure relatively quickly. This implies that after such physical factors as temperature and pH, the dispersion energy is an important factor in protein structure determination as well as in the protein folding/unfolding equilibrium. The loss of dispersion also affected the R-helical structure. On the other hand, weakening the electrostatic interactions (and thus H-bonding) affected the R-helical structure only to a minor extent.

Protein folding is often depicted as a motion along descending paths on a free energy landscape that results in a concurrent decrease in the conformational entropy of the polypeptide chain. However, to provide a description that is consistent with other natural processes, protein folding is formulated from the principle of increasing entropy. It then becomes evident that protein folding is an evolutionary process among many others. During the course of folding protein structural hierarchy builds up in succession by diminishing energy density gradients in the quest for a stationary state determined by surrounding density-in-energy. Evolution toward more probable states, eventually attaining the stationary state, naturally selects steeply ascending paths on the entropy landscape that correspond to steeply descending paths on the free energy landscape. The dissipative motion of the non-Euclidian manifold is non-deterministic by its nature which clarifies why it is so difficult to predict protein folding.

The bias exchange metadynamics (BE-META) technique was applied to investigate the folding mechanism of insulin, one of the most studied and biologically important proteins. The BE-META simulations were performed starting from an extended conformation of chain B of insulin, using only eight replicas and seven reaction coordinates. The folded state, together with the intermediate states along the folding pathway were identified and their free energy was determined. Three main basins were found separated from one another by a large free energy barrier. The characteristic native fold of chain B was observed in one basin, while the other two most populated basins contained "molten-globule" conformations stabilized by electrostatic and hydrophobic interactions, respectively. Transitions between the three basins occur on the microsecond time scale. The implications and relevance of this finding to the folding mechanisms of insulin were investigated.

Biology relies on the precise self-assembly of its molecular components. Generic principles of protein folding have emerged from extensive studies on small, water-soluble proteins, but it is unclear how these ideas are translated into more complex situations. In particular, the one-third of cellular proteins that reside in biological membranes will not fold like water-soluble proteins because membrane proteins need to expose, not hide, their hydrophobic surfaces. Here, we apply the powerful protein engineering method of Φ-value analysis to investigate the folding transition state of the alpha-helical membrane protein, bacteriorhodopsin, from a partially unfolded state. Our results imply that much of helix B of the seven-transmembrane helical protein is structured in the transition state with single-point alanine mutations in helix B giving Φ values >0.8. However, residues Y43 and T46 give lower Φ values of 0.3 and 0.5, respectively, suggesting a possible reduction in native structure in this region of the helix. Destabilizing mutations also increase the activation energy of folding, which is accompanied by an apparent movement of the transition state toward the partially unfolded state. This apparent transition state movement is most likely due to destabilization of the structured, unfolded state. These results contrast with the Hammond effect seen for several water-soluble proteins in which destabilizing mutations cause the transition state to move toward, and become closer in energy to, the folded state. We thus introduce a classic folding analysis method to membrane proteins, providing critical insight into the folding transition state.

The folding energy landscape of proteins has been suggested to be funnel-like with some degree of ruggedness on the slope. How complex the landscape, however, is still rather unclear. Many experiments for globular proteins suggested relative simplicity, whereas molecular simulations of shorter peptides implied more complexity. Here, by using complete conformational sampling of 2 globular proteins, protein G and src SH3 domain and 2 related random peptides, we investigated their energy landscapes, topological properties of folding networks, and folding dynamics. The projected energy surfaces of globular proteins were funneled in the vicinity of the native but also have other quite deep, accessible minima, whereas the randomized peptides have many local basins, including some leading to seriously misfolded forms. Dynamics in the denatured part of the network exhibited basin-hopping itinerancy among many conformations, whereas the protein reached relatively well-defined final stages that led to their native states. We also found that the folding network has the hierarchic nature characterized by the scale-free and the small-world properties.

We have characterized here the structural and dynamics properties of urea-denatured state of dSmt3 by multidimensional NMR at 27 degrees C and pH 5.6. The various results suggest that hydrophobic clusters as well as different native and non-native secondary structural elements are transiently formed. The backbone in the regions Gln26-Lys31 and Gly47-Gln60 shows conformationally restricted motions. The AABUF profile of the sequence reflected that this region has the highest tendency to undergo hydrophobic clustering and may thus assist the formation of transient structures. The secondary chemical shifts and coupling constants indicated that this region has strong tendency to occupy the broad beta-domain of (phi,psi) space. A number of NMR parameters indicated that the region Asp58-Gln60 (corresponding to beta3-beta4 turn in the folded state) has residual turn-like structure. The present structural and dynamics results on urea-denatured dSmt3 have been compared with the previously published results on denatured states of similar fold proteins e.g. human SUMO-1 (55% homologous), ubiquitin (13.8% homologous) and GB1. Although the sequence homology is rather poor between them, the residual structure in all cases seems to be largely native type. The implications of these to sequence-folding paradigm and initial folding processes have been discussed.

Proteins are held together by many weak contacts, each corresponding to a local reaction coordinate. The activation barrier for folding is distributed along a resultant global folding coordinate. Hence folding barriers are low, and could even become comparable to the thermal energy kT. In that case, proteins become downhill folders, with folding times in the microsecond region. Small barriers allow the diffusion of population along the reaction coordinate – the molecular rate – to be observed directly. Five simple free energy building blocks can explain all experimentally observed fast folding data, revealing a range of behaviors from low barrier crossings to completely downhill folding.

A “key-residue” hypothesis that a few residues’ characteristics contain the essential dynamics of the whole protein is proposed for the study of side-chain relaxation near native states. Molecular dynamics simulation is performed on the folding of Trp-cage, and four key residues are discovered and shown to be highly sensitive to the change of state of the protein away from the native state. Order parameters that characterize the geometrical properties of key residues are shown to form valuable phase plane on which one distinguishes different reaction pathways. Furthermore, one of the key residues, Trp6, is observed to display two reconfiguration processes, in which one is induced by an unconstrained torsion of the side-chain of Trp6, with a rate faster by almost an order of magnitude than the other one described by Kussell’s model. The faster process seems to occur more frequently in our simulation and thus represent a significant mechanism in folding dynamics.

One of the predictions of the energy landscape theory of protein folding is the possibility of barrierless, “downhill” folding under certain conditions. The protein 1BBL has been proposed to fold by such a downhill mechanism, though this is a matter of some dispute. We carried out extensive replica exchange molecular dynamics simulations on 1BBL in explicit solvent to address this controversy and provide a microscopic picture of its folding thermodynamics. Our simulations show two distinct structural transitions in the folding of 1BBL. A low-temperature transition involves a disordering of the protein's tertiary structure without loss of secondary structure. A distinct, higher temperature transition involves the complete loss of secondary structure and dissolution of the hydrophobic core. In contrast, control simulations of the 1BBL homolog E3BD show a single high temperature unfolding transition. Further simulations of 1BBL at high ionic strength show a significant destabilization of helix II but not helix I, suggesting that the apparent folding cooperativity of 1BBL may be highly dependent on experimental conditions. Although our simulations cannot provide definitive evidence of downhill folding in 1BBL, they clearly show evidence of a complex, non-two-state folding process.

The primary driving force for protein folding is the sequestration of hydrophobic side chains from solvent water, but the means whereby the amino acid sequence directs the folding process to form the correct final folded state is not well understood. Measurements of NMR line broadening in spin-labeled samples of unfolded apomyoglobin at pH 2.3 have been used to derive a quantitative model for transient hydrophobic interactions between various sites in the polypeptide chain, as would occur during the initiation of protein folding. Local clusters of residues with high values for the parameter “average area buried upon folding” (AABUF) form foci not only for local contacts but for long-range interactions, the relative frequencies of which can be understood in terms of differences in the extent of reduction in chain configurational entropy that occurs upon formation of nonlocal contacts. These results complement the striking correlation previously observed between the kinetic folding process of apomyoglobin and the AABUF of its amino acid sequence [Nishimura C, Lietzow MA, Dyson HJ, Wright PE (2005) J Mol Biol 351:383–392]. For the acid-unfolded states of apomyoglobin, our approach identifies multiple distinct hydrophobic clusters of differing thermodynamic stability. The most structured of these clusters, although sparsely populated, have both native-like and nonnative character; the specificity of the transient long-range contacts observed in these states suggests that they play a key role in initiating chain collapse and folding.

We have studied the folding mechanism of β-hairpins in the proteins 1GB1, 3AIT and 1A2P by conducting unfolding simulations at moderately high temperatures. The analysis of trajectories obtained from molecular dynamics simulations in explicit aqueous solution suggests that the positions of the hydrophobic core residues lead to subtle differences in the details of folding dynamics. However, the folding of three different hairpins can be explained by a unified mechanism that is a blend of the hydrogen-bond-centric and the hydrophobic-centric models. The initial stage of /?-hairpin folding involves various partially folded intermediate structures which are stabilized by both the van der Waals interactions of hydrophobic core residues and the electrostatic interactions of non-native hydrogen bonds. The native structure is obtained by forming native contacts in the final tune-up process. Depending on the relative positions of the hydrophobic residues, the actual mechanism of hairpin folding may or may not exhibit well-defined intermediates.

The 90-residue N-terminal Phox and Bem1p (PB1) domain of NBR1 forms an alpha/beta ubiquitin-like fold. Kinetic analysis using stopped-flow fluorescence reveals two-state kinetics; however, nonlinear effects in the denaturant dependence of the unfolding data demonstrate changes in the position of the rate-limiting barrier along the folding coordinate as the folding conditions change. The kinetics of wt-PB1 and several mutants show that this curvature is consistent with a single-pathway mechanism involving sequential transition states (TS1 and TS2) separated by a transiently populated high-energy intermediate, rather than movement of the transition state on a broad energy plateau. We show that the two transition states within the sequential model represent structurally and thermodynamically distinct species. TS1 is a collapsed state (alpha(TS1)=0.71) with a large enthalpic barrier to formation that is rate-limiting under conditions that strongly favour folding. TS2 is highly native-like (alpha(TS2)=0.93) and represents a late entropic barrier to formation of the native state. In support of the sequential transition state mechanism, we show that the G62A helix 2 substitution stabilises TS1 and the intermediate to such an extent that the latter becomes significantly populated, leading to the observation of a fast kinetic phase representing the initial U-->I transition, with TS2 (alpha(TS2)=0.87) becoming rate-limiting. The folding rate is not retarded by populating an intermediate, which would be expected for a misfold state, but is accelerated, suggesting that the I state is productive and on-pathway. The results show that the apparent two-state folding of the wt-PB1 domain occurs along a well-defined pathway involving structurally and thermodynamically distinct sequential transition states and an obligatory metastable intermediate that represents a productive local minimum in the energy landscape that increases the efficiency of barrier crossing through favourable effects on the entropy of activation.

The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process suggests frustration between two partially ordered forms of the protein, but recent varphi value measurements indicate that the transition structure is relatively constant over a broad range of temperatures. Here we develop a simplistic model to investigate the folding transition in which properties of the free energy landscape can be quantitatively compared with experimental data. The model is a continuation of the Muñoz-Eaton model to include the intermittency of contacts between structured parts of the protein, and the results compare variations in the landscape with denaturant and temperature to varphi value measurements and chevron plots of the kinetic rates. The topography of the model landscape (in particular, the feature of frustration) is consistent with detailed simulations even though variations in the varphi values are close to measured values. The transition barrier is smaller than indicated by the chevron data, but it agrees in order of magnitude with a similar alpha-carbon type of model. Discrepancies with the chevron plots are investigated from the point of view of solvent effects, and an approach is suggested to account for solvent participation in the model.

We present a detailed investigation of unfolded and partially folded states of a mutant apomyoglobin (apoMb) where the distal histidine has been replaced by phenylalanine (H64F). Previous studies have shown that substitution of His64, located in the E helix of the native protein, stabilizes the equilibrium molten globule and native states and leads to an increase in folding rate and a change in the folding pathway. Analysis of changes in chemical shift and in backbone flexibility, detected via [1H]-15N heteronuclear nuclear Overhauser effect measurements, indicates that the phenylalanine substitution has only minor effects on the conformational ensemble in the acid- and urea-unfolded states, but has a substantial effect on the structure, dynamics, and stability of the equilibrium molten globule intermediate formed near pH 4. In H64F apomyoglobin, additional regions of the polypeptide chain are recruited into the compact core of the molten globule. Since the phenylalanine substitution has negligible effect on the unfolded ensemble, its influence on folding rate and stability comes entirely from interactions within the compact folded or partly folded states. Replacement of His64 with Phe leads to favorable hydrophobic packing between the helix E region and the molten globule core and leads to stabilization of helix E secondary structure and overall thermodynamic stabilization of the molten globule. The secondary structure of the equilibrium molten globule parallels that of the burst phase kinetic intermediate; both intermediates contain significant helical structure in regions of the polypeptide that comprise the A, B, E, G, and H helices of the fully folded protein.

Proteins are the fundamental biopolymer responsible for much of the biochemistry of living systems. The remarkable versatility of proteins often results from their capacity to spontaneously fold into a defined conformation with specific biological or chemical function. Dysregulation of folding can result in a consequent metabolic dysregulation to give rise to debilitating pathological states. The design of synthetic proteins holds the potential to exploit their functional capacity for novel purposes, although much work remains to achieve a complete understanding of protein folding.

The first part of this paper contains an overview of protein structures, their spontaneous formation ("folding"), and the thermodynamic and kinetic aspects of this phenomenon, as revealed by in vitro experiments. It is stressed that universal features of folding are observed near the point of thermodynamic equilibrium between the native and denatured states of the protein. Here the "two-state" ("denatured state" "native state") transition proceeds without accumulation of metastable intermediates, but includes only the unstable "transition state". This state, which is the most unstable in the folding pathway, and its structured core (a "nucleus") are distinguished by their essential influence on the folding/unfolding kinetics. In the second part of the paper, a theory of protein folding rates and related phenomena is presented. First, it is shown that the protein size determines the range of a protein's folding rates in the vicinity of the point of thermodynamic equilibrium between the native and denatured states of the protein. Then, we present methods for calculating folding and unfolding rates of globular proteins from their sizes, stabilities and either 3D structures or amino acid sequences. Finally, we show that the same theory outlines the location of the protein folding nucleus (i.e., the structured part of the transition state) in reasonable agreement with experimental data.

Direct observation of the folding of a single polypeptide chain can provide important information about the thermodynamic states populated along its folding pathway. In this study, we present a lock-in force-spectroscopy technique that improves resolution of atomic-force microscopy force spectroscopy to 400 fN. Using this technique we show that immunoglobulin domain 4 from Dictyostelium discoideum filamin (ddFLN4) refolds against forces of approximately 4 pN. Our data show folding of this domain proceeds directly from an extended state and no thermodynamically distinct collapsed state of the polypeptide before folding is populated. Folding of ddFLN4 under load proceeds via an intermediate state. Three-state folding allows ddFLN4 to fold against significantly larger forces than would be possible for a mere two-state folder. We present a general model for protein folding kinetics under load that can predict refolding forces based on chain-length and zero force refolding rate.

The effects of a single-point mutation on folding thermodynamics and kinetics are usually interpreted by focusing on the native structure and the transition state. Here, the entire conformational spaces of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) and of its single-point mutant W10V are sampled close to the melting temperature by equilibrium folding-unfolding molecular dynamics simulations for a total of 40 micros. The folded state as well as the most populated free energy basins in the denatured state are isolated by grouping conformations according to fast relaxation at equilibrium. Such kinetic analysis provides more detailed and useful information than a simple projection of the free energy. The W10V mutant has the same native structure as the wild type peptide, and similar folding rate and stability. In the denatured state, the N-terminal hairpin is about 20% more structured in W10V than the wild type mainly because of van der Waals interactions. Notably, the W10V mutation influences also the van der Waals energy at the transition state ensemble causing a shift in the ratio of fluxes between two different transition state regions on parallel folding pathways corresponding to nucleation at either of the two beta-hairpins. Previous experimental studies have focused on the effects of denaturant-dependent or temperature-dependent changes in the structure of the denatured state. The atomistic simulations show that a single-point mutation in the central strand of a beta-sheet peptide results in remarkable changes in the topography of the denatured state ensemble. These changes modulate the relative accessibility of parallel folding pathways because of kinetic partitioning of the denatured state. Therefore, the observed dependence of the folding process on the starting ensemble raises questions on the biological significance of in vitro folding studies under strongly denaturing conditions.

The homochirality, or isotacticity, of the natural amino acids facilitates the formation of regular secondary structures such as alpha-helices and beta-sheets. However, many examples exist in nature where novel polypeptide topologies use both l- and d-amino acids. In this study, we explore how stereochemistry of the polypeptide backbone influences basic properties such as compactness and the size of fold space by simulating both lattice and all-atom polypeptide chains. We formulate a rectangular lattice chain model in both two and three dimensions, where monomers are chiral, having the effect of restricting local conformation. Syndiotactic chains with alternating chirality of adjacent monomers have a very large ensemble of accessible conformations characterized predominantly by extended structures. Isotactic chains on the other hand, have far fewer possible conformations and a significant fraction of these are compact. Syndiotactic chains are often unable to access maximally compact states available to their isotactic counterparts of the same length. Similar features are observed in all-atom models of isotactic versus syndiotactic polyalanine. Our results suggest that protein isotacticity has evolved to increase the enthalpy of chain collapse by facilitating compact helical states and to reduce the entropic cost of folding by restricting the size of the unfolded ensemble of competing states.

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 non-uniformly across the set of protein studied. Neverthless, the calculated prefactors k0 are found to be relatively uniform across the protein set, with variation in 1/k0 less than a factor of five. 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 30ns, we find that 1/k0 (1-5)us (with average 1/k0 4us). 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., Comment: 12 pages,6 figures,1 page supporting information.To be published in Proc.Natl.Acad.Sci.(USA)(2007)

Efficient protein folding implies a microscopic funnel-like multidimensional free-energy landscape. Macroscopically, conformational entropy reduction can manifest itself as part of an empirical barrier in the traditional view of folding, but experiments show that such barriers can also entail significant unfavorable enthalpy changes. This observation raises the puzzling possibility, irrespective of conformational entropy, that individual microscopic folding trajectories may encounter large uphill moves and thus the multidimensional free-energy landscape may not be funnel-like. Here, we investigate how nanoscale hydrophobic interactions might underpin this salient enthalpic effect in biomolecular assembly by computer simulations of the association of two preformed polyalanine or polyleucine helices in water. We observe a high, positive enthalpic signature at room temperature when the helix separation is less than a single layer of water molecules. Remarkably, this unfavorable enthalpy change, with a parallel increase in void volume, is largely compensated for by a concomitant increase in solvent entropy, netting only a small or nonexistent microscopic free-energy barrier. Thus, our findings suggest that high enthalpic folding barriers can be consistent with a funnel picture of folding and are mainly a desolvation phenomenon indicative of a cooperative mechanism of simultaneous formation of multiple side-chain contacts at the rate-limiting step.

An analysis in terms of the inherent structures (IS, local minima) of the multidimensional potential energy landscape is applied to proteins. Detailed calculations are performed for the 46 bead BLN model, which folds into a four-stranded beta-barrel. Enhanced sampling has allowed determination of 239 199 IS states, believed to encompass nearly all the compact, low-energy states, and of well-averaged thermodynamic quantities at low temperature. The density of states shows distinct lobes for compact and extended states, and entropic barriers for the collapse and local ordering transitions. A two-dimensional scatterplot or density of states clearly shows the multifunnel structure of the energy landscape. The anharmonic vibrational free energy is found to play a crucial role in protein folding. The problem of determining the folding transition in a multifunnel system is discussed, and novel indicators of folding are introduced. A particularly clear picture is obtained through the occupation probabilities, pi, of individual low-lying IS, which become finite below the collapse temperature; it is suggested that poor foldability corresponds to a large "misfolding interval" where the excited state pi0 exceeds that of the native state p0.

Conventional cooperative protein folding invokes discrete ensembles of native and denatured state structures in separate free-energy wells. Unimodal noncooperative (“downhill”) folding, however, proposes an ensemble of states occupying a single free-energy well for proteins folding at ≥4 × 10 4 s −1 at 298 K. It is difficult to falsify unimodal mechanisms for such fast folding proteins by standard equilibrium experiments because both cooperative and unimodal mechanisms can present the same time-averaged structural, spectroscopic, and thermodynamic properties when the time scale used for observation is longer than for equilibration. However, kinetics can provide the necessary evidence. Chevron plots with strongly sloping linear refolding arms are very difficult to explain by downhill folding and are a signature for cooperative folding via a transition state ensemble. The folding kinetics of the peripheral subunit binding domain POB and its mutants fit to strongly sloping chevrons at observed rate constants of >6 × 10 4 s −1 in denaturant solution, extrapolating to 2 × 10 5 s −1 in water. Protein A, which folds at 10 5 s −1 at 298 K, also has a well-defined chevron. Single-molecule fluorescence energy transfer experiments on labeled Protein A in the presence of denaturant demonstrated directly bimodal distributions of native and denatured states.

The C-terminal domain of measles virus nucleoprotein is an intrinsically disordered protein that could bind to the X domain (XD) of phosphoprotein P to exert its physiological function. Experiments reveal that the minimal binding unit is a 21-residue α-helical molecular recognition element (α-MoRE-MeV), which adopts a fully helical conformation upon binding to XD. Due to currently limited computing power, direct simulation of this coupled folding and binding process with atomic force field in explicit solvent cannot be achieved. In this work, two advanced sampling methods, metadynamics and parallel tempering, are combined to characterize the free energy surface of this process and investigate the underlying mechanism. Starting from an unbound and partially folded state of α-MoRE-MeV, multiple folding and binding events are observed during the simulation and the energy landscape was well estimated. The results demonstrate that the isolated α-MoRE-MeV resembles a molten globule and rapidly interconverts between random coil and multiple partially helical states in solution. The coupled folding and binding process occurs through the induced fit mechanism, with the residual helical conformations providing the initial binding sites. Upon binding, α-MoRE-MeV can easily fold into helical conformation without obvious energy barriers. Two mechanisms, namely, the system tending to adopt the structure in which the free energy of isolated α-MoRE-MeV is the minimum, and the binding energy of α-MoRE-MeV to its partner protein XD tending to the minimum, jointly dominate the coupled folding and binding process. With the advanced sampling approach, more IDP systems could be simulated and common mechanisms concerning the coupled folding and binding process could be investigated in the future.

A requirement for specific RNA folding is that the free-energy landscape discriminate against non-native folds. While tertiary interactions are critical for stabilizing the native fold, they are relatively non-specific, suggesting additional mechanisms contribute to tertiary folding specificity. In this study, we use coarse-grained molecular dynamics simulations to explore how secondary structure shapes the tertiary free-energy landscape of the Azoarcus ribozyme. We show that steric and connectivity constraints posed by secondary structure strongly limit the accessible conformational space of the ribozyme, and that these so-called topological constraints in turn pose strong free-energy penalties on forming different tertiary contacts. Notably, native A-minor and base-triple interactions form with low conformational free energy, while non-native tetraloop/tetraloop-receptor interactions are penalized by high conformational free energies. Topological constraints also give rise to strong cooperativity between distal tertiary interactions, quantitatively matching prior experimental measurements. The specificity of the folding landscape is further enhanced as tertiary contacts place additional constraints on the conformational space, progressively funneling the molecule to the native state. These results indicate that secondary structure assists the ribozyme in navigating the otherwise rugged tertiary folding landscape, and further emphasize topological constraints as a key force in RNA folding.

We study folding of Trp-cage miniprotein in the conditions when the native state of the protein is stable and unfolding events are improbable, which corresponds to physiological conditions. Using molecular dynamics simulations with an implicit solvent model, an ensemble of folding trajectories from unfolded (practically extended) states of the protein to the native state was generated. To get insight into the folding kinetics, the free energy surface and kinetic network projected on this surface were constructed. This, "conventional" analysis of the folding reaction was followed by a recently proposed hydrodynamic description of protein folding (Chekmarev et al. in Phys Rev Lett 100(1):018107, 2008), in which the process of the first-passage folding is viewed as a stationary flow of a folding "fluid" from the unfolded to native state. This approach is conceptually different from the previously used approaches and thus allows an alternative view of the folding dynamics and kinetics of Trp-cage, the conclusions about which are very diverse. In agreement with most previous studies, we observed two characteristic folding pathways: in one pathway (I), the collapse of the hydrophobic core precedes the formation of the [Formula: see text]-helix, and in the other pathway (II), these events occur in the reverse order. We found that although pathway II is complicated by a repeated partial protein unfolding, it contributes to the total folding flow as little as ≈10%, so that the folding kinetics remain essentially single-exponential.

Understanding the origin of the cooperativity seemingly inherent in a folding or unfolding reaction has been a major challenge. In particular, the relationship between folding cooperativity and stability is poorly understood. In this study, native state hydrogen exchange in conjunction with mass spectrometry has been used to explore the free energy landscape accessible to the small protein monellin, when the stability of the protein is varied. Mass distributions obtained in the EX1 limit of exchange have allowed a direct distinction between correlated (cooperative) and uncorrelated (noncooperative) structure-opening processes. Under conditions where the native protein is maximally stable, a continuum of partially unfolded states is gradually sampled before the globally unfolded state is transiently sampled. Under conditions that stabilize the unfolded state of the protein, the slowest structure-opening reactions leading to complete unfolding become cooperative. The present study provides experimental evidence for a gradual uphill unfolding transition on a very slow time scale, in the presence of a large free energy difference between the native and unfolded states. The results suggest that the cooperativity that manifests itself in protein folding and unfolding reactions carried out in the presence of denaturant might merely be a consequence of the effect of the denaturant on the unfolded state and transition state stabilities.

In Monte-Carlo simulations of protein folding, pathways and folding times depend on the appropriate choice of the Monte-Carlo move or process path. We developed a generalized set of process paths for a hybrid kinetic Monte Carlo—Molecular dynamics algorithm, which makes use of a novel constant time-update and allows formation of α-helical and β-stranded secondary structures. We apply our new algorithm to the folding of 3 different proteins: TrpCage, GB1, and TrpZip4. All three systems are seen to fold within the range of the experimental folding times. For the β-hairpins, we observe that loop formation is the rate-determining process followed by collapse and formation of the native core. Cluster analysis of both peptides reveals that GB1 folds with equal likelihood along a zipper or a hydrophobic collapse mechanism, while TrpZip4 follows primarily a zipper pathway. The difference observed in the folding behavior of the two proteins can be attributed to the different arrangements of their hydrophobic core, strongly packed, and dry in case of TrpZip4, and partially hydrated in the case of GB1.

The Helmholtz decomposition of the vector field of probability fluxes in a two-dimensional space of collective variables makes it possible to introduce a potential for the driving force of protein folding [Chekmarev, J. Chem. Phys. 139 (2013) 145103]. The potential has two components: one component (Φ) is responsible for the source and sink of the folding flow, which represent, respectively, the unfolded and native state of the protein, and the other (Ψ) accounts for the flow vorticity inherently generated at the periphery of the flow field and provides the canalization of the flow between the source and sink. Both components obey Poisson’s equations with the corresponding source/sink terms. In the present paper, we consider how the shape of the potential changes depending on the scenario of protein folding. To mimic protein folding dynamics projected onto a two-dimensional space of collective variables, the two-dimensional Muller and Brown potential is employed. Three characteristic scenarios are considered: a single pathway from the unfolded to the native state without intermediates, two parallel pathways without intermediates, and a single pathway with an off-pathway intermediate. To determine the probability fluxes, the hydrodynamic description of the folding reaction is used, in which the first-passage folding is viewed as a steady flow of the representative points of the protein from the unfolded to the native state. We show that despite the possible complexity of the folding process, the Φ-component is simple and universal in shape. The Ψ-component is more complex and reveals characteristic features of the process of folding. The present approach is potentially applicable to other complex reactions, for which the transition from the reactant to the product can be described in a space of two (collective) variables.

We investigate the kinetic pathways of folding and unfolding of the designed miniprotein Trp- cage in explicit solvent. Straightforward molecular dynamics and replica exchange methods both have severe convergence problems, whereas transition path sampling allows us to sample unbiased dynamical pathways between folded and unfolded states and leads to deeper understanding of the mechanisms of (un)folding. In contrast to previous predictions employing an implicit solvent, we find that Trp-cage folds primarily (80% of the paths) via a pathway forming the tertiary contacts and the salt bridge, before helix formation. The remaining 20% of the paths occur in the opposite order, by first forming the helix. The transition states of the rate-limiting steps are solvated native-like structures. Water expulsion is found to be the last step upon folding for each route. Committor analysis suggests that the dynamics of the solvent is not part of the reaction coordinate. Nevertheless, during the transition, specific water molecules are strongly bound and can play a structural role in the folding.

Characterization of the folding transition-state ensemble and the denatured-state ensemble is an important step toward a full elucidation of protein folding mechanisms. We report herein an investigation of the free-energy landscape of FSD-1 protein by a total of four sets of folding and unfolding molecular dynamics simulations with explicit solvent. The transition-state ensemble was initially identified from unfolding simulations at 500 K and was verified by simulations at 300 K starting from the ensemble structures. The denatured-state ensemble and the early-stage folding were studied by a combination of unfolding simulations at 500 K and folding simulations at 300 K starting from the extended conformation. A common feature of the transition-state ensemble was the substantial formation of the native secondary structures, including both the alpha-helix and beta-sheet, with partial exposure of the hydrophobic core in the solvent. Both the native and non-native secondary structures were observed in the denatured-state ensemble and early-stage folding, consistent with the smooth experimental melting curve. Interestingly, the contact orders of the transition-state ensemble structures were similar to that of the native structure and were notably lower than those of the compact structures found in early-stage folding, implying that chain and topological entropy might play significant roles in protein folding. Implications for FSD-1 folding mechanisms and the rate-limiting step are discussed. Analyses further revealed interesting non-native interactions in the denatured-state ensemble and early-stage folding and the possibility that destabilization of these interactions could help to enhance the stability and folding rate of the protein.

Using an all-atom free-energy model we reproducibly and predictively fold a monomeric stable tryptophane-zipper (pdb-code 1LE1) from unfolded starting conformations to experimental accuracy. We construct the folding free-energy landscape under physiological conditions with a fraction of the cost of methods that simulate the folding pathway. We identify a metastable helical ensemble of conformations in the folding funnel and discuss its impact on the folding scenario. A comparison of the energetic contributions of the competing ensembles rationalizes the stabilization of the native ensemble and illustrates opportunities for peptide design.

Globular proteins fold by minimizing the nonpolar surface that is exposed to water, while simultaneously providing hydrogen-bonding interactions for buried backbone groups, usually in the form of secondary structures such as α-helices, β-sheets, and tight turns. A primary thermodynamic driving force for the formation of globular structure is thus the sequestration of nonpolar groups, but the correlation between the parts of proteins that are observed to fold first (termed folding initiation sites) and the “hydrophobicity” (as customarily defined) of the amino acids in these regions has been quite weak. It has previously been noted that many amino acid side chains contain considerable nonpolar sections, even if they also contain polar or charged groups. For example, a lysine side chain contains four methylenes, which may undergo hydrophobic interactions if the charged ε-NH 3 + group is salt-bridged or hydrogen-bonded. Folding initiation sites might therefore contain not only accepted “hydrophobic” amino acids, but also larger charged side chains. Recent experiments on the folding of mutant apomyoglobins provides corroboration for models based on the hypothesis that folding initiation sites arise from hydrophobic interactions. A near-perfect correlation was observed between the areas of the molecule that are present in the burst-phase kinetic intermediate and both the free energy of formation of hydrophobic initiation sites and the parameter “average area buried upon folding,” which pinpoints large side chains, even those containing charged or polar portions. These results provide a putative mechanism for the control of protein-folding initiation and growth by polar/nonpolar sequence propensity alone.

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

A model of hydrophobic collapse, which is treated as the driving force for protein folding, is presented. This model is the superposition of three models commonly used in protein structure prediction: (1) 'oil-drop' model introduced by Kauzmann, (2) a lattice model introduced to decrease the number of degrees of freedom for structural changes and (3) a model of the formation of hydrophobic core as a key feature in driving the folding of proteins. These three models together helped to develop the idea of a fuzzy-oil-drop as a model for an external force field of hydrophobic character mimicking the hydrophobicity-differentiated environment for hydrophobic collapse. All amino acids in the polypeptide interact pair-wise during the folding process (energy minimization procedure) and interact with the external hydrophobic force field defined by a three-dimensional Gaussian function. The value of the Gaussian function usually interpreted as a probability distribution is treated as a normalized hydrophobicity distribution, with its maximum in the center of the ellipsoid and decreasing proportionally with the distance versus the center. The fuzzy-oil-drop is elastic and changes its shape and size during the simulated folding procedure.

The folding of naturally occurring, single-domain proteins is usually well described as a simple, single-exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers, we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity is enhanced by enhancing the nonadditivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximates single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, in part, a consequence of their remarkably cooperative folding.

Molecular dynamics simulations can be used to reveal the detailed conformational behaviors of peptides and proteins. By comparing fragment and full-length protein simulations, we can investigate the role of each peptide segment in the folding process. Here, we take advantage of information regarding the helix formation process from our previous simulations of barnase and protein A as well as new simulations of four helical fragments from these proteins at three different temperatures, starting with both helical and extended structures. Segments with high helical propensity began the folding process by tethering the chain through side chain interactions involving either polar interactions, such as salt bridges, or hydrophobic staples. These tethers were frequently nonnative (i.e., not i --i + 4 spacing) and provided a scaffold for other residues, thereby limiting the conformational search. The helical structure then propagated on both sides of the tether. Segments with low stability and propensity formed later in the folding process and utilized contacts with other portions of the protein when folding. These helices formed via a tertiary contact-assisted mechanism, primarily via hydrophobic contacts between residues distant in sequence. Thus, segments with different helical propensities appear to play different roles during protein folding. Furthermore, the active role of nonlocal side chains in helix formation highlights why we must move beyond simple hierarchical models of protein folding.

In a recent paper (J. Bredenbeck, J. Helbing, J.R. Kumita, G.A. Woolley, P. Hamm, α-helix formation in a photoswitchable peptide tracked from picoseconds to microseconds by time resolved IR spectroscopy, Proc. Natl. Acad. Sci USA 102 (2005) 2379), we have investigated the folding of a photo-switchable α-helix with a kinetics that could be fit by a stretched exponential function exp(−(t/τ)β). The stretching factor β became smaller as the temperature was lowered, a result which has been interpreted in terms of activated diffusion on a rugged energy surface. In the present paper, we discuss under which conditions diffusion problems occur with stretched exponential kinetics (β 1). We show that diffusion problems do have a strong tendency to yield stretched exponential kinetics, yet, that there are conditions (strong perturbation from equilibrium, performing the experiment in the folding direction) under which compressed exponential kinetics would be expected instead. We discuss the kinetics on free energy surfaces predicted by simple initiation-propagation models (zipper models) of α-helix folding, as well as by folding funnel models. We show that our recent experiment has been performed under condition for which models with strong downhill driving force, such as the zipper model, would predict compressed, rather than stretched exponential kinetics, in disagreement with the experimental observation. We therefore propose that the free energy surface along a reaction coordinate that governs the folding kinetics must be relatively flat and has a shape similar to a 1D golf course. We discuss how this conclusion can be unified with the thermodynamically well established zipper model by introducing an additional kinetic reaction coordinate.

We study the dependence of folding time, nucleation site, and stability of a model β-hairpin on the location of a cross-strand hydrophobic pair, using a coarse-grained off-lattice model with the aid of Monte Carlo simulations. Our simulations have produced 6500 independent folding trajectories dynamically, forming the basis for extensive statistical analysis. Four folding pathways, zipping-out, middle-out, zipping-in, and reptation, have been closely monitored and discussed in all seven sequences studied. A hydrophobic pair placed near the β-turn or in the middle section effectively speed up folding; a hydrophobic pair placed close to the terminal ends or next to the β-turn encourages stability of the entire chain. Proteins 2006. © 2006 Wiley-Liss, Inc.

The folding kinetics of a 16-residue beta-hairpin (trpzip4) and five mutants were studied by a laser-induced temperature-jump infrared method. Our results indicate that mutations which affect the strength of the hydrophobic cluster lead to a decrease in the thermal stability of the beta-hairpin, as a result of increased unfolding rates. For example, the W45Y mutant has a phi-value of approximately zero, implying a folding transition state in which the native contacts involving Trp45 are not yet formed. On the other hand, mutations in the turn or loop region mostly affect the folding rate. In particular, replacing Asp46 with Ala leads to a decrease in the folding rate by roughly 9 times. Accordingly, the phi-value for D46A is determined to be approximately 0.77, suggesting that this residue plays a key role in stabilizing the folding transition state. This is most likely due to the fact that the main chain and side chain of Asp46 form a characteristic hydrogen bond network with other residues in the turn region. Taken together, these results support the folding mechanism we proposed before, which suggests that the turn formation is the rate-limiting step in beta-hairpin folding and, consequently, a stronger turn-promoting sequence increases the stability of a beta-hairpin primarily by increasing its folding rate, whereas a stronger hydrophobic cluster increases the stability of a beta-hairpin primarily by decreasing its unfolding rate. In addition, we have examined the compactness of the thermally denatured and urea-denatured states of another 16-residue beta-hairpin, using the method of fluorescence resonance energy transfer. Our results show that the thermally denatured state of this beta-hairpin is significantly more compact than the urea-denatured state, suggesting that the very first step in beta-hairpin folding, when initiated from an extended conformation, probably corresponds to a process of hydrophobic collapse.

Protein folding is governed by a complex free energy surface whose entropic contributions are relevant because of the large number of degrees of freedom involved. Such complexity, in particular the conformational heterogeneity of the denatured state, is hidden in projections onto one or two order parameters (e.g. fraction of native contacts and/or radius of gyration), which usually results in relatively smooth surfaces. Recent approaches borrowed from network and graph theory have yielded quantitative unprojected representations of the free energy surfaces of a beta-hairpin and a three-stranded beta-sheet peptide using equilibrium folding-unfolding molecular dynamics simulations. Interestingly, the network and graph analyses of these structured peptides have revealed a very heterogeneous denatured state ensemble. It includes high-enthalpy, high-entropy conformations with fluctuating non-native secondary structure, as well as low-enthalpy, low-entropy traps.

Four versions of a β-sheet protein (CD2.d1) have been made, each with a single artificial disulfide bond inserted into hairpin structures. Folding kinetics of reduced and oxidized forms shows bridge position strongly influences its effect on the folding reaction. Bridging residues 58 and 62 does not affect the rapidly formed intermediate (I) or rate-limiting transition (t) state, whereas bridging 33 and 38, or 31 and 41, lowers the t-state energy, with the latter having the stronger influence. Bridging residues 79 and 90 stabilizes both I- and t-states. To assess additivity in the energetic effects of these bridges, four double-bridge variants have also been made. All show precise additivity of overall stability, with two showing additivity when ground states and the rate-limiting t-state are assessed, i.e. no measurable change in the folding mechanism occurs. However, combining 31-41 and 79-90 bridges produces a molecule that folds through a different pathway, with a much more stable intermediate than expected and a much higher t-state barrier. This is explained by the artificial introduction of stabilizing, non-native contacts in the I-state. More surprisingly, for another double-bridge version (58-62 and 79-90) both I- and t-states are less stable than expected, showing that conformational constraints introduced by the two bridges prevent formation of non-native contacts that would otherwise stabilize the I- and t-states, thereby lowering the energy of the folding landscape in the wild-type (unbridged) molecule. We conclude that the lowest energy path for folding has I- and t-state structures that are stabilized by non-native interactions.

Chaperonin-mediated protein fold- ing is complex. There have been diverse results on folding behavior, and the chaperonin molecules have been investigated as enhancing or retarding the folding rate. To understand the diversity of chaperonin-mediated protein folding, we report a study based on simulations using a simplified Go - type model. By considering effects of affinity be- tween the substrate protein and the chaperonin wall and spatial confinement of the chaperonin cavity, we study the thermodynamics and kinetics of folding of an unfrustrated substrate protein en- capsulated in a chaperonin cavity. The affinity makes the hydrophobic residues of the protein bind to the chaperonin wall, and a strong (or weak) affinity results in a large (or small) effect of binding. Compared with the folding in bulk, the folding in chaperonin cavity with different strengths of affin- ity shows two kinds of behaviors: one with less dependence on the affinity but more reliance on the spatial confinement effect and the other relying strongly on the affinity. It is found that the enhance- ment or retardation of the folding rate depends on the competition between the spatial confinement and the affinity due to the chaperonin cavity, and a strong affinity produces a slow folding while a weak affinity induces a fast folding. The crossover be- tween two kinds of folding behaviors happens in the case that the favorable effect of confinement is balanced by the unfavorable effect of the affinity, and a critical affinity strength is roughly defined. By analyzing the contacts formed between the residues of the protein and the chaperonin wall and between the residues of the protein themselves, the role of the affinity in the folding processes is studied. The binding of the residues with the chaperonin wall reduces the formation of both native contacts and nonnative contact or mis-contacts, providing a loose structure for further folding after allosteric change of the chaperonin cavity. In addition, 15 single-site- mutated mutants are simulated in order to test the validity of our model and to investigate the impor- tance of affinity. Inspiringly, our results of the folding rates have a good correlation with those obtained from experiments. The folding rates are inversely correlated with the strength of the bind- ing interactions, i.e., the weaker the binding, the faster the folding. We also find that the inner hydro- phobic residues have larger effects on the folding kinetics than those of the exterior hydrophobic residues. We suggest that, besides the confinement effect, the affinity acts as another important factor to affect the folding of the substrate proteins in chaperonin systems, providing an understanding of the folding mechanism of the molecular chaperonin systems. Proteins 2005;61:777-794.

Protein engineering studies suggest that the transition state for the folding of ubiquitin is highly polarised towards the N-terminal part of the sequence and involves a nucleus of residues within the beta-hairpin (residues 1-17) and main alpha-helix (residues 23-34). In contrast, the observation of small phi-values for residues in the C-terminal portion of the sequence (residues 35-76), coupled with a folding topology that results in a much higher contact order, suggests that fast folding of ubiquitin is dependent upon configurational flexibility in the C-terminal part of the polypeptide chain to ensure passage down a relatively smooth folding funnel to the native state. We show that the introduction of a small mini-hairpin motif as an extension of the native 43-50 hairpin stabilises local interactions in the C-terminal part of the sequence, resulting largely in a deceleration of the unfolding kinetics without perturbing the apparent two-state folding mechanism. However, a single-point Leu--Phe substitution within the engineered hairpin sequence leads to the premature collapse of the denatured ensemble through the stabilisation of non-native interactions and the population of a compact intermediate. Non-linear effects in the kinetic data at low concentrations of denaturant suggest that the collapsed state, which is further stabilised in the presence of cosmotropic salts, may subsequently fold directly to the native state through a "triangular" reaction scheme involving internal rearrangement rather than unfolding and refolding.

Computational studies of proteins have significantly improved our understanding of protein folding. These studies are normally carried out by using chains in isolation. However, in many systems of practical interest, proteins fold in the presence of other molecules. To obtain insight into folding in such situations, we compare the thermodynamics of folding for a Miyazawa–Jernigan model 64-mer in isolation to results obtained in the presence of additional chains. The melting temperature falls as the chain concentration increases. In multichain systems, free-energy landscapes for folding show an increased preference for misfolded states. Misfolding is accompanied by an increase in interprotein interactions; however, near the folding temperature, the transition from folded chains to misfolded and associated chains is entropically driven. A majority of the most probable interprotein contacts are also native contacts, suggesting that native topology plays a role in early stages of aggregation.

The dimeric beta-barrel domain is an unusual topology, shared only by two viral origin binding proteins, where secondary, tertiary and quaternary structure are coupled, and where the dimerization interface is composed of two four-stranded half-beta-barrels. The folding of the DNA binding domain of the E2 transcriptional regulator from human papillomavirus, strain-16, takes place through a stable and compact monomeric intermediate, with 31% the stability of the folded dimeric domain. Double jump multiple wavelength experiments allowed the reconstruction of the fluorescence spectrum of the monomeric intermediate at 100 milliseconds, indicating that tryptophan residues, otherwise buried in the folded state, are accessible to the solvent. Burial of surface area as well as differential behavior to ionic strength and pH with respect to the native ground state, plus the impossibility of having over 2500 A2 of surface area of the half-barrel exposed to the solvent, indicates that the formation of a non-native compact tertiary structure precedes the assembly of native quaternary structure. The monomeric intermediate can dimerize, albeit with a weaker affinity (approximately 1 microM), to yield a non-native dimeric intermediate, which rearranges to the native dimer through a parallel folding channel, with a unimolecular rate-limiting step. Folding pathways from either acid or urea unfolded states are identical, making the folding model robust. Unfolding takes place through a major phase accounting for apparently all the secondary structure change, with identical rate constant to that of the fluorescence unfolding experiment. In contrast to the folding direction, no unfolding intermediate was found.

Recent experimental studies have shown that alpha-helical proteins can approach the folding "speed limit", where folding switches from an activated to a downhill process in free energy. beta-sheet proteins are generally thought to fold more slowly than helix bundles. However, based on studies of hairpins, folding should still be able to approach the microsecond time scale. Here we demonstrate how the hPin1 WW domain, a triple-stranded beta-sheet protein with a sharp thermodynamic melting transition, can be engineered toward the folding "speed limit" without a significant loss in thermal denaturation cooperativity.

The N-terminal beta-hairpin sequence of ubiquitin has been implicated as a folding nucleation site. To extend and stabilise the ubiquitin folding nucleus, we have inserted an autonomously folding 14-residue peptide sequence beta4 which in isolation forms a highly populated beta-hairpin (70%) stabilised by local interactions. NMR structural analysis of the ubiquitin mutant (Ubeta4) shows that the hairpin finger is fully structured and stabilises ubiquitin by approximately 8kJmol(-1). Protein engineering and kinetic (phi(F)-value) analysis of a series of Ubeta4 mutants shows that the hairpin extension of Ubeta4 is also significantly populated in the transition state (phi(F)-values0.7) and has the effect of templating the formation of native contacts in the folding nucleus of ubiquitin. However, at low denaturant concentrations the chevron plot of Ubeta4 shows a small deviation from linearity (roll-over effect), indicative of the population of a compact collapsed state, which appears to arise from over-stabilisation of local interactions. Destabilising mutations within the native hairpin sequence and within the engineered hairpin extension, but not elsewhere, eliminate this non-linearity and restore apparent two-state behaviour. The pitfall to stabilising local interactions is to present hurdles to the rapid and efficient folding of small proteins down a smooth folding funnel by trapping partially folded or misfolded states that must unfold or rearrange before refolding.

The folding mechanism of the G29A mutant of the B-domain of protein A (BdpA) has been studied by all-atom molecular dynamics simulation using AMBER force field (ff03) and generalized Born continuum solvent model. Started from the extended chain conformation, a total of 16 simulations (400 ns each) at 300 K captured some early folding events of the G29A mutant of BdpA. In one of the 16 trajectories, the G29A mutant folded within 2.8 A (root mean square) of the wild-type NMR structure. We observed that the fast burial of hydrophobic residues was the driving force to bring the distant residues into close proximity. The initiation of the helix I and III occurred during the stage of hydrophobic collapse. The initiation and growth of the helix II was slow. Both the secondary structure formation and the development of the native tertiary contacts suggested a multistage folding process. Clustering analysis indicated that two helix species (helices I and III) could be intermediates. Further analysis revealed that the hydrophobic residues of partially folded helix II formed nativelike hydrophobic contacts with helices I and III that stabilized a nativelike state and delayed the completion of folding of the entire protein. The details of the early folding process were compared with other theoretical and experimental studies. It was found that a nativelike hydrophobic cluster was formed by residues including F 3 0 , I 3 1 , L 3 4 , L 4 4 , L 4 5 , and A 4 8 that prevented further development of the native structures, and breaking the hydrophobic cluster like this one contributed to the rate-limiting step. This was in complete agreement with the recent kinetic measurements in which mutations of these residues to Gly and Ala substantially increased the folding rates by as much as 60 times. Apparently, destabilization of nonnative states dramatically enhanced the folding rates.

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