Equilibrium and kinetic folding pathways of a TIM barrel with a funneled energy landscape

The role of native contact topology in the folding of a TIM barrel model based on the alpha-subunit of tryptophan synthase (alphaTS) from Salmonella typhimurium (Protein Data Bank structure 1BKS) was studied using both equilibrium and kinetic simulations. Equilibrium simulations of alphaTS reveal the population of two intermediate ensembles, I1 and I2, during unfolding/refolding at the folding temperature, Tf = 335 K. Equilibrium intermediate I1 demonstrates discrete structure in regions alpha0-beta6 whereas intermediate I2 is a loose ensemble of states with N-terminal structure varying from at least beta1-beta3 (denoted I2A) to alpha0-beta4 at most (denoted I2B). The structures of I1 and I2 match well with the two intermediate states detected in equilibrium folding experiments of Escherichia coli alphaTS. Kinetic folding simulations of alphaTS reveal the sequential population of four intermediate ensembles, I120Q, I200Q, I300Q, and I360Q, during refolding. Kinetic intermediates I120Q, I200Q, and I300Q are highly similar to equilibrium alphaTS intermediates I2A, I2B, and I1, respectively, consistent with kinetic experiments on alphaTS from E. coli. A small population (approximately 10%) of kinetic trajectories are trapped in the I120Q intermediate ensemble and require a slow and complete unfolding step to properly refold. Both the on-pathway and off-pathway I120Q intermediates show structure in beta1-beta3, which is also strikingly consistent with kinetic folding experiments of alphaTS. In the off-pathway intermediate I(120Q), helix alpha2 is wrapped in a nonnative chiral arrangement around strand beta3, sterically preventing the subsequent folding step between beta3 and beta4. These results demonstrate the success of combining kinetic and equilibrium simulations of minimalist protein models to explore TIM barrel folding and the folding of other large proteins.     

Outer membrane protein folding from an energy landscape perspective

The cell envelope is essential for the survival of Gram-negative bacteria. This specialised membrane is densely packed with outer membrane proteins (OMPs), which perform a variety of functions. How OMPs fold into this crowded environment remains an open question. Here, we review current knowledge about OMP folding mechanisms in vitro and discuss how the need to fold to a stable native state has shaped their folding energy landscapes. We also highlight the role of chaperones and the β-barrel assembly machinery (BAM) in assisting OMP folding in vivo and discuss proposed mechanisms by which this fascinating machinery may catalyse OMP folding.     

Probing the energy landscape of protein folding/unfolding transition states

Previous molecular dynamics (MD) simulations of the thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided atomic-resolution models of the transition state ensemble that is well supported by experimental studies. Here, we use simulations to further investigate the energy landscape around the transition state region. Nine structures within approximately 35 ps and 3 A C(alpha) RMSD of the transition state ensemble identified in a previous 498 K thermal denaturation simulation were quenched under the quasi-native conditions of 335 K and neutral pH. All of the structures underwent hydrophobically driven collapse in response to the drop in temperature. Structures less denatured than the transition state became structurally more native-like, while structures that were more denatured than the transition state tended to show additional loss of native structure. The structures in the immediate region of the transition state fluctuated between becoming more and less native-like. All of the starting structures had the same native-like topology and were quite similar (within 3.5 A C(alpha) RMSD). That the structures all shared native-like topology, yet diverged into either more or less native-like structures depending on which side of the transition state they occupied on the unfolding trajectory, indicates that topology alone does not dictate protein folding. Instead, our results suggest that a detailed interplay of packing interactions and interactions with water determine whether a partially denatured protein will become more native-like under refolding conditions.     

Effects of confinement in chaperonin assisted protein folding: rate enhancement by decreasing the roughness of the folding energy landscape

Chaperonins, such as the GroE complex of the bacteria Escherichia coli, assist the folding of proteins under non-permissive folding conditions by providing a cavity in which the newly translated or translocated protein can be encapsulated. Whether the chaperonin cage plays a passive role in protecting the protein from aggregation, or an active role in accelerating folding rates, remains a matter of debate. Here, we investigate the role of confinement in chaperonin mediated folding through molecular dynamics simulations. We designed a substrate protein with an alpha/beta sandwich fold, a common structural motif found in GroE substrate proteins and confined it to a spherical hydrophilic cage which mimicked the interior of the GroEL/ES cavity. The thermodynamics and kinetics of folding were studied over a wide range of temperature and cage radii. Confinement was seen to significantly raise the collapse temperature, T(c), as a result of the associated entropy loss of the unfolded state. The folding temperature, T(f), on the other hand, remained unaffected by encapsulation, a consequence of the folding mechanism of this protein that involves an initial collapse to a compact misfolded state prior to rearranging to the native state. Folding rates were observed to be either accelerated or retarded compared to bulk folding rates, depending on the temperature of the simulation. Rate enhancements due to confinement were observed only at temperatures above the temperature T(m), which corresponds to the temperature at which the protein folds fastest. For this protein, T(m) lies above the folding temperature, T(f), implying that encapsulation alone will not lead to a rate enhancement under conditions where the native state is stable (T相似文献   

Exploring the energy landscape of protein folding using replica-exchange and conventional molecular dynamics simulations

Two independent replica-exchange molecular dynamics (REMD) simulations with an explicit water model were performed of the Trp-cage mini-protein. In the first REMD simulation, the replicas started from the native conformation, while in the second they started from a nonnative conformation. Initially, the first simulation yielded results qualitatively similar to those of two previously published REMD simulations: the protein appeared to be over-stabilized, with the predicted melting temperature 50-150K higher than the experimental value of 315K. However, as the first REMD simulation progressed, the protein unfolded at all temperatures. In our second REMD simulation, which starts from a nonnative conformation, there was no evidence of significant folding. Transitions from the unfolded to the folded state did not occur on the timescale of these simulations, despite the expected improvement in sampling of REMD over conventional molecular dynamics (MD) simulations. The combined 1.42 micros of simulation time was insufficient for REMD simulations with different starting structures to converge. Conventional MD simulations at a range of temperatures were also performed. In contrast to REMD, the conventional MD simulations provide an estimate of Tm in good agreement with experiment. Furthermore, the conventional MD is a fraction of the cost of REMD and continuous, realistic pathways of the unfolding process at atomic resolution are obtained.     

Predicting protein folding pathways

A structured folding pathway, which is a time ordered sequence of folding events, plays an important role in the protein folding process and hence, in the conformational search. Pathway prediction, thus gives more insight into the folding process and is a valuable guiding tool to search the conformation space. In this paper, we propose a novel 'unfolding' approach to predict the folding pathway. We apply graph-based methods on a weighted secondary structure graph of a protein to predict the sequence of unfolding events. When viewed in reverse this yields the folding pathway. We demonstrate the success of our approach on several proteins whose pathway is partially known.     

Using chimeric immunity proteins to explore the energy landscape for alpha-helical protein folding

To address the role of sequence in the folding of homologous proteins, the folding and unfolding kinetics of the all-helical bacterial immunity proteins Im2 and Im9 were characterised, together with six chimeric derivatives of these proteins. We show that both Im2 and Im9 fold rapidly (k(UN)(H(2)O)) approximately 2000 s(-1) at pH 7.0, 25 degrees C) in apparent two-state transitions, through rate-limiting transition states that are highly compact (beta(TS)0.93 and 0.96, respectively). Whilst the folding and unfolding properties of three of the chimeras (Im2 (1-44)(Im9), Im2 (1-64)(Im9 )and Im2 (25-44)(Im9)) are similar to their parental counterparts, in other chimeric proteins the introduced sequence variation results in altered kinetic behaviour. At low urea concentrations, Im2 (1-29)(Im9) and Im2 (56-64)(Im9) fold in two-state transitions via transition states that are significantly less compact (beta(TS) approximately 0.7) than those characterised for the other immunity proteins presented here. At higher urea concentrations, however, the rate-limiting transition state for these two chimeras switches or moves to a more compact species (beta(TS) approximately 0.9). Surprisingly, Im2 (30-64)(Im9) populates a highly collapsed species (beta(I)=0.87) in the dead-time (2.5 ms) of stopped flow measurements. These data indicate that whilst topology may place significant constraints on the folding process, specific inter-residue interactions, revealed here through multiple sequence changes, can modulate the ruggedness of the folding energy landscape.     

Energetics of the native energy landscape of a two-domain calcium sensor protein: distinct folding features of the two domains

The protein folding energy landscape allows a thorough understanding of the protein folding problem which in turn helps in understanding various aspects of biological functions. Characterizing the cooperative unfolding units and the intermediates along the folding funnel of a protein is a challenging task. In this paper, we investigated the native energy landscape of EhCaBP, a calcium sensor, belonging to the same EF-hand superfamily as calmodulin. EhCaBP is a two-domain EF-hand protein consisting of two EF-hands in each domain and binding to four Ca2+ cations. Native-state hydrogen exchange (HX) was used to assess the folding features of the landscape and also to throw light on the structure-folding function paradigm of calcium sensor proteins. HX measurements under the EX2 regime provided the thermodynamic information about the protein folding events under native conditions. HX studies revealed that the unfolding of EhCaBP is not a two-state process. Instead, it proceeds through cooperative units. The C-terminal domain exhibits less denaturant dependence than the N-terminal domain, suggesting that the former is dominated by local fluctuations. It is interesting to note that the N- and C-terminal domains of EhCaBP have distinct folding features. In fact, these observed differences can regulate the domain-dependent target recognition of two-domain Ca2+ sensor proteins.     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

An analysis of protein folding pathways

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

Prediction of protein folding pathways.

Recent 1H nuclear magnetic resonance (n.m.r.) hydrogen exchange experiments on five different proteins have delineated the secondary structures formed in trapped, partially folded intermediates. The early forming structural elements are identifiable through a technique described in this work to predict folding pathways. The method assumes that the sequential selection of structural fragments such as alpha-helices and beta-strands involved in the folding process is founded upon the maximal burial of solvent accessible surface from both the formation of internal structure and substructure association. The substructural elements were defined objectively by major changes in main-chain direction. The predicted folding pathways are in complete correspondence with the n.m.r. results in that the formed structural fragments found in the folding intermediates are those predicted earliest in the pathways. The technique was also applied to proteins of known tertiary structure and with fold similar to one of the five proteins examined by 1H n.m.r. The pathways for these structures also showed general consistency with the n.m.r. observations, suggesting conservation of a secondary structural framework or molten globule about which folding nucleates and proceeds.     

Malleability of protein folding pathways: a simple reason for complex behaviour

Although the structures of native proteins are generally unique, the pathways by which they form are often free to vary. Some proteins fold by a multitude of different pathways, whereas others seem restricted to only one choice. An explanation for this variation in folding behaviour has recently emerged from studies of transition state changes: the number of accessible pathways is linked to the number of nucleation motifs contained within the native topology. We refer to these nucleation motifs as 'foldons', as they approach the size of an independent cooperative unit. Thus, with respect to pathway malleability and the composition of the folding funnel, proteins can be seen as modular assemblies of competing foldons. For the split beta-alpha-beta fold, these foldons are two-strand-helix motifs coupled by spatial overlap.     

Core formation in apomyoglobin: probing the upper reaches of the folding energy landscape

An acid-destabilized form of apomyoglobin, the so-called E state, consists of a set of heterogeneous structures that are all characterized by a stable hydrophobic core composed of 30-40 residues at the intersection of the A, G, and H helices of the protein, with little other secondary structure and no other tertiary structure. Relaxation kinetics studies were carried out to characterize the dynamics of core melting and formation in this protein. The unfolding and/or refolding response is induced by a laser-induced temperature jump between the folded and unfolded forms of E, and structural changes are monitored using the infrared amide I' absorbance at 1648-1651 cm(-1) that reports on the formation of solvent-protected, native-like helix in the core and by fluorescence emission changes from apomyoglobin's Trp14, a measure of burial of the indole group of this residue. The fluorescence kinetics data are monoexponential with a relaxation time of 14 micros. However, infrared kinetics data are best fit to a biexponential function with relaxation times of 14 and 59 micros. These relaxation times are very fast, close to the limits placed on folding reactions by diffusion. The 14 micros relaxation time is weakly temperature dependent and thus represents a pathway that is energetically downhill. The appearance of this relaxation time in both the fluorescence and infrared measurements indicates that this folding event proceeds by a concomitant formation of compact secondary and tertiary structures. The 59 micros relaxation time is much more strongly temperature dependent and has no fluorescence counterpart, indicating an activated process with a large energy barrier wherein nonspecific hydrophobic interactions between helix A and the G and H helices cause some helix burial but Trp14 remains solvent exposed. These results are best fit by a multiple-pathway kinetic model when U collapses to form the various folded core structures of E. Thus, the results suggest very robust dynamics for core formation involving multiple folding pathways and provide significant insight into the primary processes of protein folding.     

Prediction of protein folding pathways: Bovine pancreatic trypsin inhibitor

A previous theory for the prediction of protein folding pathways [1] is applied to bovine pancreatic trypsin inhibitor and the resulting sequence of folding events shown to corroborate well with available experimental data.     

Prediction of protein structure by simulating coarse-grained folding pathways: a preliminary report

A set of software tools designed to study protein structure and kinetics has been developed. The core of these tools is a program called Folding Machine (FM) which is able to generate low resolution folding pathways using modest computational resources. The FM is based on a coarse-grained kinetic ab initio Monte-Carlo sampler that can optionally use information extracted from secondary structure prediction servers or from fragment libraries of local structure. The model underpinning this algorithm contains two novel elements: (a) the conformational space is discretized using the Ramachandran basins defined in the local phi-psi energy maps; and (b) the solvent is treated implicitly by rescaling the pairwise terms of the non-bonded energy function according to the local solvent environments. The purpose of this hybrid ab initio/knowledge-based approach is threefold: to cover the long time scales of folding, to generate useful 3-dimensional models of protein structures, and to gain insight on the protein folding kinetics. Even though the algorithm is not yet fully developed, it has been used in a recent blind test of protein structure prediction (CASP5). The FM generated models within 6 A backbone rmsd for fragments of about 60-70 residues of alpha-helical proteins. For a CASP5 target that turned out to be natively unfolded, the trajectory obtained for this sequence uniquely failed to converge. Also, a new measure to evaluate structure predictions is presented and used along the standard CASP assessment methods. Finally, recent improvements in the prediction of beta-sheet structures are briefly described.