Absence of a stable intermediate on the folding pathway of protein A

Flexibly varying folding mechanism of a nearly symmetrical protein: B domain of protein A

The folding pathway of the B domain of protein A is the pathway most intensively studied by computer simulations. Recent systematic measurement of Phi values by Sato et al., however, has shown that none of the published computational predictions is consistent with the detailed features of the experimentally observed folding mechanism. In this article we use a statistical mechanical model of folding to show that sensitive dependence of multiple transition state ensembles on temperature and the denaturant concentration is the key to resolving the inconsistency among simulations and the experiment. Such sensitivity in multiple transition state ensembles is a natural consequence of symmetry-breaking in a nearly symmetrical protein.

Kinetic Studies of Folding of the B-domain of Staphylococcal Protein A with Molecular Dynamics and a United-residue (UNRES) Model of Polypeptide Chains

Langevin dynamics is used with our physics-based united-residue (UNRES) force field to study the folding pathways of the B-domain of staphylococcal protein A (1BDD (alpha; 46 residues)). With 400 trajectories of protein A started from the extended state (to gather meaningful statistics), and simulated for more than 35 ns each, 380 of them folded to the native structure. The simulations were carried out at the optimal folding temperature of protein A with this force field. To the best of our knowledge, this is the first simulation study of protein-folding kinetics with a physics-based force field in which reliable statistics can be gathered. In all the simulations, the C-terminal alpha-helix forms first. The ensemble of the native basin has an average RMSD value of 4 A from the native structure. There is a stable intermediate along the folding pathway, in which the N-terminal alpha-helix is unfolded; this intermediate appears on the way to the native structure in less than one-fourth of the folding pathways, while the remaining ones proceed directly to the native state. Non-native structures persist until the end of the simulations, but the native-like structures dominate. To express the kinetics of protein A folding quantitatively, two observables were used: (i) the average alpha-helix content (averaged over all trajectories within a given time window); and (ii) the fraction of conformations (averaged over all trajectories within a given time window) with Calpha RMSD values from the native structure less than 5 A (fraction of completely folded structures). The alpha-helix content grows quickly with time, and its variation fits well to a single-exponential term, suggesting fast two-state kinetics. On the other hand, the fraction of folded structures changes more slowly with time and fits to a sum of two exponentials, in agreement with the appearance of the intermediate, found when analyzing the folding pathways. This observation demonstrates that different qualitative and quantitative conclusions about folding kinetics can be drawn depending on which observable is monitored.

Transition State Ensemble for the Folding of B Domain of Protein A: A Comparison of Distributed Molecular Dynamics Simulations with Experiments

Folding pathways of the B domain of staphylococcal protein A have been sampled with a distributed computing approach. Starting from an extended structure, the method employs an index measuring topological similarity to the native structure to selectively sample trajectory branches leading to the native fold. Unperturbed and continuous folding trajectories are drawn on a physics-based atomic potential energy surface with an implicit solvent. The sampled folding trajectories demonstrate a similar sequence of events: the earlier stage involves a partial formation of helix 2 and to a less extent of helix 1 at their N terminals, followed by the hydrophobic collapse between residues F14, I17, and L18 on helix 1 and residues R28, F31, and I32 on helix 2, which results in the rigidification of the helix turn from R28 to I32. Helix 2 is then able to extend, allowing for the formation to turn 2. The above description explains one experimental result why a G30A mutant of the protein was observed to be the fastest folder among proteins of its size. And the ensemble of structures right before the final collapse is in good agreement with the transition state ensemble mapped by another recent experiment with Fersht Phi values. We emphasize that because the approach here does not provide quantifications of the free energy landscape, our model of the transition state ensemble emerges from comparisons of simulations and previous experimental results rather from the simulation results alone. On the other hand, as our approach does not rely on a low-dimensional free energy surface, it can complement methods based on the construction of free energy surfaces.

Structure and stability of a model three-helix-bundle protein on tailored surfaces

The interaction of protein molecules with surfaces is important in numerous applications. Theoretical work on protein adsorption has been limited. In particular, it is difficult to obtain quantitative predictions about the structure and stability of proteins on surfaces. In this study, density-of-states-based simulations were performed on a Gō-like model of a three-helix-bundle fragment from protein A (PDB ID: 1bdd). Both mechanical and thermal stability were investigated on neutral and attractive surfaces and compared to that in the absence of a surface. It was found that attaching the peptide to any type of surface decreases its melting temperature by as much as 9 K, depending upon orientation. Calorimetric cooperativity, as measured by van't Hoff to calorimetric enthalpy ratios, similarly decreased. It was also found that the mechanical strength of the peptide attached to surfaces is degraded to varying extents, depending upon the surface type and protein orientation. A comparison of mechanical and thermal stability showed that the two are not synonymous, but occur through different pathways, and that system configurations that are more thermally stable are not always so mechanically.

Molecular dynamics with the united-residue model of polypeptide chains. II. Langevin and Berendsen-bath dynamics and tests on model alpha-helical systems

The implementation of molecular dynamics (MD) with our physics-based protein united-residue (UNRES) force field, described in the accompanying paper, was extended to Langevin dynamics. The equations of motion are integrated by using a simplified stochastic velocity Verlet algorithm. To compare the results to those with all-atom simulations with implicit solvent in which no explicit stochastic and friction forces are present, we alternatively introduced the Berendsen thermostat. Test simulations on the Ala(10) polypeptide demonstrated that the average kinetic energy is stable with about a 5 fs time step. To determine the correspondence between the UNRES time step and the time step of all-atom molecular dynamics, all-atom simulations with the AMBER 99 force field and explicit solvent and also with implicit solvent taken into account within the framework of the generalized Born/surface area (GBSA) model were carried out on the unblocked Ala(10) polypeptide. We found that the UNRES time scale is 4 times longer than that of all-atom MD simulations because the degrees of freedom corresponding to the fastest motions in UNRES are averaged out. When the reduction of the computational cost for evaluation of the UNRES energy function is also taken into account, UNRES (with hydration included implicitly in the side chain-side chain interaction potential) offers about at least a 4000-fold speed up of computations relative to all-atom simulations with explicit solvent and at least a 65-fold speed up relative to all-atom simulations with implicit solvent. To carry out an initial full-blown test of the UNRES/MD approach, we ran Berendsen-bath and Langevin dynamics simulations of the 46-residue B-domain of staphylococcal protein A. We were able to determine the folding temperature at which all trajectories converged to nativelike structures with both approaches. For comparison, we carried out ab initio folding simulations of this protein at the AMBER 99/GBSA level. The average CPU time for folding protein A by UNRES molecular dynamics was 30 min with a single Alpha processor, compared to about 152 h for all-atom simulations with implicit solvent. It can be concluded that the UNRES/MD approach will enable us to carry out microsecond and, possibly, millisecond simulations of protein folding and, consequently, of the folding process of proteins in real time.

Folding simulations of small proteins

Understanding how a protein folds is a long-standing challenge in modern science. We have used an optimized atomistic model (united-residue force field) to simulate folding of small proteins of various structures: HP-36 (alpha protein), protein A (beta), 1fsd (alpha+beta), and betanova (beta). Extensive Monte Carlo folding simulations (ten independent runs with 10(9) Monte Carlo steps at a temperature) starting from non-native conformations are carried out for each protein. In all cases, proteins fold into their native-like conformations at appropriate temperatures, and glassy transitions occur at low temperatures. To investigate early folding trajectories, 200 independent runs with 10(6) Monte Carlo steps are also performed at a fixed temperature for a protein. There are a variety of possible pathways during non-equilibrium early processes (fast process, approximately 10(4) Monte Carlo steps). Finally, these pathways converge to the point unique for each protein. The convergence point of the early folding pathways can be determined only by direct folding simulations. The free energy surface, an equilibrium thermodynamic property, dictates the rest of the folding (slow process, approximately 10(8) Monte Carlo steps).

The folding of spectrin domains II: phi-value analysis of R16

Studies on the folding of helical proteins have shown a wide range of different mechanisms and highlighted the importance of helical propensity as a factor in determining folding mechanism. Here, we contribute to this interesting field with the protein engineering phi-value analysis of the 16th domain of chicken brain alpha-spectrin, R16. The fortuitous curvature seen in the unfolding arm of the chevron plot allows us to investigate both early and late events in folding. R16 is the first two-state helical protein for which this has been possible.

Efficient expansion, folding, and unfolding of proteins

We consider a nonstatistical, computationally fast experiment to identify important topological constraints in folding small globular proteins of about 100-200 amino acids. In this experiment, proteins are expanded mechanically along a path of steepest increase in the free space around residues. The pathways are often consistent with folding scenarios reported in kinetics experiments and most accurately describe obligatory or mechanic folding proteins. The results suggest that certain topological "defects" in proteins lead to preferred, entropically favorable channels down their free energy landscapes.

SecA folding kinetics: a large dimeric protein rapidly forms multiple native states

SecA, a 202 kDa dimeric protein, is the ATPase for the Sec-dependent translocase of precursor proteins in vivo. SecA must undergo conformational changes, which may involve dissociation into a monomer, as it translocates the precursor protein across the inner membrane. To better understand the dynamics of SecA in vivo, protein folding studies to probe the native, intermediate, and unfolded species of SecA in vitro have been done. SecA folds through a stable dimeric intermediate and dimerizes in the dead-time of a manual-mixing kinetic experiment ( approximately 5-7 seconds). Here, stopped-flow fluorescence and CD, as well as ultra-rapid continuous flow fluorescence techniques, were used to further probe the rapid folding kinetics of SecA. In the absence of urea, rapid, near diffusion-limited ( approximately 10(9)M(-1)s(-1)) SecA dimerization occurs following a rate-limiting unimolecular rearrangement of a rapidly formed intermediate. Multiple kinetic folding and unfolding phases were observed and SecA was shown to have multiple native and unfolded states. Using sequential-mixing stopped-flow experiments, SecA was determined to fold via parallel channels with sequential intermediates. These results confirm that SecA is a highly dynamic protein, consistent with the rapid, major conformational changes it must undergo in vivo.

Folding of small proteins using a single continuous potential

Extensive Monte Carlo folding simulations for four proteins of various structural classes are carried out, using a single continuous potential (united-residue force field). In all cases, collapse occurs at a very early stage, and proteins fold into their nativelike conformations at appropriate temperatures. We also observe that glassy transitions occur at low temperatures. The simulation results demonstrate that the folding mechanism is controlled not only by thermodynamic factors but also by kinetic factors: The way a protein folds into its native structure is also determined by the convergence point of early folding trajectories, which cannot be obtained by the free energy surface.

Testing protein-folding simulations by experiment: B domain of protein A

We have assessed the published predictions of the pathway of folding of the B domain of protein A, the pathway most studied by computer simulation. We analyzed the transition state for folding of the three-helix bundle protein, by using experimental Phi values on some 70 suitable mutants. Surprisingly, the third helix, which has the most stable alpha-helical structure as a peptide fragment, is poorly formed in the transition state, especially at its C terminus. The protein folds around a nearly fully formed central helix, which is stabilized by extensive hydrophobic side chain interactions. The turn connecting the poorly structured first helix to the central helix is unstructured, but the turn connecting the central helix to the third is in the process of being formed as the N-terminal region of the third helix begins to coalesce. The transition state is inconsistent with a classical framework mechanism and is closer to nucleation-condensation. None of the published atomistic simulations are fully consistent with the experimental picture although many capture important features. There is a continuing need for combining simulation with experiment to describe folding pathways, and of continued testing to improve predictive methods.

Unfolding of the cold shock protein studied with biased molecular dynamics

The cold shock protein from Bacillus caldolyticus is a small beta-barrel protein that folds in a two-state mechanism. For the native protein and for several mutants, a wealth of experimental data are available on stability and folding, so that it is an optimal system to study this process. We compare data from unfolding simulations (trajectories of 5 and up to 12 ns) obtained with a bias potential at room temperature and from unbiased thermal unfolding simulations with experimental data. The unfolding patterns derived from the trajectories starting from different native-like conformations and subject to different unfolding conditions agree. The transition state found in the simulations of unfolding is close to the native structure in agreement with experiment. Moreover, a lower value of the free energy barrier of unfolding was found for the mutant R3E than for the mutant E46A and the native protein, as indicated by experimental data. The first unfolding event involves the three-stranded beta-sheet whose decomposition corresponds to the transition state. In contrast to conclusions drawn from experiments, we found that the two-stranded beta-strand forms the most stable substructure, which decomposes very late in the unfolding process. However, assuming that this structure forms very early in the folding process, our findings would not contradict the experiments but require a different interpretation of them.

Sequence-based study of two related proteins with different folding behaviors

Z(SPA-1) is an engineered protein that binds to its parent, the three-helix-bundle Z domain of staphylococcal protein A. Uncomplexed Z(SPA-1) shows a reduced helix content and a melting behavior that is less cooperative, compared with the wild-type Z domain. Here we show that the difference in folding behavior between these two sequences can be partly understood in terms of an off-lattice model with 5-6 atoms per amino acid and a minimalistic potential, in which folding is driven by backbone hydrogen bonding and effective hydrophobic attraction.

Folding a protein in a computer: an atomic description of the folding/unfolding of protein A

We study the folding mechanism of a three-helix bundle protein at atomic resolution, including effects of explicit water. Using replica exchange molecular dynamics we perform enough sampling over a wide range of temperatures to obtain the free energy, entropy, and enthalpy surfaces as a function of structural reaction coordinates. Simulations were started from different configurations covering the folded and unfolded states. Because many transitions between all minima at the free energy surface are observed, a quantitative determination of the free energy barriers and the ensemble of configurations associated with them is now possible. The kinetic bottlenecks for folding can be determined from the thermal ensembles of structures on the free energy barriers, provided the kinetically determined transition-state ensembles are similar to those determined from free energy barriers. A mechanism incorporating the interplay among backbone ordering, sidechain packing, and desolvation arises from these calculations. Large Phi values arise not only from native contacts, which mostly form at the transition state, but also from contacts already present in the unfolded state that are partially destroyed at the transition.

Ab Initio Folding of Helix Bundle Proteins Using Molecular Dynamics Simulations

We have demonstrated that ab initio fast folding simulations at 400 K using a GB implicit solvent model with an all-atom based force field can describe the spontaneous formation of nativelike structures for the 36-residue villin headpiece and the 46-residue fragment B of Staphylococcal protein A. An implicit solvent model combined with high-temperature MD makes it possible to perform direct folding simulations of small- to medium-sized proteins by reducing the computational requirements tremendously. In the early stage of folding of the villin headpiece and protein A, initial hydrophobic collapse and rapid formation of helices were found to play important roles. For protein A, the third helix forms first in the early stage of folding and exhibits higher stability. The free energy profiles calculated from the folding simulations suggested that both of the helix-bundle proteins show a two-state thermodynamic behavior and protein A exhibits rather broad native basins.

Thermodynamics of alpha- and beta-structure formation in proteins

An atomic protein model with a minimalistic potential is developed and then tested on an alpha-helix and a beta-hairpin, using exactly the same parameters for both peptides. We find that melting curves for these sequences to a good approximation can be described by a simple two-state model, with parameters that are in reasonable quantitative agreement with experimental data. Despite the apparent two-state character of the melting curves, the energy distributions are found to lack a clear bimodal shape, which is discussed in some detail. We also perform a Monte Carlo-based kinetic study and find, in accord with experimental data, that the alpha-helix forms faster than the beta-hairpin.

Identification of rare partially unfolded states in equilibrium with the native conformation in an all beta-barrel protein

Human acidic fibroblast growth factor 1 (hFGF-1) is an all beta-barrel protein, and the secondary structural elements in the protein include 12 antiparallel beta-strands arranged into a beta-trefoil fold. In the present study, we investigate the stability of hFGF-1 by hydrogen-deuterium exchange as a function of urea concentration. Urea-induced equilibrium unfolding of hFGF-1 monitored by fluorescence and CD spectroscopy suggests that the protein unfolds by a two-state (native to denatured) mechanism. Hydrogen exchange in hFGF-1, under the experimental conditions used, occurs by the EX2 mechanism. In contrast to the equilibrium unfolding events monitored by optical probes, native state hydrogen exchange data show that the beta-trefoil architecture of hFGF-1 does not behave as a single cooperative unit. There are at least two structurally independent units with differing stabilities in hFGF-1. Beta-strands I, II, III, VI, VII, X, XI, and XII fit into the global unfolding isotherm. By contrast, residues in beta-strands IV, V, VIII, and IX exchange by the subfolding isotherm and could be responsible for the occurrence of high-energy partially unfolded state(s) in hFGF-1. There appears to be a broad continuum of stabilities among the four beta-strands (beta-strands IV, V, VIII, and IX) constituting the subglobal folding unit. The slow exchanging residues in hFGF-1 do not represent the folding nucleus of the protein.

An atomically detailed study of the folding pathways of protein A with the stochastic difference equation

An algorithm is applied here to compute folding pathways of staphylococcal protein A, fragment B. Emphasis is on studies of the complete process, starting from an ensemble of fully denatured conformations and ending at the folded state. The stochastic difference equation algorithm is based on optimization of an action that makes it possible to use a large integration step. Motions with typical displacements that change rapidly on the size scale of the step are filtered out, providing numerically stable and approximate solutions. The present approach is unique in maintaining an atomically detailed picture while providing a systematic, controlled approximation to the classical equations of motion. Analysis of 130 trajectories suggests the following folding mechanism for protein A: At an early precollapse phase of the process, a few native hydrogen bonds form near the C terminus of the protein. The hydrogen bonds are formed mostly within the third helix. The next step is chain collapse that occurs in parallel to additional growth of secondary structure seeds. Therefore, the present study does not support a pure hydrophobic collapse, or substantial early formation of secondary structure. At the last step, native tertiary contacts are formed at the same time as the completion of the secondary structure elements. To a large extent, the process is parallel and not sequential. The early formation of the third helix of protein A, fragment B (in the calculation), is consistent with experimental data.

The dual role of a loop with low loop contact distance in folding and domain swapping

Alpha helices, beta strands, and loops are the basic building blocks of protein structure. The folding kinetics of alpha helices and beta strands have been investigated extensively. However, little is known about the formation of loops. Experimental studies show that for some proteins, the formation of a single loop is the rate-determining step for folding, whereas for others, a loop (or turn) can misfold to serve as the hinge loop region for domain-swapped species. Computer simulations of an all-atom model of fragment B of Staphylococcal protein A found that the formation of a single loop initiates the dominant folding pathway. On the other hand, the stability analysis of intermediates suggests that the same loop is a likely candidate to serve as a hinge loop for domain swapping. To interpret the simulation result, we developed a simple structural parameter: the loop contact distance (LCD), or the sequence distance of contacting residues between a loop and the rest of the protein. The parameter is applied to a number of other proteins, including SH3 domains and prion protein. The results suggest that a locally interacting loop (low LCD) can either promote folding or serve as the hinge region for domain swapping. Thus, there is an intimate connection between folding and domain swapping, a possible cause of misfolding and aggregation.

Structure and functional interactions of the Tsg101 UEV domain

Human Tsg101 plays key roles in HIV budding and in cellular vacuolar protein sorting (VPS). In performing these functions, Tsg101 binds both ubiquitin (Ub) and the PTAP tetrapeptide 'late domain' motif located within the viral Gag protein. These interactions are mediated by the N-terminal domain of Tsg101, which belongs to the catalytically inactive ubiquitin E2 variant (UEV) family. We now report the structure of Tsg101 UEV and chemical shift mapping of the Ub and PTAP binding sites. Tsg101 UEV resembles canonical E2 ubiquitin conjugating enzymes, but has an additional N-terminal helix, an extended beta-hairpin that links strands 1 and 2, and lacks the two C-terminal helices normally found in E2 enzymes. PTAP-containing peptides bind in a hydrophobic cleft exposed by the absence of the C-terminal helices, whereas ubiquitin binds in a novel site surrounding the beta-hairpin. These studies provide a structural framework for understanding how Tsg101 mediates the protein-protein interactions required for HIV budding and VPS.

Folding of a small helical protein using hydrogen bonds and hydrophobicity forces

A reduced protein model with five to six atoms per amino acid and five amino acid types is developed and tested on a three-helix-bundle protein, a 46-amino acid fragment from staphylococcal protein A. The model does not rely on the widely used Go approximation, which ignores non-native interactions. We find that the collapse transition is considerably more abrupt for the protein A sequence than for random sequences with the same composition. The chain collapse is found to be at least as fast as helix formation. Energy minimization restricted to the thermodynamically favored topology gives a structure that has a root-mean-square deviation of 1.8 A from the native structure. The sequence-dependent part of our potential is pairwise additive. Our calculations suggest that fine-tuning this potential by parameter optimization is of limited use.

Application of the diffusion-collision model to the folding of three-helix bundle proteins

The diffusion-collision model has been successful in explaining many features of protein folding kinetics, particularly for helical proteins. In the model the folding reaction is described in terms of coupled chemical kinetic (Master) equations of coarse grained entities, called microdomains. Here, the diffusion-collision model is applied to compute the folding kinetics of four three-helix bundle proteins, all of which fold on a time scale of tens of microseconds and appear to have two-state folding. The native structure and the stability of the helical microdomains are used to determine the parameters of the model. The formulation allows computation of the overall rate and determination of the importance of kinetic intermediates. The proteins considered are the B domain of protein A (1BDC), the Engrailed Homeodomain (1ENH), the peripheral sub-unit-binding domain (1EBD C-chain) and the villin headpiece subdomain (1VII). The results for the folding time of protein A, the Engrailed Homeodomain, and 1EBD C-chain are in agreement with experiment, while 1VII is not stable in the present model. In the three proteins that are stable, two-state folding is predicted by the diffusion-collision model. This disagrees with published assertions that multistate kinetics would be obtained from the model. The contact order prediction agrees with experiment for protein A, but yields values that are a factor of 40, 30 and 15 too slow for 1ENH, 1EBD C-chain and 1VII. The effect of mutants on folding is described for protein A and it is demonstrated that significant intermediate concentrations (i.e. deviation from two-state folding) can occur if the stability of some of the helical microdomains is increased. A linear relationship between folding time and the length of the loop between helices B and C in protein A is demonstrated; this is not evident in the contact order description.

A structure-based method for derivation of all-atom potentials for protein folding

A method for deriving all-atom protein folding potentials is presented and tested on a three-helix bundle protein, as well as on hairpin and helical sequences. The potentials obtained are composed of a contact term between pairs of atoms, and a local density term for each atom, mimicking solvent exposure preferences. Using this potential in an all-atom protein folding simulation, we repeatedly folded the three-helix bundle, with the lowest energy conformations having a C(alpha) distance rms from the native structure of less than 2 A. Similar results were obtained for the hairpin and helices by using different potentials. We derived potentials for several different proteins and found a high correlation between the derived parameters, suggesting that a potential of this form eventually could be found that folds multiple, unrelated proteins at the atomic level of detail.

Roles of native topology and chain-length scaling in protein folding: a simulation study with a Go-like model

We perform folding simulations on 18 small proteins with using a simple Go-like protein model and analyze the folding rate constants, characteristics of the transition state ensemble, and those of the denatured states in terms of native topology and chain length. Near the folding transition temperature, the folding rate k(F) scales as k(F) approximately exp(-c RCO N(0.6)) where RCO and N are the relative contact order and number of residues, respectively. Here the topology RCO dependence of the rates is close to that found experimentally (k(F) approximately exp(-c RCO)), while the chain length N dependence is in harmony with the predicted scaling property (k(F) approximately exp(-c N(2/3))). Thus, this may provides a unified scaling law in folding rates at the transition temperature, k(F) approximately exp(-c RCO N(2/3)). The degree of residual structure in the denatured state is highly correlated with RCO, namely, proteins with smaller RCO tend to have more ordered structure in the denatured state. This is consistent with the observation that many helical proteins such as myoglobin and protein A, have partial helices, in the denatured states. The characteristics of the transition state ensemble calculated by the current model, which uses native topology but not sequence specific information, are consistent with experimental phi-value data for about half of proteins.

From folding theories to folding proteins: a review and assessment of simulation studies of protein folding and unfolding

Beginning with simplified lattice and continuum "minimalist" models and progressing to detailed atomic models, simulation studies have augmented and directed development of the modern landscape perspective of protein folding. In this review we discuss aspects of detailed atomic simulation methods applied to studies of protein folding free energy surfaces, using biased-sampling free energy methods and temperature-induced protein unfolding. We review studies from each on systems of particular experimental interest and assess the strengths and weaknesses of each approach in the context of "exact" results for both free energies and kinetics of a minimalist model for a beta-barrel protein. We illustrate in detail how each approach is implemented and discuss analysis methods that have been developed as components of these studies. We describe key insights into the relationship between protein topology and the folding mechanism emerging from folding free energy surface calculations. We further describe the determination of detailed "pathways" and models of folding transition states that have resulted from unfolding studies. Our assessment of the two methods suggests that both can provide, often complementary, details of folding mechanism and thermodynamics, but this success relies on (a) adequate sampling of diverse conformational regions for the biased-sampling free energy approach and (b) many trajectories at multiple temperatures for unfolding studies. Furthermore, we find that temperature-induced unfolding provides representatives of folding trajectories only when the topology and sequence (energy) provide a relatively funneled landscape and "off-pathway" intermediates do not exist.

Characterization of the folding kinetics of a three-helix bundle protein via a minimalist Langevin model

We use a simple off-lattice Langevin model of protein folding to characterize the folding and unfolding of a fast-folding, 46 residue three-helix bundle. Under conditions at which the C-terminal helix is 30 % stable, we observe a clear three-state folding mechanism. In the on-pathway intermediate state, the middle and C-terminal helices are folded and in contact with each other, while the N-terminal region remains disordered. Nevertheless, under these conditions this intermediate is thermodynamically unstable relative to its unfolded state. The first and highest folding barrier corresponds to the organization of the hinge between the middle and C-terminal helices. A subsequent major barrier corresponds to the organization of the hinge between the middle and N-terminal helices. Hyperstabilizing the hinge regions leads to twice the folding rate that is obtained from hyperstabilizing the helices, even though much fewer contacts are involved in hinge hyperstabilization than in helix hyperstabilization. Unfolding follows single-exponential kinetics, even at temperatures only slightly above the folding transition temperature.

The folding thermodynamics and kinetics of crambin using an all-atom Monte Carlo simulation

We present a novel Monte Carlo simulation of protein folding, in which all heavy atoms are represented as interacting hard spheres. This model includes all degrees of freedom relevant to folding, all side-chain and backbone torsions, and uses a Go potential. In this study, we focus on the 46 residue alpha/beta protein crambin and two of its structural components, the helix and helix hairpin. For a wide range of temperatures, we recorded multiple folding events of these three structures from random coils to native conformations that differ by less than 1 A C(alpha) dRMS from their crystal structure coordinates. The thermodynamics and kinetic mechanism of the helix-coil transition obtained from our simulation shows excellent agreement with currently available experimental and molecular dynamics data. Based on insights obtained from folding its smaller structural components, a possible folding mechanism for crambin is proposed. We observed that the folding occurs via a cooperative, first order-like process, and that many folding pathways to the native state exist. One particular sequence of events constitutes a "fast-folding" pathway where kinetic traps are avoided. At very low temperatures, a kinetic trap arising from the incorrect packing of side-chains was observed. These results demonstrate that folding to the native state can be observed in a reasonable amount of time on desktop computers even when an all-atom representation is used, provided the energetics sufficiently stabilize the native state.

Solution structure of an immunoactive peptide fragment of Staphylococcal protein-A

Staphylococcal protein-A (SpA) is known to bind the Fc fragment of immunoglobin G in vitro and induce a myriad of immunogenic responses in vivo. The latter is ascribed to be due to the interaction of Fc and SpA. It has also been proposed that in vivo proteolytically cleaved fragments of SpA may be functioning in the same manner. One such fragment (EQQNAFYEILHLPNLNEEQR), fragment 8-27 of the B-domain (SpA-B), was recently shown to exhibit in vivo immunogenic response [Sinha, P., Sengupta, J., and Ray, P. K. (1999) Biochem. Biophys. Res. Commun. 258, 141-147]. As a first step towards understanding the mode of interaction of this peptide with the Fc fragment, we have studied the solution conformation of this isolated peptide by CD and NMR. The peptide, with 7 contact residues in the crystal structure of the SpA-B/Fc complex and comprising of mostly helixI and part of helixII of the 3-helix bundle of SpA-B, was found to be present predominantly in extended structure. However it showed nascent turn/helix like conformations around F14 & Y15. These two residues are known to play a vital role in SpA-B/Fc interaction as deciphered from crystal structure and NMR studies of SpA-B/Fc complex and mutational studies. The implications of our results, especially the nascent conformations found around F14 & Y15, in design of SpA-B mimetic small molecules are discussed.

Three-helix-bundle protein in a Ramachandran model

We study the thermodynamic behavior of a model protein with 54 amino acids that forms a three-helix bundle in its native state. The model contains three types of amino acids and five to six atoms per amino acid and has the Ramachandran torsional angles phi(i), psi(i) as its degrees of freedom. The force field is based on hydrogen bonds and effective hydrophobicity forces. For a suitable choice of the relative strength of these interactions, we find that the three-helix-bundle protein undergoes an abrupt folding transition from an expanded state to the native state. Also shown is that the corresponding one- and two-helix segments are less stable than the three-helix sequence.

Formation of hydrogen bonds precedes the rate-limiting formation of persistent structure in the folding of ACBP

A burst phase in the early folding of the four-helix two-state folder protein acyl-coenzyme A binding protein (ACBP) has been detected using quenched-flow in combination with site-specific NMR-detected hydrogen exchange. Several of the burst phase structures coincide with a structure consisting of eight conserved hydrophobic residues at the interface between the two N and C-terminal helices. Previous mutation studies have shown that the formation of this structure is rate limiting for the final folding of ACBP. The burst phase structures observed in ACBP are different from the previously reported collapsed types of burst phase intermediates observed in the folding of other proteins.

Generating ensemble averages for small proteins from extended conformations by Monte Carlo simulations

Since it is not feasible to determine the structure of every protein by experiment, algorithms delivering the folded conformation of a protein solely from its amino acid sequence are desirable. Here the diffusion-process controlled-Monte Carlo approach has been applied to generating ensemble averages for three small proteins with 31, 36, and 46 residues. Starting from extended conformations and using an energy model that was developed on other protein models, the simulations find nativelike structures deviating by 3 A rms from the experimental structures for the main chain atoms. The balance between long-range and short-range interactions is discussed briefly in the context of stability and folding.

Long timescale simulations

Computers are becoming increasingly fast, making it possible to perform simulations of macromolecules on timescales that were previously inaccessible. Questions have arisen concerning how well we are keeping up with computer power and the state of the art with respect to long molecular dynamics simulations in solvent. More importantly, however, simulations of macromolecules are performed to aid the understanding of biochemical phenomena. So, what are we learning from longer simulations and are they providing reliable insight into protein dynamics, conformational behavior and function?

Thermal unfolding of an intermediate is associated with non-Arrhenius kinetics in the folding of hen lysozyme

A variety of techniques, including quenched-flow hydrogen exchange labelling monitored by electrospray ionization mass spectrometry, and stopped-flow absorbance, fluorescence and circular dichroism spectroscopy, has been used to investigate the refolding kinetics of hen lysozyme over a temperature range from 2 degrees C to 50 degrees C. Simple Arrhenius behaviour is not observed, and although the overall rate of folding increases from 2 to 40 degrees C, it decreases above 40 degrees C. In addition, the transient intermediate on the major folding pathway at 20 degrees C, in which the alpha-domain is persistently structured in the absence of a stable beta-domain, is thermally unfolded in a sigmoidal transition (T(m) approximately 40 degrees C) indicative of a cooperatively folded state. At all temperatures, however, there is evidence for fast ( approximately 25 %) and slow ( approximately 75 %) populations of refolding molecules. By using transition state theory, the kinetic data from various experiments were jointly fitted to a sequential three-state model for the slow folding pathway. Together with previous findings, these results indicate that the alpha-domain intermediate is a productive species on the folding route between the denatured and native states, and which accumulates as a consequence of its intrinsic stability. Our analysis suggests that the temperature dependence of the rate constant for lysozyme folding depends on both the total change in the heat capacity between the ground and transition states (the dominant factor at low temperatures) and the heat-induced destabilization of the alpha-domain intermediate (the dominant factor at high temperatures). Destabilization of such kinetically competent intermediate species is likely to be a determining factor in the non-Arrhenius temperature dependence of the folding rate of those proteins for which one or more intermediates are populated.

Staphylococcal protein A: unfolding pathways, unfolded states, and differences between the B and E domains

We present multiple native and denaturation simulations of the B and E domains of the three-helix bundle protein A, totaling 60 ns. The C-terminal helix (H3) consistently denatures later than either of the other two helices and contains residual helical structure in the denatured state. These results are consistent with experiments suggesting that the isolated H3 fragment is more stable than H1 and H2 and that H3 forms early in folding. Interestingly, the denatured state of the B domain is much more compact than that of the E domain. This sequence-dependent effect on the dimensions of the denatured state and the lack of correlation with structure suggest that the radius of gyration can be a misleading reaction coordinate for unfolding/folding. Various unfolding and refolding events are observed in the denaturation simulations. In some cases, the transitions are facilitated through interactions with other portions of the protein-contact-assisted helix formation. In the native simulations, the E domain is very stable: after 6 ns, the C(alpha) root-mean-square deviation from the starting structure is less than 1.4 A. In contrast, the native state of the B domain deviates more and its inter-helical angles fluctuate. In apparent contrast, we note that the B domain is thermodynamically more stable than the E domain. The simulations suggest that the increased stability of the B domain may be due to heightened mobility, and therefore entropy, in the native state and decreased mobility/entropy in the more compact denatured state.

Rate and equilibrium constants for protein unfolding and refolding determined by hydrogen exchange-mass spectrometry

Studies of protein unfolding and refolding may help us understand the more general problem of protein folding. Recent studies from this laboratory demonstrated that the unfolding and refolding of a large protein, rabbit muscle aldolase (M(r) 157 kDa), can be studied by combining amide hydrogen exchange and mass spectrometry. Results of these studies indicated that aldolase has three unfolding domains which likely unfold sequentially. Urea was used to increase the populations of partially unfolded states which were labeled with deuterium following a brief exposure to D(2)O. Electrospray ionization mass spectra of both the intact protein and its peptic fragments had multiple envelopes of isotope peaks from which the populations of unfolded forms were determined. The present study extends the previous investigations to include different urea concentrations and kinetic modeling of data taken as the system approaches equilibrium. Analysis of these results gives rate and equilibrium constants describing the unfolding and refolding processes characteristic of aldolase destabilized in urea. The change in solvent-accessible surface, which has been used as a reaction coordinate for protein folding, is estimated from the dependence of the equilibrium and rate constants on the concentration of urea.

Folding of a model three-helix bundle protein: a thermodynamic and kinetic analysis

The kinetics and thermodynamics of an off-lattice model for a three-helix bundle protein are investigated as a function of a bias gap parameter that determines the energy difference between native and non-native contacts. A simple dihedral potential is used to introduce the tendency to form right-handed helices. For each value of the bias parameter, 100 trajectories of up to one microsecond are performed. Such statistically valid sampling of the kinetics is made possible by the use of the discrete molecular dynamics method with square-well interactions. This permits much faster simulations for off-lattice models than do continuous potentials. It is found that major folding pathways can be defined, although ensembles with considerable structural variation are involved. The large gap models generally fold faster than those with a smaller gap. For the large gap models, the kinetic intermediates are non-obligatory, while both obligatory and non-obligatory intermediates are present for small gap models. Certain large gap intermediates have a two-helix microdomain with one helix extended outward (as in domain-swapped dimers); the small gap intermediates have more diverse structures. The importance of studying the kinetic, as well as the thermodynamics, of folding for an understanding of the mechanism is discussed and the relation between kinetic and equilibrium intermediates is examined. It is found that the behavior of this model system has aspects that encompass both the "new" view and the "old" view of protein folding.

Exploring the origins of topological frustration: design of a minimally frustrated model of fragment B of protein A

Topological frustration in an energetically unfrustrated off-lattice model of the helical protein fragment B of protein A from Staphylococcus aureus was investigated. This G-type model exhibited thermodynamic and kinetic signatures of a well-designed two-state folder with concurrent collapse and folding transitions and single exponential kinetics at the transition temperature. Topological frustration is determined in the absence of energetic frustration by the distribution of Fersht phi values. Topologically unfrustrated systems present a unimodal distribution sharply peaked at intermediate phi, whereas highly frustrated systems display a bimodal distribution peaked at low and high phi values. The distribution of phi values in protein A was determined both thermodynamically and kinetically. Both methods yielded a unimodal distribution centered at phi = 0.3 with tails extending to low and high phi values, indicating the presence of a small amount of topological frustration. The contacts with high phi values were located in the turn regions between helices I and II and II and III, intimating that these hairpins are in large part required in the transition state. Our results are in good agreement with all-atom simulations of protein A, as well as lattice simulations of a three- letter code 27-mer (which can be compared with a 60-residue helical protein). The relatively broad unimodal distribution of phi values obtained from the all-atom simulations and that from the minimalist model for the same native fold suggest that the structure of the transition state ensemble is determined mostly by the protein topology and not energetic frustration.

The hydrogen exchange core and protein folding

A database of hydrogen-deuterium exchange results has been compiled for proteins for which there are published rates of out-exchange in the native state, protection against exchange during folding, and out-exchange in partially folded forms. The question of whether the slow exchange core is the folding core (Woodward C, 1993, Trends Biochem Sci 18:359-360) is reexamined in a detailed comparison of the specific amide protons (NHs) and the elements of secondary structure on which they are located. For each pulsed exchange or competition experiment, probe NHs are shown explicitly; the large number and broad distribution of probe NHs support the validity of comparing out-exchange with pulsed-exchange/competition experiments. There is a strong tendency for the same elements of secondary structure to carry NHs most protected in the native state, NHs first protected during folding, and NHs most protected in partially folded species. There is not a one-to-one correspondence of individual NHs. Proteins for which there are published data for native state out-exchange and theta values are also reviewed. The elements of secondary structure containing the slowest exchanging NHs in native proteins tend to contain side chains with high theta values or be connected to a turn/loop with high theta values. A definition for a protein core is proposed, and the implications for protein folding are discussed. Apparently, during folding and in the native state, nonlocal interactions between core sequences are favored more than other possible nonlocal interactions. Other studies of partially folded bovine pancreatic trypsin inhibitor (Barbar E, Barany G, Woodward C, 1995, Biochemistry 34:11423-11434; Barber E, Hare M, Daragan V, Barany G, Woodward C, 1998, Biochemistry 37:7822-7833), suggest that developing cores have site-specific energy barriers between microstates, one disordered, and the other(s) more ordered.

Comparison of continuous and pulsed labeling amide hydrogen exchange/mass spectrometry for studies of protein dynamics

In contrast to the rigid structures portrayed by X-ray diffraction, proteins in solution display constant motion which leads to populations that are momentarily unfolded. To begin to understand protein dynamics, we must have experimental methods for determining rates of folding and unfolding, as well as for identifying structures of folding and unfolding intermediates. Amide hydrogen exchange has become an important tool for such measurements. When urea is used to stabilize unfolded forms of proteins, the refolding rates may become slower than the rates of isotope exchange. In such cases, the intermolecular distribution of deuterium among the entire population of molecules may become bimodal, giving rise to a bimodal distribution of isotope peaks in mass spectra of the protein or its peptic fragments. When the protein is exposed continuously to D2O, the relative intensities of the two envelopes of isotope peaks give an integrated account of populations participating in the folding/unfolding process. However, when the protein is exposed only briefly to D2O, the relative intensities of the two envelopes of isotope peaks give an instantaneous measure of the folded/unfolded populations. Application of these two labeling methods to a large protein, aldolase, is described along with a discussion of specific parameters required to optimize these experiments.

Conservation of rapid two-state folding in mesophilic, thermophilic and hyperthermophilic cold shock proteins

The cold shock protein CspB from Bacillus subtilis is only marginally stable, but it folds extremely fast in a simple N reversible U two-state reaction. The corresponding cold shock proteins from the thermophile Bacillus caldolyticus and the hyperthermophile Thermotoga maritima show strongly increased conformational stabilities, but unchanged very fast two-state refolding kinetics. The absence of intermediates in the folding of B. subtilis CspB is thus not a corollary of its low stability. Rather, two-state folding and an unusually native-like activated state of folding seem to be inherent properties of these small all-beta proteins. There is no link between stability and folding rate, and numerous sequence positions exist which can be varied to modulate the stability without affecting the rate and mechanism of folding.

Pathways for protein folding: is a new view needed?

Theoretical studies using simplified models of proteins have shed light on the general heteropolymeric aspects of the folding problem. Recent work has emphasized the statistical aspects of folding pathways. In particular, progress has been made in characterizing the ensemble of transition state conformations and elucidating the role of intermediates. These advances suggest a reconciliation between the new ensemble approaches and the classical view of a folding pathway.