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.     

Analysis of long-range interactions in a model denatured state of staphylococcal nuclease based on correlated changes in backbone dynamics.

An expanded, highly dynamic denatured state of staphylococcal nuclease exhibits a native-like topology in the apparent absence of tight packing and fixed hydrogen bonds (Gillespie JR, Shortle D, 1997, J Mol Biol 268:158-169, 170-184). To address the physical basis of the long-range spatial ordering of this molecule, we probe the effects of perturbations of the sequence and solution conditions on the local chain dynamics of a denatured 101-residue fragment that is missing the first three beta strands. Structural interactions between chain segments are inferred from correlated changes in the motional behavior of residues monitored by 15N NMR relaxation measurements. Restoration of the sequence corresponding to the first three beta strands significantly increases the average order of all chain segments that form the five strand beta barrel including loops but has no effect on the carboxy terminal 30 residues. Addition of the denaturing salt sodium perchlorate enhances ordering over the entire sequence of this fragment. Analysis of seven different substitution mutants points to a complex set of interactions between the hydrophobic segment corresponding to beta strand 5 and the remainder of the chain. General patterns in the data suggest there is a hierarchy of native-like interactions that occur transiently in the denatured state and are consistent with the overall topology of the denatured state ensemble being determined by many coupled local interactions rather than a few highly specific long-range interactions.     

Phi-analysis at the experimental limits: mechanism of beta-hairpin formation

The 37-residue Formin-binding protein, FBP28, is a canonical three-stranded beta-sheet WW domain. Because of its small size, it is so insensitive to chemical denaturation that it is barely possible to determine accurately a denaturation curve, as the transition spans 0-7 M guanidinium hydrochloride (GdmCl). It is also only marginally stable, with a free energy of denaturation of just 2.3 kcal/mol at 10 degrees Celsius so only small changes in energy upon mutation can be tolerated. But these properties and relaxation times for folding of 25 micros-400 micros conspire to allow the rapid acquisition of accurate and reproducible kinetic data for Phi-analysis using classical temperature-jump methods. The transition state for folding is highly polarized with some regions having Phi-values of 0 and others 1, as readily seen in chevron plots, with Phi-values of 0 having the refolding arms overlaying and those of 1 the unfolding arms superimposable. Good agreement is seen with transition state structures identified from independent molecular dynamics (MD) simulations at 60, 75, and 100 degrees Celsius, which allows us to explore further the details of the folding and unfolding pathway of FBP28. The first beta-turn is near native-like in the transition state for folding (experimental) and unfolding (MD and experiment). The simulations show that there are transient contacts between the aromatic side-chains of the beta-strands in the denatured state and that these interactions provide the driving force for folding of the first beta-hairpin of this three-stranded sheet. Only after the backbone hydrogen bonds are formed between beta1 and beta2 does a hydrogen bond form to stabilize the intervening turn, or the first beta-turn.     

Increasing temperature accelerates protein unfolding without changing the pathway of unfolding

We have traditionally relied on extremely elevated temperatures (498K, 225 degrees C) to investigate the unfolding process of proteins within the timescale available to molecular dynamics simulations with explicit solvent. However, recent advances in computer hardware have allowed us to extend our thermal denaturation studies to much lower temperatures. Here we describe the results of simulations of chymotrypsin inhibitor 2 at seven temperatures, ranging from 298K to 498K. The simulation lengths vary from 94ns to 20ns, for a total simulation time of 344ns, or 0.34 micros. At 298K, the protein is very stable over the full 50ns simulation. At 348K, corresponding to the experimentally observed melting temperature of CI2, the protein unfolds over the first 25ns, explores partially unfolded conformations for 20ns, and then refolds over the last 35ns. Above its melting temperature, complete thermal denaturation occurs in an activated process. Early unfolding is characterized by sliding or breathing motions in the protein core, leading to an unfolding transition state with a weakened core and some loss of secondary structure. After the unfolding transition, the core contacts are rapidly lost as the protein passes on to the fully denatured ensemble. While the overall character and order of events in the unfolding process are well conserved across temperatures, there are substantial differences in the timescales over which these events take place. We conclude that 498K simulations are suitable for elucidating the details of protein unfolding at a minimum of computational expense.     

Molecular dynamics simulations of hydrophobic collapse of ubiquitin.

Nine nonnative conformations of ubiquitin, generated during two different thermal denaturation trajectories, were simulated under nearly native conditions (62 degrees C). The simulations included all protein and solvent atoms explicitly, and simulation times ranged from 1-2.4 ns. The starting structures had alpha-carbon root-mean-square deviations (RMSDs) from the crystal structure of 4-12 A and radii of gyration as high as 1.3 times that of the native state. In all but one case, the protein collapsed when the temperature was lowered and sampled conformations as compact as those reached in a control simulation beginning from the crystal structure. In contrast, the protein did not collapse when simulated in a 60% methanol:water mixture. The behavior of the protein depended on the starting structure: during simulation of the most native-like starting structures (<5 A RMSD to the crystal structure) the RMSD decreased, the number of native hydrogen bonds increased, and the secondary and tertiary structure increased. Intermediate starting structures (5-10 A RMSD) collapsed to the radius of gyration of the control simulation, hydrophobic residues were preferentially buried, and the protein acquired some native contacts. However, the protein did not refold. The least native starting structures (10-12 A RMSD) did not collapse as completely as the more native-like structures; instead, they experienced large fluctuations in radius of gyration and went through cycles of expansion and collapse, with improved burial of hydrophobic residues in successive collapsed states.     

Transition state contact orders correlate with protein folding rates

We have used molecular dynamics simulations restrained by experimental phi values derived from protein engineering experiments to determine the structures of the transition state ensembles of ten proteins that fold with two-state kinetics. For each of these proteins we then calculated the average contact order in the transition state ensemble and compared it with the corresponding experimental folding rate. The resulting correlation coefficient is similar to that computed for the contact orders of the native structures, supporting the use of native state contact orders for predicting folding rates. The native contacts in the transition state also correlate with those of the native state but are found to be about 30% lower. These results show that, despite the high levels of heterogeneity in the transition state ensemble, the large majority of contributing structures have native-like topologies and that the native state contact order captures this phenomenon.     

Towards a complete description of the structural and dynamic properties of the denatured state of barnase and the role of residual structure in folding

The detailed characterization of denatured proteins remains elusive due to their mobility and conformational heterogeneity. NMR studies are beginning to provide clues regarding residual structure in the denatured state but the resulting data are too sparse to be transformed into molecular models using conventional techniques. Molecular dynamics simulations can complement NMR by providing detailed structural information for components of the denatured ensemble. Here, we describe three independent 4 ns high-temperature molecular dynamics simulations of barnase in water. The simulated denatured state was conformationally heterogeneous with respect to the conformations populated both within a single simulation and between simulations. Nonetheless, there were some persistent interactions that occurred to varying degrees in all simulations and primarily involved the formation of fluid hydrophobic clusters with participating residues changing over time. The region of the beta(3-4) hairpin contained a particularly high degree of such side-chain interactions but it lacked beta-structure in two of the three denatured ensembles: beta(3-4) was the only portion of the beta-structure to contain significant residual structure in the denatured state. The two principal alpha-helices (alpha1 and alpha2) adopted dynamic helical structure. In addition, there were persistent contacts that pinched off core 2 from the body of the protein. The rest of the protein was unstructured, aside from transient and mostly local side-chain interactions. Overall, the simulated denatured state contains residual structure in the form of dynamic, fluctuating secondary structure in alpha1 and alpha2, as well as fluctuating tertiary contacts in the beta(3-4) region, and between alpha1 and beta(3-4), in agreement with previous NMR studies. Here, we also show that these regions containing residual structure display impaired mobility by both molecular dynamics and NMR relaxation experiments. The residual structure was important in decreasing the conformational states available to the chain and in repairing disrupted regions. For example, tertiary contacts between beta(3-4) and alpha1 assisted in the refolding of alpha1. This contact-assisted helix formation was confirmed in fragment simulations of beta(3-4) and alpha1 alone and complexed, and, as such, alpha1 and beta(3-4) appear to be folding initiation sites. The role of these sites in folding was investigated by working backwards and considering the simulation in reverse, noting that earlier time-points from the simulations provide models of the major intermediate and transition states in quantitative agreement with data from both unfolding and refolding experiments. Both beta(3-4) and alpha1 are dynamic in the denatured state but when they collide and make enough contacts, they provide a loose structural scaffold onto which further beta-strands pack. The beta-structure condenses about beta(3-4), while alpha1 aids in stabilizing beta(3-4) and maintaining its orientation. The resulting beta-structure is relatively planar and loose in the major intermediate. Further packing ensues, and as a result the beta-sheet twists, leading to the major transition state. The structure is still expanded and loops are not well formed at this point. Fine-tuning of the packing interactions and the final condensation of the structure then occurs to yield the native state.     

Identification and characterization of key substructures involved in the early folding events of a (beta/alpha)8-barrel protein as studied by experimental and computational methods

A number of studies have examined the structural properties of late folding intermediates of (beta/alpha)8-barrel proteins involved in tryptophan biosynthesis, whereas there is little information available about the early folding events of these proteins. To identify the contiguous polypeptide segments important to the folding of the (beta/alpha)8-barrel protein Escherichia coli N-(5'-phosphoribosyl)anthranilate isomerase, we structurally characterized fragments and circularly permuted forms of the protein. We also simulated thermal unfolding of the protein using molecular dynamics. Our fragmentation experiments demonstrate that the isolated (beta/alpha)(1-4)beta5 fragment is almost as stable as the full-length protein. The far and near-UV CD spectra of this fragment are indicative of native-like secondary and tertiary structures. Structural analysis of the circularly permutated proteins shows that if the protein is cleaved within the two N-terminal betaalpha modules, the amount of secondary structure is unaffected, whereas, when cleaved within the central (beta/alpha)(3-4)beta5 segment, the protein simply cannot fold. An ensemble of the denatured structures produced by thermal unfolding simulations contains a persistent local structure comprised of beta3, beta4 and beta5. The presence of this three-stranded beta-barrel suggests that it may be an important early-stage folding intermediate. Interactions found in (beta/alpha)(3-4)beta5 may be essential for the early events of ePRAI folding if they provide a nucleation site that directs folding.     

Energetics of the native and non-native states of the glycophorin transmembrane helix dimer

Using an implicit membrane model (IMM1), we examine whether the structure of the transmembrane domain of Glycophorin A (GpA) could be predicted based on energetic considerations alone. The energetics of native GpA shows that van der Waals interactions make the largest contribution to stability. Although specific electrostatic interactions are stabilizing, the overall electrostatic contribution is close to zero. The GXXXG motif contributes significantly to stability, but residues outside this motif contribute almost twice as much. To generate non-native states a global conformational search was done on two segments of GpA: an 18-residue peptide (GpA74-91) that is embedded in the membrane and a 29-residue peptide (GpA70-98) that has additional polar residues flanking the transmembrane region. Simulated annealing was done on a large number of conformations generated from parallel, antiparallel, left- and right-handed starting structures by rotating each helix at 20 degrees intervals around its helical axis. Several crossing points along the helix dimer were considered. For 18-residue parallel topology, an ensemble of native-like structures was found at the lowest effective energy region; the effective energy is lowest for a right-handed structure with an RMSD of 1.0 A from the solid-state NMR structure with correct orientation of the helices. For the 29-residue peptide, the effective energies of several left-handed structures were lower than that of the native, right-handed structure. This could be due to deficiencies in modeling the interactions between charged sidechains and/or omission of the sidechain entropy contribution to the free energy. For 18-residue antiparallel topology, both IMM1 and a Generalized Born model give effective energies that are lower than that of the native structure. In contrast, the Poisson-Boltzmann solvation model gives lower effective energy for the parallel topology, largely because the electrostatic solvation energy is more favorable for the parallel structure. IMM1 seems to underestimate the solvation free energy advantage when the CO and NH dipoles just outside the membrane are parallel. This highlights the importance of electrostatic interactions even when these are not obvious by looking at the structures.     

Mutational analysis demonstrates that specific electrostatic interactions can play a key role in the denatured state ensemble of proteins

The nature of the denatured state ensemble has been controversial for decades owing, in large part, to the difficulty in characterizing the structure and energetics of denatured state interactions. There is increasing evidence for relatively non-specific hydrophobic clustering in the denatured states of some proteins but other types of interactions are much less well characterized. Here, we report the characterization of highly specific electrostatic interactions in the denatured state of a small alpha-beta protein, the N-terminal domain of the ribosomal protein L9 (NTL9). Mutation of Lys12 to Met has been shown to increase the stability of NTL9 significantly through the disruption of denatured state interactions. Here, we describe the analysis of the pH-dependent stability of 13 mutants designed to probe the nature of the Lys12 denatured state interaction. Lys12 is located in a lysine-rich region of the protein but analysis of a set of Lys to Met mutants shows that it plays a unique role in the denatured state. Analysis of mutants of all of the acidic residues in NTL9 shows that Lys12 forms a specific non-native electrostatic interaction with Asp8 in the denatured state ensemble. Thus the distribution of charge-charge interactions in the denatured state ensemble of NTL9 appears to be biased by few key interactions and is very different from that expected in a random coil. We propose that these interactions are not encoded by local sequence effects but rather reflect interactions among residues more distant in sequence. These results demonstrate that electrostatic as well as hydrophobic interactions can play an important role in the denatured state ensemble.     

Charge-charge interactions in the denatured state influence the folding kinetics of ribonuclease Sa

Gaining a better understanding of the denatured state ensemble of proteins is important for understanding protein stability and the mechanism of protein folding. We studied the folding kinetics of ribonuclease Sa (RNase Sa) and a charge-reversal variant (D17R). The refolding kinetics are similar, but the unfolding rate constant is 10-fold greater for the variant. This suggests that charge-charge interactions in the denatured state and the transition state ensembles are more favorable in the variant than in RNase Sa, and shows that charge-charge interactions can influence the kinetics and mechanism of protein folding.     

NMR characterization of residual structure in the denatured state of protein L

Triple-resonance NMR experiments were used to assign the (13)C(alpha), (13)C(beta), (15)N and NH resonances for all the residues in the denatured state of a destabilized protein L variant in 2 M guanidine. The chemical shifts of most resonances were very close to their random coil values. Significant deviations were observed for G22, L38 and K39; increasing the denaturant concentration shifted the chemical shifts of these residues towards theory random coil values. Medium-range nuclear Overhauser enhancements were detected in segments corresponding to the turn between the first two strands, the end of the second strand through the turn between the second strand and the helix, and the turn between the helix and the third strand in 3D H(1), N(15)-HSQC-NOESY-HSQC experiments on perdeuterated samples. Longer-range interactions were probed by measuring the paramagnetic relaxation enhancement produced by nitroxide spin labels introduced via cysteine residues at five sites around the molecule. Damped oscillations in the magnitude of the paramagnetic relaxation enhancement as a function of distance along the sequence suggested native-like chain reversals in the same three turn regions. The more extensive interactions within the region corresponding to the first beta-turn than in the region corresponding to the second beta-turn suggests that the asymmetry in the folding reaction evident in previous studies of the protein L folding transition state is already established in the denatured state.     

Ultra-fast barrier-limited folding in the peripheral subunit-binding domain family

We have determined the solution structures, equilibrium properties and ultra-fast folding kinetics for three bacterial homologues of the peripheral subunit-binding domain (PSBD) family. The mesophilic homologue, BBL, was less stable than the thermophilic and hyper-thermophilic variants (E3BD and POB, respectively). The broad unfolding transitions of each PSBD, when probed by different techniques, were essentially superimposable, consistent with co-operative denaturation. Temperature-jump and continuous-flow fluorescence methods were used to measure the folding kinetics for E3BD, POB and BBL. E3BD folded fairly rapidly at 298K (folding half-time approximately 25 micros) and BBL and POB folded even faster (folding half-times approximately 3-5 micros). The variations in equilibrium and kinetic behaviour observed for the PSBD family resembles that of the homeodomain family, where the folding pattern changes from apparent two-state transitions to multi-state kinetics as the denatured state becomes more structured. The faster folding of POB may be a consequence of its higher propensity to form helical structure in the region corresponding to the folding nucleus of E3BD. The ultra-fast folding of BBL appears to be a consequence of residual structure in the denatured ensemble, as with engrailed homeodomain. We discuss issues concerning "one-state", downhill folding, and find no evidence for, and strong evidence against, it occurring in these PSBDs. The shorter construct used previously for BBL was destabilized significantly and the stability further perturbed by the introduction of fluorescent probes. Thermal titrations for 11 side-chains scattered around the protein, when probed by (13)C-NMR experiments, could be fit globally to a common co-operative transition.     

Influence of denatured and intermediate states of folding on protein aggregation

We simulate the aggregation thermodynamics and kinetics of proteins L and G, each of which self-assembles to the same alpha/beta [corrected] topology through distinct folding mechanisms. We find that the aggregation kinetics of both proteins at an experimentally relevant concentration exhibit both fast and slow aggregation pathways, although a greater proportion of protein G aggregation events are slow relative to those of found for protein L. These kinetic differences are correlated with the amount and distribution of intrachain contacts formed in the denatured state ensemble (DSE), or an intermediate state ensemble (ISE) if it exists, as well as the folding timescales of the two proteins. Protein G aggregates more slowly than protein L due to its rapidly formed folding intermediate, which exhibits native intrachain contacts spread across the protein, suggesting that certain early folding intermediates may be selected for by evolution due to their protective role against unwanted aggregation. Protein L shows only localized native structure in the DSE with timescales of folding that are commensurate with the aggregation timescale, leaving it vulnerable to domain swapping or nonnative interactions with other chains that increase the aggregation rate. Folding experiments that characterize the structural signatures of the DSE, ISE, or the transition state ensemble (TSE) under nonaggregating conditions should be able to predict regions where interchain contacts will be made in the aggregate, and to predict slower aggregation rates for proteins with contacts that are dispersed across the fold. Since proteins L and G can both form amyloid fibrils, this work also provides mechanistic and structural insight into the formation of prefibrillar species.     

Perturbations of the denatured state ensemble: modeling their effects on protein stability and folding kinetics.

By considering the denatured state of a protein as an ensemble of conformations with varying numbers of sequence-specific interactions, the effects on stability, folding kinetics, and aggregation of perturbing these interactions can be predicted from changes in the molecular partition function. From general considerations, the following conclusions are drawn: (1) A perturbation that enhances a native interaction in denatured state conformations always increases the stability of the native state. (2) A perturbation that promotes a non-native interaction in the denatured state always decreases the stability of the native state. (3) A change in the denatured state ensemble can alter the kinetics of aggregation and folding. (4) The loss (or increase) in stability accompanying two mutations, each of which lowers (or raises) the free energy of the denatured state, will be less than the sum of the effects of the single mutations, except in cases where both mutations affect the same set of partially folded conformations. By modeling the denatured state as the ensemble of all non-native conformations of hydrophobic-polar (HP) chains configured on a square lattice, it can be shown that the stabilization obtained from enhancement of native interactions derives in large measure from the avoidance of non-native interactions in the D state. In addition, the kinetic effects of fixing single native contacts in the denatured state or imposing linear gradients in the HH contact probabilities are found, for some sequences, to significantly enhance the efficiency of folding by a simple hydrophobic zippering algorithm. Again, the dominant mechanism appears to be avoidance of non-native interactions. These results suggest stabilization of native interactions and imposition of gradients in the stability of local structure are two plausible mechanisms involving the denatured state that could play a role in the evolution of protein folding and stability.     

Scaling behavior and structure of denatured proteins

An ensemble of random-coil conformations with no persistent structures has long been accepted as the classical model of denatured proteins due to its consistency with the experimentally determined scaling of protein sizes. However, recent NMR spectroscopy studies on proteins at high chemical denaturant concentrations suggest the presence of significant amounts of native-like structures, in contrast to the classical random-coil picture. To reconcile these seemingly controversial observations, we examine thermally denatured states of experimentally characterized proteins by using molecular dynamics simulations. For all studied proteins, we find that denatured states indeed have strong local conformational bias toward native states while a random-coil power law scaling of protein sizes is preserved. In addition, we explain why experimentally determined size of the protein creatine kinase does not follow general scaling. In simulations, we observe that this protein exhibits a stable intermediate state, the size of which is consistent with the reported experimental observation.     

Irreversible thermal denaturation of elongation factor Ts from Thermus thermophilus effect of the residual structure and intermonomer disulfide bond

The homodimeric wild-type elongation factor Ts, EF-Ts(wt), and its C190A mutant, EF-Ts(C190A), from Thermus thermophilus goes through thermal denaturation in a way consistent with a two state irreversible model with a relatively high activation energy, approximately 530 kJ/mol (Supplemental materials provides a list of 98 activation energies from 54 proteins in various solvent conditions). Removing the intermonomeric disulfide bond by substituting alanine for cysteine 190 affects the rate constant of the irreversible thermal transition. At physiological temperatures, the half-life of the native conformations was estimated to be approximately 21 days for wt and 1.3 days for C190A. Thermally denatured EF-Ts refolds into a molten-globule-like state as indicated by its native-like circular dichroism spectrum in the far UV region and the enhanced fluorescence of the hydrophobic probe, 1-anilinonaphtalene-8-sulphonate. The residual secondary structure observed in the thermally denatured state of EF-Ts at high temperatures affects its apparent temperature of thermal transition, T(trs), independent of the presence or absence of the intermonomeric disulfide bond. The effect of the GdmHCl concentration on the activation energy, E(a), and the temperature, T*, i.e., the temperature at which the rate of the irreversible step is 1 min(-1), indicates that the intermonomeric disulfide bond contributes to the irreversibility of thermal transition of EF-Ts.     

Formation of the folding nucleus of an SH3 domain investigated by loosely coupled molecular dynamics simulations

The experimentally well-established folding mechanism of the src-SH3 domain, and in particular the phi-value analysis of its transition state, represents a sort of testing table for computational investigations of protein folding. Here, parallel molecular dynamics simulations of the src-SH3 domain have been performed starting from denatured conformations. By rescuing and restarting only trajectories approaching the folding transition state, an ensemble of conformations was obtained with a completely structured central beta-sheet and a native-like packing of residues Ile-110, Ala-121, and Ile-132. An analysis of the trajectories shows that there are several pathways leading to the formation of the central beta-sheet whereas its two hairpins form in a different but consistent way.