Role of native topology investigated by multiple unfolding simulations of four SH3 domains

The relative importance of amino acid sequence and native topology in the unfolding process of two SH3 domains and two circular permutants was investigated by 120 molecular dynamics runs at 375 K for a total simulation time of 0.72 micros. The alpha-spectrin (aSH3) and src SH3 (sSH3) domains, which have the same topology and a sequence identity of only 34%, show similar unfolding pathways. The disappearance of the three-stranded antiparallel beta-sheet is the last unfolding event, in agreement with a large repertoire of kinetic data derived from point mutations as well as glycine insertions and disulfide crosslinks. Two alternative routes of beta-sheet unfolding have emerged from the analysis of the trajectories. One is statistically preferred in aSH3 (n-src loop breaks before distal hair-pin) and the inverse in sSH3. An elongation of the beta2-beta3 hairpin was observed during the unfolding of sSH3 at 375 K and in 300 K simulations started from the putative transition state of sSH3 in accord with unusual kinetic data for point mutations at the n-src loop. The change of connectivity in the permutants influenced the sequence of unfolding events mainly at the permutation site. Regions where the connectivity remained unaffected showed the same chronology of contact disappearance. Taken together with previous folding simulations of two designed three-stranded antiparallel beta-sheet peptides, these results indicate that, at least for small beta-sheet proteins, the folding mechanism is primarily defined by the native state topology, whilst specific interactions determine the statistically predominant folding route.     

Beta-hairpin folding mechanism of a nine-residue peptide revealed from molecular dynamics simulations in explicit water

The beta-hairpin fold mechanism of a nine-residue peptide, which is modified from the beta-hairpin of alpha-amylase inhibitor tendamistat (residues 15-23), is studied through direct folding simulations in explicit water at native folding conditions. Three 300-nanosecond self-guided molecular dynamics (SGMD) simulations have revealed a series of beta-hairpin folding events. During these simulations, the peptide folds repeatedly into a major cluster of beta-hairpin structures, which agree well with nuclear magnetic resonance experimental observations. This major cluster is found to have the minimum conformational free energy among all sampled conformations. This peptide also folds into many other beta-hairpin structures, which represent some local free energy minimum states. In the unfolded state, the N-terminal residues of the peptide, Tyr-1, Gln-2, and Asn-3, have a confined conformational distribution. This confinement makes beta-hairpin the only energetically favored structure to fold. The unfolded state of this peptide is populated with conformations with non-native intrapeptide interactions. This peptide goes through fully hydrated conformations to eliminate non-native interactions before folding into a beta-hairpin. The folding of a beta-hairpin starts with side-chain interactions, which bring two strands together to form interstrand hydrogen bonds. The unfolding of the beta-hairpin is not simply the reverse of the folding process. Comparing unfolding simulations using MD and SGMD methods demonstrate that SGMD simulations can qualitatively reproduce the kinetics of the peptide system.     

Native topology or specific interactions: what is more important for protein folding?

Fifty-five molecular dynamics runs of two three-stranded antiparallel beta-sheet peptides were performed to investigate the relative importance of amino acid sequence and native topology. The two peptides consist of 20 residues each and have a sequence identity of 15 %. One peptide has Gly-Ser (GS) at both turns, while the other has d-Pro-Gly ((D)PG). The simulations successfully reproduce the NMR solution conformations, irrespective of the starting structure. The large number of folding events sampled along the trajectories at 360 K (total simulation time of about 5 micros) yield a projection of the free-energy landscape onto two significant progress variables. The two peptides have compact denatured states, similar free-energy surfaces, and folding pathways that involve the formation of a beta-hairpin followed by consolidation of the unstructured strand. For the GS peptide, there are 33 folding events that start by the formation of the 2-3 beta-hairpin and 17 with first the 1-2 beta-hairpin. For the (D)PG peptide, the statistical predominance is opposite, 16 and 47 folding events start from the 2-3 beta-hairpin and the 1-2 beta-hairpin, respectively. These simulation results indicate that the overall shape of the free-energy surface is defined primarily by the native-state topology, in agreement with an ever-increasing amount of experimental and theoretical evidence, while the amino acid sequence determines the statistically predominant order of the events.     

Conformational transition states of a beta-hairpin peptide between the ordered and disordered conformations in explicit water

The conformational transition states of a beta-hairpin peptide in explicit water were identified from the free energy landscapes obtained from the multicanonical ensemble, using an enhanced conformational sampling calculation. The beta-hairpin conformations were significant at 300 K in the landscape, and the typical nuclear Overhauser effect signals were reproduced, consistent with the previously reported experiment. In contrast, the disordered conformations were predominant at higher temperatures. Among the stable conformations at 300 K, there were several free energy barriers, which were not visible in the landscapes formed with the conventional parameters. We identified the transition states around the saddle points along the putative folding and unfolding paths between the beta-hairpin and the disordered conformations in the landscape. The characteristic features of these transition states are the predominant hydrophobic contacts and the several hydrogen bonds among the side-chains, as well as some of the backbone hydrogen bonds. The unfolding simulations at high temperatures, 400 K and 500 K, and their principal component analyses also provided estimates for the transition state conformations, which agreed well with those at 400 K and 500 K deduced from the current free energy landscapes at 400 K and 500 K, respectively. However, the transition states at high temperatures were much more widely distributed on the landscape than those at 300 K, and their conformations were different.     

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.     

Loop propensity of the sequence YKGQP from staphylococcal nuclease: implications for the folding of nuclease.

Recently we performed molecular dynamics (MD) simulations on the folding of the hairpin peptide DTVKLMYKGQPMTFR from staphylococcal nuclease in explicit water. We found that the peptide folds into a hairpin conformation with native and nonnative hydrogen-bonding patterns. In all the folding events observed in the folding of the hairpin peptide, loop formation involving the region YKGQP was an important event. In order to trace the origins of the loop propensity of the sequence YKGQP, we performed MD simulations on the sequence starting from extended, polyproline II and native type I' turn conformations for a total simulation length of 300 ns, using the GROMOS96 force field under constant volume and temperature (NVT) conditions. The free-energy landscape of the peptide YKGQP shows minima corresponding to loop conformation with Tyr and Pro side-chain association, turn and extended conformational forms, with modest free-energy barriers separating the minima. To elucidate the role of Gly in facilitating loop formation, we also performed MD simulations of the mutated peptide YKAQP (Gly --> Ala mutation) under similar conditions starting from polyproline II conformation for 100 ns. Two minima corresponding to bend/turn and extended conformations were observed in the free-energy landscape for the peptide YKAQP. The free-energy barrier between the minima in the free-energy landscape of the peptide YKAQP was also modest. Loop conformation is largely sampled by the YKGQP peptide, while extended conformation is largely sampled by the YKAQP peptide. We also explain why the YKGQP sequence samples type II turn conformation in these simulations, whereas the sequence as part of the hairpin peptide DTVKLMYKGQPMTFR samples type I' turn conformation both in the X-ray crystal structure and in our earlier simulations on the folding of the hairpin peptide. We discuss the implications of our results to the folding of the staphylococcal nuclease.     

beta-hairpin stability and folding: molecular dynamics studies of the first beta-hairpin of tendamistat

The stability and (un)folding of the 19-residue peptide, SCVTLYQSWRYSQADNGCA, corresponding to the first beta-hairpin (residues 10 to 28) of the alpha-amylase inhibitor tendamistat (PDB entry 3AIT) has been studied by molecular dynamics simulations in explicit water under periodic boundary conditions at several temperatures (300 K, 360 K and 400 K), starting from various conformations for simulation lengths, ranging from 10 to 30 ns. Comparison of trajectories of the reduced and oxidized native peptides reveals the importance of the disulphide bridge closing the beta-hairpin in maintaining a proper turn conformation, thereby insuring a proper side-chain arrangement of the conserved turn residues. This allows rationalization of the conservation of those cysteine residues among the family of alpha-amylase inhibitors. High temperature simulations starting from widely different initial configurations (native beta-hairpin, alpha and left-handed helical and extended conformations) begin sampling similar regions of the conformational space within tens of nanoseconds, and both native and non-native beta-hairpin conformations are recovered. Transitions between conformational clusters are accompanied by an increase in energy fluctuations, which is consistent with the increase in heat capacity measured experimentally upon protein folding. The folding events observed in the various simulations support a model for beta-hairpin formation in which the turn is formed first, followed by hydrogen bond formation closing the hairpin, and subsequent stabilization by side-chain hydrophobic interactions.     

Ubiquitin folds via a flip-twist-lock mechanism

To perform specific functional activities, the majority of proteins should fold into their distinct three-dimensional conformations. However, the biologically active conformation of a protein is generally found to be marginally stable than the other conformations that the chain can adopt. How a protein finds its native conformation from its post-synthesis unfolded structure in a complex conformational landscape is the unsolved question that still drives the protein folding community. Here, we report the folding mechanism of a globular protein, ubiquitin, from its chemically denatured state using all-atom molecular dynamics simulations. From the kinetic analysis of the simulated trajectories we show that the folding process can be described by the hydrophobic collapse mechanism, initiated by the “dewetting transition”, and subsequently assisted by the origination of an N-terminal folding nucleus, and finally supported by a native salt-bridge interaction between K11 and E34. We show that ubiquitin folds via an intermediate. Finally, we confirm the presence of “biological water” and explain its role to the folding process.     

Reproducible polypeptide folding and structure prediction using molecular dynamics simulations

The folding of a polypeptide from an extended state to a well-defined conformation is studied using microsecond classical molecular dynamics (MD) simulations and replica exchange molecular dynamics (REMD) simulations in explicit solvent and in vacuo. It is shown that the solvated peptide folds many times in the REMD simulations but only a few times in the conventional simulations. From the folding events in the classical simulations we estimate an approximate folding time of 1-2 micros. The REMD simulations allow enough sampling to deduce a detailed Gibbs free energy landscape in three dimensions. The global minimum of the energy landscape corresponds to the native state of the peptide as determined previously by nuclear magnetic resonance (NMR) experiments. Starting from an extended state it takes about 50 ns before the native structure appears in the REMD simulations, about an order of magnitude faster than conventional MD. The calculated melting curve is in good qualitative agreement with experiment. In vacuo, the peptide collapses rapidly to a conformation that is substantially different from the native state in solvent.     

RNA simulations: probing hairpin unfolding and the dynamics of a GNRA tetraloop

Simulations of an RNA hairpin containing a GNRA tetraloop were conducted to allow the characterization of its secondary structure formation and dynamics. Ten 10 ns trajectories of the folded hairpin 5'-GGGC[GCAA]GCCU-3' were generated using stochastic dynamics and the GB/SA implicit solvent model at 300 K. Overall, we find the stem to be a very stable subunit of this molecule, whereas multiple loop conformations and transitions between them were observed. These trajectories strongly suggest that extension of the C6 base away from the loop occurs cooperatively with an N-type-->S-type sugar pucker conversion in that residue and that similar pucker transitions are necessary to stabilize other looped-out bases. In addition, a short-lived conformer with an extended fourth loop residue (A8) lacking this stabilizing 2'-endo pucker mode was observed. Results of thermal perturbation at 400 K support this model of loop dynamics. Unfolding trajectories were produced using this same methodology at temperatures of 500 to 700 K. The observed unfolding events display three-state behavior kinetically (including native, globular, and unfolded populations) and, based on these observations, we propose a folding mechanism that consists of three distinct events: (i) collapse of the random unfolded structure and sampling of the globular state; (ii) passage into the folded region of configurational space as stem base-pairs form and gain helicity; and (iii) attainment of proper loop geometry and organization of loop pairing and stacking interactions. These results are considered in the context of current experimental knowledge of this and similar nucleic acid hairpins.     

Thermal unfolding simulations of apo-calmodulin using leap-dynamics

The simulation method leap-dynamics (LD) has been applied to protein thermal unfolding simulations to investigate domain-specific unfolding behavior. Thermal unfolding simulations of the 148-residue protein apo-calmodulin with implicit solvent were performed at temperatures 290 K, 325 K, and 360 K and compared with the corresponding molecular dynamics trajectories in terms of a number of calculated conformational parameters. The main experimental results of unfolding are reproduced in showing the lower stability of the C-domain: at 290 K, both the N- and C-domains are essentially stable; at 325 K, the C-domain unfolds, whereas the N-domain remains folded; and at 360 K, both domains unfold extensively. This behavior could not be reproduced by molecular dynamics simulations alone under the same conditions. These results show an encouraging degree of convergence between experiment and LD simulation. The simulations are able to describe the overall plasticity of the apo-calmodulin structure and to reveal details such as reversible folding/unfolding events within single helices. The results show that by using the combined application of a fast and efficient sampling routine with a detailed molecular dynamics force field, unfolding simulations of proteins at atomic resolution are within the scope of current computational power.     

Heterogeneity even at the speed limit of folding: large-scale molecular dynamics study of a fast-folding variant of the villin headpiece

We have performed molecular dynamics simulations on a set of nine unfolded conformations of the fastest-folding protein yet discovered, a variant of the villin headpiece subdomain (HP-35 NleNle). The simulations were generated using a new distributed computing method, yielding hundreds of trajectories each on a time scale comparable to the experimental folding time, despite the large (10,000 atom) size of the simulation system. This strategy eliminates the need to assume a two-state kinetic model or to build a Markov state model. The relaxation to the folded state at 300 K from the unfolded configurations (generated by simulation at 373 K) was monitored by a method intended to reflect the experimental observable (quenching of tryptophan by histidine). We also monitored the relaxation to the native state by directly comparing structural snapshots with the native state. The rate of relaxation to the native state and the number of resolvable kinetic time scales both depend upon starting structure. Moreover, starting structures with folding rates most similar to experiment show some native-like structure in the N-terminal helix (helix 1) and the phenylalanine residues constituting the hydrophobic core, suggesting that these elements may exist in the experimentally relevant unfolded state. Our large-scale simulation data reveal kinetic complexity not resolved in the experimental data. Based on these findings, we propose additional experiments to further probe the kinetics of villin folding.     

Hierarchy of structure loss in MD simulations of src SH3 domain unfolding.

To complement experimental studies of the src SH3 domain folding, we studied 30 independent, high-temperature, molecular dynamics simulations of src SH3 domain unfolding. These trajectories were observed to differ widely from each other. Thus, rather than analyzing individual trajectories, we sought to identify the recurrent features of the high-temperature unfolding process. The conformations from all simulations were combined and then divided into groups based on the number of native contacts. Average occupancies of each side-chain hydrophobic contact and hydrogen bond in the protein were then determined. In the symmetric funnel limit, the occupancies of all contacts should decrease in concert with the loss in total number of native contacts. If there is a lack of symmetry or hierarchy to the unfolding process, the occupancies of some contacts should decrease more slowly, and others more rapidly. Despite the heterogeneity of the individual trajectories, the ensemble averaging revealed an order to the unfolding process: contacts between the N and C-terminal strands are the first to disappear, whereas contacts within the distal beta-hairpin and a hydrogen-bonding network involving the distal loop beta-turn and the diverging turn persist well after the majority of the native contacts are lost. This hierarchy of events resembles but is somewhat less pronounced than that observed in our experimental studies of the folding of src SH3 domain.     

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.     

Kinetic partitioning mechanism governs the folding of the third FnIII domain of tenascin-C: evidence at the single-molecule level

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

Wild type, mutant protein unfolding and phase transition detected by single-nanopore recording

Understanding protein folding remains a challenge. A difficulty is to investigate experimentally all the conformations in the energy landscape. Only single molecule methods, fluorescence and force spectroscopy, allow observing individual molecules along their folding pathway. Here we observe that single-nanopore recording can be used as a new single molecule method to explore the unfolding transition and to examine the conformational space of native or variant proteins. We show that we can distinguish unfolded states from partially folded ones with the aerolysin pore. The unfolding transition curves of the destabilized variant are shifted toward the lower values of the denaturant agent compared to the wild type protein. The dynamics of the partially unfolded wild type protein follows a first-order transition. The denaturation curve obtained with the aerolysin pore is similar to that obtained with the α-hemolysin pore. The nanopore geometry or net charge does not influence the folding transition but changes the dynamics.