Salt effects on hydrophobic‐core formation in folding of a helical miniprotein studied by molecular dynamics simulations

We have investigated effects of salt ions on folding events of a helical miniprotein chicken villin headpiece subdomain HP36. Low concentrations of ions alter electrostatic interactions between charged groups of a protein and can change the populations of conformers. Here, we compare two data sets of folding simulations of HP36 in explicit water solvent with or without ions. For efficient sampling of the conformational space of HP36, the multicanonical replica‐exchange molecular dynamics method was employed. Our analyses suggest that salt alters salt‐bridging nature of the protein at later stages of folding at room temperature. Especially, more nonnative, nonlocal salt bridges are formed at near‐native conformations in pure water. Our analyses also show that such salt‐bridge formation hinders the fully native hydrophobic‐core packing at the final stages of folding. Proteins 2014; 82:933–943. © 2013 Wiley Periodicals, Inc.     

All-atom fast protein folding simulations: the villin headpiece

We provide a fast folding simulation using an all-atom solute, implicit solvent method that eliminates the need for treating solvent degrees of freedom. The folding simulations for the 36-residue villin headpiece exhibit close correspondence with the landmark all-atom explicit solvent molecular dynamics simulations by Duan and Kollman (Duan & Kollman, Science 1998;282:740-744; Duan, Wang, & Kollman, Proc Natl Acad Sci USA 1998;95:9897-9902). Our implicit solvent approach uses only an entry-level single CPU PC with comparable throughput ( approximately 4 nsec/day) to the DK supercomputer simulation. The native state is shown to be stable. Our 200-nsec folding trajectory agrees with the DK simulation in displaying a burst phase, a rapid initial shrinkage, a highly native-like binding site structure, and more.     

Folding network of villin headpiece subdomain

Protein folding is a complex multidimensional process that is difficult to illustrate by the traditional analyses based on one- or two-dimensional profiles. Analyses based on transition networks have become an alternative approach that has the potential to reveal detailed features of protein folding dynamics. However, due to the lack of successful reversible folding of proteins from conventional molecular-dynamics simulations, this approach has rarely been utilized. Here, we analyzed the folding network from several 10 μs conventional molecular-dynamics reversible folding trajectories of villin headpiece subdomain (HP35). The folding network revealed more complexity than the traditional two-dimensional map and demonstrated a variety of conformations in the unfolded state, intermediate states, and the native state. Of note, deep enthalpic traps at the unfolded state were observed on the folding landscape. Furthermore, in contrast to the clear separation of the native state and the primary intermediate state shown on the two-dimensional map, the two states were mingled on the folding network, and prevalent interstate transitions were observed between these two states. A more complete picture of the folding mechanism of HP35 emerged when the traditional and network analyses were considered together.     

Large-scale context in protein folding: villin headpiece

The villin headpiece folds autonomously in vitro forming three alpha-helical regions. Local propensities, however, strongly disfavor the formation of the C-terminal helix because most native residue pairs in that helix are hydrophobic/polar mismatches. Even the N-terminal helix is unfavored according to the AGADIR criterion. Our coarse-grained ab initio simulations reveal three-body correlations in which hydrophobic residues position to protect amide-carbonyl hydrogen bonds from attack by water, thus inducing the growth of the C-terminal helix and guiding the folding process. Similar correlations are also found in all-atom simulations with an implicit solvent model that accurately reproduces the results of simulations with explicit solvent molecules. The correlations establish a large-scale, many-body context that may be probed experimentally by introducing mutations of certain nonobvious residues that reside outside the native hydrophobic core but that are predicted to affect the folding rates and dynamics dramatically.     

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.     

Experimental tests of villin subdomain folding simulations

We have used laser temperature-jump to investigate the kinetics and mechanism of folding the 35 residue subdomain of the villin headpiece. The relaxation kinetics are biphasic with a sub-microsecond phase corresponding to a helix-coil transition and a slower microsecond phase corresponding to overall unfolding/refolding. At 300 K, the folding time is 4.3(+/-0.6) micros, making it the fastest folding, naturally occurring protein, with a rate close to the theoretical speed limit. This time is in remarkable agreement with the prediction of 5 (+11,-3) micros by Zagrovic et al. from atomistic molecular dynamics simulations using an implicit solvent model. We test their prediction that replacement of the C-terminal phenylalanine residue with alanine will increase the folding rate by removing a transient non-native interaction. We find that the alanine substitution has no effect on the folding rate or on the equilibrium constant. Implications of this result for the validity of the simulated folding mechanism are discussed.     

Local structure formation in simulations of two small proteins

Massively parallel all-atom, explicit solvent molecular dynamics simulations were used to explore the formation and existence of local structure in two small alpha-helical proteins, the villin headpiece and the helical fragment B of protein A. We report on the existence of transient helices and combinations of helices in the unfolded ensemble, and on the order of formation of helices, which appears to largely agree with previous experimental results. Transient local structure is observed even in the absence of overall native structure. We also calculate sets of residue-residue pairs that are statistically predictive of the formation of given local structures in our simulations.     

Simulation of folding of a small alpha-helical protein in atomistic detail using worldwide-distributed computing

By employing thousands of PCs and new worldwide-distributed computing techniques, we have simulated in atomistic detail the folding of a fast-folding 36-residue alpha-helical protein from the villin headpiece. The total simulated time exceeds 300 micros, orders of magnitude more than previous simulations of a molecule of this size. Starting from an extended state, we obtained an ensemble of folded structures, which is on average 1.7A and 1.9A away from the native state in C(alpha) distance-based root-mean-square deviation (dRMS) and C(beta) dRMS sense, respectively. The folding mechanism of villin is most consistent with the hydrophobic collapse view of folding: the molecule collapses non-specifically very quickly ( approximately 20ns), which greatly reduces the size of the conformational space that needs to be explored in search of the native state. The conformational search in the collapsed state appears to be rate-limited by the formation of the aromatic core: in a significant fraction of our simulations, the C-terminal phenylalanine residue packs improperly with the rest of the hydrophobic core. We suggest that the breaking of this interaction may be the rate-determining step in the course of folding. On the basis of our simulations we estimate the folding rate of villin to be approximately 5micros. By analyzing the average features of the folded ensemble obtained by simulation, we see that the mean folded structure is more similar to the native fold than any individual folded structure. This finding highlights the need for simulating ensembles of molecules and averaging the results in an experiment-like fashion if meaningful comparison between simulation and experiment is to be attempted. Moreover, our results demonstrate that (1) the computational methodology exists to simulate the multi-microsecond regime using distributed computing and (2) that potential sets used to describe interatomic interactions may be sufficiently accurate to reach the folded state, at least for small proteins. We conclude with a comparison between our results and current protein-folding theory.     

An all-atom force field for tertiary structure prediction of helical proteins

We have developed an all-atom free-energy force field (PFF01) for protein tertiary structure prediction. PFF01 is based on physical interactions and was parameterized using experimental structures of a family of proteins believed to span a wide variety of possible folds. It contains empirical, although sequence-independent terms for hydrogen bonding. Its solvent-accessible surface area solvent model was first fit to transfer energies of small peptides. The parameters of the solvent model were then further optimized to stabilize the native structure of a single protein, the autonomously folding villin headpiece, against competing low-energy decoys. Here we validate the force field for five nonhomologous helical proteins with 20-60 amino acids. For each protein, decoys with 2-3 A backbone root mean-square deviation and correct experimental Cbeta-Cbeta distance constraints emerge as those with the lowest energy.     

Sub-microsecond protein folding

We have investigated the structure, equilibria, and folding kinetics of an engineered 35-residue subdomain of the chicken villin headpiece, an ultrafast-folding protein. Substitution of two buried lysine residues by norleucine residues stabilizes the protein by 1 kcal/mol and increases the folding rate sixfold, as measured by nanosecond laser T-jump. The folding rate at 300 K is (0.7 micros)(-1) with little or no temperature dependence, making this protein the first sub-microsecond folder, with a rate only twofold slower than the theoretically predicted speed limit. Using the 70 ns process to obtain the effective diffusion coefficient, the free energy barrier height is estimated from Kramers theory to be less than approximately 1 kcal/mol. X-ray crystallographic determination at 1A resolution shows no significant change in structure compared to the single-norleucine-substituted molecule and suggests that the increased stability is electrostatic in origin. The ultrafast folding rate, very accurate X-ray structure, and small size make this engineered villin subdomain an ideal system for simulation by atomistic molecular dynamics with explicit solvent.     

Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing

Atomistic simulations of protein folding have the potential to be a great complement to experimental studies, but have been severely limited by the time scales accessible with current computer hardware and algorithms. By employing a worldwide distributed computing network of tens of thousands of PCs and algorithms designed to efficiently utilize this new many-processor, highly heterogeneous, loosely coupled distributed computing paradigm, we have been able to simulate hundreds of microseconds of atomistic molecular dynamics. This has allowed us to directly simulate the folding mechanism and to accurately predict the folding rate of several fast-folding proteins and polymers, including a nonbiological helix, polypeptide alpha-helices, a beta-hairpin, and a three-helix bundle protein from the villin headpiece. Our results demonstrate that one can reach the time scales needed to simulate fast folding using distributed computing, and that potential sets used to describe interatomic interactions are sufficiently accurate to reach the folded state with experimentally validated rates, at least for small proteins.     

Optimum folding pathways for growing protein chains

The folding of a protein is studied as it grows residue by residue from the N-terminus and enters an environment that stabilizes the folded state. This mode of folding of a growing chain is different from refolding where the full chain folds from a disordered initial configuration to the native state. We propose a sequential dynamic optimization method that computes the evolution of optimum folding pathways as amino acid residues are added to the peptide chain one by one. The dynamic optimization formulation is deterministic and uses Newton's equations of motion and a Go-type potential that establishes the native contacts and excluded volume effects. The method predicts the optimal energy-minimizing path among all the alternative feasible pathways. As two examples, the folding of the chicken villin headpiece, a 36-residue protein, and chymotrypsin inhibitor 2 (CI2), a 64-residue protein, are studied. Results on the villin headpiece show significant differences from the refolding of the same chain studied previously. Results on CI2 mostly agree with the results of refolding experiments and computational work.     

The unfolded state of the villin headpiece helical subdomain: computational studies of the role of locally stabilized structure

The 36 residue villin headpiece helical subdomain (HP36) is one of the fastest cooperatively folding proteins, folding on the microsecond timescale. HP36's simple three helix topology, fast folding and small size have made it an attractive model system for computational and experimental studies of protein folding. Recent experimental studies have explored the denatured state of HP36 using fragment analysis coupled with relatively low-resolution spectroscopic techniques. These studies have shown that there is apparently only a small tendency to form locally stabilized secondary structure. Here, we complement the experimental studies by using replica exchange molecular dynamics with explicit solvent to investigate the structural features of these peptide models of unfolded HP36. To ensure convergence, two sets of simulations for each fragment were performed with different initial structures, and simulations were continued until these generated very similar final ensembles. These simulations reveal low populations of native-like structure and early folding events that cannot be resolved by experiment. For each fragment, calculated J-coupling constants and helical propensities are in good agreement with experimental trends. HP-1, corresponding to residues 41 to 53 and including the first alpha-helix, contains the highest helical population. HP-3, corresponding to residues 62 through 75 and including the third alpha-helix, contains a small population of helical turn residing at the N terminus while HP-2, corresponding to residues 52 through 61 and including the second alpha-helix, formed little to no structure in isolation. Overall, HP-1 was the only fragment to adopt a native-like conformation, but the low population suggests that formation of significant structure only occurs after formation of specific tertiary interactions.     

Dependence of Protein Crystal Stability on Residue Charge States and Ion Content of Crystal Solvent

Protein crystallization is frequently induced by the addition of various precipitants, which directly affect protein solubility. In addition to organic cosolvents and long-chain polymers, salts belong to the most widely used precipitants in protein crystallography. However, despite such widespread usage, their mode of action at the atomistic level is still largely unknown. Here, we perform extensive molecular dynamics simulations of the villin headpiece crystal unit cell to examine its stability at different concentrations of sodium sulfate. We show that the inclusion of ions in crystal solvent at high concentration can prevent large rearrangements of the asymmetric units and a loss of symmetry of the unit cell without significantly affecting protein dynamics. Of importance, a similar result can be achieved by neutralizing several specific charged residues suggesting that they may play an active role in crystal destabilization due to unfavorable electrostatic interactions. Our results provide a microscopic picture behind salt-induced stabilization of a protein crystal and further suggest that adequate modeling of realistic crystallization conditions may be necessary for successful molecular dynamics simulations of protein crystals.     

Multistate folding of the villin headpiece domain

The villin headpiece (HP67) is a 67 residue, monomeric protein derived from the C-terminal domain of villin. Wild-type HP67 (WT HP67) is the smallest fragment of villin that retains strong in vitro actin-binding activity. WT HP67 is made up of two subdomains, which form a tightly packed interface. The C-terminal subdomain of WT HP67, denoted HP35, is rich in helical structure, folds in isolation, and has been widely used as a model system for folding studies. In contrast, very little is known about the folding of the intact villin headpiece domain. Here, NMR, CD and H/2H amide exchange measurements are used to follow the pH, thermal and urea-induced unfolding of WT HP67 and a mutant (HP67 H41Y) in which a buried conserved histidine in the N-terminal subdomain, His41, has been mutated to Tyr. Although most small proteins display two-state equilibrium unfolding, the results presented here demonstrate that unfolding of the villin headpiece is a multistate process. The presence of a folded N-terminal subdomain is shown to stabilize the C-terminal subdomain, increasing the midpoints of the thermal and urea-induced unfolding transitions and increasing protection factors for H/2H exchange. Histidine 41 has been shown to act as a pH-dependent switch in wild-type HP67: the N-terminal subdomain is unfolded when His41 is protonated, while the C-terminal subdomain remains folded irrespective of the protonation state of His41. Mutation of His41 to Tyr eliminates the segmental pH-dependent unfolding of the headpiece. The mutation stabilizes both domains, but folding is still multistate, indicating that His41 is not solely responsible for the unusual equilibrium unfolding behavior of villin headpiece domain.     

Conformation spaces of proteins

We report a simple method for measuring the accessible conformational space explored by an ensemble of protein structures. The method is useful for diverse ensembles derived from molecular dynamics trajectories, molecular modeling, and molecular structure determinations. It can be used to examine a wide range of time scales. The central tactic we use, which has been previously employed, is to replace the true mechanical degrees of freedom of a molecular system with the conformationally effective degrees of freedom as measured by the root-mean squared cartesian distances among all pairs of conformations. Each protein conformation is treated as a point in a high dimensional euclidean space. In this article, we model this space in a novel way by representing it as an N-dimensional hypercube, describable with only two parameters: the number of dimensions and the edge length. To validate this approach, we provide a number of elementary test cases and then use the N-cube method for measuring the size and shape of conformational space covered by molecular dynamics trajectories spanning 10 orders of magnitude in time. These calculations were performed on a small protein, the villin headpiece subdomain, exploring both the native state and the misfolded/folding regime. Distinct features include single, vibrationally averaged, substate minima on the 0.1-1-ps time scale, thermally averaged conformational states that persist for 1-100 ps and transitions between these local minima on nanosecond time scales. Large-scale refolding modes appear to become uncorrelated on the microsecond time scale. Associated length scales for these events are 0.2 A for the vibrational minima; 0.5 A for the conformational minima; and 1-2 A for the nanosecond events. We find that the conformational space that is dynamically accessible during folding of villin has enough volume for approximately 10(9) minima of the variety that persist for picoseconds. Molecular dynamics trajectories of the native protein and experimentally derived solution ensembles suggest the native state to be composed of approximately 10(2) of these thermally accessible minima. Thus, based on random exploration of accessible folding space alone, protein folding for a small protein is predicted to be a milliseconds time scale event. This time can be compared with the experimental folding time for villin of 10-100 micros. One possible explanation for the 10-100-fold discrepancy is that the slope of the "folding funnel" increases the rate 1-2 orders of magnitude above random exploration of substates.     

Theoretical investigation of the photoinitiated folding of HP-36

A computational model was developed to examine the phototriggered folding of a caged protein, a protein modified with an organic photolabile cross-linker. Molecular dynamics simulations of the modified 36-residue fragment of subdomain B of chicken villin head piece with a photolabile linker were performed, starting from both the caged and the uncaged structures. Construction of a free-energy landscape, based on principal components as well as on radius of gyration versus root-mean-square deviation, and circular dichroism calculations were employed to characterize folding behavior and structures. The folded structures observed in the molecular dynamics trajectories were found to be similar to that of the wild-type protein, in agreement with the published experimental results. The free-energy landscapes of the modified and wild-type proteins have similar topology, suggesting common thermodynamic/kinetic behavior. The existence of small differences in the free-energy surface of the modified protein from that of the native protein, however, indicates subtle differences in the folding behavior.     

Free-energy landscape of the villin headpiece in an all-atom force field

We investigate the landscape of the internal free-energy of the 36 amino acid villin headpiece with a modified basin hopping method in the all-atom force field PFF01, which was previously used to predictively fold several helical proteins with atomic resolution. We identify near native conformations of the protein as the global optimum of the force field. More than half of the twenty best simulations started from random initial conditions converge to the folding funnel of the native conformation, but several competing low-energy metastable conformations were observed. From 76,000 independently generated conformations we derived a decoy tree which illustrates the topological structure of the entire low-energy part of the free-energy landscape and characterizes the ensemble of metastable conformations. These emerge as similar in secondary content, but differ in tertiary arrangement.