Two-stage folding of HP-35 from ab initio simulations

Common structural transitions in explicit-solvent simulations of villin headpiece folding

Molecular dynamics simulations of protein folding can provide very high-resolution data on the folding process; however, due to computational challenges most studies of protein folding have been limited to small peptides, or made use of approximations such as Gō potentials or implicit solvent models. We have performed a set of molecular dynamics simulations totaling >50 micros on the villin headpiece subdomain, one of the most stable and fastest-folding naturally occurring proteins, in explicit solvent. We find that the wild-type villin headpiece reliably folds to a native conformation on timescales similar to experimentally observed folding, but that a fast folding double-norleucine mutant shows significantly more heterogeneous behavior. Along with other recent simulation studies, we note the occurrence of nonnative structures intermediates, which may yield a nativelike signal in the fluorescence measurements typically used to study villin folding. Based on the wild-type simulations, we propose alternative approaches to measure the formation of the native state.

Dual folding pathways of an alpha/beta protein from all-atom ab initio folding simulations

Successful ab initio folding of proteins with both alpha-helix and beta-sheet requires a delicate balance among a variety of forces in the simulation model, which may explain that the successful folding of any alpha/beta proteins to within experimental error has yet to be reported. Here we demonstrate that it is an achievable goal to fold alpha/beta proteins with a force field emphasizing the balance between the two major secondary structures. Using our newly developed force field, we conducted extensive ab initio folding simulations on an alpha/beta protein full sequence design (FSD) employing both conventional molecular dynamics and replica exchange molecular dynamics in combination with a generalized-Born solvation model. In these simulations, the folding of FSD to the native state with high population (>64.2%) and high fidelity (C(alpha)-Root Mean Square Deviation of 1.29 A for the most sampled conformation when compared to the experimental structure) was achieved. The folding of FSD was found to follow two pathways. In the major pathway, the folding started from the formation of the helix. In the minor pathway, however, folding of the beta-hairpin started first. Further examination revealed that the helix initiated from the C-terminus and propagated toward the N-terminus. The formation of the hydrophobic contacts coincided with the global folding. Therefore the hydrophobic force does not appear to be the driving force of the folding of this protein.

Native like structure in the unfolded state of the villin headpiece helical subdomain, an ultrafast folding protein

The villin headpiece subdomain, HP36, is the smallest naturally occurring protein that folds cooperatively. Its small size, rapid folding, and simple three-helix topology have made it an extremely popular system for computational studies of protein folding. The role of unfolded state structure in rapid folding is an area of active investigation, but relatively little is known about the properties of unfolded states under native conditions. A peptide fragment, HP21, which contains the first and second helices of HP36 has been shown to be a good model for structure in the unfolded state of the intact domain but a detailed description of the conformational propensities of HP21 is lacking and the balance between native and nonnative interactions is not known. A series of three-dimensional NMR experiments were performed on (13)C, (15)N-labeled HP21 to investigate in detail its conformational propensities. Analysis of (13)C(alpha), (13)C(beta), (13)CO chemical shifts, Deltadelta(13)C(alpha) - Deltadelta(13)C(beta) secondary shifts, the secondary structure propensity scores, NOEs, (15)N R(2) values and comparison of experimental chemical shifts with those of HP36 and with chemical shifts calculated using the SHIFTS and SHIFTX programs all indicate that there is significant native like structure in the HP21 ensemble, and thus by implication in the unfolded state of HP36.

Polarizable intermolecular potentials for water and benzene interacting with halide and metal ions

A complete derivation of polarizable intermolecular potentials based on high-level, gas-phase quantum-mechanical calculations is proposed. The importance of appreciable accuracy together with inherent simplicity represents a significant endeavor when enhancement of existing force fields for biological systems is sought. Toward this end, symmetry-adapted perturbation theory (SAPT) can provide an expansion of the total interaction energy into physically meaningful e.g. electrostatic, induction and van der Waals terms. Each contribution can be readily compared with its counterpart in classical force fields. Since the complexity of the different intermolecular terms cannot be fully embraced using a minimalist description, it is necessary to resort to polyvalent expressions capable of encapsulating overlooked contributions from the quantum-mechanical expansion. This choice results in consistent force field components that reflect the underlying physical principles of the phenomena. This simplified potential energy function is detailed and definitive guidelines are drawn. As a proof of concept, the methodology is illustrated through a series of test cases that include the interaction of water and benzene with halide and metal ions. In each case considered, the total energy is reproduced accurately over a range of biologically relevant distances.

Probing the folding transition state structure of the villin headpiece subdomain via side chain and backbone mutagenesis

Backbone-backbone hydrogen bonds are a common feature of native protein structures, yet their thermodynamic and kinetic influence on folding has long been debated. This is reflected by the disparity between current protein folding models, which place hydrogen bond formation at different stages along the folding trajectory. For example, previous studies have suggested that the denatured state of the villin headpiece subdomain contains a residual helical structure that may provide a bias toward the folded state by confining the conformational search associated with its folding. Although helical hydrogen bonds clearly stabilize the folded state, here we show, using an amide-to-ester mutation strategy, that the formation of backbone hydrogen bonds within helices is not rate-limiting in the folding of the subdomain, thereby suggesting that such hydrogen bonds are unlikely to be formed en route from the denatured to the transition state. On the other hand, elimination of hydrogen bonds within the turn region elicits a slower folding rate, consistent with the hypothesis that these residues are involved in the formation of a folding nucleus. While illustrating a potentially conserved aspect of helix-turn-helix folding, our results further underscore the inherent importance of turns in protein supersecondary structure formation.

Quantitative determination of site-specific conformational distributions in an unfolded protein by solid-state nuclear magnetic resonance

Solid-state nuclear magnetic resonance (NMR) techniques are used to investigate the structure of the 35-residue villin headpiece subdomain (HP35) in folded, partially denatured, and fully denatured states. Experiments are carried out in frozen glycerol/water solutions, with chemical denaturation by guanidine hydrochloride (GdnHCl). Without GdnHCl, two-dimensional solid-state (13)C NMR spectra of samples prepared with uniform (13)C labeling of selected residues show relatively sharp cross-peaks at chemical shifts that are consistent with the known three-helix bundle structure of folded HP35. At high GdnHCl concentrations, most cross-peaks broaden and shift, qualitatively indicating disruption of the folded structure and development of static conformational disorder in the frozen denatured state. Conformational distributions at one residue in each helical segment are probed quantitatively with three solid-state NMR techniques that provide independent constraints on backbone varphi and psi torsion angles in samples with sequential pairs of carbonyl (13)C labels. Without GdnHCl, the combined data are well fit by alpha-helical conformations. At [GdnHCl]=4.5 M, corresponding to the approximate denaturation midpoint, the combined data are well fit by a combination of alpha-helical and partially extended conformations at each site, but with a site-dependent population ratio. At [GdnHCl]=7.0 M, corresponding to the fully denatured state, the combined data are well fit by a combination of partially extended and polyproline II conformations, again with a site-dependent population ratio. Two entirely different models for conformational distributions lead to nearly the same best-fit distributions, demonstrating the robustness of these conclusions. This work represents the first quantitative investigation of site-specific conformational distributions in partially folded and unfolded states of a protein by solid-state NMR.

Blind test of physics-based prediction of protein structures

We report here a multiprotein blind test of a computer method to predict native protein structures based solely on an all-atom physics-based force field. We use the AMBER 96 potential function with an implicit (GB/SA) model of solvation, combined with replica-exchange molecular-dynamics simulations. Coarse conformational sampling is performed using the zipping and assembly method (ZAM), an approach that is designed to mimic the putative physical routes of protein folding. ZAM was applied to the folding of six proteins, from 76 to 112 monomers in length, in CASP7, a community-wide blind test of protein structure prediction. Because these predictions have about the same level of accuracy as typical bioinformatics methods, and do not utilize information from databases of known native structures, this work opens up the possibility of predicting the structures of membrane proteins, synthetic peptides, or other foldable polymers, for which there is little prior knowledge of native structures. This approach may also be useful for predicting physical protein folding routes, non-native conformations, and other physical properties from amino acid sequences.

The fast-folding HP35 double mutant has a substantially reduced primary folding free energy barrier

The LYS24/29NLE double mutant of villin headpiece subdomain (HP35) is the fastest folding protein known so far with a folding time constant of 0.6 micros. In this work, the folding mechanism of the mutant has been investigated by both conventional and replica exchange molecular dynamics (CMD and REMD) simulations with AMBER FF03 force field and a generalized-Born solvation model. Direct comparison to the ab initio folding of the wild type HP35 enabled a close examination on the mutational effect on the folding process. The mutant folded to the native state, as demonstrated by the 0.50 A C(alpha)-root mean square deviation (RMSD) sampled in both CMD and REMD simulations and the high population of the folded conformation compared with the denatured conformations. Consistent with experiments, the significantly reduced primary folding free energy barrier makes the mutant closer to a downhill folder than the wild type HP35 that directly leads to the faster transition and higher melting temperature. However, unlike the proposed downhill folding which envisages a smooth shift between unfolded and folded states without transition barrier, we observed a well-defined folding transition that was consistent with experiments. Further examination of the secondary structures revealed that the two mutated residues have higher intrinsic helical preference that facilitated the formation of both helix III and the intermediate state which contains the folded segment helix II/III. Other factors contributing to the faster folding include the more favorable electrostatic interactions in the transition state with the removal of the charged NH(3)(+) groups from LYS. In addition, both transition state ensemble and denatured state ensemble are shifted in the mutant.

Chemical, physical, and theoretical kinetics of an ultrafast folding protein

An extensive set of equilibrium and kinetic data is presented and analyzed for an ultrafast folding protein--the villin subdomain. The equilibrium data consist of the excess heat capacity, tryptophan fluorescence quantum yield, and natural circular-dichroism spectrum as a function of temperature, and the kinetic data consist of time courses of the quantum yield from nanosecond-laser temperature-jump experiments. The data are well fit with three kinds of models--a three-state chemical-kinetics model, a physical-kinetics model, and an Ising-like theoretical model that considers 10(5) possible conformations (microstates). In both the physical-kinetics and theoretical models, folding is described as diffusion on a one-dimensional free-energy surface. In the physical-kinetics model the reaction coordinate is unspecified, whereas in the theoretical model, order parameters, either the fraction of native contacts or the number of native residues, are used as reaction coordinates. The validity of these two reaction coordinates is demonstrated from calculation of the splitting probability from the rate matrix of the master equation for all 10(5) microstates. The analysis of the data on site-directed mutants using the chemical-kinetics model provides information on the structure of the transition-state ensemble; the physical-kinetics model allows an estimate of the height of the free-energy barrier separating the folded and unfolded states; and the theoretical model provides a detailed picture of the free-energy surface and a residue-by-residue description of the evolution of the folded structure, yet contains many fewer adjustable parameters than either the chemical- or physical-kinetics models.

Using an amino acid fluorescence resonance energy transfer pair to probe protein unfolding: application to the villin headpiece subdomain and the LysM domain

Previously, we have shown that p-cyanophenylalanine (Phe CN) and tryptophan (Trp) constitute an efficient fluorescence resonance energy transfer (FRET) pair that has several advantages over commonly used dye pairs. Here, we aim to examine the general applicability of this FRET pair in protein folding-unfolding studies by applying it to the urea-induced unfolding transitions of two small proteins, the villin headpiece subdomain (HP35) and the lysin motif (LysM) domain. Depending on whether Phe CN is exposed to solvent, we are able to extract either qualitative information about the folding pathway, as demonstrated by HP35, which has been suggested to unfold in a stepwise manner, or quantitative thermodynamic and structural information, as demonstrated by LysM, which has been shown to be an ideal two-state folder. Our results show that the unfolding transition of HP35 reported by FRET occurs at a denaturant concentration lower than that measured by circular dichroism (CD) and that the loop linking helix 2 and helix 3 remains compact in the denatured state, which are consistent with the notion that HP35 unfolds in discrete steps and that its unfolded state contains residual structures. On the other hand, our FRET results on the LysM domain allow us to develop a model for extracting structural and thermodynamic parameters about its unfolding, and we find that our results are in agreement with those obtained by other methods. Given the fact that Phe CN is a non-natural amino acid and, thus, amenable to incorporation into peptides and proteins via existing peptide synthesis and protein expression methods, we believe that the FRET method demonstrated here is widely applicable to protein conformational studies, especially to the study of relatively small proteins.

Amyloid beta-protein monomer folding: free-energy surfaces reveal alloform-specific differences

Alloform-specific differences in structural dynamics between amyloid beta-protein (Abeta) 40 and Abeta42 appear to underlie the pathogenesis of Alzheimer's disease. To elucidate these differences, we performed microsecond timescale replica-exchange molecular dynamics simulations to sample the conformational space of the Abeta monomer and constructed its free-energy surface. We find that neither peptide monomer is unstructured, but rather that each may be described as a unique statistical coil in which five relatively independent folding units exist, comprising residues 1-5, 10-13, 17-22, 28-37, and 39-42, which are connected by four turn structures. The free-energy surfaces of both peptides are characterized by two large basins, comprising conformers with either substantial alpha-helix or beta-sheet content. Conformational transitions within and between these basins are rapid. The two additional hydrophobic residues at the Abeta42 C-terminus, Ile41 and Ala42, significantly increase contacts within the C-terminus, and between the C-terminus and the central hydrophobic cluster (Leu17-Ala21). As a result, the beta-structure of Abeta42 is more stable than that of Abeta40, and the conformational equilibrium in Abeta42 shifts towards beta-structure. These results suggest that drugs stabilizing alpha-helical Abeta conformers (or destabilizing the beta-sheet state) would block formation of neurotoxic oligomers. The atomic-resolution conformer structures determined in our simulations may serve as useful targets for this purpose. The conformers also provide starting points for simulations of Abeta oligomerization-a process postulated to be the key pathogenetic event in Alzheimer's disease.

Vulnerability in Popular Molecular Dynamics Packages Concerning Langevin and Andersen Dynamics

We report a serious problem associated with a number of current implementations of Andersen and Langevin dynamics algorithms. When long simulations are run in many segments, it is sometimes possible to have a repeating sequence of pseudorandom numbers enter the calcuation. We show that, if the sequence repeats rapidly, the resulting artifacts can quickly denature biomolecules and are then easily detectable. However, if the sequence repeats less frequently, the artifacts become subtle and easily overlooked. We derive a formula for the underlying cause of artifacts in the case of the Langevin thermostat, and find it vanishes slowly as the inverse square root of the number of time steps per simulation segment. Numerous examples of simulation artifacts are presented, including dissociation of a tetrameric protein after 110 ns of dynamics, reductions in atomic fluctuations for a small protein in implicit solvent, altered thermodynamic properties of a box of water molecules, and changes in the transition free energies between dihedral angle conformations. Finally, in the case of strong thermocoupling, we link the observed artifacts to previous work in nonlinear dynamics and show that it is possible to drive a 20-residue, implicitly solvated protein into periodic trajectories if the thermostat is not used properly. Our findings should help other investigators re-evaluate simulations that may have been corrupted and obtain more accurate results.

Folding processes of the B domain of protein A to the native state observed in all-atom ab initio folding simulations

Reaching the native states of small proteins, a necessary step towards a comprehensive understanding of the folding mechanisms, has remained a tremendous challenge to ab initio protein folding simulations despite the extensive effort. In this work, the folding process of the B domain of protein A (BdpA) has been simulated by both conventional and replica exchange molecular dynamics using AMBER FF03 all-atom force field. Started from an extended chain, a total of 40 conventional (each to 1.0 micros) and two sets of replica exchange (each to 200.0 ns per replica) molecular dynamics simulations were performed with different generalized-Born solvation models and temperature control schemes. The improvements in both the force field and solvent model allowed successful simulations of the folding process to the native state as demonstrated by the 0.80 A C(alpha) root mean square deviation (RMSD) of the best folded structure. The most populated conformation was the native folded structure with a high population. This was a significant improvement over the 2.8 A C(alpha) RMSD of the best nativelike structures from previous ab initio folding studies on BdpA. To the best of our knowledge, our results demonstrate, for the first time, that ab initio simulations can reach the native state of BdpA. Consistent with experimental observations, including Phi-value analyses, formation of helix II/III hairpin was a crucial step that provides a template upon which helix I could form and the folding process could complete. Early formation of helix III was observed which is consistent with the experimental results of higher residual helical content of isolated helix III among the three helices. The calculated temperature-dependent profile and the melting temperature were in close agreement with the experimental results. The simulations further revealed that phenylalanine 31 may play critical to achieve the correct packing of the three helices which is consistent with the experimental observation. In addition to the mechanistic studies, an ab initio structure prediction was also conducted based on both the physical energy and a statistical potential. Based on the lowest physical energy, the predicted structure was 2.0 A C(alpha) RMSD away from the experimentally determined structure.

A test on peptide stability of AMBER force fields with implicit solvation

We used replica exchange molecular dynamics (REMD) simulations to evaluate four different AMBER force fields and three different implicit solvent models. Our aim was to determine if these physics-based models captured the correct secondary structures of two alpha-helical and two beta-peptides: the 14-mer EK helix of Baldwin and co-workers, the C-terminal helix of ribonuclease, the 16-mer C-terminal hairpin of protein G, and the trpzip2 miniprotein. The different models gave different results, but generally we found that AMBER ff96 plus the implicit solvent model of Onufriev, Bashford, and Case gave reasonable structures, and is fairly well-balanced between helix and sheet. We also observed differences in the strength of ion pairing in the solvent models, we but found that the native secondary structures were retained even when salt bridges were prevented in the conformational sampling. Overall, this work indicates that some of these all-atom physics-based force fields may be good starting points for protein folding and protein structure prediction.

Ten-microsecond molecular dynamics simulation of a fast-folding WW domain

All-atom molecular dynamics (MD) simulations of protein folding allow analysis of the folding process at an unprecedented level of detail. Unfortunately, such simulations have not yet reached their full potential both due to difficulties in sufficiently sampling the microsecond timescales needed for folding, and because the force field used may yield neither the correct dynamical sequence of events nor the folded structure. The ongoing study of protein folding through computational methods thus requires both improvements in the performance of molecular dynamics programs to make longer timescales accessible, and testing of force fields in the context of folding simulations. We report a ten-microsecond simulation of an incipient downhill-folding WW domain mutant along with measurement of a molecular time and activated folding time of 1.5 microseconds and 13.3 microseconds, respectively. The protein simulated in explicit solvent exhibits several metastable states with incorrect topology and does not assume the native state during the present simulations.

Combining experiment and simulation in protein folding: closing the gap for small model systems

All-atom molecular dynamics (MD) simulations on increasingly powerful computers have been combined with experiments to characterize protein folding in detail over wider time ranges. The folding of small ultrafast folding proteins is being simulated on micros timescales, leading to improved structural predictions and folding rates. To what extent is 'closing the gap' between simulation and experiment for such systems providing insights into general mechanisms of protein folding?

The protein folding problem

The "protein folding problem" consists of three closely related puzzles: (a) What is the folding code? (b) What is the folding mechanism? (c) Can we predict the native structure of a protein from its amino acid sequence? Once regarded as a grand challenge, protein folding has seen great progress in recent years. Now, foldable proteins and nonbiological polymers are being designed routinely and moving toward successful applications. The structures of small proteins are now often well predicted by computer methods. And, there is now a testable explanation for how a protein can fold so quickly: A protein solves its large global optimization problem as a series of smaller local optimization problems, growing and assembling the native structure from peptide fragments, local structures first.

Implicit modeling of nonpolar solvation for simulating protein folding and conformational transitions

Accurate description of the solvent environment is critical in computer simulations of protein structure and dynamics. An implicit treatment of solvent aims to capture the mean influence of water molecules on the solute via direct estimation of the solvation free energy. It has emerged as a powerful alternative to explicit solvent, and provides a favorable compromise between computational cost and level of detail. We review the current theory and techniques for implicit modeling of nonpolar solvation in the context of simulating protein folding and conformational transitions, and discuss the main directions for further development. It is demonstrated that the current surface area based nonpolar models have severe limitations, including insufficient description of the conformational dependence of solvation, over-estimation of the strength of pair-wise nonpolar interactions, and incorrect prediction of anti-cooperativity for three-body hydrophobic associations. We argue that, to improve beyond current level of accuracy of implicit solvent models, two important aspects of nonpolar solvation need to be incorporated, namely, the length-scale dependence of hydrophobic association and solvent screening of solute-solute dispersion interactions. We recognize that substantial challenges exist in constructing a sufficiently balanced, yet reasonably efficient, implicit solvent protein force field. Nonetheless, most of the fundamental problems are understood, and exciting progress has been made over the last few years. We believe that continual work along the frontiers outlined will greatly improve one's ability to study protein folding and large conformational transitions at atomistic detail.

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.