All-atom folding of the three-helix HIV accessory protein with an adaptive parallel tempering method

All-atom protein structure prediction from the amino acid sequence alone remains an important goal of biophysical chemistry. Recent progress in force field development and validation suggests that the PFF01 free-energy force field correctly predicts the native conformation of various helical proteins as the global optimum of its free-energy surface. Reproducible protein structure prediction requires the availability of efficient optimization methods to locate the global minima of such complex potentials. Here we investigate an adapted version of the parallel tempering method as an efficient parallel stochastic optimization method for protein structure prediction. Using this approach we report the reproducible all-atom folding of the three-helix 40 amino acid HIV accessory protein from random conformations to within 2.4 A backbone RMS deviation from the experimental structure with modest computational resources.     

A Free-Energy Approach for All-Atom Protein Simulation

All-atom free-energy methods offer a promising alternative to kinetic molecular mechanics simulations of protein folding and association. Here we report an accurate, transferable all-atom biophysical force field (PFF02) that stabilizes the native conformation of a wide range of proteins as the global optimum of the free-energy landscape. For 32 proteins of the ROSETTA decoy set and six proteins that we have previously folded with PFF01, we find near-native conformations with an average backbone RMSD of 2.14 Å to the native conformation and an average Z-score of −3.46 to the corresponding decoy set. We used nonequilibrium sampling techniques starting from completely extended conformations to exhaustively sample the energy surface of three nonhomologous hairpin-peptides, a three-stranded β-sheet, the all-helical 40 amino-acid HIV accessory protein, and a zinc-finger ββα motif, and find near-native conformations for the minimal energy for each protein. Using a massively parallel evolutionary algorithm, we also obtain a near-native low-energy conformation for the 54 amino-acid engrailed homeodomain. Our force field thus stabilized near-native conformations for a total of 20 proteins of all structure classes with an average RMSD of only 3.06 Å to their respective experimental conformations.     

Protein structure prediction by all-atom free-energy refinement

Background  

The reliable prediction of protein tertiary structure from the amino acid sequence remains challenging even for small proteins. We have developed an all-atom free-energy protein forcefield (PFF01) that we could use to fold several small proteins from completely extended conformations. Because the computational cost of de-novo folding studies rises steeply with system size, this approach is unsuitable for structure prediction purposes. We therefore investigate here a low-cost free-energy relaxation protocol for protein structure prediction that combines heuristic methods for model generation with all-atom free-energy relaxation in PFF01.     

A new pairwise folding potential based on improved decoy generation and side-chain packing

A new force field for pairwise residue interactions as a function of C(alpha) to C(alpha) distances is presented. The force field was developed through the solution of a linear programming formulation with large sets of constraints. The constraints are based on the construction of >80,000 low-energy decoys for a set of proteins and requiring the decoy energies for each protein system to be higher than the native conformation of that particular protein. The generation of a robust force field was facilitated by the use of a novel decoy generation process, which involved the rational selection of proteins to add to the training set and included a significant energy minimization of the decoys. The force field was tested on a large set of decoys for various proteins not included in the training set and shown to perform well compared with a leading force field in identifying the native conformation for these proteins.     

Use of decoys to optimize an all-atom force field including hydration

A novel method of parameter optimization is proposed. It makes use of large sets of decoys generated for six nonhomologous proteins with different architecture. Parameter optimization is achieved by creating a free energy gap between sets of nativelike and nonnative conformations. The method is applied to optimize the parameters of a physics-based scoring function consisting of the all-atom ECEPP05 force field coupled with an implicit solvent model (a solvent-accessible surface area model). The optimized force field is able to discriminate near-native from nonnative conformations of the six training proteins when used either for local energy minimization or for short Monte Carlo simulated annealing runs after local energy minimization. The resulting force field is validated with an independent set of six nonhomologous proteins, and appears to be transferable to proteins not included in the optimization; i.e., for five out of the six test proteins, decoys with 1.7- to 4.0-Å all-heavy-atom root mean-square deviations emerge as those with the lowest energy. In addition, we examined the set of misfolded structures created by Park and Levitt using a four-state reduced model. The results from these additional calculations confirm the good discriminative ability of the optimized force field obtained with our decoy sets.     

Development of a physics-based force field for the scoring and refinement of protein models

The minimal requirements of a physics-based potential that can refine protein structures are the existence of a correlation between the energy with native similarity and the scoring of the native structure as the lowest in energy. To develop such a force field, the relative weights of the Amber ff03 all-atom potential supplemented by an explicit hydrogen-bond potential were adjusted by global optimization of energetic and structural criteria for a large set of protein decoys generated for a set of 58 nonhomologous proteins. The average correlation coefficient of the energy with TM-score significantly improved from 0.25 for the original ff03 potential to 0.65 for the optimized force field. The fraction of proteins for which the native structure had lowest energy increased from 0.22 to 0.90. Moreover, use of an explicit hydrogen-bond potential improves scoring performance of the force field. Promising preliminary results were obtained in applying the optimized potentials to refine protein decoys using only an energy criterion to choose the best decoy among sampled structures. For a set of seven proteins, 63% of the decoys improve, 18% get worse, and 19% are not changed.     

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.     

A novel high resolution Calpha--Calpha distance dependent force field based on a high quality decoy set

This work presents a novel C(alpha)--C(alpha) distance dependent force field which is successful in selecting native structures from an ensemble of high resolution near-native conformers. An enhanced and diverse protein set, along with an improved decoy generation technique, contributes to the effectiveness of this potential. High quality decoys were generated for 1489 nonhomologous proteins and used to train an optimization based linear programming formulation. The goal in developing a set of high resolution decoys was to develop a simple, distance-dependent force field that yields the native structure as the lowest energy structure and assigns higher energies to decoy structures that are quite similar as well as those that are less similar. The model also includes a set of physical constraints that were based on experimentally observed physical behavior of the amino acids. The force field was tested on two sets of test decoys not in the training set and was found to excel on all the metrics that are widely used to measure the effectiveness of a force field. The high resolution force field was successful in correctly identifying 113 native structures out of 150 test cases and the average rank obtained for this test was 1.87. All the high resolution structures (training and testing) used for this work are available online and can be downloaded from http://titan.princeton.edu/HRDecoys.     

An evolutionary strategy for all-atom folding of the 60-amino-acid bacterial ribosomal protein l20

We have investigated an evolutionary algorithm for de novo all-atom folding of the bacterial ribosomal protein L20. We report results of two simulations that converge to near-native conformations of this 60-amino-acid, four-helix protein. We observe a steady increase of "native content" in both simulated ensembles and a large number of near-native conformations in their final populations. We argue that these structures represent a significant fraction of the low-energy metastable conformations, which characterize the folding funnel of this protein. These data validate our all-atom free-energy force field PFF01 for tertiary structure prediction of a previously inaccessible structural family of proteins. We also compare folding simulations of the evolutionary algorithm with the basin-hopping technique for the Trp-cage protein. We find that the evolutionary algorithm generates a dynamic memory in the simulated population, which leads to faster overall convergence.     

Free energy determinants of tertiary structure and the evaluation of protein models

We develop a protocol for estimating the free energy difference between different conformations of the same polypeptide chain. The conformational free energy evaluation combines the CHARMM force field with a continuum treatment of the solvent. In almost all cases studied, experimentally determined structures are predicted to be more stable than misfolded "decoys." This is due in part to the fact that the Coulomb energy of the native protein is consistently lower than that of the decoys. The solvation free energy generally favors the decoys, although the total electrostatic free energy (sum of Coulomb and solvation terms) favors the native structure. The behavior of the solvation free energy is somewhat counterintuitive and, surprisingly, is not correlated with differences in the burial of polar area between native structures and decoys. Rather. the effect is due to a more favorable charge distribution in the native protein, which, as is discussed, will tend to decrease its interaction with the solvent. Our results thus suggest, in keeping with a number of recent studies, that electrostatic interactions may play an important role in determining the native topology of a folded protein. On this basis, a simplified scoring function is derived that combines a Coulomb term with a hydrophobic contact term. This function performs as well as the more complete free energy evaluation in distinguishing the native structure from misfolded decoys. Its computational efficiency suggests that it can be used in protein structure prediction applications, and that it provides a physically well-defined alternative to statistically derived scoring functions.     

Hydrophobic potential of mean force as a solvation function for protein structure prediction

We have developed a solvation function that combines a Generalized Born model for polarization of protein charge by the high dielectric solvent, with a hydrophobic potential of mean force (HPMF) as a model for hydrophobic interaction, to aid in the discrimination of native structures from other misfolded states in protein structure prediction. We find that our energy function outperforms other reported scoring functions in terms of correct native ranking for 91% of proteins and low Z scores for a variety of decoy sets, including the challenging Rosetta decoys. This work shows that the stabilizing effect of hydrophobic exposure to aqueous solvent that defines the HPMF hydration physics is an apparent improvement over solvent-accessible surface area models that penalize hydrophobic exposure. Decoys generated by thermal sampling around the native-state basin reveal a potentially important role for side-chain entropy in the future development of even more accurate free energy surfaces.     

Structure refinement of protein model decoys requires accurate side‐chain placement

In this study, the application of temperature‐based replica‐exchange (T‐ReX) simulations for structure refinement of decoys taken from the I‐TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self‐guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T‐ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T‐ReX simulation model is provided. Additionally, the effect of side‐chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near‐native backbone conformations among the starting decoys, the determinant of their refinement is side‐chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T‐ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I‐TASSER decoy sets and a 25% reduction in values of C_α root‐mean‐square deviation. The hybrid model succeeded in obtaining a sharper funnel to low‐energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near‐native packing of side chains, the T‐ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem. Proteins 2013. 2012 Published by Wiley Periodicals, Inc.     

Folding of Globular Proteins by Energy Minimization and Monte Carlo Simulations with Hydrophobic Surface Area Potentials

We describe an efficient method to calculate analytically the solvent accessible surface areas and their gradients in proteins for empirical force field calculations on serial and parallel computers. In an application to the small three helix bundle protein Er-10, energy minimizations and Monte Carlo simulations were performed with the empirical ECEPP/2 force field, which was extended by a protein solvent interaction term. We show that the NMR structure is stable when refined with the force field including the protein solvent interaction term, but large structural deviations are observed in energy minimization in vacuo. When we started from random structures with preformed helices and maintained the helical segments by dihedral angle constraints, the final structures with the lowest energies resembled the native form. The root-mean-square deviations for the backbone atoms of the three helices compared to the experimentally determined structure was 3 Å to 4 Å.     

Spatial profiling of protein hydrophobicity: native vs. decoy structures

A recent study of 30 soluble globular protein structures revealed a quasi-invariant called the hydrophobic ratio. This invariant, which is the ratio of the distance at which the second order hydrophobic moment vanished to the distance at which the zero order moment vanished, was found to be 0.75 +/- 0.05 for 30 protein structures. This report first describes the results of the hydrophobic profiling of 5,387 non-redundant globular protein domains of the Protein Data Bank, which yields a hydrophobic ratio of 0.71 +/- 0.08. Then, a new hydrophobic score is defined based on the hydrophobic profiling to discriminate native-like proteins from decoy structures. This is tested on three widely used decoy sets, namely the Holm and Sander decoys, Park and Levitt decoys, and Baker decoys. Since the hydrophobic moment profiling characterizes a global feature and requires reasonably good statistics, this imposes a constraint upon the size of the protein structures in order to yield relatively smooth moment profiles. We show that even subject to the limitations of protein size (both Park & Levitt and Baker sets are small protein decoys), the hydrophobic moment profiling and hydrophobic score can provide useful information that should be complementary to the information provided by force field calculations.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.     

Why the OPLS-AA force field cannot produce the β-hairpin structure of H1 peptide in solution when comparing with the GROMOS 43A1 force field?

The optimal combination of force field and water model is an essential problem that is able to increase molecular dynamics simulation quality for different types of proteins and peptides. In this work, an attempt has been made to explore the problem by studying H1 peptide using four different models based on different force fields, water models and electrostatic schemes. The driving force for H1 peptide conformation transition and the reason why the OPLS-AA force field cannot produce the β-hairpin structure of H1 peptide in solution while the GROMOS 43A1 force field can do were investigated by temperature replica exchange molecular dynamics simulation (T-REMD). The simulation using the GROMOS 43A1 force field preferred to adopt a β-hairpin structure, which was in good agreement with the several other simulations and the experimental evidences. However, the simulation using the OPLS-AA force field has a significant difference from the simulations with the GROMOS 43A1 force field simulation. The results show that the driving force in H1 peptide conformation transition is solvent exposure of its hydrophobic residues. However, the subtle balances between residue-residue interactions and residue-solvent interaction are disrupted by using the OPLS-AA force field, which induced the reduction in the number of residue-residue contact. Similar solvent exposure of the hydrophobic residues is observed for all the conformations sampled using the OPLS-AA force field. For H1 peptide which exhibits large solvent exposure of the hydrophobic residues, the GROMOS 43A1 force field with the SPC water model can provide more accurate results.     

How well can we predict native contacts in proteins based on decoy structures and their energies?

One strategy for ab initio protein structure prediction is to generate a large number of possible structures (decoys) and select the most fitting ones based on a scoring or free energy function. The conformational space of a protein is huge, and chances are rare that any heuristically generated structure will directly fall in the neighborhood of the native structure. It is desirable that, instead of being thrown away, the unfitting decoy structures can provide insights into native structures so prediction can be made progressively. First, we demonstrate that a recently parameterized physics-based effective free energy function based on the GROMOS96 force field and a generalized Born/surface area solvent model is, as several other physics-based and knowledge-based models, capable of distinguishing native structures from decoy structures for a number of widely used decoy databases. Second, we observe a substantial increase in correlations of the effective free energies with the degree of similarity between the decoys and the native structure, if the similarity is measured by the content of native inter-residue contacts in a decoy structure rather than its root-mean-square deviation from the native structure. Finally, we investigate the possibility of predicting native contacts based on the frequency of occurrence of contacts in decoy structures. For most proteins contained in the decoy databases, a meaningful amount of native contacts can be predicted based on plain frequencies of occurrence at a relatively high level of accuracy. Relative to using plain frequencies, overwhelming improvements in sensitivity of the predictions are observed for the 4_state_reduced decoy sets by applying energy-dependent weighting of decoy structures in determining the frequency. There, approximately 80% native contacts can be predicted at an accuracy of approximately 80% using energy-weighted frequencies. The sensitivity of the plain frequency approach is much lower (20% to 40%). Such improvements are, however, not observed for the other decoy databases. The rationalization and implications of the results are discussed.     

Protein decoy assembly using short fragments under geometric constraints

A small set of protein fragments can represent adequately all known local protein structure. This set of fragments, along with a construction scheme that assembles these fragments into structures, defines a discrete (relatively small) conformation space, which approximates protein structures accurately. We generate protein decoys by sampling geometrically valid structures from this conformation space, biased by the secondary structure prediction for the protein. Unlike other methods, secondary structure prediction is the only protein-specific information used for generating the decoys. Nevertheless, these decoys are qualitatively similar to those found by others. The method works well for all-alpha proteins, and shows promising results for alpha and beta proteins.