Discrimination of the native from misfolded protein models with an energy function including implicit solvation.

An essential requirement for theoretical protein structure prediction is an energy function that can discriminate the native from non-native protein conformations. To date most of the energy functions used for this purpose have been extracted from a statistical analysis of the protein structure database, without explicit reference to the physical interactions responsible for protein stability. The use of the statistical functions has been supported by the widespread belief that they are superior for such discrimination to physics-based energy functions. An effective energy function which combined the CHARMM vacuum potential with a Gaussian model for the solvation free energy is tested for its ability to discriminate the native structure of a protein from misfolded conformations; the results are compared with those obtained with the vacuum CHARMM potential. The test is performed on several sets of misfolded structures prepared by others, including sets of about 650 good decoys for six proteins, as well as on misfolded structures of chymotrypsin inhibitor 2. The vacuum CHARMM potential is successful in most cases when energy minimized conformations are considered, but fails when applied to structures relaxed by molecular dynamics. With the effective energy function the native state is always more stable than grossly misfolded conformations both in energy minimized and molecular dynamics-relaxed structures. The present results suggest that molecular mechanics (physics-based) energy functions, complemented by a simple model for the solvation free energy, should be tested for use in the inverse folding problem, and supports their use in studies of the effective energy surface of proteins in solution. Moreover, the study suggests that the belief in the superiority of statistical functions for these purposes may be ill founded.     

The non-polar solvent potential of mean force for the dimerization of alanine dipeptide: the role of solute-solvent van der Waals interactions

The non-polar component of the potential of mean force of dimerization of alanine dipeptide has been calculated in explicit solvent by free energy perturbation. We observe that the calculated PMF is inconsistent with a non-polar hydration free energy model based solely on the solute surface area. The non-linear behavior of the solute-solvent van der Waals energy is primarily responsible for the non-linear dependence of the potential of mean force with respect to the surface area. The calculated potential of mean force is reproduced by an implicit solvent model based on a solvent continuum model for the solute-solvent van der Waals interaction energy and the surface area for the work of forming the solute cavity.     

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.     

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.     

Free energy landscape of protein folding in water: explicit vs. implicit solvent

The Generalized Born (GB) continuum solvent model is arguably the most widely used implicit solvent model in protein folding and protein structure prediction simulations; however, it still remains an open question on how well the model behaves in these large-scale simulations. The current study uses the beta-hairpin from C-terminus of protein G as an example to explore the folding free energy landscape with various GB models, and the results are compared to the explicit solvent simulations and experiments. All free energy landscapes are obtained from extensive conformation space sampling with a highly parallel replica exchange method. Because solvation model parameters are strongly coupled with force fields, five different force field/solvation model combinations are examined and compared in this study, namely the explicit solvent model: OPLSAA/SPC model, and the implicit solvent models: OPLSAA/SGB (Surface GB), AMBER94/GBSA (GB with Solvent Accessible Surface Area), AMBER96/GBSA, and AMBER99/GBSA. Surprisingly, we find that the free energy landscapes from implicit solvent models are quite different from that of the explicit solvent model. Except for AMBER96/GBSA, all other implicit solvent models find the lowest free energy state not the native state. All implicit solvent models show erroneous salt-bridge effects between charged residues, particularly in OPLSAA/SGB model, where the overly strong salt-bridge effect results in an overweighting of a non-native structure with one hydrophobic residue F52 expelled from the hydrophobic core in order to make better salt bridges. On the other hand, both AMBER94/GBSA and AMBER99/GBSA models turn the beta-hairpin in to an alpha-helix, and the alpha-helical content is much higher than the previously reported alpha-helices in an explicit solvent simulation with AMBER94 (AMBER94/TIP3P). Only AMBER96/GBSA shows a reasonable free energy landscape with the lowest free energy structure the native one despite an erroneous salt-bridge between D47 and K50. Detailed results on free energy contour maps, lowest free energy structures, distribution of native contacts, alpha-helical content during the folding process, NOE comparison with NMR, and temperature dependences are reported and discussed for all five models.     

Protein molecular dynamics with the generalized Born/ACE solvent model

Implicit solvent models are increasingly important for the study of proteins in aqueous solution. Here, the generalized Born (GB) solvent polarization model as implemented in the analytical ACE potential [Schaefer and Karplus (1996) J Phys Chem 100:1578] is used to perform molecular dynamics simulations of two small, homologous proteins: the immunoglobulin-binding domain of streptococcal protein G and the Ras binding domain of Raf. Several model parameterizations are compared through more than 60 ns of simulation. Results are compared with two simpler solvent models-an accessible surface area model and a distant-dependent dielectric model, with finite-difference Poisson calculations, with existing explicit solvent simulations, and with experimental data. The simpler models yield stable but distorted structures. The best GB/ACE implementation uses a set of atomic Voronoi volumes reported recently, obtained by averaging over a large database of crystallographic protein structures. A 20% reduction is applied to the volumes, compensating in an average sense for an excessive de-screening of individual charges inherent in the ACE self-energy and for an undersolvation of dipolar groups inherent in the GB screening function. This GB/ACE parameterization yields stable trajectories on the 0.5-1-ns time scale that deviate moderately (approximately 1.5-2.5 A) from the X-ray structure, reproduce approximately the surface distribution of charged, polar, and hydrophobic groups, and reproduce accurately backbone flexibility as measured by amide NMR-order parameters. Over longer time scales (1.5-3 ns), some of the protein G runs escape from the native energy basin and deviate strongly (3 A) from the native structure. The conformations sampled during the transition out of the native energy basin are overstabilized by the GB/ACE solvation model, as compared with a numerical treatment of the full dielectric continuum model.     

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.     

A CFF 91-based Continuum Solvation Model: Solvation Free Energies of Small Organic Molecules and Conformations of the Alanine Dipeptide in Solution

Abstract

For molecular mechanics simulations of solvated molecules, it is important to use a consistent approach for calculating both the force field energy and the solvation free energy. A continuum solvation model based upon the atomic charges provided with the CFF91 force field is derived. The electrostatic component of the solvation free energy is described by the Poisson-Bolzmann equation while the nonpolar comonent of the solvation energy is assumed to be proportional to the solvent accessible surface area of the solute. Solute atomic radii used to describe the interface between the solute and solvent are fitted to reproduce the energies of small organic molecules. Data for 140 compounds are presented and compared to experiment and to the results from the well-characterized quantum mechanical solvation model AM1-SM2. In particular, accurate results are obtained for amino acid neutral analogues (mean unsigned error of 0.3 kcal/mol). The conformational energetics of the solvated alanine dipeptide is discussed.     

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.     

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.     

Microfolding: conformational probability map for the alanine dipeptide in water from molecular dynamics simulations

A direct attack on the protein-folding problem has been initiated with the free energy perturbation methods of molecular dynamics. The complete conformational probability map for the alanine dipeptide is presented. This work uses the SPC model for the explicit hydration of the dipeptide. Free energy differences for the four observed minima (beta, alpha R, alpha L, C7ax) are given, and the free energy barriers between minima are outlined.     

Folding, misfolding, and amyloid protofibril formation of WW domain FBP28

We study the folding mechanism of a triple beta-strand WW domain from the Formin binding protein 28 (FBP28) at atomic resolution with explicit water model using replica exchange molecular dynamics computer simulations. Extended sampling over a wide range of temperatures to obtain the free energy, enthalpy, and entropy surfaces as a function of structural coordinates has been performed. Simulations were started from different configurations covering the folded and unfolded states. In the free energy landscape a transition state is identified and its structures and -values are compared with experimental data from a homologous protein, the prolyl-isomerase Pin1 WW domain. A stable intermediate state is found to accumulate during the simulation characterized by the carboxyl-terminal beta-strand 3 having misregistered hydrogen bonds and where the structural heterogeneity is due to nonnative turn II formation. Furthermore, the aggregation behavior of the FBP28 WW domain may be related to one such misfolded structure, which has a much lower free energy of dimer formation than that of the native dimer. Based on the misfolded dimer, aggregation to form protofibril structure is discussed.     

Conformational characteristics of unstructured peptides: alpha-synuclein

We have performed replica-exchange molecular dynamics simulations on 41 residue peptides containing NAC region of alpha-synuclein in various force fields and solvent conditions. Alpha-synuclein is known to be the major cause of Parkinson's disease by amyloid-like aggregation, and one of the natively unfolded proteins. To investigate conformational characteristics of intrinsically unstructured peptides, we carried out structural analysis by introducing 'representative structure' for ensemble of structures occurring during the overall trajectory. Representative structures may be defined by using either coordinate averaging or distance averaging. When applied to the natively folded proteins such as villin headpiece, structural analysis based on representative structure was found to yield consistent results with those obtained from conventional analysis. Individual conformations obtained from the simulations of NAC peptide for various conditions show flexible structures close to random coil. Secondary structure contents and free energy surfaces showed dependency on solvent conditions, which may be interpreted as another manifestation of structural diversity. It is found that representative structures can provide useful information about structural characteristics of intrinsically unstructured proteins.     

Criteria that discriminate between native proteins and incorrectly folded models

Various theoretical concepts, such as free energy potentials, electrostatic interaction potentials, atomic packing, solvent-exposed surface, and surface charge distribution, were tested for their ability to discriminate between native proteins and misfolded protein models. Misfolded models were constructed by introducing incorrect side chains onto polypeptide backbones: side chains of the alpha-helical hemerythrin were modeled on the beta-sheeted backbone of immunoglobulin VL domain, whereas those of the VL domain were similarly modeled on the hemerythrin backbone. CONGEN, a conformational space sampling program, was used to construct the side chains, in contrast to the previous work, where incorrect side chains were modeled in all trans conformations. Capability of the conformational search procedure to reproduce native conformations was gauged first by rebuilding (the correct) side chains in hemerythrin and the VL domain: constructs with r.m.s. differences from the x-ray side chains 2.2-2.4 A were produced, and many calculated conformations matched the native ones quite well. Incorrectly folded models were then constructed by the same conformational protocol applied to incorrect amino acid sequences. All CONGEN constructs, both correctly and incorrectly folded, were characterized by exceptionally small molecular surfaces and low potential energies. Surface charge density, atomic packing, and Coulomb formula-based electrostatic interactions of the misfolded structures and the correctly folded proteins were similar, and therefore of little interest for diagnosing incorrect folds. The following criteria clearly favored the native structures over the misfolded ones: 1) solvent-exposed side-chain nonpolar surface, 2) number of buried ionizable groups, and 3) empirical free energy functions that incorporate solvent effects.     

Extracting knowledge from protein structure geometry

Protein structure prediction techniques proceed in two steps, namely the generation of many structural models for the protein of interest, followed by an evaluation of all these models to identify those that are native‐like. In theory, the second step is easy, as native structures correspond to minima of their free energy surfaces. It is well known however that the situation is more complicated as the current force fields used for molecular simulations fail to recognize native states from misfolded structures. In an attempt to solve this problem, we follow an alternate approach and derive a new potential from geometric knowledge extracted from native and misfolded conformers of protein structures. This new potential, Metric Protein Potential (MPP), has two main features that are key to its success. Firstly, it is composite in that it includes local and nonlocal geometric information on proteins. At the short range level, it captures and quantifies the mapping between the sequences and structures of short (7‐mer) fragments of protein backbones through the introduction of a new local energy term. The local energy term is then augmented with a nonlocal residue‐based pairwise potential, and a solvent potential. Secondly, it is optimized to yield a maximized correlation between the energy of a structural model and its root mean square (RMS) to the native structure of the corresponding protein. We have shown that MPP yields high correlation values between RMS and energy and that it is able to retrieve the native structure of a protein from a set of high‐resolution decoys. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Exploratory studies of ab initio protein structure prediction: multiple copy simulated annealing, AMBER energy functions, and a generalized born/solvent accessibility solvation model.

A theoretical and computational approach to ab initio structure prediction for polypeptides in water is described and applied to selected amino acid sequences for testing and preliminary validation. The method builds systematically on the extensive efforts applied to parameterization of molecular dynamics (MD) force fields, employs an empirically well-validated continuum dielectric model for solvation, and an eminently parallelizable approach to conformational search. The effective free energy of polypeptide chains is estimated from AMBER united atom potential functions, with internal degrees of freedom for both backbone and amino acid side chains explicitly treated. The hydration free energy of each structure is determined using the Generalized Born/Solvent Accessibility (GBSA) method, modified and reparameterized to include atom types consistent with the AMBER force field. The conformational search procedure employs a multiple copy, Monte Carlo simulated annealing (MCSA) protocol in full torsion angle space, applied iteratively on sets of structures of progressively lower free energy until a prediction of a structure with lowest effective free energy is obtained. Calibration tests for the effective energy function and search algorithm are performed on the alanine dipeptide, selected protein crystal structures, and united atom decoys on barnase, crambin, and six examples from the Rosetta set. Specific demonstration cases of the method are provided for the 8-mer sequence of Ala residues, a 12-residue peptide with longer side chains QLLKKLLQQLKQ, a de novo designed 16 residue peptide of sequence (AAQAA)3Y, a 15-residue sequence with a beta sheet motif, GEWTWDATKTFTVTE, and a 36 residue small protein, Villin headpiece. The Ala 8-mer readily formed an alpha-helix. An alpha-helix structure was predicted for the 16-mer, consistent with observed results from IR and CD spectroscopy and with the pattern in psi/straight phi angles of known protein structures. The predicted structure for the 12-mer, composed of a mix of helix and less regular elements of secondary structure, lies 2.65 A RMS from the observed crystal structure. Structure prediction for the 8-mer beta-motif resulted in form 4.50 A RMS from the crystal geometry. For Villin, the predicted native form is very close to the crystal structure, RMS values of 3.5 A (including sidechains), and 1.01 A (main chain only). The methodology permits a detailed analysis of the molecular forces which dominate various segments of the predicted folding trajectory. Analysis of the results in terms of internal torsional, electrostatic and van der Waals and the electrostatic and non-electrostatic contributions to hydration, including the hydrophobic effect, is presented.     

A model for the simulation of an aqueous dipeptide solution

A model for the simulation of a solution of an alanine dipeptide in water is presented that combines a previous model for bulk water (ST2) with that used in conformational energy studies on small molecules and proteins. The results of a pilot molecular dynamics study indicate that the model leads to reasonable solvent–solute interactions. No evidence is found for substantial changes in the structure or dynamics of the dipeptide in solution as compared to in vacuo. Furthermore, at the elevated temperature examined, there appear to be no significant effects on the dynamics or intermolecular bonding of the water molecules in contact with the solute.     

Computer simulation studies of the fully solvated wild-type and mutated GnRH in extended and beta-turn conformations

The conformational preference of the gonadotropin-releasing hormone (GnRH) and its Lys-8 mutant, studied earlier with a continuum model, was revisited using an explicit solvent model and thermodynamic integration to calculate the solvents contribution to the conformation-dependence of its free energy. In addition, the Proximity Criterion was used to further analyze the effects of conformational changes.     

The sensitivity of conformational free energies of the alanine dipeptide to atomic site charges

Different atomic point charge sets are obtained for the α_R and C_7.eq conformations of the alanine dipeptide by fitting the charges of each conformation to the respective ab initio electrostatic potential surfaces both individually and simultaneously, in both the united atom and the all-atom representations. Using these charge sets, the sensitivity of the relative conformational aqueous free energies to the atomic site charges is investigated. For this particular system, we find that the solute-water contributions to the conformational free energy differences have a rather weak dependence on site charges; the calculated intramolecular contributions, however, show a rather strong dependence on the atomic site charges. It is suggested that the calculated results for the alanine dipeptide using a single, simultaneously fit set of charges for both conformations are in better agreement with experiments than the calculations carried out with charges determined individually for each conformation. © 1997 John Wiley & Sons, Inc.