Physical scoring function based on AMBER force field and Poisson-Boltzmann implicit solvent for protein structure prediction

A well-behaved physics-based all-atom scoring function for protein structure prediction is analyzed with several widely used all-atom decoy sets. The scoring function, termed AMBER/Poisson-Boltzmann (PB), is based on a refined AMBER force field for intramolecular interactions and an efficient PB model for solvation interactions. Testing on the chosen decoy sets shows that the scoring function, which is designed to consider detailed chemical environments, is able to consistently discriminate all 62 native crystal structures after considering the heteroatom groups, disulfide bonds, and crystal packing effects that are not included in the decoy structures. When NMR structures are considered in the testing, the scoring function is able to discriminate 8 out of 10 targets. In the more challenging test of selecting near-native structures, the scoring function also performs very well: for the majority of the targets studied, the scoring function is able to select decoys that are close to the corresponding native structures as evaluated by ranking numbers and backbone Calpha root mean square deviations. Various important components of the scoring function are also studied to understand their discriminative contributions toward the rankings of native and near-native structures. It is found that neither the nonpolar solvation energy as modeled by the surface area model nor a higher protein dielectric constant improves its discriminative power. The terms remaining to be improved are related to 1-4 interactions. The most troublesome term is found to be the large and highly fluctuating 1-4 electrostatics term, not the dihedral-angle term. These data support ongoing efforts in the community to develop protein structure prediction methods with physics-based potentials that are competitive with knowledge-based potentials.     

Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures

In this study, we have developed a statistical mechanics-based iterative method to extract statistical atomic interaction potentials from known, nonredundant protein structures. Our method circumvents the long-standing reference state problem in deriving traditional knowledge-based scoring functions, by using rapid iterations through a physical, global convergence function. The rapid convergence of this physics-based method, unlike other parameter optimization methods, warrants the feasibility of deriving distance-dependent, all-atom statistical potentials to keep the scoring accuracy. The derived potentials, referred to as ITScore/Pro, have been validated using three diverse benchmarks: the high-resolution decoy set, the AMBER benchmark decoy set, and the CASP8 decoy set. Significant improvement in performance has been achieved. Finally, comparisons between the potentials of our model and potentials of a knowledge-based scoring function with a randomized reference state have revealed the reason for the better performance of our scoring function, which could provide useful insight into the development of other physical scoring functions. The potentials developed in this study are generally applicable for structural selection in protein structure prediction.     

Comparison between Generalized-Born and Poisson–Boltzmann methods in physics-based scoring functions for protein structure prediction

Continuum solvent models such as Generalized-Born and Poisson–Boltzmann methods hold the promise to treat solvation effect efficiently and to enable rapid scoring of protein structures when they are combined with physics-based energy functions. Yet, direct comparison of these two approaches on large protein data set is lacking. Building on our previous work with a scoring function based on a Generalized-Born (GB) solvation model, and short molecular-dynamics simulations, we further extended the scoring function to compare with the MM-PBSA method to treat the solvent effect. We benchmarked this scoring function against seven publicly available decoy sets. We found that, somewhat surprisingly, the results of MM-PBSA approach are comparable to the previous GB-based scoring function. We also discussed the effect to the scoring function accuracy due to presence of large ligands and ions in some native structures of the decoy sets.     

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.     

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.     

Design of an optimal Chebyshev-expanded discrimination function for globular proteins

We describe the construction of a scoring function designed to model the free energy of protein folding. An optimization technique is used to determine the best functional forms of the hydrophobic, residue-residue and hydrogen-bonding components of the potential. The scoring function is expanded by use of Chebyshev polynomials, the coefficients of which are determined by minimizing the score, in units of standard deviation, of native structures in the ensembles of alternate decoy conformations. The derived effective potential is then tested on decoy sets used conventionally in such studies. Using our scoring function, we achieve a high level of discrimination between correct and incorrect folds. In addition, our method is able to represent functions of arbitrary shape with fewer parameters than the usual histogram potentials of similar resolution. Finally, our representation can be combined easily with many optimization methods, because the total energy is a linear function of the parameters. Our results show that the techniques of Z-score optimization and Chebyshev expansion work well.     

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 energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.     

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 simple Cα-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C_α-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.     

Protein structure evaluation using an all-atom energy based empirical scoring function

Arriving at the native conformation of a polypeptide chain characterized by minimum most free energy is a problem of long standing interest in protein structure prediction endeavors. Owing to the computational requirements in developing free energy estimates, scoring functions--energy based or statistical--have received considerable renewed attention in recent years for distinguishing native structures of proteins from non-native like structures. Several cleverly designed decoy sets, CASP (Critical Assessment of Techniques for Protein Structure Prediction) structures and homology based internet accessible three dimensional model builders are now available for validating the scoring functions. We describe here an all-atom energy based empirical scoring function and examine its performance on a wide series of publicly available decoys. Barring two protein sequences where native structure is ranked second and seventh, native is identified as the lowest energy structure in 67 protein sequences from among 61,659 decoys belonging to 12 different decoy sets. We further illustrate a potential application of the scoring function in bracketing native-like structures of two small mixed alpha/beta globular proteins starting from sequence and secondary structural information. The scoring function has been web enabled at www.scfbio-iitd.res.in/utility/proteomics/energy.jsp.     

An accurate, residue-level, pair potential of mean force for folding and binding based on the distance-scaled, ideal-gas reference state

Structure prediction on a genomic scale requires a simplified energy function that can efficiently sample the conformational space of polypeptide chains. A good energy function at minimum should discriminate native structures against decoys. Here, we show that a recently developed, residue-specific, all-atom knowledge-based potential (167 atomic types) based on distance-scaled, finite ideal-gas reference state (DFIRE-all-atom) can be substantially simplified to 20 residue types located at side-chain center of mass (DFIRE-SCM) without a significant change in its capability of structure discrimination. Using 96 standard multiple decoy sets, we show that there is only a small reduction (from 80% to 78%) in success rate of ranking native structures as the top 1. The success rate is higher than two previously developed, all-atom distance-dependent statistical pair potentials. Applied to structure selections of 21 docking decoys without modification, the DFIRE-SCM potential is 29% more successful in recognizing native complex structures than an all-atom statistical potential trained by a database of dimeric interfaces. The potential also achieves 92% accuracy in distinguishing true dimeric interfaces from artificial crystal interfaces. In addition, the DFIRE potential with the C(alpha) positions as the interaction centers recognizes 123 native structures out of a comprehensive 125-protein TOUCHSTONE decoy set in which each protein has 24,000 decoys with only C(alpha) positions. Furthermore, the performance by DFIRE-SCM on newly established 25 monomeric and 31 docking Rosetta-decoy sets is comparable to (or better than in the case of monomeric decoy sets) that of a recently developed, all-atom Rosetta energy function enhanced with an orientation-dependent hydrogen bonding potential.     

A distance-dependent atomic knowledge-based potential for improved protein structure selection.

A heavy atom distance-dependent knowledge-based pairwise potential has been developed. This statistical potential is first evaluated and optimized with the native structure z-scores from gapless threading. The potential is then used to recognize the native and near-native structures from both published decoy test sets, as well as decoys obtained from our group's protein structure prediction program. In the gapless threading test, there is an average z-score improvement of 4 units in the optimized atomic potential over the residue-based quasichemical potential. Examination of the z-scores for individual pairwise distance shells indicates that the specificity for the native protein structure is greatest at pairwise distances of 3.5-6.5 A, i.e., in the first solvation shell. On applying the current atomic potential to test sets obtained from the web, composed of native protein and decoy structures, the current generation of the potential performs better than residue-based potentials as well as the other published atomic potentials in the task of selecting native and near-native structures. This newly developed potential is also applied to structures of varying quality generated by our group's protein structure prediction program. The current atomic potential tends to pick lower RMSD structures than do residue-based contact potentials. In particular, this atomic pairwise interaction potential has better selectivity especially for near-native structures. As such, it can be used to select near-native folds generated by structure prediction algorithms as well as for protein structure refinement.     

Recognizing protein–protein interfaces with empirical potentials and reduced amino acid alphabets

Background  

In structural genomics, an important goal is the detection and classification of protein–protein interactions, given the structures of the interacting partners. We have developed empirical energy functions to identify native structures of protein–protein complexes among sets of decoy structures. To understand the role of amino acid diversity, we parameterized a series of functions, using a hierarchy of amino acid alphabets of increasing complexity, with 2, 3, 4, 6, and 20 amino acid groups. Compared to previous work, we used the simplest possible functional form, with residue–residue interactions and a stepwise distance-dependence. We used increased computational ressources, however, constructing 290,000 decoys for 219 protein–protein complexes, with a realistic docking protocol where the protein partners are flexible and interact through a molecular mechanics energy function. The energy parameters were optimized to correctly assign as many native complexes as possible. To resolve the multiple minimum problem in parameter space, over 64000 starting parameter guesses were tried for each energy function. The optimized functions were tested by cross validation on subsets of our native and decoy structures, by blind tests on series of native and decoy structures available on the Web, and on models for 13 complexes submitted to the CAPRI structure prediction experiment.     

Discrimination of native loop conformations in membrane proteins: decoy library design and evaluation of effective energy scoring functions

The recent determination of crystal structures for several important membrane proteins opens the way for comparative modeling of their membrane-spanning regions. However, the ability to predict correctly the structures of loop regions, which may be critical, for example, in ligand binding, remains a considerable challenge. To meet this challenge, accurate scoring methods have to discriminate between candidate conformations of an unknown loop structure. Some success in loop prediction has been reported for globular proteins; however, the proximity of membrane protein loops to the lipid bilayer casts doubt on the applicability of the same scoring methods to this problem. In this work, we develop "decoy libraries" of non-native folds generated, using the structures of two membrane proteins, with molecular dynamics and Monte Carlo techniques over a range of temperatures. We introduce a new approach for decoy library generation by constructing a flat distribution of conformations covering a wide range of Calpha-root-mean-square deviation (RMSD) from the native structure; this removes possible bias in subsequent scoring stages. We then score these decoy conformations with effective energy functions, using increasingly more cpu-intensive implicit solvent models, including (1) simple Coulombic electrostatics with constant or distance-dependent dielectrics; (2) atomic solvation parameters; (3) the effective energy function (EEF1) of Lazaridis and Karplus; (4) generalized Born/Analytical Continuum Solvent; and (5) finite-difference Poisson-Boltzmann energy functions. We show that distinction of native-like membrane protein loops may be achieved using effective energies with the assumption of a homogenous environment; thus, the absence of the adjacent lipid bilayer does not affect the scoring ability. In particular, the Analytical Continuum Solvent and finite-difference Poisson-Boltzmann energy functions are seen to be the most powerful scoring functions. Interestingly, the use of the uncharged states of ionizable sidechains is shown to aid prediction, particularly for the simplest energy functions.     

SVR_CAF: An integrated score function for detecting native protein structures among decoys

An accurate score function for detecting the most native‐like models among a huge number of decoy sets is essential to the protein structure prediction. In this work, we developed a novel integrated score function (SVR_CAF) to discriminate native structures from decoys, as well as to rank near‐native structures and select best decoys when native structures are absent. SVR_CAF is a machine learning score, which incorporates the contact energy based score ( C E_score), amino acid network based score ( A AN_score), and the fast Fourier transform based score ( F FT_score). The score function was evaluated with four decoy sets for its discriminative ability and it shows higher overall performance than the state‐of‐the‐art score functions. Proteins 2014; 82:556–564. © 2013 Wiley Periodicals, Inc.     

Evaluating CASP4 predictions with physical energy functions

Physical energy scoring functions based on implicit solvation models are tested by evaluating predictions from the most recent CASP4 competition. The best performing scoring functions are identified along with the best protocol for preparing structures before energies are evaluated. Ranking of structures with the best scoring functions is compared across CASP4 targets to establish when physical scoring functions can be expected to reliably distinguish structures that are most similar to the native fold in a set of misfolded or unfolded protein conformations. The results are used to interpret previous studies where scoring functions were tested on the standard decoy sets by Park, Levitt, and Baker. We show that the best physical scoring functions can be applied successfully in automated consensus scoring applications where a single best conformation has to be selected from a set of structures from different sources. Finally, the potential for better protein structure scoring functions is discussed with a suggestion for an empirically parameterized linear combination of energy components.     

Free-energy function for discriminating the native fold of a protein from misfolded decoys

In this study, free-energy function (FEF) for discriminating the native fold of a protein from misfolded decoys was investigated. It is a physics-based function using an all-atom model, which comprises the hydration entropy (HE) and the total dehydration penalty (TDP). The HE is calculated using a hybrid of a statistical-mechanical theory applied to a molecular model for water and the morphometric approach. The energetic component is suitably taken into account in a simple manner as the TDP. On the basis of the results from a careful test of the FEF, which have been performed for 118 proteins in representative decoy sets, we show that its performance is distinctly superior to that of any other function. The FEF varies largely from model to model for the candidate models for the native structure (NS) obtained from nuclear magnetic resonance experiments, but we can find models or a model for which the FEF becomes lower than for any of the decoy structures. A decoy set is not suited to the test of a free-energy or potential function in cases where a protein isolated from a protein complex is considered and the structure in the complex is used as the model NS of the isolated protein without any change or where portions of the terminus sides of a protein are removed and the percentage of the secondary structures lost due to the removal is significantly high. As these findings are made possible, we can assume that our FEF precisely captures the features of the true NS.     

Distance-dependent, pair potential for protein folding: results from linear optimization

The results of an optimization of a folding potential are reported. The complete energy function is modeled as a sum of pairwise interactions with a flexible functional form. The relevant distance between two amino acids (2 - 9 A) is divided into 13 intervals, and the energy of each interval is optimized independently. We show, in accord with a previous publication (Tobi et al., Proteins 2000;40:71-85) that it is impossible to find a pair potential with the above flexible form that recognizes all native folds. Nevertheless, a potential that rates correctly a subset of the decoy structures was constructed and optimized. The resulting potential is compared with a distance-dependent statistical potential of Bahar and Jernigan. It is further tested against decoy structures that were created in the Levitt's group. On average, the new potential places native shapes lower in energy and provides higher Z scores than other potentials.