Distance dependent centroid to centroid force fields using high resolution decoys

Simplified force fields play an important role in protein structure prediction and de novo protein design by requiring less computational effort than detailed atomistic potentials. A side chain centroid based, distance dependent pairwise interaction potential has been developed. A linear programming based formulation was used in which non-native "decoy" conformers are forced to take a higher energy compared with the corresponding native structure. This model was trained on an enhanced and diverse protein set. High quality decoy structures were generated for approximately 1400 nonhomologous proteins using torsion angle dynamics along with restricted variations of the hydrophobic cores of the native structure. The resulting decoy set was used to train the model yielding two different side chain centroid based force fields that differ in the way distance dependence has been used to calculate energy parameters. These force fields were tested on an independent set of 148 test proteins with 500 decoy structures for each protein. The side chain centroid force fields were successful in correctly identifying approximately 86% native structures. The Z-scores produced by the proposed centroid-centroid distance dependent force fields improved compared with other distance dependent C(alpha)-C(alpha) or side chain based force fields.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

Protein Structure Evaluation using an All-Atom Energy Based Empirical Scoring Function

Abstract

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     

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.     

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.     

The victor/FRST function for model quality estimation.

Scoring functions are widely used in the final step of model selection in protein structure prediction. This is of interest both for comparative modeling targets, where it is important to select the best model among a set of many good, "correct" ones, as well as for other (fold recognition or novel fold) targets, where the set may contain many incorrect models. A novel combination of four knowledge-based potentials recognizing different features of native protein structures is introduced and tested. The pairwise, solvation, hydrogen bond, and torsion angle potentials contain largely orthogonal information. Of these, the torsion angle potential is found to show the strongest correlation with model quality. Combining these features with a linear weighting function, it was possible to construct a robust energy function capable of discriminating native-like structures on several benchmarking sets. In a recent blind test (CAFASP-4 MQAP), the scoring function ranked consistently well and was able to reliably distinguish the correct template from an ensemble of high quality decoys in 52 of 70 cases (33 of 34 for comparative modeling). An executable version of the Victor/FRST function for Linux PCs is available for download from the URL http://protein.cribi.unipd.it/frst/.     

Steiner minimal trees, twist angles, and the protein folding problem

The Steiner Minimal Tree (SMT) problem determines the minimal length network for connecting a given set of vertices in three-dimensional space. SMTs have been shown to be useful in the geometric modeling and characterization of proteins. Even though the SMT problem is an NP-Hard Optimization problem, one can define planes within the amino acids that have a surprising regularity property for the twist angles of the planes. This angular property is quantified for all amino acids through the Steiner tree topology structure. The twist angle properties and other associated geometric properties unique for the remaining amino acids are documented in this paper. We also examine the relationship between the Steiner ratio rho and the torsion energy in amino acids with respect to the side chain torsion angle chi(1). The rho value is shown to be inversely proportional to the torsion energy. Hence, it should be a useful approximation to the potential energy function. Finally, the Steiner ratio is used to evaluate folded and misfolded protein structures. We examine all the native proteins and their decoys at http://dd.stanford.edu. and compare their Steiner ratio values. Because these decoy structures have been delicately misfolded, they look even more favorable than the native proteins from the potential energy viewpoint. However, the rho value of a decoy folded protein is shown to be much closer to the average value of an empirical Steiner ratio for each residue involved than that of the corresponding native one, so that we recognize the native folded structure more easily. The inverse relationship between the Steiner ratio and the energy level in the protein is shown to be a significant measure to distinguish native and decoy structures. These properties should be ultimately useful in the ab initio protein folding prediction.     

ProVal: a protein-scoring function for the selection of native and near-native folds

A low-resolution scoring function for the selection of native and near-native structures from a set of predicted structures for a given protein sequence has been developed. The scoring function, ProVal (Protein Validate), used several variables that describe an aspect of protein structure for which the proximity to the native structure can be assessed quantitatively. Among the parameters included are a packing estimate, surface areas, and the contact order. A partial least squares for latent variables (PLS) model was built for each candidate set of the 28 decoy sets of structures generated for 22 different proteins using the described parameters as independent variables. The C(alpha) RMS of the candidate structures versus the experimental structure was used as the dependent variable. The final generalized scoring function was an average of all models derived, ensuring that the function was not optimized for specific fold classes or method of structure generation of the candidate folds. The results show that the crystal structure was scored best in 64% of the 28 test sets and was clearly separated from the decoys in many examples. In all the other cases in which the crystal structure did not rank first, it ranked within the top 10%. Thus, although ProVal could not distinguish between predicted structures that were similar overall in fold quality due to its inherently low resolution, it can clearly be used as a primary filter to eliminate approximately 90% of fold candidates generated by current prediction methods from all-atom modeling and further evaluation. The correlation between the predicted and actual C(alpha) RMS values varies considerably between the candidate fold sets.     

Native fold and docking pose discrimination by the same residue‐based scoring function

Structure prediction and quality assessment are crucial steps in modeling native protein conformations. Statistical potentials are widely used in related algorithms, with different parametrizations typically developed for different contexts such as folding protein monomers or docking protein complexes. Here, we describe BACH‐SixthSense, a single residue‐based statistical potential that can be successfully employed in both contexts. BACH‐SixthSense shares the same approach as BACH, a knowledge‐based potential originally developed to score monomeric protein structures. A term that penalizes steric clashes as well as the distinction between polar and apolar sidechain‐sidechain contacts are crucial novel features of BACH‐SixthSense. The performance of BACH‐SixthSense in discriminating correctly the native structure among a competing set of decoys is significantly higher than other state‐of‐the‐art scoring functions, that were specifically trained for a single context, for both monomeric proteins (QMEAN, Rosetta, RF_CB_SRS_OD, benchmarked on CASP targets) and protein dimers (IRAD, Rosetta, PIE*PISA, HADDOCK, FireDock, benchmarked on 14 CAPRI targets). The performance of BACH‐SixthSense in recognizing near‐native docking poses within CAPRI decoy sets is good as well. Proteins 2015; 83:621–630. © 2015 Wiley Periodicals, Inc.     

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.     

Sampling and scoring: A marriage made in heaven

Most structure prediction algorithms consist of initial sampling of the conformational space, followed by rescoring and possibly refinement of a number of selected structures. Here we focus on protein docking, and show that while decoupling sampling and scoring facilitates method development, integration of the two steps can lead to substantial improvements in docking results. Since decoupling is usually achieved by generating a decoy set containing both non‐native and near‐native docked structures, which can be then used for scoring function construction, we first review the roles and potential pitfalls of decoys in protein–protein docking, and show that some type of decoys are better than others for method development. We then describe three case studies showing that complete decoupling of scoring from sampling is not the best choice for solving realistic docking problems. Although some of the examples are based on our own experience, the results of the CAPRI docking and scoring experiments also show that performing both sampling and scoring generally yields better results than scoring the structures generated by all predictors. Next we investigate how the selection of training and decoy sets affects the performance of the scoring functions obtained. Finally, we discuss pathways to better alignment of the two steps, and show some algorithms that achieve a certain level of integration. Although we focus on protein–protein docking, our observations most likely also apply to other conformational search problems, including protein structure prediction and the docking of small molecules to proteins.Proteins 2013; 81:1874–1884. © 2013 Wiley Periodicals, Inc.     

A reduced protein model with accurate native-structure identification ability

A protein model that is simple enough to be used in protein-folding simulations but accurate enough to identify a protein native fold is described. Its geometry consists of describing the residues by one, two, or three pseudoatoms, depending on the residue size. Its energy is given by a pairwise, knowledge-based potential obtained for all the pseudoatoms as a function of their relative distance. The pseudoatomic potential is also a function of the primary chain separation and residue order. The model is tested by gapless threading on a large, representative set of known protein and decoy structures obtained from the "Decoys 'R' Us" database. It is also tested by threading on gapped decoys generated for proteins with many homologs. The gapless threading tests show near 98% native-structure recognition as the lowest energy structure and almost 100% as one of the three lowest energy structures for over 2200 test proteins. In decoy threading tests, the model recognized the majority of the native structures. It is also able to recognize native structures among gapped decoys, in spite of close structural similarities. The results indicate that the pseudoatomic model has native recognition ability similar to comparable atomic-based models but much better than equivalent residue-based models.     

Distinguish protein decoys by using a scoring function based on a new AMBER force field, short molecular dynamics simulations, and the generalized born solvent model

Recent works have shown the ability of physics-based potentials (e.g., CHARMM and OPLS-AA) and energy minimization to differentiate the native protein structures from large ensemble of non-native structures. In this study, we extended previous work by other authors and developed an energy scoring function using a new set of AMBER parameters (also recently developed in our laboratory) in conjunction with molecular dynamics and the Generalized Born solvent model. We evaluated the performance of our new scoring function by examining its ability to distinguish between the native and decoy protein structures. Here we present a systematic comparison of our results with those obtained with use of other physics-based potentials by previous authors. A total of 7 decoy sets, 117 protein sequences, and more than 41,000 structures were evaluated. The results of our study showed that our new scoring function represents a significant improvement over previously published physics-based scoring functions.     

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.     

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.     

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.     

Statistical potential for assessment and prediction of protein structures

Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distance-dependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.     

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.