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.     

Protein loop structure prediction with flexible stem geometries

The structure prediction of loops with flexible stem residues is addressed in this article. While the secondary structure of the stem residues is assumed to be known, the geometry of the protein into which the loop must fit is considered to be unknown in our methodology. As a consequence, the compatibility of the loop with the remainder of the protein is not used as a criterion to reject loop decoys. The loop structure prediction with flexible stems is more difficult than fitting loops into a known protein structure in that a larger conformational space has to be covered. The main focus of the study is to assess the precision of loop structure prediction if no information on the protein geometry is available. The proposed approach is based on (1) dihedral angle sampling, (2) structure optimization by energy minimization with a physically based energy function, (3) clustering, and (4) a comparison of strategies for the selection of loops identified in (3). Steps (1) and (2) have similarities to previous approaches to loop structure prediction with fixed stems. Step (3) is based on a new iterative approach to clustering that is tailored for the loop structure prediction problem with flexible stems. In this new approach, clustering is not only used to identify conformers that are likely to be close to the native structure, but clustering is also employed to identify far-from-native decoys. By discarding these decoys iteratively, the overall quality of the ensemble and the loop structure prediction is improved. Step (4) provides a comparative study of criteria for loop selection based on energy, colony energy, cluster density, and a hybrid criterion introduced here. The proposed method is tested on a large set of 3215 loops from proteins in the Pdb-Select25 set and to 179 loops from proteins from the Casp6 experiment.     

Capturing native/native like structures with a physico-chemical metric (pcSM) in protein folding

Specification of the three dimensional structure of a protein from its amino acid sequence, also called a “Grand Challenge” problem, has eluded a solution for over six decades. A modestly successful strategy has evolved over the last couple of decades based on development of scoring functions (e.g. mimicking free energy) that can capture native or native-like structures from an ensemble of decoys generated as plausible candidates for the native structure. A scoring function must be fast enough in discriminating the native from unfolded/misfolded structures, and requires validation on a large data set(s) to generate sufficient confidence in the score. Here we develop a scoring function called pcSM that detects true native structure in the top 5 with 93% accuracy from an ensemble of candidate structures. If we eliminate the native from ensemble of decoys then pcSM is able to capture near native structure (RMSD < = 5 ?) in top 10 with 86% accuracy. The parameters considered in pcSM are a C-alpha Euclidean metric, secondary structural propensity, surface areas and an intramolecular energy function. pcSM has been tested on 415 systems consisting 142,698 decoys (public and CASP—largest reported hitherto in literature). The average rank for the native is 2.38, a significant improvement over that existing in literature. In-silico protein structure prediction requires robust scoring technique(s). Therefore, pcSM is easily amenable to integration into a successful protein structure prediction strategy. The tool is freely available at http://www.scfbio-iitd.res.in/software/pcsm.jsp.     

Simultaneous single-structure and bundle representation of protein NMR structures in torsion angle space

A method is introduced to represent an ensemble of conformers of a protein by a single structure in torsion angle space that lies closest to the averaged Cartesian coordinates while maintaining perfect covalent geometry and on average equal steric quality and an equally good fit to the experimental (e.g. NMR) data as the individual conformers of the ensemble. The single representative ‘regmean structure’ is obtained by simulated annealing in torsion angle space with the program CYANA using as input data the experimental restraints, restraints for the atom positions relative to the average Cartesian coordinates, and restraints for the torsion angles relative to the corresponding principal cluster average values of the ensemble. The method was applied to 11 proteins for which NMR structure ensembles are available, and compared to alternative, commonly used simple approaches for selecting a single representative structure, e.g. the structure from the ensemble that best fulfills the experimental and steric restraints, or the structure from the ensemble that has the lowest RMSD value to the average Cartesian coordinates. In all cases our method found a structure in torsion angle space that is significantly closer to the mean coordinates than the alternatives while maintaining the same quality as individual conformers. The method is thus suitable to generate representative single structure representations of protein structure ensembles in torsion angle space. Since in the case of NMR structure calculations with CYANA the single structure is calculated in the same way as the individual conformers except that weak positional and torsion angle restraints are added, we propose to represent new NMR structures by a ‘regmean bundle’ consisting of the single representative structure as the first conformer and all but one original individual conformers (the original conformer with the highest target function value is discarded in order to keep the number of conformers in the bundle constant). In this way, analyses that require a single structure can be carried out in the most meaningful way using the first model, while at the same time the additional information contained in the ensemble remains available.     

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.     

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein ‘structure prediction’ problem.     

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein 'structure prediction' problem.     

A simple procedure to weight empirical potentials in a fitness function so as to optimize its performance in ab initio protein-folding problem

In an approach to the protein folding problem by a Genetic Algorithm, the fitness function plays a critical role. Empirical potentials are generally used to build the fitness function, and they must be weighted to obtain a valuable one. The weights are generally found by the comparison with a set of misfolded structures (decoys), but a dependence of the obtained fitness generally arises on the used decoys. Here we describe a general procedure to find out, from a given set of potentials, their better linear combination that could either identify the wild structure or prove their powerlessness. We use topological considerations over the hyperspace of the potentials, and a multiple linear inequalities solver. The iterated method flows through the following steps: it determines a direction in the hyperspace of the potentials, which identifies the native structure as a vertex among a set of misfolded decoys. A multiple linear inequalities solver obtains the direction. A Genetic Algorithm, tailored to the specific problem, uses the fitness function defined by this direction and generally reaches a new structure better than the experimental one, which is added to the ensemble. The decoys so generated are not dependent on a deterministic criterion. This iterative procedure can be stopped either by identifying an effective fitness function or by proving the impossibility of its achievement. In order to test the method under the hardest conditions, we choose numerous and heterogeneous quantities as components of the fitness function. This method could be a useful tool for the scientific community in order to test any fitness proposed and to recognize the most important components on which it is built.     

Prospects for ab initio protein structural genomics

We present the results of a large-scale testing of the ROSETTA method for ab initio protein structure prediction. Models were generated for two independently generated lists of small proteins (up to 150 amino acid residues), and the results were evaluated using traditional rmsd based measures and a novel measure based on the structure-based comparison of the models to the structures in the PDB using DALI. For 111 of 136 all alpha and alpha/beta proteins 50 to 150 residues in length, the method produced at least one model within 7 A rmsd of the native structure in 1000 attempts. For 60 of these proteins, the closest structure match in the PDB to at least one of the ten most frequently generated conformations was found to be structurally related (four standard deviations above background) to the native protein. These results suggest that ab initio structure prediction approaches may soon be useful for generating low resolution models and identifying distantly related proteins with similar structures and perhaps functions for these classes of proteins on the genome scale.     

A pair-to-pair amino acids substitution matrix and its applications for protein structure prediction

We present a new structurally derived pair-to-pair substitution matrix (P2PMAT). This matrix is constructed from a very large amount of integrated high quality multiple sequence alignments (Blocks) and protein structures. It evaluates the likelihoods of all 160,000 pair-to-pair substitutions. P2PMAT matrix implicitly accounts for evolutionary conservation, correlated mutations, and residue-residue contact potentials. The usefulness of the matrix for structural predictions is shown in this article. Predicting protein residue-residue contacts from sequence information alone, by our method (P2PConPred) is particularly accurate in the protein cores, where it performs better than other basic contact prediction methods (increasing accuracy by 25-60%). The method mean accuracy for protein cores is 24% for 59 diverse families and 34% for a subset of proteins shorter than 100 residues. This is above the level that was recently shown to be sufficient to significantly improve ab initio protein structure prediction. We also demonstrate the ability of our approach to identify native structures within large sets of (300-2000) protein decoys. On the basis of evolutionary information alone our method ranks the native structure in the top 0.3% of the decoys in 4/10 of the sets, and in 8/10 of sets the native structure is ranked in the top 10% of the decoys. The method can, thus, be used to assist filtering wrong models, complementing traditional scoring functions.     

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.     

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.     

SimFold energy function for de novo protein structure prediction: consensus with Rosetta

Predicting protein tertiary structures by in silico folding is still very difficult for proteins that have new folds. Here, we developed a coarse-grained energy function, SimFold, for de novo structure prediction, performed a benchmark test of prediction with fragment assembly simulations for 38 test proteins, and proposed consensus prediction with Rosetta. The SimFold energy consists of many terms that take into account solvent-induced effects on the basis of physicochemical consideration. In the benchmark test, SimFold succeeded in predicting native structures within 6.5 A for 12 of 38 proteins; this success rate was the same as that by the publicly available version of Rosetta (ab initio version 1.2) run with default parameters. We investigated which energy terms in SimFold contribute to structure prediction performance, finding that the hydrophobic interaction is the most crucial for the prediction, whereas other sequence-specific terms have weak but positive roles. In the benchmark, well-predicted proteins by SimFold and by Rosetta were not the same for 5 of 12 proteins, which led us to introduce consensus prediction. With combined decoys, we succeeded in prediction for 16 proteins, four more than SimFold or Rosetta separately. For each of 38 proteins, structural ensembles generated by SimFold and by Rosetta were qualitatively compared by mapping sampled structural space onto two dimensions. For proteins of which one of the two methods succeeded and the other failed in prediction, the former had a less scattered ensemble located around the native. For proteins of which both methods succeeded in prediction, often two ensembles were mixed up.     

Coarse-Grained Prediction of RNA Loop Structures

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.     

A correlation-based method for the enhancement of scoring functions on funnel-shaped energy landscapes

A correlation-based approach is introduced for enhancing the ability of structure-scoring methods to identify and distinguish native-like conformations. The proposed method relies on a funnel-shaped scoring function that decreases steadily toward the native state. It takes advantage of the idea that the structure from a given ensemble that is closest to the native basin leads to the highest correlation coefficient between a given score and distance to that structure as an approximation of the native state for the entire ensemble. The method is applied successfully to a number of different test cases that demonstrate substantial improvements in the correlation of the score with the distance from the true native state but also result in the selection of more native-like structures compared to the original score.     

X‐ray vs. NMR structures as templates for computational protein design

Certain protein‐design calculations involve using an experimentally determined high‐resolution structure as a template to identify new sequences that can adopt the same fold. This approach has led to the successful design of many novel, well‐folded, native‐like proteins. Although any atomic‐resolution structure can serve as a template in such calculations, most successful designs have used high‐resolution crystal structures. Because there are many proteins for which crystal structures are not available, it is of interest whether nuclear magnetic resonance (NMR) templates are also appropriate. We have analyzed differences between using X‐ray and NMR templates in side‐chain repacking and design calculations. We assembled a database of 29 proteins for which both a high‐resolution X‐ray structure and an ensemble of NMR structures are available. Using these pairs, we compared the rotamericity, χ₁‐angle recovery, and native‐sequence recovery of X‐ray and NMR templates. We carried out design using RosettaDesign on both types of templates, and compared the energies and packing qualities of the resulting structures. Overall, the X‐ray structures were better templates for use with Rosetta. However, for ～20% of proteins, a member of the reported NMR ensemble gave rise to designs with similar properties. Re‐evaluating RosettaDesign structures with other energy functions indicated much smaller differences between the two types of templates. Ultimately, experiments are required to confirm the utility of particular X‐ray and NMR templates. But our data suggest that the lack of a high‐resolution X‐ray structure should not preclude attempts at computational design if an NMR ensemble is available. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

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.