Decoy Structures Research Articles

A knowledge-based orientation potential for transcription factor-DNA docking

Computational modeling of protein-DNA complexes remains a challenging problem in structural bioinformatics. One of the key factors for a successful protein-DNA docking is a potential function that can accurately discriminate the near-native structures from decoy complexes and at the same time make conformational sampling more efficient. Here, we developed a novel orientation-dependent, knowledge-based, residue-level potential for improving transcription factor (TF)-DNA docking. We demonstrated the performance of this new potential in TF-DNA binding affinity prediction, discrimination of native protein-DNA complex from decoy structures, and most importantly in rigid TF-DNA docking. The rigid TF-DNA docking with the new orientation potential, on a benchmark of 38 complexes, successfully predicts 42% of the cases with root mean square deviations lower than 1 Å and 55% of the cases with root mean square deviations lower than 3 Å. The results suggest that docking with this new orientation-dependent, coarse-grained statistical potential can achieve high-docking accuracy and can serve as a crucial first step in multi-stage flexible protein-DNA docking. The new potential is available at http://bioinfozen.uncc.edu/Protein_DNA_orientation_potential.tar.

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

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

Statistical analyses and computational prediction of helical kinks in membrane proteins

We have carried out statistical analyses and computer simulations of helical kinks for TM helices in the PDBTM database. About 59% of 1562 TM helices showed a significant kink, and 38% of these kinks are associated with prolines in a range of ±4 residues. Our analyses show that helical kinks are more populated in the central region of helices, particularly in the range of 1-3 residues away from the helix center. Among 1,053 helical kinks analyzed, 88% of kinks are bends (change in helix axis without loss of helical character) and 12% are disruptions (change in helix axis and loss of helical character). It is found that proline residues tend to cause larger kink angles in helical bends, while this effect is not observed in helical disruptions. A further analysis of these kinked helices suggests that a kinked helix usually has 1-2 broken backbone hydrogen bonds with the corresponding N-O distance in the range of 4.2-8.7Å, whose distribution is sharply peaked at 4.9Å followed by an exponential decay with increasing distance. Our main aims of this study are to understand the formation of helical kinks and to predict their structural features. Therefore we further performed molecular dynamics (MD) simulations under four simulation scenarios to investigate kink formation in 37 kinked TM helices and 5 unkinked TM helices. The representative models of these kinked helices are predicted by a clustering algorithm, SPICKER, from numerous decoy structures possessing the above generic features of kinked helices. Our results show an accuracy of 95% in predicting the kink position of kinked TM helices and an error less than 10° in the angle prediction of 71.4% kinked helices. For unkinked helices, based on various structure similarity tests, our predicted models are highly consistent with their crystal structure. These results provide strong supports for the validity of our method in predicting the structure of TM helices.

A Protein Solvation Model Based on Residue Burial.

The influence of solvent on the individual amino acids of a protein depends not simply on their surface exposure but rather on the degree of their burial within the structure. This property can be related to a simple geometrical measure termed circular variance. Circular variance depends on the spatial distribution of neighboring residues and varies from zero to one as a residue becomes buried. Its only adjustable parameter is a cutoff distance for selecting neighbors. Here, we show that circular variance can be used to build a fast and effective model of protein solvation energies. For this, we combine a coarse-grain protein representation with statistical potentials derived by Boltzmann inversion of circular variance probability distributions for different classes of pseudoatom within a large protein structure database. The method is shown to work well for distinguishing native protein structures from decoy structures generated in a variety of ways. It can also be used to detect specific residues in unfavorable solvent environments. Compared to surface accessibility, circular variance calculations are faster, less sensitive to small conformational changes, and able to account for the longer-range interactions that characterize the electrostatic component of solvent effects. The resulting solvation energies can be used alone or as part of a more general coarse-grain protein model.

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.

Distance‐dependent atomic knowledge‐based force in protein fold recognition

We have recently introduced a novel model for discriminating the correctly folded proteins from well-designed decoy structures using mechanical interatomic forces. In the model, we considered a protein as a collection of springs and the force imposed to each atom was calculated by using the relation between the potential energy and the force. A mean force potential function is obtained from statistical contact preferences within the known protein structures. In this article, the interatomic forces are calculated by numerical derivation of the potential function. For assessing the knowledge-based force function we consider an optimal structure and define a score function on the 3D structure of a protein. We compare the force imposed to each atom of a protein with the corresponding atom in the optimum structure. Afterwards we assign larger scores to those atoms with the lower forces. The total score is the sum of partial scores of atoms. The optimal structure is assumed to be the one with the highest score in the dataset. Finally, several decoy sets are applied in order to evaluate the performance of our model.

Quality Assessment of Protein Models

Quality assessment (QA) is to judge the quality of a protein model without knowing its native structure. It plays an important role in the process of protein structure prediction by guiding us to select an appropriate combination of templates out of many possibilities [1]. We formulate the QA problem as mapping and regression. Protein models are mapped into R n space by extracting n features from each model, and the space is divided into subspaces according to the feature values in order to represent models’ closeness (between 0 and 1) to the native structure. For the feature values, we measure the degree of agreement between the predicted property from the sequence analysis and the calculated one from the 3D model. Properties that we use include the secondary structure, solvent accessibility, hydrophobicity, and energy components from MODELLER [2], DFIRE [3], and TASSER [4]. One advantage of using the consensustype feature is that models with similar quality are prone to be clustered together in R n space, and thus they tend to be well classified. Assigning closeness values to regions of R n space is carried out using decoy structures generated during the CASP7 with known native structures [1] by applying Support Vector Machine regression techniques (SVM). SVM that we used has the character of non-linearity which can be applied to the linearly non-separable cases. In other words, for given features, SVM is more efficient than the linear method such as linear programming. The proposed method was used to select final models during the CASP8 prediction. We will discuss both the usefulness and the limitation of the method for better protein modeling.

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.

Automated RNA tertiary structure prediction from secondary structure and low-resolution restraints.

A novel protocol for all-atom RNA tertiary structure prediction is presented that uses restrained molecular mechanics and simulated annealing. The restraints are from secondary structure, covariation analysis, coaxial stacking predictions for helices in junctions, and, when available, cross-linking data. Results are demonstrated on the Alu domain of the mammalian signal recognition particle RNA, the Saccharomyces cerevisiae phenylalanine tRNA, the hammerhead ribozyme, the hepatitis C virus internal ribosomal entry site, and the P4-P6 domain of the Tetrahymena thermophila group I intron. The predicted structure is selected from a pool of decoy structures with a score that maximizes radius of gyration and base-base contacts, which was empirically found to select higher quality decoys. This simple ab initio approach is sufficient to make good predictions of the structure of RNAs compared to current crystal structures using both root mean square deviation and the accuracy of base-base contacts.

Application of biasing-potential replica exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative protein modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Frequently, the quality of the target- template sequence alignment is non-uniform along the sequence: parts can be modeled with a high confidence, whereas other parts differ strongly from the template. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loops in homology modeled protein structures, but it is limited by the currently accessible simulation time scales. In the current work we have used a recently developed biasing potential replica exchange (BP-Rex) MD [1] method to refine and to model loops in homology modeled protein structure at atomic resolution including explicit solvent. In standard Rex MD [2] simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP-Rex MD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with standard temperature Rex MD. Starting from incorrect loop conformations this BP-Rex MD method samples the correct loop conformations as dominant conformations in all the cases. Application of BP-Rex MD to several protein loops indicates improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP-Rex MD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations [3].

Absolute quality evaluation of protein model structures using statistical potentials with respect to the native and reference states

In protein structure prediction, it is crucial to evaluate the degree of native-likeness of given model structures. Statistical potentials extracted from protein structure data sets are widely used for such quality assessment problems, but they are only applicable for comparing different models of the same protein. Although various other methods, such as machine learning approaches, were developed to predict the absolute similarity of model structures to the native ones, they required a set of decoy structures in addition to the model structures. In this paper, we tried to reformulate the statistical potentials as absolute quality scores, without using the information from decoy structures. For this purpose, we regarded the native state and the reference state, which are necessary components of statistical potentials, as the good and bad standard states, respectively, and first showed that the statistical potentials can be regarded as the state functions, which relate a model structure to the native and reference states. Then, we proposed a standardized measure of protein structure, called native-likeness, by interpolating the score of a model structure between the native and reference state scores defined for each protein. The native-likeness correlated with the similarity to the native structures and discriminated the native structures from the models, with better accuracy than the raw score. Our results show that statistical potentials can quantify the native-like properties of protein structures, if they fully utilize the statistical information obtained from the data set.

Novel Nonlinear Knowledge-Based Mean Force Potentials Based on Machine Learning

The prediction of 3D structures of proteins from amino acid sequences is one of the most challenging problems in molecular biology. An essential task for solving this problem with coarse-grained models is to deduce effective interaction potentials. The development and evaluation of new energy functions is critical to accurately modeling the properties of biological macromolecules. Knowledge-based mean force potentials are derived from statistical analysis of proteins of known structures. Current knowledge-based potentials are almost in the form of weighted linear sum of interaction pairs. In this study, a class of novel nonlinear knowledge-based mean force potentials is presented. The potential parameters are obtained by nonlinear classifiers, instead of relative frequencies of interaction pairs against a reference state or linear classifiers. The support vector machine is used to derive the potential parameters on data sets that contain both native structures and decoy structures. Five knowledge-based mean force Boltzmann-based or linear potentials are introduced and their corresponding nonlinear potentials are implemented. They are the DIH potential (single-body residue-level Boltzmann-based potential), the DFIRE-SCM potential (two-body residue-level Boltzmann-based potential), the FS potential (two-body atom-level Boltzmann-based potential), the HR potential (two-body residue-level linear potential), and the T32S3 potential (two-body atom-level linear potential). Experiments are performed on well-established decoy sets, including the LKF data set, the CASP7 data set, and the Decoys “R”Us data set. The evaluation metrics include the energy Z score and the ability of each potential to discriminate native structures from a set of decoy structures. Experimental results show that all nonlinear potentials significantly outperform the corresponding Boltzmann-based or linear potentials, and the proposed discriminative framework is effective in developing knowledge-based mean force potentials. The nonlinear potentials can be widely used for ab initio protein structure prediction, model quality assessment, protein docking, and other challenging problems in computational biology.

Extending the PRIME model for protein aggregation to all 20 amino acids

We extend PRIME, an intermediate-resolution protein model previously used in simulations of the aggregation of polyalanine and polyglutamine, to the description of the geometry and energetics of peptides containing all 20 amino acid residues. The 20 amino acid side chains are classified into 14 groups according to their hydrophobicity, polarity, size, charge, and potential for side chain hydrogen bonding. The parameters for extended PRIME, called PRIME 20, include hydrogen-bonding energies, side chain interaction range and energy, and excluded volume. The parameters are obtained by applying a perceptron-learning algorithm and a modified stochastic learning algorithm that optimizes the energy gap between 711 known native states from the PDB and decoy structures generated by gapless threading. The number of independent pair interaction parameters is chosen to be small enough to be physically meaningful yet large enough to give reasonably accurate results in discriminating decoys from native structures. The most physically meaningful results are obtained with 19 energy parameters.

Application of biasing‐potential replica‐exchange simulations for loop modeling and refinement of proteins in explicit solvent

Comparative or homology modeling of a target protein based on sequence similarity to a protein with known structure is widely used to provide structural models of proteins. Depending on the target-template similarity these model structures may contain regions of limited structural accuracy. In principle, molecular dynamics (MD) simulations can be used to refine protein model structures and also to model loop regions that connect structurally conserved regions but it is limited by the currently accessible simulation time scales. A recently developed biasing potential replica exchange (BP-REMD) method was used to refine loops and complete decoy protein structures at atomic resolution including explicit solvent. In standard REMD simulations several replicas of a system are run in parallel at different temperatures allowing exchanges at preset time intervals. In a BP-REMD simulation replicas are controlled by various levels of a biasing potential to reduce the energy barriers associated with peptide backbone dihedral transitions. The method requires much fewer replicas for efficient sampling compared with T-REMD. Application of the approach to several protein loops indicated improved conformational sampling of backbone dihedral angle of loop residues compared to conventional MD simulations. BP-REMD refinement simulations on several test cases starting from decoy structures deviating significantly from the native structure resulted in final structures in much closer agreement with experiment compared to conventional MD simulations.

ATRIPPI: AN ATOM-RESIDUE PREFERENCE SCORING FUNCTION FOR PROTEIN–PROTEIN INTERACTIONS

We present an ATRIPPI model for analyzing protein–protein interactions. This model is a 167-atom-type and residue-specific interaction preferences with distance bins derived from 641 co-crystallized protein–protein interfaces. The ATRIPPI model is able to yield physical meanings of hydrogen bonding, disulfide bonding, electrostatic interactions, van der Waals and aromatic–aromatic interactions. We applied this model to identify the native states and near-native complex structures on 17 bound and 17 unbound complexes from thousands of decoy structures. On average, 77.5% structures (155 structures) of top rank 200 structures are closed to the native structure. These results suggest that the ATRIPPI model is able to keep the advantages of both atom–atom and residue–residue interactions and is a potential knowledge-based scoring function for protein–protein docking methods. We believe that our model is robust and provides biological meanings to support protein–protein interactions.

Evaluation of the information content of RNA structure mapping data for secondary structure prediction.

Structure mapping experiments (using probes such as dimethyl sulfate [DMS], kethoxal, and T1 and V1 RNases) are used to determine the secondary structures of RNA molecules. The process is iterative, combining the results of several probes with constrained minimum free-energy calculations to produce a model of the structure. We aim to evaluate whether particular probes provide more structural information, and specifically, how noise in the data affects the predictions. Our approach involves generating "decoy" RNA structures (using the sFold Boltzmann sampling procedure) and evaluating whether we are able to identify the correct structure from this ensemble of structures. We show that with perfect information, we are always able to identify the optimal structure for five RNAs of known structure. We then collected orthogonal structure mapping data (DMS and RNase T1 digest) under several solution conditions using our high-throughput capillary automated footprinting analysis (CAFA) technique on two group I introns of known structure. Analysis of these data reveals the error rates in the data under optimal (low salt) and suboptimal solution conditions (high MgCl(2)). We show that despite these errors, our computational approach is less sensitive to experimental noise than traditional constraint-based structure prediction algorithms. Finally, we propose a novel approach for visualizing the interaction of chemical and enzymatic mapping data with RNA structure. We project the data onto the first two dimensions of a multidimensional scaling of the sFold-generated decoy structures. We are able to directly visualize the structural information content of structure mapping data and reconcile multiple data sets.

Electronic Polarization Is Important in Stabilizing the Native Structures of Proteins

Quantum mechanical computations of proteins based on the molecular fragment approach have been carried out, and polarized protein-specific charges have been derived to provide accurate electrostatic interactions for a benchmark set of proteins. Our study shows that, under the polarized protein-specific force field, the native structure indeed corresponds to the lowest-energy conformation for these proteins. In contrast, when a standard mean-field force field such as AMBER is used, the energies of many decoy structures of proteins could be lower than those of the native structures. Furthermore, MD simulations were carried out and verified that the native structures of these proteins not only are statically more stable but are also dynamically more stable under the polarized protein-specific force field. The present results, together with several recent studies, provide strong evidence that protein polarization is critical to stabilizing the native structures of proteins.

A distance‐dependent atomic knowledge‐based potential and force for discrimination of native structures from decoys

The purpose of this article is to introduce a novel model for discriminating correctly folded proteins from well designed decoy structures using mechanical interatomic forces. In our model, we consider a protein as a collection of springs and the force imposed to each atom is calculated. A potential function is obtained from statistical contact preferences within known protein structures. Combining this function with the spring equation, the interatomic forces are calculated. Finally, we consider a structure and define a score function on the 3D structure of a protein. We compare the force imposed to each atom of a protein with the corresponding atom in the other structures. We then assign larger scores to those atoms with lower forces. The total score is the sum of partial scores of atoms. The optimal structure is assumed to be the one with the highest score in the data set. To evaluate the performance of our model, we apply it on several decoy sets.

Importance of dispersion and electron correlation in ab initio protein folding.

Dispersion is well-known to be important in biological systems, but the effect of electron correlation in such systems remains unclear. In order to assess the relationship between the structure of a protein and its electron correlation energy, we employed both full system Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) calculations in conjunction with the Polarizable Continuum Model (PCM) on the native structures of two proteins and their corresponding computer-generated decoy sets. Because of the expense of the MP2 calculation, we have utilized the fragment molecular orbital method (FMO) in this study. We show that the sum of the Hartree-Fock (HF) energy and force field (LJ6)-derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order Møller-Plesset perturbation (MP2) theory. In one of the two examples studied, the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discrimination capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly. Furthermore, when we randomly scrambled the Lennard-Jones parameters, the correlation between the MP2 energy and the sum of the HF energy and dispersive energy (HF+LJ6) significantly drops, which indicates that the choice of Lennard-Jones parameters is important.

A coarse‐grained potential for fold recognition and molecular dynamics simulations of proteins

A coarse-grained potential for protein simulations and fold ranking is presented. The potential is based on a two-point model of individual amino acids and a specific implementation of hydrogen bonding. Parameters are determined for distance dependent pair interactions, pseudo bonds, angles, and torsions. A scaling factor for a hydrogen bonding term is also determined. Iterative sampling for 4867 proteins reproduces distributions of internal coordinates and distances observed in the Protein Data Bank. The adjustment of the potential and resampling are in the spirit of the generalized ensemble approach. No native structure information (e.g., secondary structure) is used in the calculation of the potential or in the simulation of a particular protein. The potential is subject to two tests as follows: (i) simulations of 956 globular proteins in the neighborhood of their native folds (these proteins were not used in the training set) and (ii) discrimination between native and decoy structures for 2470 proteins with 305,000 decoys and the "Decoys 'R' Us" dataset. In the first test, 58% of tested proteins stay within 5 A from the native fold in Molecular Dynamics simulations of more than 20 nanoseconds using the new potential. The potential is also useful in differentiating between correct and approximate folds providing significant signal for structure prediction algorithms. Sampling with the potential consistently regenerates the distribution of distances and internal coordinates it learned. Nevertheless, during Molecular Dynamics simulations structures are found that reproduce the learned distributions but are far from the native fold.