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ABSTRACT Knowledge-based protein potentials are simplified potentials designed to improve the quality of protein models, which is important as more accurate models are more useful for biological and pharmaceutical studies. Consequently, knowledge-based potentials often are designed to be efficient in ordering a given set of deformed structures denoted decoys according to how close they are to the relevant native protein structure. This, however, does not necessarily imply that energy minimization of this potential will bring the decoys closer to the native structure. In this study, we introduce an iterative strategy to improve the convergence of decoy structures. It works by adding energy optimized decoys to the pool of decoys used to construct the next and improved knowledge-based potential. We demonstrate that this strategy results in significantly improved decoy convergence on Titan high resolution decoys and refinement targets from Critical Assessment of protein Structure Prediction competitions. Our potential is formulated in Cartesian coordinates and has a fixed backbone potential to restricts motions to be close to those of a dihedral model, a fixed hydrogen-bonding potential and a variable coarse grained carbon alpha potential consisting of a pair potential and a novel solvent potential that are b-spline based as we use explicit gradient and Hessian for efficient energy optimization. Proteins 2015; 83:1616-1624. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Exponential growth in the number of available protein sequences is unmatched by the slower growth in the number of structures. As a result, the development of efficient and fast protein secondary structure prediction methods is essential for the broad comprehension of protein structures. Computational methods that can efficiently determine secondary structure can in turn facilitate protein tertiary structure prediction, since most methods rely initially on secondary structure predictions. Recently, we have developed a fast learning optimized prediction methodology (FLOPRED) for predicting protein secondary structure (Saraswathi et al. in JMM 18:4275, ). Data are generated by using knowledge-based potentials combined with structure information from the CATH database. A neural network-based extreme learning machine (ELM) and advanced particle swarm optimization (PSO) are used with this data to obtain better and faster convergence to more accurate secondary structure predicted results. A five-fold cross-validated testing accuracy of 83.8 % and a segment overlap (SOV) score of 78.3 % are obtained in this study. Secondary structure predictions and their accuracy are usually presented for three secondary structure elements: α-helix, β-strand and coil but rarely have the results been analyzed with respect to their constituent amino acids. In this paper, we use the results obtained with FLOPRED to provide detailed behaviors for different amino acid types in the secondary structure prediction. We investigate the influence of the composition, physico-chemical properties and position specific occurrence preferences of amino acids within secondary structure elements. In addition, we identify the correlation between these properties and prediction accuracy. The present detailed results suggest several important ways that secondary structure predictions can be improved in the future that might lead to improved protein design and engineering. [ABSTRACT FROM AUTHOR]

Protein structure prediction methods typically use statistical potentials, which rely on statistics derived from a database of know protein structures. In the vast majority of cases, these potentials involve pairwise distances or contacts between amino acids or atoms. Although some potentials beyond pairwise interactions have been described, the formulation of a general multibody potential is seen as intractable due to the perceived limited amount of data. In this article, we show that it is possible to formulate a probabilistic model of higher order interactions in proteins, without arbitrarily limiting the number of contacts. The success of this approach is based on replacing a naive table-based approach with a simple hierarchical model involving suitable probability distributions and conditional independence assumptions. The model captures the joint probability distribution of an amino acid and its neighbors, local structure and solvent exposure. We show that this model can be used to approximate the conditional probability distribution of an amino acid sequence given a structure using a pseudo-likelihood approach. We verify the model by decoy recognition and site-specific amino acid predictions. Our coarse-grained model is compared to state-of-art methods that use full atomic detail. This article illustrates how the use of simple probabilistic models can lead to new opportunities in the treatment of nonlocal interactions in knowledge-based protein structure prediction and design. Proteins 2013; 81:1340-1350. © 2013 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Computational methods are rapidly gaining importance in the field of structural biology, mostly due to the explosive progress in genome sequencing projects and the large disparity between the number of sequences and the number of structures. There has been an exponential growth in the number of available protein sequences and a slower growth in the number of structures. There is therefore an urgent need to develop computational methods to predict structures and identify their functions from the sequence. Developing methods that will satisfy these needs both efficiently and accurately is of paramount importance for advances in many biomedical fields, including drug development and discovery of biomarkers. A novel method called fast learning optimized prediction methodology (FLOPRED) is proposed for predicting protein secondary structure, using knowledge-based potentials combined with structure information from the CATH database. A neural network-based extreme learning machine (ELM) and advanced particle swarm optimization (PSO) are used with this data that yield better and faster convergence to produce more accurate results. Protein secondary structures are predicted reliably, more efficiently and more accurately using FLOPRED. These techniques yield superior classification of secondary structure elements, with a training accuracy ranging between 83 % and 87 % over a widerange of hidden neurons and a cross-validated testing accuracy ranging between 81 % and 84 % and a segment overlap (SOV) score of 78 % that are obtained with different sets of proteins. These results are comparable to other recently published studies, but are obtained with greater efficiencies, in terms of time and cost. [ABSTRACT FROM AUTHOR]

Empirical potentials for interaction of proteins with intracellular ions are presented. We derive the potentials using a training dataset of the protein 3D structure bank, PDB, based on the statistical analysis of contacts between ions and protein atoms of different types. The potentials are derived using Monte Carlo Reference State, simulating non-interacting structure elements as random 3D points in the structure space. The resulting potentials are detailed, continuous, and cover a wide range of contact distances. The obtained potentials were tested for prediction of ion-binding sites in proteins and are shown to reproduce locations and specificities of ion-binding sites with a high accuracy. A web server is created for predictions of ion-binding sites in proteins. [ABSTRACT FROM AUTHOR]

Empirical or knowledge‐based potentials have many applications in structural biology such as the prediction of protein structure, protein–protein, and protein–ligand interactions and in the evaluation of stability for mutant proteins, the assessment of errors in experimentally solved structures, and the design of new proteins. Here, we describe a simple procedure to derive and use pairwise distance‐dependent potentials that rely on the definition of effective atomic interactions, which attempt to capture interactions that are more likely to be physically relevant. Based on a difficult benchmark test composed of proteins with different secondary structure composition and representing many different folds, we show that the use of effective atomic interactions significantly improves the performance of potentials at discriminating between native and near‐native conformations. We also found that, in agreement with previous reports, the potentials derived from the observed effective atomic interactions in native protein structures contain a larger amount of mutual information. A detailed analysis of the effective energy functions shows that atom connectivity effects, which mostly arise when deriving the potential by the incorporation of those indirect atomic interactions occurring beyond the first atomic shell, are clearly filtered out. The shape of the energy functions for direct atomic interactions representing hydrogen bonding and disulfide and salt bridges formation is almost unaffected when effective interactions are taken into account. On the contrary, the shape of the energy functions for indirect atom interactions (i.e., those describing the interaction between two atoms bound to a direct interacting pair) is clearly different when effective interactions are considered. Effective energy functions for indirect interacting atom pairs are not influenced by the shape or the energy minimum observed for the corresponding direct interacting atom pair. Our results suggest that the dependency between the signals in different energy functions is a key aspect that need to be addressed when empirical energy functions are derived and used, and also highlight the importance of additivity assumptions in the use of potential energy functions. [ABSTRACT FROM AUTHOR]

Knowledge-based potentials are extensively used to represent atomic interactions in modeling the protein structure. We consider a number of problems in constructing efficient knowledge-based potentials for biopolymer modeling. We show that some limitations can be overcome by normalizing estimated interactions through the distribution of distances between noninteracting random probes in protein structure space. We demonstrate that knowledge-based potentials thus constructed can be efficiently applied for analysis of the hydration state of proteins atoms. With this approach, one can predict the locations of structural water molecules in a protein globule. We have also succeeded in recognizing the correctly folded protein structure among many misfolded decoys in cases when the interaction with water solvent is dominant for structure formation. [ABSTRACT FROM AUTHOR]

Abstract: How eukaryotic genomes encode the folding of DNA into nucleosomes and how this intrinsic organization of chromatin guides biological function are questions of wide interest. The physical basis of nucleosome positioning lies in the sequence-dependent propensity of DNA to adopt the tightly bent configuration imposed by the binding of the histone proteins. Traditionally, only DNA bending and twisting deformations are considered, while the effects of the lateral displacements of adjacent base pairs are neglected. We demonstrate, however, that these displacements have a much more important structural role than ever imagined. Specifically, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. Furthermore, the computed cost of deforming DNA on the nucleosome is sequence-specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA bends into the minor groove). These conclusions rest upon a treatment of DNA that goes beyond the conventional ribbon model, incorporating all essential degrees of freedom of “real” duplexes in the estimation of DNA deformation energies. Indeed, only after lateral Slide displacements are considered are we able to account for the sequence-specific folding of DNA found in nucleosome structures. The close correspondence between the predicted and observed nucleosome locations demonstrates the potential advantage of our “structural” approach in the computer mapping of nucleosome positioning. [Copyright &y& Elsevier]

The accurate assessment of structural errors plays a key role in protein structure prediction, constitutes the first step of protein structure refinement, and has a major impact on subsequent functional inference from structural data. In this study, we assess and compare the ability of different full atom knowledge-based potentials to detect small and localized errors in comparative protein structure models of known accuracy. We have evaluated the effect of incorporating close nonbonded pairwise atom terms on the task of classifying residue modeling accuracy. Since the direct and unbiased derivation of close nonbonded terms from current experimental data is not possible, we extrapolated those terms from the corresponding pseudo-energy functions of a nonlocal knowledge-based potential. It is shown that this methodology clearly improves the detection of errors in protein models, suggesting that a proper description of close nonbonded terms is important to achieve a more complete and accurate description of native protein conformations. The use of close nonbonded terms directly derived from experimental data exhibited a poor performance, demonstrating that these terms cannot be accurately obtained by using the current data and methodology. Some external knowledge-based energy functions that are widely used in model assessment also performed poorly, which suggests that the benchmark of models and the specific error detection task tested in this study constituted a difficult challenge. The methodology presented here could be useful to detect localized structural errors not only in high-quality protein models, but also in experimental protein structures. [ABSTRACT FROM AUTHOR]

Abstract: We describe the application of knowledge-based potentials implemented in the MOE program to compare the ligand-binding sites of several proteins. The binding probabilities for a polar and a hydrophobic probe are calculated on a grid to allow easy comparison of binding sites of superimposed related proteins. The method is fast and simple enough to simultaneously use structural information of multiple proteins of a target family. The method can be used to rapidly cluster proteins into subfamilies according to the similarity of hydrophobic and polar fields of their ligand-binding sites. Regions of the binding site which are common within a protein family can be identified and analysed for the design of family-targeted libraries or those which differ for improvement of ligand selectivity. The field-based hierarchical clustering is demonstrated for three protein families: the ligand-binding domains of nuclear receptors, the ATP-binding sites of protein kinases and the substrate binding sites of proteases. More detailed comparisons are presented for serine proteases of the chymotrypsin family, for the peroxisome proliferator-activated receptor subfamily of nuclear receptors and for progesterone and androgen receptor. The results are in good accordance with structure-based analysis and highlight important differences of the binding sites, which have been also described in the literature. [Copyright &y& Elsevier]

Abstract: The variational approach of evaluation for knowledge-based potentials is considered for the first time. In this approach, the problem to derive knowledge-based potentials is solved as the optimization task in the multiparametric model of atom types, reference states and interaction cutoff radii. Using analogy to liquid state theory we offered four new reference states and derived corresponding knowledge-based potentials. The cutoff radii and atom types are optimized to minimize averaged root-mean square deviations (RMSD) of the ligand docked positions regarding to the experimentally determined poses. The number of atom types is varied on the developed atom type tree with 6 root (C, N, O, S, P and the halogen type) and 49 apical atom types. We showed a pronounced effect of atom type choice on docking accuracy and proved that splitting of elements C, N and O of the periodic system up to the 18 optimal atom types essentially improves docking accuracy. [Copyright &y& Elsevier]

Modifications of the amino acid sequence generally affect protein stability. Here, we use knowledge-based potentials to estimate the stability of protein structures under sequence variation. Calculations on a variety of protein scaffolds result in a clear distinction of known mutable regions from arbitrarily chosen control patches. For example, randomly changing the sequence of an antibody paratope yields a significantly lower number of destabilized mutants as compared to the randomization of comparable regions on the protein surface. The technique is computationally efficient and can be used to screen protein structures for regions that are amenable to molecular tinkering by preserving the stability of the mutated proteins. [Copyright &y& Elsevier]

Consensus design methods have been used successfully to engineer proteins with a particular fold, and moreover to engineer thermostable exemplars of particular folds. Here, we consider how a statistical free energy approach can expand upon current methods of phylogenetic design. As an example, we have analyzed the tetratricopeptide repeat (TPR) motif, using multiple sequence alignment to identify the significance of each position in the TPR. The results provide information above and beyond that revealed by consensus design alone, especially at poorly conserved positions. A particularly striking finding is that certain residues, which TPR-peptide co-crystal structures show are in direct contact with the ligand, display a marked hypervariability. This suggests a novel means of identifying ligand-binding sites, and also implies that TPRs generally function as ligand-binding domains. Using perturbation analysis (or statistical coupling analysis), we examined site–site interactions within the TPR motif. Correlated occurrences of amino acid residues at poorly conserved positions explain how TPRs achieve their near-neutral surface charge distributions, and why a TPR designed from straight consensus has an unusually high net charge. Networks of interacting sites revealed that TPRs fall into two unrecognized families with distinct sets of interactions related to the identity of position 7 (Leu or Lys/Arg). Statistical free energy analysis provides a more complete description of “What makes a TPR a TPR?” than consensus alone, and it suggests general approaches to extend and improve the phylogenetic design of proteins. [Copyright &y& Elsevier]

We have developed PLASS (Protein-Ligand Affinity Statistical Score), a pair-wise potential of mean-force for rapid estimation of the binding affinity of a ligand molecule to a protein active site. This scoring function is derived from the frequency of occurrence of atom-type pairs in crystallographic complexes taken from the Protein Data Bank (PDB). Statistical distributions are converted into distance-dependent contributions to the Gibbs free interaction energy for 10 atomic types using the Boltzmann hypothesis, with only one adjustable parameter. For a representative set of 72 protein-ligand structures, PLASS scores correlate well with the experimentally measured dissociation constants: a correlation coefficient R of 0.82 and RMS error of 2.0 kcal/mol. Such high accuracy results from our novel treatment of the volume correction term, which takes into account the inhomogeneous properties of the protein-ligand complexes. PLASS is able to rank reliably the affinity of complexes which have as much diversity as in the PDB. [ABSTRACT FROM AUTHOR]

A new approach, MOBILE, is presented that models protein binding-sites including bound ligand molecules as restraints. Initially generated, homology models of the target protein are refined iteratively by including information about bioactive ligands as spatial restraints and optimising the mutual interactions between the ligands and the binding-sites. Thus optimised models can be used for structure-based drug design and virtual screening.In a first step, ligands are docked into an averaged ensemble of crude homology models of the target protein. In the next step, improved homology models are generated, considering explicitly the previously placed ligands by defining restraints between protein and ligand atoms. These restraints are expressed in terms of knowledge-based distance-dependent pair potentials, which were compiled from crystallographically determined protein–ligand complexes. Subsequently, the most favourable models are selected by ranking the interactions between the ligands and the generated pockets using these potentials. Final models are obtained by selecting the best-ranked side-chain conformers from various models, followed by an energy optimisation of the entire complex using a common force-field.Application of the knowledge-based pair potentials proved efficient to restrain the homology modelling process and to score and optimise the modelled protein–ligand complexes. For a test set of 46 protein–ligand complexes, taken from the Protein Data Bank (PDB), the success rate of producing near-native binding-site geometries (rmsd<2.0 A˚) with MODELLER is 70% when the ligand restrains the homology modelling process in its native orientation. Scoring these complexes with the knowledge-based potentials, in 66% of the cases a pose with rmsd <2.0 A˚ is found on rank 1. Finally, MOBILE has been applied to two case studies modelling factor Xa based on trypsin and aldose reductase based on aldehyde reductase. [Copyright &y& Elsevier]

The relative strengths of interactions involving polypeptide chains can be estimated with reasonable accuracy with statistical potentials, free-energy functions derived from the frequency of occurrence of structural arrangements of residues or atoms in collections of protein structures. Recent published work has shown that the energetics of side-chain/backbone interactions can be modeled by the ϕ/Ψ propensities of the 20 amino acids. In this report, the more commonly used ϕ/Ψ probabilities are demonstrated to fail in evaluating the free energies of protein conformations because of an overriding preference for all helical structures. Comparison of the hypothetical reactions implied by these two different statistics-propensities versus probabilities-leads to the conclusion that the Boltzmann hypothesis may only be applicable for the calculation of statistical potentials after the starting conformation has been specified. This conclusion supports a simple conjecture: The surprising success of the Boltzmann hypothesis in explaining the energetics of protein structures is a direct consequence of a real equilibrium, one extending over evolutionary time that has maintained the stability of each protein within a narrow range of values. [ABSTRACT FROM AUTHOR]

Whether knowledge-based intra-molecular inter-residue potentials are valid to represent inter-molecular interactions taking place at protein-protein interfaces has been questioned in several studies. Differences in the chain connectivity effect and in residue packing geometry between interfaces and single chain monomers have been pointed out as possible sources of distinct energetics for the two cases. In the present study, the interfacial regions of protein-protein complexes are examined to extract inter-molecular inter-residue potentials, using the same statistical methods as those previously adopted for intra-molecular residue pairs. Two sets of energy parameters are derived, corresponding to solvent-mediation and 'average residue' mediation. The former set is shown to be highly correlated (correlation coefficient 0.89) with that previously obtained for inter-residue interactions within single chain monomers, while the latter exhibits a weaker correlation (0.69) with its intra-molecular counterpart. In addition to the close similarity of intra- and inter-molecular solvent-mediated potentials, they are shown to be significantly more residue-specific and thereby discriminative compared to the residue-mediated ones, indicating that solvent-mediation plays a major role in controlling the effective inter-residue interactions, either at interfaces, or within single monomers. Based on this observation, a reduced set of energy parameters comprising 20 one-body and 3 two-body terms is proposed (as opposed to the 20 × 20 tables of inter-residue potentials), which reproduces the conventional 20 × 20 tables with a correlation coefficient of 0.99. [ABSTRACT FROM AUTHOR]

The Z-score of a protein is defined as the energy separation between the native fold and the average of an ensemble of misfolds in the units of the standard deviation of the ensemble. The Z-score is often used as a way of testing the knowledge-based potentials for their ability to recognize the native fold from other alternatives. However, it is not known what range of values the Z-scores should have if one had a correct potential. Here, we offer an estimate of Z-scores extracted from calorimetric measurements of proteins. The energies obtained from these experimental data are compared with those from computer simulations of a lattice model protein. It is suggested that the Z-scores calculated from different knowledge-based potentials are generally too small in comparison with the experimental values. [ABSTRACT FROM AUTHOR]

Proteases recognize specific substrate sequences and catalyze the hydrolysis of targeted peptide bonds to activate or degrade them. It is particularly important to identify the recognition and binding mechanisms of protease-substrate complex structures in studies of drug development. Cleavage specificity in protease systems is generally determined by the amino acid profile, structural features, and distinct molecular interactions. In this work, substrate variability and substrate specificity of the NS3/4A serine protease encoded by the hepatitis C virus (HCV) was investigated by the biased sequence search threading (BSST) methodology. The available crystal structures of peptide-bound protease were used as templates as well as new complex structures that were generated via docking calculations. Threading various binding and nonbinding sequences as starting sequences over multiple templates, the potential sequence space was efficiently explored by a low-resolution knowledge-based scoring potential. The low-energy substrate sequences generated by the biased search are correlated with the natural substrates with conserved amino acid preferences, although some positions exhibit variability. Specifically, the amino acids which play essential roles in cleavage are mostly preferred. Potential substrate sequences were predicted by statistical probability approaches that consider the pairwise and triplewise interdependencies among residue positions in the low-energy sequences. The predicted substrate sequences also reproduce most of the natural substrate sequences, implying the complex interdependence between the different substrate residues. Consequently, the BSST seems to provide a powerful methodology for predicting the substrate specificity for the NS3/4A protease, which is a target in drug discovery studies for HCV.

Despite the significant increase in computational power, molecular modeling of protein structure using classical all-atom approaches remains inefficient, at least for most of the protein targets in the focus of biomedical research. Perhaps the most successful strategy to overcome the inefficiency problem is multiscale modeling to merge all-atom and coarse-grained models. This chapter describes a well-established CABS coarse-grained protein model. The CABS (C-Alpha, C-Beta, and Side chains) model assumes a 2-4 united-atom representation of amino acids, knowledge-based force field (derived from the statistical regularities seen in known protein sequences and structures) and efficient Monte Carlo sampling schemes (MC dynamics, MC replica-exchange, and combinations). A particular emphasis is given to the unique design of the CABS force-field, which is largely defined using one-dimensional structural properties of proteins, including protein secondary structure. This chapter also presents CABS-based modeling methods, including multiscale tools for de novo structure prediction, modeling of protein dynamics and prediction of protein-peptide complexes. CABS-based tools are freely available at http://biocomp.chem.uw.edu.pl/tools.

Proteins are the bricks and mortar of cells, playing structural and functional roles. In order to perform their function, they interact with each other as well as with other biomolecules such as DNA or RNA. Therefore, to fathom the function of a protein, we require knowing its partners and the atomic details of its interactions (i.e., the structure of the complex). However, the amount of protein interactions with an experimentally determined three-dimensional structure is scarce. Therefore, computational techniques such as homology modeling are foremost to fill this gap. Protein interactions can be modeled using as templates the interactions of homologous proteins, if the structure of the complex is known, or using docking methods. In both approaches, the estimation of the quality of models is essential. There are several ways to address this problem. In this review, we focus on the use of knowledge-based potentials for the analysis of protein interactions. We describe the procedure to derive statistical potentials and split them into different energetic terms that can be used for different purposes. We extensively discuss the fields where knowledge-based potentials have been successfully applied to (1) model protein-protein, protein-DNA, and protein-RNA interactions and (2) predict binding sites (in the protein and in the DNA). Moreover, we provide ready-to-use resources for docking and benchmarking protein interactions., (© 2014 Elsevier Inc. All rights reserved.)

Structural refinement of predicted models of biological macromolecules using atomistic or coarse-grained molecular force fields having various degree of error is investigated. The goal of this analysis is to estimate what is the probability for designing an effective structural refinement based on computations of conformational energies using force field, and starting from a structure predicted from the sequence (using template-based or template-free modeling), and refining it to bring the structure into closer proximity to the native state. It is widely believed that it should be possible to develop such a successful structure refinement algorithm by applying an iterative procedure with stochastic sampling and appropriate energy function, which assesses the quality (correctness) of protein decoys. Here, an analysis of noise in an artificially introduced scoring function is investigated for a model of an ideal sampling scheme, where the underlying distribution of RMSDs is assumed to be Gaussian. Sampling of the conformational space is performed by random generation of RMSD values. We demonstrate that whenever the random noise in a force field exceeds some level, it is impossible to obtain reliable structural refinement. The magnitude of the noise, above which a structural refinement, on average is impossible, depends strongly on the quality of sampling scheme and a size of the protein. Finally, possible strategies to overcome the intrinsic limitations in the force fields for impacting the development of successful refinement algorithms are discussed., (Copyright © 2011 Wiley Periodicals, Inc.)