Protein decoy sets for evaluating energy functions

Ranking the quality of protein structure models using sidechain based network properties

Determining the correct structure of a protein given its sequence still remains an arduous task with many researchers working towards this goal. Most structure prediction methodologies result in the generation of a large number of probable candidates with the final challenge being to select the best amongst these. In this work, we have used Protein Structure Networks of native and modeled proteins in combination with Support Vector Machines to estimate the quality of a protein structure model and finally to provide ranks for these models. Model ranking is performed using regression analysis and helps in model selection from a group of many similar and good quality structures. Our results show that structures with a rank greater than 16 exhibit native protein-like properties while those below 10 are non-native like. The tool is also made available as a web-server ( http://vishgraph.mbu.iisc.ernet.in/GraProStr/native_non_native_ranking.html), where, 5 modelled structures can be evaluated at a given time.

The use of soluble protein structures in modeling helical proteins in a layered membrane

Major advances have been made in the prediction of soluble protein structures, led by the knowledge-based modeling methods that extract useful structural trends from known protein structures and incorporate them into scoring functions. The same cannot be reported for the class of transmembrane proteins, primarily due to the lack of high-resolution structural data for transmembrane proteins, which render many of the knowledge-based method unreliable or invalid. We have developed a method that harnesses the vast structural knowledge available in soluble protein data for use in the modeling of transmembrane proteins. At the core of the method, a set of transmembrane protein decoy sets that allow us to filter and train features recognized from soluble proteins for transmembrane protein modeling into a set of scoring functions. We have demonstrated that structures of soluble proteins can provide significant insight into transmembrane protein structures. A complementary novel two-stage modeling/selection process that mimics the two-stage helical membrane protein folding was developed. Combined with the scoring function, the method was successfully applied to model 5 transmembrane proteins. The root mean square deviations of the predicted models ranged from 5.0 to 8.8 Å to the native structures.

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

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

Multibody coarse-grained potentials for native structure recognition and quality assessment of protein models

Multibody potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Our goal was to combine long range multibody potentials and short range potentials to improve recognition of native structure among misfolded decoys. We optimized the weights for four-body nonsequential, four-body sequential, and short range potentials to obtain optimal model ranking results for threading and have compared these data against results obtained with other potentials (26 different coarse-grained potentials from the Potentials 'R'Us web server have been used). Our optimized multibody potentials outperform all other contact potentials in the recognition of the native structure among decoys, both for models from homology template-based modeling and from template-free modeling in CASP8 decoy sets. We have compared the results obtained for this optimized coarse-grained potentials, where each residue is represented by a single point, with results obtained by using the DFIRE potential, which takes into account atomic level information of proteins. We found that for all proteins larger than 80 amino acids our optimized coarse-grained potentials yield results comparable to those obtained with the atomic DFIRE potential.

Amino acid interaction preferences in proteins

Understanding the key factors that influence the interaction preferences of amino acids in the folding of proteins have remained a challenge. Here we present a knowledge-based approach for determining the effective interactions between amino acids based on amino acid type, their secondary structure, and the contact based environment that they find themselves in the native state structure as measured by their number of neighbors. We find that the optimal information is approximately encoded in a 60 x 60 matrix describing the 20 types of amino acids in three distinct secondary structures (helix, beta strand, and loop). We carry out a clustering scheme to understand the similarity between these interactions and to elucidate a nonredundant set. We demonstrate that the inferred energy parameters can be used for assessing the fit of a given sequence into a putative native state structure.

Explicit orientation dependence in empirical potentials and its significance to side-chain modeling

Protein structure modeling and prediction have important applications throughout the biological sciences, from the design of pharmaceuticals to the elucidation of enzyme mechanisms. At the core of most protein modeling is an energy function, the minimum of which represents the free energy "cost" for forming a correct protein structure. The most commonly used energy functions are knowledge-based statistical potential functions; that is, they are empirically derived from statistical analysis of a set of high-resolution protein structures. When that kind of potential function is constructed, the anisotropic orientation dependence between the interacting groups is a critical component for accurately representing key molecular interactions, such as those involved in protein side-chain packing. In the literature, however, many potential functions are limited in their ability to describe orientation dependence. In all-atom potentials, they typically ignore heterogeneous chemical-bond connectivity. In coarse-grained potentials, such as (semi)-residue-based potentials, the simplified representation of residues often reduces the sensitivity of the potential to side-chain orientation. Recently, in an effort to maximally capture the orientation dependence in side-chain interactions, a new type of all-atom statistical potential was developed: OPUS-PSP (potential derived from side-chain packing). The key feature of this potential is its explicit description of orientation dependence in molecular interactions, which is achieved with a basis set of 19 rigid-body blocks extracted from the chemical structures of 20 amino acid residues. This basis set is specifically designed to maximally capture the essential elements of orientation dependence in molecular packing interactions. The potential is constructed from the orientation-specific packing statistics of pairs of those blocks in a nonredundant structural database. On decoy set tests, OPUS-PSP significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and its consistency in achieving high Z scores across decoy sets. The application of OPUS-PSP to conformational modeling of side chains has led to another method, called OPUS-Rota. In terms of combined speed and accuracy, OPUS-Rota outperforms all of the other methods in modeling side-chain conformation. In this Account, we briefly outline the basic scheme of the OPUS-PSP potential and its application to side-chain modeling via OPUS-Rota. Future perspectives on the modeling of orientation dependence are also discussed. The computer programs for OPUS-PSP and OPUS-Rota can be downloaded at http://sigler.bioch.bcm.tmc.edu/MaLab . They are free for academic users.

An estimate of the numbers and density of low-energy structures (or decoys) in the conformational landscape of proteins

BACKGROUND

The conformational energy landscape of a protein, as calculated by known potential energy functions, has several minima, and one of these corresponds to its native structure. It is however difficult to comprehensively estimate the actual numbers of low energy structures (or decoys), the relationships between them, and how the numbers scale with the size of the protein.

METHODOLOGY

We have developed an algorithm to rapidly and efficiently identify the low energy conformers of oligo peptides by using mutually orthogonal Latin squares to sample the potential energy hyper surface. Using this algorithm, and the ECEPP/3 potential function, we have made an exhaustive enumeration of the low-energy structures of peptides of different lengths, and have extrapolated these results to larger polypeptides.

CONCLUSIONS AND SIGNIFICANCE

We show that the number of native-like structures for a polypeptide is, in general, an exponential function of its sequence length. The density of these structures in conformational space remains more or less constant and all the increase appears to come from an expansion in the volume of the space. These results are consistent with earlier reports that were based on other models and techniques.

MetaMQAP: a meta-server for the quality assessment of protein models

Background

Computational models of protein structure are usually inaccurate and exhibit significant deviations from the true structure. The utility of models depends on the degree of these deviations. A number of predictive methods have been developed to discriminate between the globally incorrect and approximately correct models. However, only a few methods predict correctness of different parts of computational models. Several Model Quality Assessment Programs (MQAPs) have been developed to detect local inaccuracies in unrefined crystallographic models, but it is not known if they are useful for computational models, which usually exhibit different and much more severe errors.

Results

The ability to identify local errors in models was tested for eight MQAPs: VERIFY3D, PROSA, BALA, ANOLEA, PROVE, TUNE, REFINER, PROQRES on 8251 models from the CASP-5 and CASP-6 experiments, by calculating the Spearman's rank correlation coefficients between per-residue scores of these methods and local deviations between C-alpha atoms in the models vs. experimental structures. As a reference, we calculated the value of correlation between the local deviations and trivial features that can be calculated for each residue directly from the models, i.e. solvent accessibility, depth in the structure, and the number of local and non-local neighbours. We found that absolute correlations of scores returned by the MQAPs and local deviations were poor for all methods. In addition, scores of PROQRES and several other MQAPs strongly correlate with 'trivial' features. Therefore, we developed MetaMQAP, a meta-predictor based on a multivariate regression model, which uses scores of the above-mentioned methods, but in which trivial parameters are controlled. MetaMQAP predicts the absolute deviation (in Ångströms) of individual C-alpha atoms between the model and the unknown true structure as well as global deviations (expressed as root mean square deviation and GDT_TS scores). Local model accuracy predicted by MetaMQAP shows an impressive correlation coefficient of 0.7 with true deviations from native structures, a significant improvement over all constituent primary MQAP scores. The global MetaMQAP score is correlated with model GDT_TS on the level of 0.89.

Conclusion

Finally, we compared our method with the MQAPs that scored best in the 7th edition of CASP, using CASP7 server models (not included in the MetaMQAP training set) as the test data. In our benchmark, MetaMQAP is outperformed only by PCONS6 and method QA_556 – methods that require comparison of multiple alternative models and score each of them depending on its similarity to other models. MetaMQAP is however the best among methods capable of evaluating just single models.

We implemented the MetaMQAP as a web server available for free use by all academic users at the URL

OPUS-PSP: an orientation-dependent statistical all-atom potential derived from side-chain packing

Here we report an orientation-dependent statistical all-atom potential derived from side-chain packing, named OPUS-PSP. It features a basis set of 19 rigid-body blocks extracted from the chemical structures of all 20 amino acid residues. The potential is generated from the orientation-specific packing statistics of pairs of those blocks in a non-redundant structural database. The purpose of such an approach is to capture the essential elements of orientation dependence in molecular packing interactions. Tests of OPUS-PSP on commonly used decoy sets demonstrate that it significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and consistency in achieving high Z-scores across decoy sets. As OPUS-PSP excludes interactions among main-chain atoms, its success highlights the crucial importance of side-chain packing in forming native protein structures. Moreover, OPUS-PSP does not explicitly include solvation terms, and thus the potential should perform well when the solvation effect is difficult to determine, such as in membrane proteins. Overall, OPUS-PSP is a generally applicable potential for protein structure modeling, especially for handling side-chain conformations, one of the most difficult steps in high-accuracy protein structure prediction and refinement.

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.

Potential for assessing quality of protein structure based on contact number prediction

We developed a novel knowledge-based residue environment potential for assessing the quality of protein structures in protein structure prediction. The potential uses the contact number of residues in a protein structure and the absolute contact number of residues predicted from its amino acid sequence using a new prediction method based on a support vector regression (SVR). The contact number of an amino acid residue in a protein structure is defined by the number of residues around a given residue. First, the contact number of each residue is predicted using SVR from an amino acid sequence of a target protein. Then, the potential of the protein structure is calculated from the probability distribution of the native contact numbers corresponding to the predicted ones. The performance of this potential is compared with other score functions using decoy structures to identify both native structure from other structures and near-native structures from nonnative structures. This potential improves not only the ability to identify native structures from other structures but also the ability to discriminate near-native structures from nonnative structures.

The change of protein intradomain mobility on ligand binding: is it a commonly observed phenomenon?

Analysis of changes in the dynamics of protein domains on ligand binding is important in several aspects: for the understanding of the hierarchical nature of protein folding and dynamics at equilibrium; for analysis of signal transduction mechanisms triggered by ligand binding, including allostery; for drug design; and for construction of biosensors reporting on the presence of target ligand in studied media. In this work we use the recently developed HCCP computational technique for the analysis of stabilities of dynamic domains in proteins, their intrinsic motions and of their changes on ligand binding. The work is based on comparative studies of 157 ligand binding proteins, for which several crystal structures (in ligand-free and ligand-bound forms) are available. We demonstrate that the domains of the proteins presented in the Protein DataBank are far more robust than it was thought before: in the majority of the studied proteins (152 out of 157), the ligand binding does not lead to significant change of domain stability. The exceptions from this rule are only four bacterial periplasmic transport proteins and calmodulin. Thus, as a rule, the pattern of correlated motions in dynamic domains, which determines their stability, is insensitive to ligand binding. This rule may be the general feature for a vast majority of proteins.