Pairwise Contact Potentials Research Articles

Feature extraction by statistical contact potentials and wavelet transform for predicting subcellular localizations in gram negative bacterial proteins

Predicting the localization of a protein has become a useful practice for inferring its function. Most of the reported methods to predict subcellular localizations in Gram-negative bacterial proteins make use of standard protein representations that generally do not take into account the distribution of the amino acids and the structural information of the proteins. Here, we propose a protein representation based on the structural information contained in the pairwise statistical contact potentials. The wavelet transform decodes the information contained in the primary structure of the proteins, allowing the identification of patterns along the proteins, which are used to characterize the subcellular localizations. Then, a support vector machine classifier is trained to categorize them. Cellular compartments like periplasm and extracellular medium are difficult to predict, having a high false negative rate. The wavelet-based method achieves an overall high performance while maintaining a low false negative rate, particularly, on “periplasm” and “extracellular medium”. Our results suggest the proposed protein characterization is a useful alternative to representing and predicting protein sequences over the classical and cutting edge protein depictions.

Predicting residue contacts for protein-protein interactions by integration of multiple information

Detailed knowledge of interfacial region between interacting proteins is not only helpful in annotating function for proteins, but also very important for structure-based drug design and disease treatment. However, this is one of the most difficult tasks and current methods are constrained by some factors. In this study, we developed a new method to predict residue-residue contacts of two interacting protein domains by integrating information about evolutionary couplings andamino acid pairwise contact potentials, as well as domain-domain interaction interfaces. The experimental results showed that our proposed method outperformed the previous method with the same datasets. Moreover, the method promises an improvement in the source of template-based protein docking.

EpicCapo: epitope prediction using combined information of amino acid pairwise contact potentials and HLA-peptide contact site information

BackgroundEpitope identification is an essential step toward synthetic vaccine development since epitopes play an important role in activating immune response. Classical experimental approaches are laborious and time-consuming, and therefore computational methods for generating epitope candidates have been actively studied. Most of these methods, however, are based on sophisticated nonlinear techniques for achieving higher predictive performance. The use of these techniques tend to diminish their interpretability with respect to binding potential: that is, they do not provide much insight into binding mechanisms.ResultsWe have developed a novel epitope prediction method named EpicCapo and its variants, EpicCapo+ and EpicCapo+REF. Nonapeptides were encoded numerically using a novel peptide-encoding scheme for machine learning algorithms by utilizing 40 amino acid pairwise contact potentials (referred to as AAPPs throughout this paper). The predictive performances of EpicCapo+ and EpicCapo+REF outperformed other state-of-the-art methods without losing interpretability. Interestingly, the most informative AAPPs estimated by our study were those developed by Micheletti and Simons while previous studies utilized two AAPPs developed by Miyazawa & Jernigan and Betancourt & Thirumalai. In addition, we found that all amino acid positions in nonapeptides could effect on performances of the predictive models including non-anchor positions. Finally, EpicCapo+REF was applied to identify candidates of promiscuous epitopes. As a result, 67.1% of the predicted nonapeptides epitopes were consistent with preceding studies based on immunological experiments.ConclusionsOur method achieved high performance in testing with benchmark datasets. In addition, our study identified a number of candidates of promiscuous CTL epitopes consistent with previously reported immunological experiments. We speculate that our techniques may be useful in the development of new vaccines. The R implementation of EpicCapo+REF is available at http://pirun.ku.ac.th/~fsciiok/EpicCapoREF.zip. Datasets are available at http://pirun.ku.ac.th/~fsciiok/Datasets.zip.

PAAQD: Predicting immunogenicity of MHC class I binding peptides using amino acid pairwise contact potentials and quantum topological molecular similarity descriptors

Prediction of peptide immunogenicity is a promising approach for novel vaccine discovery. Conventionally, epitope prediction methods have been developed to accelerate the process of vaccine production by searching for candidate peptides from pathogenic proteins. However, recent studies revealed that peptides with high binding affinity to major histocompatibility complex molecules (MHCs) do not always result in high immunogenicity. Therefore, it is promising to predict the peptide immunogenicity rather than epitopes in order to discover new vaccines more effectively. To this end, we developed a novel T-cell reactivity predictor which we call PAAQD. Nonapeptides were encoded numerically, using combining information of amino acid pairwise contact potentials (AAPPs) and quantum topological molecular similarity (QTMS) descriptors. Encoded data were used in the construction of our classification model. Our numerical experiments suggested that the predictive performance of PAAQD is at least comparable with POPISK, one of the pioneering techniques for T-cell reactivity prediction. Also, our experiment suggested that the first and eighth positions of nonapeptides are the most important for immunogenicity and most of the anchor residues in epitope prediction were not important in T-cell reactivity prediction. The R implementation of PAAQD is available at http://pirun.ku.ac.th/~fsciiok/PAAQD.rar.

Methyl side-chain dynamics prediction based on protein structure

Protein dynamics is believed to influence protein function through a variety of mechanisms, some of which are not fully understood. Thus, prediction of protein flexibility from sequence or structural characteristics would assist in comprehension of the ways dynamics is linked to function, and would be important in protein modeling and design. In particular, quantitative description of side-chain dynamics would allow us to understand the role of side-chain flexibility in different functional processes, such as protein-ligand and protein-protein interactions. Using a dataset of 18 proteins, we trained a neural network for the prediction of methyl-bearing side-chain dynamics as described by the methyl side-chain generalized order parameters (S(2)) inferred from NMR data. The network uses 10 input parameters extracted from 3D structures. The average correlation coefficient between the experimental and predicted generalized order parameters is r = 0.71 +/- 0.029. Further analysis revealed that the order parameter depends more strongly on the methyl carbon packing density, the methyl carbon distance to the C(alpha) atom, and the knowledge-based pair-wise contact potential between the methyl carbon and neighboring amino acids. In general, we observed an improvement in the prediction of methyl order parameters by our network in comparison with molecular dynamics simulations. The sensitivity of the predictions to minor structural changes was illustrated in two examples (calmodulin and barnase) by comparing the S(2) predictions for the unbound and ligand-bound structures. The method was able to correctly predict most of the significant changes in side-chain dynamics upon ligand binding, and identified some residues involved in long-range communications or protein-ligand binding. http://epigenomique.genopole.fr/ approximately carbonell

Ranking of binding and nonbinding peptides to MHC class I molecules using inverse folding approach: Implications for vaccine design

T cell recognition of the peptide-MHC complex initiates a cascade of immunological events necessary for immune responses. Accurate T-cell epitope prediction is an important part of the vaccine designing. Development of predictive algorithms based on sequence profile requires a very large number of experimental binding peptide data to major histocompatibility complex (MHC) molecules. Here we used inverse folding approach to study the peptide specificity of MHC Class-I molecule with the aim of obtaining a better differentiation between binding and nonbinding sequence. Overlapping peptides, spanning the entire protein sequence, are threaded through the backbone coordinates of a known peptide fold in the MHC groove, and their interaction energies are evaluated using statistical pairwise contact potentials. We used the Miyazawa & Jernigan and Betancourt & Thirumalai tables for pairwise contact potentials, and two distance criteria (Nearest atom >> 4.0 A & C-beta >> 7.0 A) for ranking the peptides in an ascending order according to their energy values, and in most cases, known antigenic peptides are highly ranked. The predictions from threading improved when used multiple templates and average scoring scheme. In general, when structural information about a protein-peptide complex is available, the current application of the threading approach can be used to screen a large library of peptides for selection of the best binders to the target protein. The proposed scheme may significantly reduce the number of peptides to be tested in wet laboratory for epitope based vaccine design.

Hypergraph Model of Multi-Residue Interactions in Proteins: Sequentially-Constrained Partitioning Algorithms for Optimization of Site-Directed Protein Recombination

Relationships among amino acids determine stability and function and are also constrained by evolutionary history. We develop a probabilistic hypergraph model of residue relationships that generalizes traditional pairwise contact potentials to account for the statistics of multi-residue interactions. Using this model, we detected non-random associations in protein families and in the protein database. We also use this model in optimizing site-directed recombination experiments to preserve significant interactions and thereby increase the frequency of generating useful recombinants. We formulate the optimization as a sequentially-constrained hypergraph partitioning problem; the quality of recombinant libraries with respect to a set of breakpoints is characterized by the total perturbation to edge weights. We prove this problem to be NP-hard in general, but develop exact and heuristic polynomial-time algorithms for a number of important cases. Application to the beta-lactamase family demonstrates the utility of our algorithms in planning site-directed recombination.

A maximum likelihood framework for protein design

BackgroundThe aim of protein design is to predict amino-acid sequences compatible with a given target structure. Traditionally envisioned as a purely thermodynamic question, this problem can also be understood in a wider context, where additional constraints are captured by learning the sequence patterns displayed by natural proteins of known conformation. In this latter perspective, however, we still need a theoretical formalization of the question, leading to general and efficient learning methods, and allowing for the selection of fast and accurate objective functions quantifying sequence/structure compatibility.ResultsWe propose a formulation of the protein design problem in terms of model-based statistical inference. Our framework uses the maximum likelihood principle to optimize the unknown parameters of a statistical potential, which we call an inverse potential to contrast with classical potentials used for structure prediction. We propose an implementation based on Markov chain Monte Carlo, in which the likelihood is maximized by gradient descent and is numerically estimated by thermodynamic integration. The fit of the models is evaluated by cross-validation. We apply this to a simple pairwise contact potential, supplemented with a solvent-accessibility term, and show that the resulting models have a better predictive power than currently available pairwise potentials. Furthermore, the model comparison method presented here allows one to measure the relative contribution of each component of the potential, and to choose the optimal number of accessibility classes, which turns out to be much higher than classically considered.ConclusionAltogether, this reformulation makes it possible to test a wide diversity of models, using different forms of potentials, or accounting for other factors than just the constraint of thermodynamic stability. Ultimately, such model-based statistical analyses may help to understand the forces shaping protein sequences, and driving their evolution.

Assessing Site-Interdependent Phylogenetic Models of Sequence Evolution

In recent works, methods have been proposed for applying phylogenetic models that allow for a general interdependence between the amino acid positions of a protein. As of yet, such models have focused on site interdependencies resulting from sequence-structure compatibility constraints, using simplified structural representations in combination with a set of statistical potentials. This structural compatibility criterion is meant as a proxy for sequence fitness, and the methods developed thus far can incorporate different site-interdependent fitness proxies based on other measurements. However, no methods have been proposed for comparing and evaluating the adequacy of alternative fitness proxies in this context, or for more general comparisons with canonical models of protein evolution. In the present work, we apply Bayesian methods of model selection-based on numerical calculations of marginal likelihoods and posterior predictive checks-to evaluate models encompassing the site-interdependent framework. Our application of these methods indicates that considering site-interdependencies, as done here, leads to an improved model fit for all data sets studied. Yet, we find that the use of pairwise contact potentials alone does not suitably account for across-site rate heterogeneity or amino acid exchange propensities; for such complexities, site-independent treatments are still called for. The most favored models combine the use of statistical potentials with a suitably rich site-independent model. Altogether, the methodology employed here should allow for a more rigorous and systematic exploration of different ways of modeling explicit structural constraints, or any other site-interdependent criterion, while best exploiting the richness of previously proposed models.

Assessing methods for identifying pair-wise atomic contacts across binding interfaces

An essential step in understanding the molecular basis of protein–protein interactions is the accurate identification of inter-protein contacts. We evaluate a number of common methods used in analyzing protein–protein interfaces: a Voronoi polyhedra-based approach, changes in solvent accessible surface area (ΔSASA) and various radial cutoffs (closest atom, Cβ, and centroid). First, we compared the Voronoi polyhedra-based analysis to the ΔSASA and show that using Voronoi polyhedra finds knob-in-hole contacts. To assess the accuracy between the Voronoi polyhedra-based approach and the various radial cutoff methods, two sets of data were used: a small set of 75 experimental mutants and a larger one of 592 structures of protein–protein interfaces. In an assessment using the small set, the Voronoi polyhedra-based methods, a solvent accessible surface area method, and the closest atom radial method identified 100% of the direct contacts defined by mutagenesis data, but only the Voronoi polyhedra-based method found no false positives. The other radial methods were not able to find all of the direct contacts even using a cutoff of 9 Å. With the larger set of structures, we compared the overall number contacts using the Voronoi polyhedra-based method as a standard. All the radial methods using a 6-Å cutoff identified more interactions, but these putative contacts included many false positives as well as missed many false negatives. While radial cutoffs are quicker to calculate as well as to implement, this result highlights why radial cutoff methods do not have the proper resolution to detail the non-homogeneous packing within protein interfaces, and suggests an inappropriate bias in pair-wise contact potentials. Of the radial cutoff methods, using the closest atom approach exhibits the best approximation to the more intensive Voronoi calculation. Our version of the Voronoi polyhedra-based method QContacts is available at http://tsailab.tamu.edu/Qcons.

An Atomic Environment Potential for use in Protein Structure Prediction

We describe the derivation and testing of a knowledge-based atomic environment potential for the modeling of protein structural energetics. An analysis of the probabilities of atomic interactions in a dataset of high-resolution protein structures shows that the probabilities of non-bonded inter-atomic contacts are not statistically independent events, and that the multi-body contact frequencies are poorly predicted from pairwise contact potentials. A pseudo-energy function is defined that measures the preferences for protein atoms to be in a given microenvironment defined by the number of contacting atoms in the environment and its atomic composition. This functional form is tested for its ability to recognize native protein structures amongst an ensemble of decoy structures and a detailed relative performance comparison is made with a number of common functions used in protein structure prediction.

Inferring ideal amino acid interaction forms from statistical protein contact potentials

We have analyzed 29 different published matrices of protein pairwise contact potentials (CPs) between amino acids derived from different sets of proteins, either crystallographic structures taken from the Protein Data Bank (PDB) or computer-generated decoys. Each of the CPs is similar to 1 of the 2 matrices derived in the work of Miyazawa and Jernigan (Proteins 1999;34:49-68). The CP matrices of the first class can be approximated with a correlation of order 0.9 by the formula e(ij) = h(i) + h(j), 1 <or= i, j <or= 20, where the residue-type dependent factor h is highly correlated with the frequency of occurrence of a given amino acid type inside proteins. Electrostatic interactions for the potentials of this class are almost negligible. In the potentials belonging to this class, the major contribution to the potentials is the one-body transfer energy of the amino acid from water to the protein environment. Potentials belonging to the second class can be approximated with a correlation of 0.9 by the formula e(ij) = c(0) - h(i)h(j) + q(i)q(j), where c(0) is a constant, h is highly correlated with the Kyte-Doolittle hydrophobicity scale, and a new, less dominant, residue-type dependent factor q is correlated ( approximately 0.9) with amino acid isoelectric points pI. Including electrostatic interactions significantly improves the approximation for this class of potentials. While, the high correlation between potentials of the first class and the hydrophobic transfer energies is well known, the fact that this approximation can work well also for the second class of potentials is a new finding. We interpret potentials of this class as representing energies of contact of amino acid pairs within an average protein environment.

Optimal potentials for predicting inter-helical packing in transmembrane proteins.

A set of pairwise contact potentials between amino acid residues in transmembrane helices was determined from the known native structure of the transmembrane protein (TMP) bacteriorhodopsin by the method of perceptron learning, using Monte Carlo dynamics to generate suitable "decoy" structures. The procedure of finding these decoys is simpler than for globular proteins, since it is reasonable to assume that helices behave as independent, stable objects and, therefore, the search in the conformational space is greatly reduced. With the learnt potentials, the association of the helices in bacteriorhodopsin was successfully simulated. The folding of a second TMP (the helix-dimer glycophorin A) was then accomplished with only a refinement of the potentials from a small number of decoys.

Information-theoretic dissection of pairwise contact potentials.

Pairwise contact potentials have a long, successful history in protein structure prediction. They provide an easily-estimated representation of many attributes of protein structures, such as the hydrophobic effect. In order to improve on existing potentials, one should develop a clear understanding of precisely what information they convey. Here, using mutual information, we quantified the information in amino acid potentials, and the importance of hydropathy, charge, disulfide bonding, and burial. Sampling error in mutual information was controlled for by estimating how much information cannot be attributed to sampling bias. We found the information in amino acid contacts to be modest: 0.04 bits per contact. Of that, only 0.01 bits of information could not be attributed to hydropathy, charge, disulfide bonding, or burial.

Application of PROSPECT in CASP4: characterizing protein structures with new folds.

In the Fourth Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP4), we predicted all 43 targets using our threading application PROSPECT. PROSPECT guarantees to find an optimal alignment between a protein sequence and a structural fold for a general energy function with pairwise contact potential. For each prediction, it gives a reliability assessment based on a neural network approach. In addition, PROSPECT has been added to the Genomic Integrated Supercomputing Toolkit (GIST) and is deployed on terascale computing resources. Structural predictions in CASP4 included three categories, that is comparative modeling, fold recognition, and prediction for structures with new folds. In the fold recognition category, PROSPECT correctly identified 8 of a total of 22 and finished the sixth in the total scores among 127 assessed groups. In the "new fold" category, it found important structural features for most targets, and its overall performance is among the best of all prediction methods. Our CASP4 performance demonstrates that PROSPECT is a powerful tool to quickly characterize structures with new folds, and it may provide useful structural restraints for ab initio prediction methods.

Can a pairwise contact potential stabilize native protein folds against decoys obtained by threading?

We present a method to derive contact energy parameters from large sets of proteins. The basic requirement on which our method is based is that for each protein in the database the native contact map has lower energy than all its decoy conformations that are obtained by threading. Only when this condition is satisfied one can use the proposed energy function for fold identification. Such a set of parameters can be found (by perceptron learning) if Mp, the number of proteins in the database, is not too large. Other aspects that influence the existence of such a solution are the exact definition of contact and the value of the critical distance Rc, below which two residues are considered to be in contact. Another important novel feature of our approach is its ability to determine whether an energy function of some suitable proposed form can or cannot be parameterized in a way that satisfies our basic requirement. As a demonstration of this, we determine the region in the (Rc, Mp) plane in which the problem is solvable, i.e., we can find a set of contact parameters that stabilize simultaneously all the native conformations. We show that for large enough databases the contact approximation to the energy cannot stabilize all the native folds even against the decoys obtained by gapless threading.

Analysis of knowledge-based protein-ligand potentials using a self-consistent method.

We propose a self-consistent approach to analyze knowledge-based atom-atom potentials used to calculate protein-ligand binding energies. Ligands complexed to actual protein structures were first built using the SMoG growth procedure (DeWitte & Shakhnovich, 1996) with a chosen input potential. These model protein-ligand complexes were used to construct databases from which knowledge-based protein-ligand potentials were derived. We then tested several different modifications to such potentials and evaluated their performance on their ability to reconstruct the input potential using the statistical information available from a database composed of model complexes. Our data indicate that the most significant improvement resulted from properly accounting for the following key issues when estimating the reference state: (1) the presence of significant nonenergetic effects that influence the contact frequencies and (2) the presence of correlations in contact patterns due to chemical structure. The most successful procedure was applied to derive an atom-atom potential for real protein-ligand complexes. Despite the simplicity of the model (pairwise contact potential with a single interaction distance), the derived binding free energies showed a statistically significant correlation (approximately 0.65) with experimental binding scores for a diverse set of complexes.

Folding Lennard-Jones proteins by a contact potential.

We studied the possibility to approximate a Lennard-Jones interaction by a pairwise contact potential. First we used a Lennard-Jones potential to design off-lattice, protein-like heteropolymer sequences, whose lowest energy (native) conformations were then identified by molecular dynamics. Then we turned to investigate whether one can find a pairwise contact potential, whose ground states are the contact maps associated with these native conformations. We show that such a requirement cannot be satisfied exactly, i.e., no such contact parameters exist. Nevertheless, we found that one can find contact energy parameters for which an energy minimization procedure, acting in the space of contact maps, yields maps whose corresponding structures are close to the native ones. Finally, we show that when these structures are used as the initial point of a molecular dynamics energy minimization process, the correct native folds are recovered with high probability.

An empirical energy potential with a reference state for protein fold and sequence recognition

We consider modifications of an empirical energy potential for fold and sequence recognition to represent approximately the stabilities of proteins in various environments. A potential used here includes a secondary structure potential representing short-range interactions for secondary structures of proteins, and a tertiary structure potential consisting of a long-range, pairwise contact potential and a repulsive packing potential. This potential is devised to evaluate together the total conformational energy of a protein at the coarse grained residue level. It was previously estimated from the observed frequencies of secondary structures, from contact frequencies between residues, and from the distributions of the number of residues in contact in known protein structures by regarding those distributions as the equilibrium distributions with the Boltzmann factor of these interaction energies. The stability of native structures is assumed as a primary requirement for proteins to fold into their native structures. A collapse energy is subtracted from the contact energies to remove the protein size dependence and to represent protein stabilities for monomeric and multimeric states. The free energy of the whole ensemble of protein conformations that is subtracted from the conformational energy to represent protein stability is approximated as the average energy expected for a typical native structure with the same amino acid composition. This term may be constant in fold recognition but essentially varies in sequence recognition. A simple test of threading sequences into structures without gaps is employed to demonstrate the importance of the present modifications that permit the same potential to be utilized for both fold and sequence recognition. Proteins 1999;36:357-369. Published 1999 Wiley-Liss, Inc.

An empirical energy potential with a reference state for protein fold and sequence recognition

We consider modifications of an empirical energy potential for fold and sequence recognition to represent approximately the stabilities of proteins in various environments. A potential used here includes a secondary structure potential representing short-range interactions for secondary structures of proteins, and a tertiary structure potential consisting of a long-range, pairwise contact potential and a repulsive packing potential. This potential is devised to evaluate together the total conformational energy of a protein at the coarse grained residue level. It was previously estimated from the observed frequencies of secondary structures, from contact frequencies between residues, and from the distributions of the number of residues in contact in known protein structures by regarding those distributions as the equilibrium distributions with the Boltzmann factor of these interaction energies. The stability of native structures is assumed as a primary requirement for proteins to fold into their native structures. A collapse energy is subtracted from the contact energies to remove the protein size dependence and to represent protein stabilities for monomeric and multimeric states. The free energy of the whole ensemble of protein conformations that is subtracted from the conformational energy to represent protein stability is approximated as the average energy expected for a typical native structure with the same amino acid composition. This term may be constant in fold recognition but essentially varies in sequence recognition. A simple test of threading sequences into structures without gaps is employed to demonstrate the importance of the present modifications that permit the same potential to be utilized for both fold and sequence recognition. Proteins 1999;36:357–369. Published 1999 Wiley-Liss, Inc.