Visualization analysis of inter-fragment interaction energies of CRP-cAMP-DNA complex based on the fragment molecular orbital method

A visualization method for inter-fragment interaction energies (IFIEs) of biopolymers is presented on the basis of the fragment molecular orbital (FMO) method. The IFIEs appropriately illustrate the information about the interaction energies between the fragments consisting of amino acids, nucleotides and other molecules. The IFIEs are usually analyzed in a matrix form called an IFIE matrix. Analyzing the IFIE matrix, we detect important fragments for the function of biomolecular systems and quantify the strength of interaction energies based on quantum chemistry, including the effects of charge transfer, electronic polarization and dispersion force. In this study, by analyzing a protein-DNA complex, we report a visual representation of the IFIE matrix, a so-called IFIE map. We comprehensively examine what information the IFIE map contains concerning structures and stabilities of the protein-DNA complex.     

Evolution and similarity evaluation of protein structures in contact map space

Prediction of fold from amino acid sequence of a protein has been an active area of research in the past few years, but the limited accuracy of existing techniques emphasizes the need to develop newer approaches to tackle this task. In this study, we use contact map prediction as an intermediate step in fold prediction from sequence. Contact map is a reduced graph-theoretic representation of proteins that models the local and global inter-residue contacts in the structure. We start with a population of random contact maps for the protein sequence and "evolve" the population to a "high-feasibility" configuration using a genetic algorithm. A neural network is employed to assess the feasibility of contact maps based on their 4 physically relevant properties. We also introduce 5 parameters, based on algebraic graph theory and physical considerations, that can be used to judge the structural similarity between proteins through contact maps. To predict the fold of a given amino acid sequence, we predict a contact map that will sufficiently approximate the structure of the corresponding protein. Then we assess the similarity of this contact map with the representative contact map of each fold; the fold that corresponds to the closest match is our predicted fold for the input sequence. We have found that our feasibility measure is able to differentiate between feasible and infeasible contact maps. Further, this novel approach is able to predict the folds from sequences significantly better than a random predictor.     

Prediction of the location of structural domains in globular proteins

The location of structural domains in proteins is predicted from the amino acid sequence, based on the analysis of a computed contact map for the protein, the average distance map (ADM). Interactions between residues i and j in a protein are subdivided into several ranges, according to the separation |i-j| in the amino acid sequence. Within each range, average spatial distances between every pair of amino acid residues are computed from a data base of known protein structures. Infrequently occurring pairs are omitted as being statistically insignificant. The average distances are used to construct a predicted ADM. The ADM is analyzed for the occurrence of regions with high densities of contacts (compact regions). Locations of rapid changes of density between various parts of the map are determined by the use of scanning plots of contact densities. These locations serve to pinpoint the distribution of compact regions. This distribution, in turn, is used to predict boundaries of domains in the protein. The technique provides an objective method for the location of domains both on a contact map derived from a known three-dimensional protein structure, the real distance map (RDM), and on an ADM. While most other published methods for the identification of domains locate them in the known three-dimensional structure of a protein, the technique presented here also permits the prediction of domains in proteins of unknown spatial structure, as the construction of the ADM for a given protein requires knowledge of only its amino acid sequence.     

Driving Forces for Transmembrane α-Helix Oligomerization

We present what we believe to be a novel statistical contact potential based on solved structures of transmembrane (TM) α-helical bundles, and we use this contact potential to investigate the amino acid likelihood of stabilizing helix-helix interfaces. To increase statistical significance, we have reduced the full contact energy matrix to a four-flavor alphabet of amino acids, automatically determined by our methodology, in which we find that polarity is a more dominant factor of group identity than is size, with charged or polar groups most often occupying the same face, whereas polar/apolar residue pairs tend to occupy opposite faces. We found that the most polar residues strongly influence interhelical contact formation, although they occur rarely in TM helical bundles. Two-body contact energies in the reduced letter code are capable of determining native structure from a large decoy set for a majority of test TM proteins, at the same time illustrating that certain higher-order sequence correlations are necessary for more accurate structure predictions.     

Folding Pathways of a Knotted Protein with a Realistic Atomistic Force Field

We report on atomistic simulation of the folding of a natively-knotted protein, MJ0366, based on a realistic force field. To the best of our knowledge this is the first reported effort where a realistic force field is used to investigate the folding pathways of a protein with complex native topology. By using the dominant-reaction pathway scheme we collected about 30 successful folding trajectories for the 82-amino acid long trefoil-knotted protein. Despite the dissimilarity of their initial unfolded configuration, these trajectories reach the natively-knotted state through a remarkably similar succession of steps. In particular it is found that knotting occurs essentially through a threading mechanism, involving the passage of the C-terminal through an open region created by the formation of the native -sheet at an earlier stage. The dominance of the knotting by threading mechanism is not observed in MJ0366 folding simulations using simplified, native-centric models. This points to a previously underappreciated role of concerted amino acid interactions, including non-native ones, in aiding the appropriate order of contact formation to achieve knotting.     

Analyses of protein sequences using inter-residue average distance statistics to study folding processes and the significance of their partial sequences

One of the goals of molecular bioinformatics is decoding amino acid sequences to extract information on the principles of protein folding. However, this is difficult to perform with standard bioinformatics techniques such as multiple sequence alignment and so on. Thus, we propose a technique based on inter-residue average distance statistics to make predictions regarding the protein folding mechanisms of amino acid sequences. Our method involves constructing a kind of predicted contact map called an Average Distance Map (ADM) based on average distance statistics to pinpoint regions of possible folding nuclei for proteins. Only information on the amino acid sequence of a given protein is required for the present method. In this article, we summarize the results of studies using our method to analyze how specific protein sequences affect folding properties. In particular, we present studies on proteins in the phage lysozyme, such as the globin, fatty acid binding protein-like, and the cupredoxin-like fold families. In the present review, we characterize the 3D architectures of these proteins through the properties of the protein ADMs. Furthermore, we combine the information on the conserved residues within the regions predicted by the ADMs with our results obtained so far. Such information may help identify the folding characteristics of each protein. We discuss this possibility in the present review.     

The helical hairpin structure of the influenza fusion peptide can be seen on a hydrophobic moment map

An assignment of the helical hairpin of the influenza fusion peptide has been made based on the hydrophobic moments, represented in a form of two-dimensional map. Such assignment holds for all serotypes, even for the cases of mutations altering the amino acid character. Similar results are obtained for the experimentally developed hydrophobicity scales, whose values reflect the transfer energies between aqueous and membrane environments. A distinct, however still structure-related hydrophobic map corresponds to a helical and contiguous HIV gp41 fp. The method may be used as a simple tool for sequence-based prediction of structures adopted by viral fusion peptides.     

Prediction of probable pathways of folding in globular proteins

A method is described for the prediction of probable folding pathways of globular proteins, based on the analysis of distance maps. It is applicable to proteins of unknown spatial structure but known amino acid sequence as well as to proteins of known structure. It is based on an objective procedure for the determination of the boundary of compact regions that contain high densities of interresidue contacts on the distance map of a globular protein. The procedure can be used both with contact maps derived from a known three-dimensional protein structure and with predicted contact maps computed by means of a statistical procedure from the amino acid sequence alone. The computed contact map can also be used to predict the location of compact short-range structures, viz. -helices and -turns, thereby complementing other statistical predictive procedures. The method provides an objective basis for the derivation of a theoretically predicted pathway of protein folding, proposed by us earlier [Tanaka and Scheraga (1977) Macromolecules10, 291–304; Némethy and Scheraga (1979) Proc. Natl. Acad. Sci., U.S.A.76, 6050–6054].     

Can contact potentials reliably predict stability of proteins?

The simplest approximation of interaction potential between amino acid residues in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein's thermodynamic stabilities (DeltaDeltaG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental (DeltaDeltaG) values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters may yield reliable predictions of DeltaDeltaG for datasets of mutations confined to the same amino acid positions in the sequence of a single protein.     

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.     

Information and discrimination in pairwise contact potentials

We examine the information-theoretic characteristics of statistical potentials that describe pairwise long-range contacts between amino acid residues in proteins. In our work, we seek to map out an efficient information-based strategy to detect and optimally utilize the structural information latent in empirical data, to make contact potentials, and other statistically derived folding potentials, more effective tools in protein structure prediction. Foremost, we establish fundamental connections between basic information-theoretic quantities (including the ubiquitous Z-score) and contact "energies" or scores used routinely in protein structure prediction, and demonstrate that the informatic quantity that mediates fold discrimination is the total divergence. We find that pairwise contacts between residues bear a moderate amount of fold information, and if optimized, can assist in the discrimination of native conformations from large ensembles of native-like decoys. Using an extensive battery of threading tests, we demonstrate that parameters that affect the information content of contact potentials (e.g., choice of atoms to define residue location and the cut-off distance between pairs) have a significant influence in their performance in fold recognition. We conclude that potentials that have been optimized for mutual information and that have high number of score events per sequence-structure alignment are superior in identifying the correct fold. We derive the quantity "information product" that embodies these two critical factors. We demonstrate that the information product, which does not require explicit threading to compute, is as effective as the Z-score, which requires expensive decoy threading to evaluate. This new objective function may be able to speed up the multidimensional parameter search for better statistical potentials. Lastly, by demonstrating the functional equivalence of quasi-chemically approximated "energies" to fundamental informatic quantities, we make statistical potentials less dependent on theoretically tenuous biophysical formalisms and more amenable to direct bioinformatic optimization.     

A combined bioinformatic approach oriented to the analysis and design of peptides with high affinity to MHC class I molecules

We report on a new method to compute the antigenic degree of peptides from available experimental data on peptide binding affinity to class I MHC molecules. The methodology is a combination of two strategies at different levels of information. The first, at the primary structure level, consists in expressing the peptides binding activity as a profile of amino acid contributions, amino acid similarity being accounted for by their characteristic physicochemical properties and their position within the sequence. The higher level of the strategy is based on a meticulous analysis of the contact interface of the peptides with the cleft constituting the receptor region of a particular class I MHC molecule. Interaction interfaces are inferred by docking the peptide onto the receptor groove of the MHC molecule; evaluation of the affinity of the peptide to the receptor is then performed by analysis of the electrostatic and hydrophobic energies on points of the interaction interface.The result is a robust system for analysis of peptide affinity to class I MHC molecules since while the first analysis dictates the composition of active sequences at the amino acid level, the second translates this information to the atomic level, where the molecular interaction can be analyzed in terms of the intrinsic interatomic forces and energies. Evaluation results for the methodology are encouraging since high affinity peptides are reflected by high scores at both levels of information, and are proportionally lower for peptides of medium and lower affinity for which interaction surfaces show relatively lower electrostatic complementarity and hydrophobic correlation than for the former.     

Pair potentials for protein folding: choice of reference states and sensitivity of predicted native states to variations in the interaction schemes

We examine the similarities and differences between two widely used knowledge-based potentials, which are expressed as contact matrices (consisting of 210 elements) that gives a scale for interaction energies between the naturally occurring amino acid residues. These are the Miyazawa-Jernigan contact interaction matrix M and the potential matrix S derived by Skolnick J et al., 1997, Protein Sci 6:676-688. Although the correlation between the two matrices is good, there is a relatively large dispersion between the elements. We show that when Thr is chosen as a reference solvent within the Miyazawa and Jernigan scheme, the dispersion between the M and S matrices is reduced. The resulting interaction matrix B gives hydrophobicities that are in very good agreement with experiment. The small dispersion between the S and B matrices, which arises due to differing reference states, is shown to have dramatic effect on the predicted native states of lattice models of proteins. These findings and other arguments are used to suggest that for reliable predictions of protein structures, pairwise additive potentials are not sufficient. We also establish that optimized protein sequences can tolerate relatively large random errors in the pair potentials. We conjecture that three body interaction may be needed to predict the folds of proteins in a reliable manner.     

A New Method to Characterize Hydrophobic Organization of Proteins: Application to Rational Protein Engineering of Barnase

Abstract

We present a new algorithm for characterization of protein spatial structure basing on the molecular hydrophobicity potential approach. The method is illustrated by the analysis of three-dimensional structure of barnase and barnase-barstar complex. Current approach enables identification of amino acid residues situated in unfavorable environment (these residues may be “active” for binding), and to map quantitatively hydrophobic, hydrophilic and unfavorable hydrophobic-hydrophilic intra-and inter-molecular contacts involving backbone and side-chain segments of amino acid residues. Calculation of individual contributions of amino acid residues to such contacts permits identification of structurally-important residues. The contact plots obtained with molecular hydrophobicity potential calculations, provide easy rules to choose sites for mutations, which can increase a strength of intra- or inter-molecular hydrophobic interactions. The unfavorable hydrophobic-hydrophilic contact can be mutated to favorable hydrophobic, and already existing weak hydrophobic contact can be strengthen by increasing hydrophobicity of residues in contact. Basing on the analysis of the contact plots, we suggest several mutations of barnase which are supposed to increase intramolecular hydrophobic interactions, and thus might lead to increased stability of the protein. Part of these mutations was studied previously experimentally, and indeed stabilized barnase. The other of predicted mutations were not studied experimentally yet. Several new mutations of barnase and barstar are also proposed to enhance the hydrophobic interactions on their binding interface.     

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 × 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.     

Atomic solvation parameters in the analysis of protein-protein docking results.

Several sets of amino acid surface areas and transfer free energies were used to derive a total of nine sets of atomic solvation parameters (ASPs). We tested the accuracy of each of these sets of parameters in predicting the experimentally determined transfer free energies of the amino acid derivatives from which the parameters were derived. In all cases, the calculated and experimental values correlated well. We then chose three parameter sets and examined the effect of adding an energetic correction for desolvation based on these three parameter sets to the simple potential function used in our multiple start Monte Carlo docking method. A variety of protein-protein interactions and docking results were examined. In the docking simulations studied, the desolvation correction was only applied during the final energy calculation of each simulation. For most of the docking results we analyzed, the use of an octanol-water-based ASP set marginally improved the energetic ranking of the low-energy dockings, whereas the other ASP sets we tested disturbed the ranking of the low-energy dockings in many of the same systems. We also examined the correlation between the experimental free energies of association and our calculated interaction energies for a series of proteinase-inhibitor complexes. Again, the octanol-water-based ASP set was compatible with our standard potential function, whereas ASP sets derived from other solvent systems were not.     

A machine learning based method for the prediction of G protein-coupled receptor-binding PDZ domain proteins

G protein-coupled receptors (GPCRs) are part of multi-protein networks called ‘receptosomes’. These GPCR interacting proteins (GIPs) in the receptosomes control the targeting, trafficking and signaling of GPCRs. PDZ domain proteins constitute the largest protein family among the GIPs, and the predominant function of the PDZ domain proteins is to assemble signaling pathway components into close proximity by recognition of the last four C-terminal amino acids of GPCRs. We present here a machine learning based approach for the identification of GPCR-binding PDZ domain proteins. In order to characterize the network of interactions between amino acid residues that contribute to the stability of the PDZ domain-ligand complex and to encode the complex into a feature vector, amino acid contact matrices and physicochemical distance matrix were constructed and adopted. This novel machine learning based method displayed high performance for the identification of PDZ domain-ligand interactions and allowed the identification of novel GPCR-PDZ domain protein interactions.     

Main-chain conformational tendencies of amino acids

A Ramachandran plot is a visual representation of the main-chain conformational tendencies of an amino acid. Despite forty years of research, the shape of Ramachandran plots is still a matter of debate. The issue in making a Ramachandran plot based on experimental data is deciding whether sparse data represent genuine conformations. We present here a simple solution to settle the ambiguities of the sparse data, and explain how we verified the accuracies of our plots using an independent dataset. To obtain our results, we then measured the pair-wise distances of main-chain conformational tendencies among amino acids, and showed that the conformational relationships of amino acids are well preserved in a two-dimensional map, leading to the conclusion that the conformational diversity space of amino acids is largely two dimensional. We further noticed that amino acids in early and late evolutionary stages are located in different zones in the two-dimensional map. In addition to these conclusions, we here present an amino acid substitution table derived from experimental data.     

Solvent accessibility, residue charge and residue volume, the three ingredients of a robust amino acid substitution matrix

Cost measure matrices or different amino acid indices have been widely used for studies in many fields of biology. One major criticism of these studies might be based on the unavailability of an unbiased and yet effective amino acid substitution matrix. Throughout this study we have devised a cost measure matrix based on the solvent accessibility, residue charge, and residue volume indices. Performed analyses on this novel substitution matrix (i.e. solvent accessibility charge volume (SCV) matrix) support the uncontaminated nature of this matrix regarding the genetic code. Although highly similar to a number of previously available cost measure matrices, the SCV matrix results in a more significant optimality in the error-buffering capacity of the genetic code when compared to many other amino acid substitution matrices. Besides, a method to compare an SCV-based scoring matrix with a number of widely used matrices has been devised, the results of which highlights the robustness of this matrix in protein family discrimination.