Influence of protein structure databases on the predictive power of statistical pair potentials

DistAA: Database of amino acid distances in proteins and web application for statistical review of distances

Three-dimensional structure of a protein chain is determined by its amino acid interactions. One approach to the analysis of amino acid interactions refers to geometric distances of amino acid pairs in polypeptide chains. For a detailed analysis of the amino acid distances, the database with three types of amino acid distances in a set of chains was created. Web application Distances of Amino Acids has also been developed to enable scientists to explore interactions of amino acids with different properties based on distances stored in the database. Web application calculates and displays descriptive statistics and graphs of amino acid pair distances with selected properties, such as geometric distance threshold, corresponding SCOP class of proteins and secondary structure types. In addition to the analysis of pre-calculated distances stored in the database, the amino acid distances of a single protein with the specified PDB identifier can also be analyzed. The web application is available at http://andromeda.matf.bg.ac.rs/aadis_dynamic/.

Diverse effects of distance cutoff and residue interval on the performance of distance-dependent atom-pair potential in protein structure prediction

BACKGROUND

As one of the most successful knowledge-based energy functions, the distance-dependent atom-pair potential is widely used in all aspects of protein structure prediction, including conformational search, model refinement, and model assessment. During the last two decades, great efforts have been made to improve the reference state of the potential, while other factors that also strongly affect the performance of the potential have been relatively less investigated.

RESULTS

Based on different distance cutoffs (from 5 to 22 Å) and residue intervals (from 0 to 15) as well as six different reference states, we constructed a series of distance-dependent atom-pair potentials and tested them on several groups of structural decoy sets collected from diverse sources. A comprehensive investigation has been performed to clarify the effects of distance cutoff and residue interval on the potential's performance. Our results provide a new perspective as well as a practical guidance for optimizing distance-dependent statistical potentials.

CONCLUSIONS

The optimal distance cutoff and residue interval are highly related with the reference state that the potential is based on, the measurements of the potential's performance, and the decoy sets that the potential is applied to. The performance of distance-dependent statistical potential can be significantly improved when the best statistical parameters for the specific application environment are adopted.

Pairwise contact energy statistical potentials can help to find probability of point mutations

To adopt a particular fold, a protein requires several interactions between its amino acid residues. The energetic contribution of these residue-residue interactions can be approximated by extracting statistical potentials from known high resolution structures. Several methods based on statistical potentials extracted from unrelated proteins are found to make a better prediction of probability of point mutations. We postulate that the statistical potentials extracted from known structures of similar folds with varying sequence identity can be a powerful tool to examine probability of point mutation. By keeping this in mind, we have derived pairwise residue and atomic contact energy potentials for the different functional families that adopt the (α/β)₈ TIM-Barrel fold. We carried out computational point mutations at various conserved residue positions in yeast Triose phosphate isomerase enzyme for which experimental results are already reported. We have also performed molecular dynamics simulations on a subset of point mutants to make a comparative study. The difference in pairwise residue and atomic contact energy of wildtype and various point mutations reveals probability of mutations at a particular position. Interestingly, we found that our computational prediction agrees with the experimental studies of Silverman et al. (Proc Natl Acad Sci 2001;98:3092-3097) and perform better prediction than i_Mutant and Cologne University Protein Stability Analysis Tool. The present work thus suggests deriving pairwise contact energy potentials and molecular dynamics simulations of functionally important folds could help us to predict probability of point mutations which may ultimately reduce the time and cost of mutation experiments. Proteins 2016; 85:54-64. © 2016 Wiley Periodicals, Inc.

An Atomistic Statistically Effective Energy Function for Computational Protein Design

Shortcomings in the definition of effective free-energy surfaces of proteins are recognized to be a major contributory factor responsible for the low success rates of existing automated methods for computational protein design (CPD). The formulation of an atomistic statistically effective energy function (SEEF) suitable for a wide range of CPD applications and its derivation from structural data extracted from protein domains and protein-ligand complexes are described here. The proposed energy function comprises nonlocal atom-based and local residue-based SEEFs, which are coupled using a novel atom connectivity number factor to scale short-range, pairwise, nonbonded atomic interaction energies and a surface-area-dependent cavity energy term. This energy function was used to derive additional SEEFs describing the unfolded-state ensemble of any given residue sequence based on computed average energies for partially or fully solvent-exposed fragments in regions of irregular structure in native proteins. Relative thermal stabilities of 97 T4 bacteriophage lysozyme mutants were predicted from calculated energy differences for folded and unfolded states with an average unsigned error (AUE) of 0.84 kcal mol(-1) when compared to experiment. To demonstrate the utility of the energy function for CPD, further validation was carried out in tests of its capacity to recover cognate protein sequences and to discriminate native and near-native protein folds, loop conformers, and small-molecule ligand binding poses from non-native benchmark decoys. Experimental ligand binding free energies for a diverse set of 80 protein complexes could be predicted with an AUE of 2.4 kcal mol(-1) using an additional energy term to account for the loss in ligand configurational entropy upon binding. The atomistic SEEF is expected to improve the accuracy of residue-based coarse-grained SEEFs currently used in CPD and to extend the range of applications of extant atom-based protein statistical potentials.

Extracting knowledge from protein structure geometry

Protein structure prediction techniques proceed in two steps, namely the generation of many structural models for the protein of interest, followed by an evaluation of all these models to identify those that are native-like. In theory, the second step is easy, as native structures correspond to minima of their free energy surfaces. It is well known however that the situation is more complicated as the current force fields used for molecular simulations fail to recognize native states from misfolded structures. In an attempt to solve this problem, we follow an alternate approach and derive a new potential from geometric knowledge extracted from native and misfolded conformers of protein structures. This new potential, Metric Protein Potential (MPP), has two main features that are key to its success. Firstly, it is composite in that it includes local and nonlocal geometric information on proteins. At the short range level, it captures and quantifies the mapping between the sequences and structures of short (7-mer) fragments of protein backbones through the introduction of a new local energy term. The local energy term is then augmented with a nonlocal residue-based pairwise potential, and a solvent potential. Secondly, it is optimized to yield a maximized correlation between the energy of a structural model and its root mean square (RMS) to the native structure of the corresponding protein. We have shown that MPP yields high correlation values between RMS and energy and that it is able to retrieve the native structure of a protein from a set of high-resolution decoys.

Statistical potential for modeling and ranking of protein-ligand interactions

Applications in structural biology and medicinal chemistry require protein-ligand scoring functions for two distinct tasks: (i) ranking different poses of a small molecule in a protein binding site and (ii) ranking different small molecules by their complementarity to a protein site. Using probability theory, we developed two atomic distance-dependent statistical scoring functions: PoseScore was optimized for recognizing native binding geometries of ligands from other poses and RankScore was optimized for distinguishing ligands from nonbinding molecules. Both scores are based on a set of 8,885 crystallographic structures of protein-ligand complexes but differ in the values of three key parameters. Factors influencing the accuracy of scoring were investigated, including the maximal atomic distance and non-native ligand geometries used for scoring, as well as the use of protein models instead of crystallographic structures for training and testing the scoring function. For the test set of 19 targets, RankScore improved the ligand enrichment (logAUC) and early enrichment (EF(1)) scores computed by DOCK 3.6 for 13 and 14 targets, respectively. In addition, RankScore performed better at rescoring than each of seven other scoring functions tested. Accepting both the crystal structure and decoy geometries with all-atom root-mean-square errors of up to 2 Å from the crystal structure as correct binding poses, PoseScore gave the best score to a correct binding pose among 100 decoys for 88% of all cases in a benchmark set containing 100 protein-ligand complexes. PoseScore accuracy is comparable to that of DrugScore(CSD) and ITScore/SE and superior to 12 other tested scoring functions. Therefore, RankScore can facilitate ligand discovery, by ranking complexes of the target with different small molecules; PoseScore can be used for protein-ligand complex structure prediction, by ranking different conformations of a given protein-ligand pair. The statistical potentials are available through the Integrative Modeling Platform (IMP) software package (http://salilab.org/imp) and the LigScore Web server (http://salilab.org/ligscore/).

Protein structure modelling and evaluation based on a 4-distance description of side-chain interactions

Background

Accurate evaluation and modelling of residue-residue interactions within and between proteins is a key aspect of computational structure prediction including homology modelling, protein-protein docking, refinement of low-resolution structures, and computational protein design.

Results

Here we introduce a method for accurate protein structure modelling and evaluation based on a novel 4-distance description of residue-residue interaction geometry. Statistical 4-distance preferences were extracted from high-resolution protein structures and were used as a basis for a knowledge-based potential, called Hunter. We demonstrate that 4-distance description of side chain interactions can be used reliably to discriminate the native structure from a set of decoys. Hunter ranked the native structure as the top one in 217 out of 220 high-resolution decoy sets, in 25 out of 28 "Decoys 'R' Us" decoy sets and in 24 out of 27 high-resolution CASP7/8 decoy sets. The same concept was applied to side chain modelling in protein structures. On a set of very high-resolution protein structures the average RMSD was 1.47 Å for all residues and 0.73 Å for buried residues, which is in the range of attainable accuracy for a model. Finally, we show that Hunter performs as good or better than other top methods in homology modelling based on results from the CASP7 experiment. The supporting web site http://bioinfo.weizmann.ac.il/hunter/ was developed to enable the use of Hunter and for visualization and interactive exploration of 4-distance distributions.

Conclusions

Our results suggest that Hunter can be used as a tool for evaluation and for accurate modelling of residue-residue interactions in protein structures. The same methodology is applicable to other areas involving high-resolution modelling of biomolecules.

Adenosine A(2A) receptors in psychopharmacology: modulators of behavior, mood and cognition

The adenosine A(2A) receptor (A(2A)R) is in the center of a neuromodulatory network affecting a wide range of neuropsychiatric functions by interacting with and integrating several neurotransmitter systems, especially dopaminergic and glutamatergic neurotransmission. These interactions and integrations occur at multiple levels, including (1) direct receptor- receptor cross-talk at the cell membrane, (2) intracellular second messenger systems, (3) trans-synaptic actions via striatal collaterals or interneurons in the striatum, (4) and interactions at the network level of the basal ganglia. Consequently, A(2A)Rs constitute a novel target to modulate various psychiatric conditions. In the present review we will first summarize the molecular interaction of adenosine receptors with other neurotransmitter systems and then discuss the potential applications of A(2A)R agonists and antagonists in physiological and pathophysiological conditions, such as psychostimulant action, drug addiction, anxiety, depression, schizophrenia and learning and memory.

Information-theoretic analysis of the reference state in contact potentials used for protein structure prediction

Using information-theoretic concepts, we examine the role of the reference state, a crucial component of empirical potential functions, in protein fold recognition. We derive an information-based connection between the probability distribution functions of the reference state and those that characterize the decoy set used in threading. In examining commonly used contact reference states, we find that the quasi-chemical approximation is informatically superior to other variant models designed to include characteristics of real protein chains, such as finite length and variable amino acid composition from protein to protein. We observe that in these variant models, the total divergence, the operative function that quantifies discrimination, decreases along with threading performance. We find that any amount of nativeness encoded in the reference state model does not significantly improve threading performance. A promising avenue for the development of better potentials is suggested by our information-theoretic analysis of the action of contact potentials on individual protein sequences. Our results show that contact potentials perform better when the compositional properties of the data set used to derive the score function probabilities are similar to the properties of the sequence of interest. Results also suggest to use only sequences of similar composition in deriving contact potentials, to tailor the contact potential specifically for a test sequence.

Helix-sheet packing in proteins

The three-dimensional structure of a protein is organized around the packing of its secondary structure elements. Although much is known about the packing geometry observed between alpha-helices and between beta-sheets, there has been little progress on characterizing helix-sheet interactions. We present an analysis of the conformation of alphabeta(2) motifs in proteins, corresponding to all occurrences of helices in contact with two strands that are hydrogen bonded. The geometry of the alphabeta(2) motif is characterized by the azimuthal angle theta between the helix axis and an average vector representing the two strands, the elevation angle psi between the helix axis and the plane containing the two strands, and the distance D between the helix and the strands. We observe that the helix tends to align to the two strands, with a preference for an antiparallel orientation if the two strands are parallel; this preference is diminished for other topologies of the beta-sheet. Side-chain packing at the interface between the helix and the strands is mostly hydrophobic, with a preference for aliphatic amino acids in the strand and aromatic amino acids in the helix. From the knowledge of the geometry and amino acid propensities of alphabeta(2) motifs in proteins, we have derived different statistical potentials that are shown to be efficient in picking native-like conformations among a set of non-native conformations in well-known decoy datasets. The information on the geometry of alphabeta(2) motifs as well as the related statistical potentials have applications in the field of protein structure prediction.

Effective knowledge-based potentials

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.

Four distances between pairs of amino acids provide a precise description of their interaction

The three-dimensional structures of proteins are stabilized by the interactions between amino acid residues. Here we report a method where four distances are calculated between any two side chains to provide an exact spatial definition of their bonds. The data were binned into a four-dimensional grid and compared to a random model, from which the preference for specific four-distances was calculated. A clear relation between the quality of the experimental data and the tightness of the distance distribution was observed, with crystal structure data providing far tighter distance distributions than NMR data. Since the four-distance data have higher information content than classical bond descriptions, we were able to identify many unique inter-residue features not found previously in proteins. For example, we found that the side chains of Arg, Glu, Val and Leu are not symmetrical in respect to the interactions of their head groups. The described method may be developed into a function, which computationally models accurately protein structures.

Another look at the conditions for the extraction of protein knowledge-based potentials

Protein knowledge-based potentials are effective free energies obtained from databases of known protein structures. They are used to parameterize coarse-grained protein models in many folding simulation and structure prediction methods. Two common approaches are used in the derivation of knowledge-based potentials. One assumes that the energy parameters optimize the native structure stability. The other assumes that interaction events are related to their energies according to the Boltzmann distribution, and that they are distributed independently of other events, that is, the quasi-chemical approximation. Here, these assumptions are systematically tested by extracting contact energies from artificial databases of lattice proteins with predefined pairwise contact energies. Databases of protein sequences are designed to either satisfy the Boltzmann distribution at high or low temperatures, or to simultaneously optimize the native stability and folding kinetics. It is found that the quasi-chemical approximation, with the ideal reference state, accurately reproduce the true energies for high temperature Boltzmann distributed sequences (weakly interacting residues), but less accurately at low temperatures, where the sequences correspond to energy minima and the residues are strongly interacting. To overcome this problem, an iterative procedure for Boltzmann distributed sequences is introduced, which accounts for interacting residue correlations and eliminates the need for the quasi-chemical approximation. In this case, the energies are accurately reproduced at any ensemble temperature. However, when the database of sequences designed for optimal stability and kinetics is used, the energy correlation is less than optimal using either method, exhibiting random and systematic deviations from linearity. Therefore, the assumption that native structures are maximally stable or that sequences are determined according to the Boltzmann distribution seems to be inadequate for obtaining accurate energies. The limited number of sequences in the database and the inhomogeneous concentration of amino acids from one structure to another do not seem to be major obstacles for improving the quality of the extracted pairwise energies, with the exception of repulsive interactions.

Effects of amino acid composition, finite size of proteins, and sparse statistics on distance-dependent statistical pair potentials

Statistical distance dependent pair potentials are frequently used in a variety of folding, threading, and modeling studies of proteins. The applicability of these types of potentials is tightly connected to the reliability of statistical observations. We explored the possible origin and extent of false positive signals in statistical potentials by analyzing their distance dependence in a variety of randomized protein-like models. While on average potentials derived from such models are expected to equal zero at any distance, we demonstrate that systematic and significant distortions exist. These distortions originate from the limited statistical counts in local environments of proteins and from the limited size of protein structures at large distances. We suggest that these systematic errors in statistical potentials are connected to the dependence of amino acid composition on protein size and to variation in protein sizes. Additionally, atom-based potentials are dominated by a false positive signal that is due to correlation among distances measured from atoms of one residue to atoms of another residue. The significance of residue-based pairwise potentials at various spatial pair separations was assessed in this study and it was found that as few as approximately 50% of potential values were statistically significant at distances below 4 A, and only at most approximately 80% of them were significant at larger pair separations. A new definition for reference state, free of the observed systematic errors, is suggested. It has been demonstrated to generate statistical potentials that compare favorably to other publicly available ones.

Near-native structure refinement using in vacuo energy minimization

One of the greatest shortcomings of macromolecular energy minimization and molecular dynamics techniques is that they generally do not preserve the native structure of proteins as observed by x-ray crystallography. This deformation of the native structure means that these methods are not generally used to refine structures produced by homology-modeling techniques. Here, we use a database of 75 proteins to test the ability of a variety of popular molecular mechanics force fields to maintain the native structure. Minimization from the native structure is a weak test of potential energy functions: It is complemented by a much stronger test in which the same methods are compared for their ability to attract a near-native decoy protein structure toward the native structure. We use a powerfully convergent energy-minimization method and show that, of the traditional molecular mechanics potentials tested, only one showed a modest net improvement over a large data set of structurally diverse proteins. A smooth, differentiable knowledge-based pairwise atomic potential performs better on this test than traditional potential functions. This work is expected to have important implications for protein structure refinement, homology modeling, and structure prediction.

Statistical potential for assessment and prediction of protein structures

Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distance-dependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.

PIPER: an FFT-based protein docking program with pairwise potentials

The Fast Fourier Transform (FFT) correlation approach to protein-protein docking can evaluate the energies of billions of docked conformations on a grid if the energy is described in the form of a correlation function. Here, this restriction is removed, and the approach is efficiently used with pairwise interaction potentials that substantially improve the docking results. The basic idea is approximating the interaction matrix by its eigenvectors corresponding to the few dominant eigenvalues, resulting in an energy expression written as the sum of a few correlation functions, and solving the problem by repeated FFT calculations. In addition to describing how the method is implemented, we present a novel class of structure-based pairwise intermolecular potentials. The DARS (Decoys As the Reference State) potentials are extracted from structures of protein-protein complexes and use large sets of docked conformations as decoys to derive atom pair distributions in the reference state. The current version of the DARS potential works well for enzyme-inhibitor complexes. With the new FFT-based program, DARS provides much better docking results than the earlier approaches, in many cases generating 50% more near-native docked conformations. Although the potential is far from optimal for antibody-antigen pairs, the results are still slightly better than those given by an earlier FFT method. The docking program PIPER is freely available for noncommercial applications.

A new generation of statistical potentials for proteins

We propose a novel and flexible derivation scheme of statistical, database-derived, potentials, which allows one to take simultaneously into account specific correlations between several sequence and structure descriptors. This scheme leads to the decomposition of the total folding free energy of a protein into a sum of lower order terms, thereby giving the possibility to analyze independently each contribution and clarify its significance and importance, to avoid overcounting certain contributions, and to deal more efficiently with the limited size of the database. In addition, this derivation scheme appears as quite general, for many previously developed potentials can be expressed as particular cases of our formalism. We use this formalism as a framework to generate different residue-based energy functions, whose performances are assessed on the basis of their ability to discriminate genuine proteins from decoy models. The optimal potential is generated as a combination of several coupling terms, measuring correlations between residue types, backbone torsion angles, solvent accessibilities, relative positions along the sequence, and interresidue distances. This potential outperforms all tested residue-based potentials, and even several atom-based potentials. Its incorporation in algorithms aiming at predicting protein structure and stability should therefore substantially improve their performances.

A knowledge-based energy function for protein-ligand, protein-protein, and protein-DNA complexes

We developed a knowledge-based statistical energy function for protein-ligand, protein-protein, and protein-DNA complexes by using 19 atom types and a distance-scale finite ideal-gas reference (DFIRE) state. The correlation coefficients between experimentally measured protein-ligand binding affinities and those predicted by the DFIRE energy function are around 0.63 for one training set and two testing sets. The energy function also makes highly accurate predictions of binding affinities of protein-protein and protein-DNA complexes. Correlation coefficients between theoretical and experimental results are 0.73 for 82 protein-protein (peptide) complexes and 0.83 for 45 protein-DNA complexes, despite the fact that the structures of protein-protein (peptide) and protein-DNA complexes were not used in training the energy function. The results of the DFIRE energy function on protein-ligand complexes are compared to the published results of 12 other scoring functions generated from either physical-based, knowledge-based, or empirical methods. They include AutoDock, X-Score, DrugScore, four scoring functions in Cerius 2 (LigScore, PLP, PMF, and LUDI), four scoring functions in SYBYL (F-Score, G-Score, D-Score, and ChemScore), and BLEEP. While the DFIRE energy function is only moderately successful in ranking native or near native conformations, it yields the strongest correlation between theoretical and experimental binding affinities of the testing sets and between rmsd values and energy scores of docking decoys in a benchmark of 100 protein-ligand complexes. The parameters and the program of the all-atom DFIRE energy function are freely available for academic users at http://theory.med.buffalo.edu.

Database-derived potentials dependent on protein size for in silico folding and design

Knowledge-based potentials are widely used in simulations of protein folding, structure prediction, and protein design. Their advantages include limited computational requirements and the ability to deal with low-resolution protein models compatible with long-scale simulations. Their drawbacks comprehend their dependence on specific features of the dataset from which they are derived, such as the size of the proteins it contains, and their physical meaning is still a subject of debate. We address these issues by probing the theoretical validity of these potentials as mean-force potentials that take the solvent implicitly into account and involve entropic contributions due to atomic degrees of freedom and solvation. The dependence on the size of the system is checked on distance-dependent amino acid pair potentials, derived from six protein structure sets containing proteins of increasing length N. For large inter-residue distances, they are found to display the theoretically predicted 1/N behavior weighted by a factor depending on the boundaries and the compressibility of the system. For short distances, different trends are observed according to the nature of the residue pairs and their ability to form, for example, electrostatic, cation-pi or pi-pi interactions, or hydrophobic packing. The results of this analysis are used to devise a novel protein size-dependent distance potential, which displays an improved performance in discriminating native sequence-structure matches among decoy models.

The dependence of all-atom statistical potentials on structural training database

An accurate statistical energy function that is suitable for the prediction of protein structures of all classes should be independent of the structural database used for energy extraction. Here, two high-resolution, low-sequence-identity structural databases of 333 alpha-proteins and 271 beta-proteins were built for examining the database dependence of three all-atom statistical energy functions. They are RAPDF (residue-specific all-atom conditional probability discriminatory function), atomic KBP (atomic knowledge-based potential), and DFIRE (statistical potential based on distance-scaled finite ideal-gas reference state). These energy functions differ in the reference states used for energy derivation. The energy functions extracted from the different structural databases are used to select native structures from multiple decoys of 64 alpha-proteins and 28 beta-proteins. The performance in native structure selections indicates that the DFIRE-based energy function is mostly independent of the structural database whereas RAPDF and KBP have a significant dependence. The construction of two additional structural databases of alpha/beta and alpha + beta-proteins further confirmed the weak dependence of DFIRE on the structural databases of various structural classes. The possible source for the difference between the three all-atom statistical energy functions is that the physical reference state of ideal gas used in the DFIRE-based energy function is least dependent on the structural database.

Inter-residue interactions in protein folding and stability

During the process of protein folding, the amino acid residues along the polypeptide chain interact with each other in a cooperative manner to form the stable native structure. The knowledge about inter-residue interactions in protein structures is very helpful to understand the mechanism of protein folding and stability. In this review, we introduce the classification of inter-residue interactions into short, medium and long range based on a simple geometric approach. The features of these interactions in different structural classes of globular and membrane proteins, and in various folds have been delineated. The development of contact potentials and the application of inter-residue contacts for predicting the structural class and secondary structures of globular proteins, solvent accessibility, fold recognition and ab initio tertiary structure prediction have been evaluated. Further, the relationship between inter-residue contacts and protein-folding rates has been highlighted. Moreover, the importance of inter-residue interactions in protein-folding kinetics and for understanding the stability of proteins has been discussed. In essence, the information gained from the studies on inter-residue interactions provides valuable insights for understanding protein folding and de novo protein design.

Effect of chain connectivity on the structure of Lennard-Jones liquid and its implicationon statistical potentials for protein folding

Statistical contact potentials and bead-spring models have been widely used for computational studies of protein folding. However, there has been speculation that systematic error may arise in the contact energy calculations when the statistical potentials are deduced under the assumption that the chain connectivity in proteins can be ignored. To address this issue, we have performed molecular-dynamics simulations to study the structure and dynamics of a simple liquid system in which the beads are either connected or unconnected with springs. Results from the present study provide useful information for assessing the accuracy of the statistical potentials for protein structure simulations.

An Empirical Backbone−Backbone Hydrogen-Bonding Potential in Proteins and Its Applications to NMR Structure Refinement and Validation

A new multidimensional potential is described that encodes for the relative spatial arrangement of the peptidyl backbone units as observed within a large database of high-resolution X-ray structures. The detailed description afforded by such an analysis provides an opportunity to study the atomic details of hydrogen bonding in proteins. The specification of the corresponding potential of mean force (PMF) is based on a defined set of physical principles and optimized to yield the maximum advantage when applied to protein structure refinement. The observed intricate differences between hydrogen-bonding geometries within various patterns of secondary structure allow application of the PMF to both validation of protein structures and their refinement. A pronounced improvement of several aspects of structural quality is observed following the application of such a potential to a variety of NMR-derived models, including a noticeable decrease in backbone coordinate root-mean-square deviation relative to the X-ray structures and a considerable improvement in the Ramachandran map statistics.

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.

Statistical potentials for fold assessment

A protein structure model generally needs to be evaluated to assess whether or not it has the correct fold. To improve fold assessment, four types of a residue-level statistical potential were optimized, including distance-dependent, contact, Phi/Psi dihedral angle, and accessible surface statistical potentials. Approximately 10,000 test models with the correct and incorrect folds were built by automated comparative modeling of protein sequences of known structure. The criterion used to discriminate between the correct and incorrect models was the Z-score of the model energy. The performance of a Z-score was determined as a function of many variables in the derivation and use of the corresponding statistical potential. The performance was measured by the fractions of the correctly and incorrectly assessed test models. The most discriminating combination of any one of the four tested potentials is the sum of the normalized distance-dependent and accessible surface potentials. The distance-dependent potential that is optimal for assessing models of all sizes uses both C(alpha) and C(beta) atoms as interaction centers, distinguishes between all 20 standard residue types, has the distance range of 30 A, and is derived and used by taking into account the sequence separation of the interacting atom pairs. The terms for the sequentially local interactions are significantly less informative than those for the sequentially nonlocal interactions. The accessible surface potential that is optimal for assessing models of all sizes uses C(beta) atoms as interaction centers and distinguishes between all 20 standard residue types. The performance of the tested statistical potentials is not likely to improve significantly with an increase in the number of known protein structures used in their derivation. The parameters of fold assessment whose optimal values vary significantly with model size include the size of the known protein structures used to derive the potential and the distance range of the accessible surface potential. Fold assessment by statistical potentials is most difficult for the very small models. This difficulty presents a challenge to fold assessment in large-scale comparative modeling, which produces many small and incomplete models. The results described in this study provide a basis for an optimal use of statistical potentials in fold assessment.