Delaunay‐based nonlocal interactions are sufficient and accurate in protein fold recognition

This study is aimed at showing that considering only nonlocal interactions (interactions of two atoms with a sequence separation larger than five amino acids) extracted using Delaunay tessellation is sufficient and accurate for protein fold recognition. An atomic knowledge‐based potential was extracted based on a Delaunay tessellation with 167 atom types from a sample of the native structures and the normalized energy was calculated for only nonlocal interactions in each structure. The performance of this method was tested on several decoy sets and compared to a method considering all interactions extracted by Delaunay tessellation and three other popular scoring functions. Features such as the contents of different types of interactions and atoms with the highest number of interactions were also studied. The results suggest that considering only nonlocal interactions in a Delaunay tessellation of protein structure is a discrete structure catching deep properties of the three‐dimensional protein data. Proteins 2014; 82:415–423. © 2013 Wiley Periodicals, Inc.     

Development of a four-body statistical pseudo-potential to discriminate native from non-native protein conformations

MOTIVATION: Most scoring functions used in protein fold recognition employ two-body (pseudo) potential energies. The use of higher-order terms may improve the performance of current algorithms. Methods: Proteins are represented by the side chain centroids of amino acids. Delaunay tessellation of this representation defines all sets of nearest neighbor quadruplets of amino acids. Four-body contact scoring function (log likelihoods of residue quadruplet compositions) is derived by the analysis of a diverse set of proteins with known structures. A test protein is characterized by the total score calculated as the sum of the individual log likelihoods of composing amino acid quadruplets. RESULTS: The scoring function distinguishes native from partially unfolded or deliberately misfolded structures. It also discriminates between pre- and post-transition state and native structures in the folding simulations trajectory of Chymotrypsin Inhibitor 2 (CI2).     

Sequence periodicity and secondary structure propensity in model proteins

We explore the question of whether local effects (originating from the amino acids intrinsic secondary structure propensities) or nonlocal effects (reflecting the sequence of amino acids as a whole) play a larger role in determining the fold of globular proteins. Earlier circular dichroism studies have shown that the pattern of polar, non polar amino acids (nonlocal effect) dominates over the amino acid intrinsic propensity (local effect) in determining the secondary structure of oligomeric peptides. In this article, we present a coarse grained computational model that allows us to quantitatively estimate the role of local and nonlocal factors in determining both the secondary and tertiary structure of small, globular proteins. The amino acid intrinsic secondary structure propensity is modeled by a dihedral potential term. This dihedral potential is parametrized to match with experimental measurements of secondary structure propensity. Similarly, the magnitude of the attraction between hydrophobic residues is parametrized to match the experimental transfer free energies of hydrophobic amino acids. Under these parametrization conditions, we systematically explore the degree of frustration a given polar, non polar pattern can tolerate when the secondary structure intrinsic propensities are in opposition to it. When the parameters are in the biophysically relevant range, we observe that the fold of small, globular proteins is determined by the pattern of polar, non polar amino acids regardless of their instrinsic secondary structure propensities. Our simulations shed new light on previous observations that tertiary interactions are more influential in determining protein structure than secondary structure propensity. The fact that this can be inferred using a simple polymer model that lacks most of the biochemical details points to the fundamental importance of binary patterning in governing folding.     

Self-complementarity within proteins: bridging the gap between binding and folding

Complementarity, in terms of both shape and electrostatic potential, has been quantitatively estimated at protein-protein interfaces and used extensively to predict the specific geometry of association between interacting proteins. In this work, we attempted to place both binding and folding on a common conceptual platform based on complementarity. To that end, we estimated (for the first time to our knowledge) electrostatic complementarity (Em) for residues buried within proteins. Em measures the correlation of surface electrostatic potential at protein interiors. The results show fairly uniform and significant values for all amino acids. Interestingly, hydrophobic side chains also attain appreciable complementarity primarily due to the trajectory of the main chain. Previous work from our laboratory characterized the surface (or shape) complementarity (Sm) of interior residues, and both of these measures have now been combined to derive two scoring functions to identify the native fold amid a set of decoys. These scoring functions are somewhat similar to functions that discriminate among multiple solutions in a protein-protein docking exercise. The performances of both of these functions on state-of-the-art databases were comparable if not better than most currently available scoring functions. Thus, analogously to interfacial residues of protein chains associated (docked) with specific geometry, amino acids found in the native interior have to satisfy fairly stringent constraints in terms of both Sm and Em. The functions were also found to be useful for correctly identifying the same fold for two sequences with low sequence identity. Finally, inspired by the Ramachandran plot, we developed a plot of Sm versus Em (referred to as the complementarity plot) that identifies residues with suboptimal packing and electrostatics which appear to be correlated to coordinate errors.     

Using a Hydrophobic Contact Potential to Evaluate Native and Near-native Folds Generated by Molecular Dynamics Simulations

There are several knowledge-based energy functions that can distinguish the native fold from a pool of grossly misfolded decoys for a given sequence of amino acids. These decoys, which are typically generated by mounting, or “threading”, the sequence onto the backbones of unrelated protein structures, tend to be non-compact and quite different from the native structure: the root-mean-squared (RMS) deviations from the native are commonly in the range of 15 to 20 Å. Effective energy functions should also demonstrate a similar recognition capability when presented with compact decoys that depart only slightly in conformation from the correct structure (i.e. those with RMS deviations of ∼5 Å or less). Recently, we developed a simple yet powerful method for native fold recognition based on the tendency for native folds to form hydrophobic cores. Our energy measure, which we call the hydrophobic fitness score, is challenged to recognize the native fold from 2000 near-native structures generated for each of five small monomeric proteins. First, 1000 conformations for each protein were generated by molecular dynamics simulation at room temperature. The average RMS deviation of this set of 5000 was 1.5 Å. A total of 323 decoys had energies lower than native; however, none of these had RMS deviations greater than 2 Å. Another 1000 structures were generated for each at high temperature, in which a greater range of conformational space was explored (4.3 Å average RMS deviation). Out of this set, only seven decoys were misrecognized. The hydrophobic fitness energy of a conformation is strongly dependent upon the RMS deviation. On average our potential yields energy values which are lowest for the population of structures generated at room temperature, intermediate for those produced at high temperature and highest for those constructed by threading methods. In general, the lowest energy decoy conformations have backbones very close to native structure. The possible utility of our method for screening backbone candidates for the purpose of modelling by side-chain packing optimization is discussed.     

A simple Cα-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C_α-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.     

Distance‐dependent classification of amino acids by information theory

Reduced amino acid alphabets are useful to understand molecular evolution as they reveal basal, shared properties of amino acids, which the structures and functions of proteins rely on. Several previous studies derived such reduced alphabets and linked them to the origin of life and biotechnological applications. However, all this previous work presupposes that only direct contacts of amino acids in native protein structures are relevant. We show in this work, using information–theoretical measures, that an appropriate alphabet reduction scheme is in fact a function of the maximum distance amino acids interact at. Although for small distances our results agree with previous ones, we show how long‐range interactions change the overall picture and prompt for a revised understanding of the protein design process. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Detecting local residue environment similarity for recognizing near‐native structure models

We developed a new representation of local amino acid environments in protein structures called the Side‐chain Depth Environment (SDE). An SDE defines a local structural environment of a residue considering the coordinates and the depth of amino acids that locate in the vicinity of the side‐chain centroid of the residue. SDEs are general enough that similar SDEs are found in protein structures with globally different folds. Using SDEs, we developed a procedure called PRESCO (Protein Residue Environment SCOre) for selecting native or near‐native models from a pool of computational models. The procedure searches similar residue environments observed in a query model against a set of representative native protein structures to quantify how native‐like SDEs in the model are. When benchmarked on commonly used computational model datasets, our PRESCO compared favorably with the other existing scoring functions in selecting native and near‐native models. Proteins 2014; 82:3255–3272. © 2014 Wiley Periodicals, Inc.     

Amino acid alphabet reduction preserves fold information contained in contact interactions in proteins

To reduce complexity, understand generalized rules of protein folding, and facilitate de novo protein design, the 20‐letter amino acid alphabet is commonly reduced to a smaller alphabet by clustering amino acids based on some measure of similarity. In this work, we seek the optimal alphabet that preserves as much of the structural information found in long‐range (contact) interactions among amino acids in natively‐folded proteins. We employ the Information Maximization Device, based on information theory, to partition the amino acids into well‐defined clusters. Numbering from 2 to 19 groups, these optimal clusters of amino acids, while generated automatically, embody well‐known properties of amino acids such as hydrophobicity/polarity, charge, size, and aromaticity, and are demonstrated to maintain the discriminative power of long‐range interactions with minimal loss of mutual information. Our measurements suggest that reduced alphabets (of less than 10) are able to capture virtually all of the information residing in native contacts and may be sufficient for fold recognition, as demonstrated by extensive threading tests. In an expansive survey of the literature, we observe that alphabets derived from various approaches—including those derived from physicochemical intuition, local structure considerations, and sequence alignments of remote homologs—fare consistently well in preserving contact interaction information, highlighting a convergence in the various factors thought to be relevant to the folding code. Moreover, we find that alphabets commonly used in experimental protein design are nearly optimal and are largely coherent with observations that have arisen in this work. Proteins 2015; 83:2198–2216. © 2015 Wiley Periodicals, Inc.     

A coarse‐grained potential for fold recognition and molecular dynamics simulations of proteins

A coarse‐grained potential for protein simulations and fold ranking is presented. The potential is based on a two‐point model of individual amino acids and a specific implementation of hydrogen bonding. Parameters are determined for distance dependent pair interactions, pseudo bonds, angles, and torsions. A scaling factor for a hydrogen bonding term is also determined. Iterative sampling for 4867 proteins reproduces distributions of internal coordinates and distances observed in the Protein Data Bank. The adjustment of the potential and resampling are in the spirit of the generalized ensemble approach. No native structure information (e.g., secondary structure) is used in the calculation of the potential or in the simulation of a particular protein. The potential is subject to two tests as follows: (i) simulations of 956 globular proteins in the neighborhood of their native folds (these proteins were not used in the training set) and (ii) discrimination between native and decoy structures for 2470 proteins with 305,000 decoys and the “Decoys ‘R’ Us” dataset. In the first test, 58% of tested proteins stay within 5 Å from the native fold in Molecular Dynamics simulations of more than 20 nanoseconds using the new potential. The potential is also useful in differentiating between correct and approximate folds providing significant signal for structure prediction algorithms. Sampling with the potential consistently regenerates the distribution of distances and internal coordinates it learned. Nevertheless, during Molecular Dynamics simulations structures are found that reproduce the learned distributions but are far from the native fold. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

How different from random are docking predictions when ranked by scoring functions?

Docking algorithms predict the structure of protein–protein interactions. They sample the orientation of two unbound proteins to produce various predictions about their interactions, followed by a scoring step to rank the predictions. We present a statistical assessment of scoring functions used to rank near‐native orientations, applying our statistical analysis to a benchmark dataset of decoys of protein–protein complexes and assessing the statistical significance of the outcome in the Critical Assessment of PRedicted Interactions (CAPRI) scoring experiment. A P value was assigned that depended on the number of near‐native structures in the sampling. We studied the effect of filtering out redundant structures and tested the use of pair‐potentials derived using ZDock and ZRank. Our results show that for many targets, it is not possible to determine when a successful reranking performed by scoring functions results merely from random choice. This analysis reveals that changes should be made in the design of the CAPRI scoring experiment. We propose including the statistical assessment in this experiment either at the preprocessing or the evaluation step. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

A simple probabilistic model of multibody interactions in proteins

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

Local interactions in protein folding determined through an inverse folding model

We adopt a model of inverse folding in which folding stability results from the combination of the hydrophobic effect with local interactions responsible for secondary structure preferences. Site-specific amino acid distributions can be calculated analytically for this model. We determine optimal parameters for the local interactions by fitting the complete inverse folding model to the site-specific amino acid distributions found in the Protein Data Bank. This procedure reduces drastically the influence on the derived parameters of the preference of different secondary structures for buriedness, which affects local interaction parameters determined through the standard approach based on amino acid propensities. The quality of the fit is evaluated through the likelihood of the observed amino acid distributions given the model and the Bayesian Information Criterion, which indicate that the model with optimal local interaction parameters is strongly preferable to the model where local interaction parameters are determined through propensities. The optimal model yields a mean correlation coefficient r = 0.96 between observed and predicted amino acid distributions. The local interaction parameters are then tested in threading experiments, in combination with contact interactions, for their capacity to recognize the native structure and structures similar to the native against unrelated ones. In a challenging test, proteins structurally aligned with the Mammoth algorithm are scored with the effective free energy function. The native structure gets the highest stability score in 100% of the cases, a high recognition rate comparable to that achieved against easier decoys generated by gapless threading. We then examine proteins for which at least one highly similar template exists. In 61% of the cases, the structure with the highest stability score excluding the native belongs to the native fold, compared to 60% if we use local interaction parameters derived from the usual amino acid propensities and 52% if we use only contact interactions. A highly similar structure is present within the five best stability scores in 82%, 81%, and 76% of the cases, for local interactions determined through inverse folding, through propensity, and set to zero, respectively. These results indicate that local interactions improve substantially the performances of contact free energy functions in fold recognition, and that similar structures tend to get high stability scores, although they are often not high enough to discriminate them from unrelated structures. This work highlights the importance to apply more challenging tests, as the recognition of homologous structures, for testing stability scores for protein folding.     

Local and nonlocal interactions in globular proteins and mechanisms of alcohol denaturation.

How important are helical propensities in determining the conformations of globular proteins? Using the two-dimensional lattice model and two monomer types, H (hydrophobic) and P (polar), we explore both nonlocal interactions, through an HH contact energy, as developed in earlier work, and local interactions, through a helix energy, σ. By computer enumeration, the partition functions for short chains are obtained without approximation for the full range of both types of energy. When nonlocal interactions dominate, some sequences undergo coil-globule collapse to a unique native structure. When local interactions dominate, all sequences undergo helix–coil transitions. For two different conformational properties, the closest correspondence between the lattice model and proteins in the Protein Data Bank is obtained if the model local interactions are made small compared to the HH contact interaction, suggesting that helical propensities may be only weak determinants of globular protein structures in water. For some HP sequences, varying σ/ leads to additional sharp transitions (sometimes several) and to “conformational switching” between unique conformations. This behavior resembles the transitions of globular proteins in water to helical states in alcohols. In particular, comparison with experiments shows that whereas urea as a denaturant is best modeled as weakening both local and nonlocal interactions, trifluoroethanol is best modeled as mainly weakening HH interactions and slightly enhancing local helical interactions.     

Distinguishing native conformations of proteins from decoys with an effective free energy estimator based on the OPLS all-atom force field and the Surface Generalized Born solvent model

Protein decoy data sets provide a benchmark for testing scoring functions designed for fold recognition and protein homology modeling problems. It is commonly believed that statistical potentials based on reduced atomic models are better able to discriminate native-like from misfolded decoys than scoring functions based on more detailed molecular mechanics models. Recent benchmark tests on small data sets, however, suggest otherwise. In this work, we report the results of extensive decoy detection tests using an effective free energy function based on the OPLS all-atom (OPLS-AA) force field and the Surface Generalized Born (SGB) model for the solvent electrostatic effects. The OPLS-AA/SGB effective free energy is used as a scoring function to detect native protein folds among a total of 48,832 decoys for 32 different proteins from Park and Levitt's 4-state-reduced, Levitt's local-minima, Baker's ROSETTA all-atom, and Skolnick's decoy sets. Solvent electrostatic effects are included through the Surface Generalized Born (SGB) model. All structures are locally minimized without restraints. From an analysis of the individual energy components of the OPLS-AA/SGB energy function for the native and the best-ranked decoy, it is determined that a balance of the terms of the potential is responsible for the minimized energies that most successfully distinguish the native from the misfolded conformations. Different combinations of individual energy terms provide less discrimination than the total energy. The results are consistent with observations that all-atom molecular potentials coupled with intermediate level solvent dielectric models are competitive with knowledge-based potentials for decoy detection and protein modeling problems such as fold recognition and homology modeling.     

Peptide fragment studies on the folding elements of dihydrofolate reductase from Escherichia coli

One of the necessary conditions for a protein to be foldable is the presence of a complete set of “folding elements” (FEs) that are short, contiguous peptide segments distributed over an amino acid sequence. The FE‐assembly model of protein folding has been proposed, in which the FEs play a role in guiding structure formation through FE–FE interactions early in folding. However, two major issues remain to be clarified regarding the roles of the FEs in determining protein foldability. Are the FEs AFUs that can form nativelike structures in isolation? Is the presence of only the FEs without mutual connections a sufficient condition for a protein to be foldable? Here, we address these questions using peptide fragments corresponding to the FEs of DHFR from Escherichia coli. We show by CD measurement that the FE peptides are unfolded under the native conditions, and some of them have the propensities toward non‐native helices. MD simulations also show the non‐native helical propensities of the peptides, and the helix contents estimated from the simulations are well correlated with those estimated from the CD in TFE. Thus, the FEs of DHFR are not AFUs, suggesting the importance of the FEs in nonlocal interactions. We also show that equimolar mixtures of the FE peptides do not induce any structural formation. Therefore, mutual connections between the FEs, which should strengthen the nonlocal FE–FE interactions, are also one of the necessary conditions for a protein to be foldable. Proteins 2006. © 2005 Wiley‐Liss, Inc.     

Can molecular dynamics simulations help in discriminating correct from erroneous protein 3D models?

Background  

Recent approaches for predicting the three-dimensional (3D) structure of proteins such asde novoor fold recognition methods mostly rely on simplified energy potential functions and a reduced representation of the polypeptide chain. These simplifications facilitate the exploration of the protein conformational space but do not permit to capture entirely the subtle relationship that exists between the amino acid sequence and its native structure. It has been proposed that physics-based energy functions together with techniques for sampling the conformational space, e.g., Monte Carlo or molecular dynamics (MD) simulations, are better suited to the task of modelling proteins at higher resolutions than those of models obtained with the former type of methods. In this study we monitor different protein structural properties along MD trajectories to discriminate correct from erroneous models. These models are based on the sequence-structure alignments provided by our fold recognition method, FROST. We define correct models as being built from alignments of sequences with structures similar to their native structures and erroneous models from alignments of sequences with structures unrelated to their native structures.     

Network properties of protein-decoy structures

Convergence of the vast sequence space of proteins into a highly restricted fold/conformational space suggests a simple yet unique underlying mechanism of protein folding that has been the subject of much debate in the last several decades. One of the major challenges related to the understanding of protein folding or in silico protein structure prediction is the discrimination of non-native structures/decoys from the native structure. Applications of knowledge-based potentials to attain this goal have been extensively reported in the literature. Also, scoring functions based on accessible surface area and amino acid neighbourhood considerations were used in discriminating the decoys from native structures. In this article, we have explored the potential of protein structure network (PSN) parameters to validate the native proteins against a large number of decoy structures generated by diverse methods. We are guided by two principles: (a) the PSNs capture the local properties from a global perspective and (b) inclusion of non-covalent interactions, at all-atom level, including the side-chain atoms, in the network construction accommodates the sequence dependent features. Several network parameters such as the size of the largest cluster, community size, clustering coefficient are evaluated and scored on the basis of the rank of the native structures and the Z-scores. The network analysis of decoy structures highlights the importance of the global properties contributing to the uniqueness of native structures. The analysis also exhibits that the network parameters can be used as metrics to identify the native structures and filter out non-native structures/decoys in a large number of data-sets; thus also has a potential to be used in the protein ‘structure prediction’ problem.     

Hydrophobic clusters in protein structures

Globular proteins fold such that the hydrophobic groups are packed inside forming hydrophobic clusters, and the hydrophilic groups are present on the surface. In this article we analyze clusters of hydrophobic groups of atoms in 781 protein structures selected from the PDB. Our analysis showed that every structure consists of two types of clusters: at least one large cluster that forms the hydrophobic core and probably dictates the protein fold; and numerous smaller clusters, which might be involved in the stabilization of the fold. We also analyzed the preference of the hydrophobic groups in each of the amino acids toward forming hydrophobic clusters. We find that hydrophobic groups from the hydrophilic amino acids also contribute toward cluster formation. Proteins 2008. © 2008 Wiley‐Liss, Inc.