Discriminative ability with respect to amino acid types: assessing the performance of knowledge-based potentials without threading

We present a novel method designed to analyze the discriminative ability of knowledge-based potentials with respect to the 20 residue types. The method is based on the preference of amino acids for specific types of protein environment, and uses a virtual mutagenesis experiment to estimate how much information a given potential can provide about environments of each amino acid type. This allows one to test and optimize the performance of real potentials at the level of individual amino acids, using actual data on residue environments from a dataset of known protein structures. We have applied our method to long-range and medium-range pairwise distance-dependent potentials. The results of our study indicate that these potentials are only able to discriminate between a very limited number of residue types, and that discriminative ability is extremely sensitive to the choice of parameters used to construct the potentials, and even to the size of the training dataset. We also show that different types of pairwise distance potentials are dominated by different types of interactions. These dominant interactions strongly depend on the type of approximation used to define residue position. For each potential, our methodology is able to identify a potential-specific amino acid distance matrix and a reduced amino acid alphabet of any specified size, which may have implications for sequence alignment and multibody models.     

Geometric cooperativity and anticooperativity of three-body interactions in native proteins

Characterizing multibody interactions of hydrophobic, polar, and ionizable residues in protein is important for understanding the stability of protein structures. We introduce a geometric model for quantifying 3-body interactions in native proteins. With this model, empirical propensity values for many types of 3-body interactions can be reliably estimated from a database of native protein structures, despite the overwhelming presence of pairwise contacts. In addition, we define a nonadditive coefficient that characterizes cooperativity and anticooperativity of residue interactions in native proteins by measuring the deviation of 3-body interactions from 3 independent pairwise interactions. It compares the 3-body propensity value from what would be expected if only pairwise interactions were considered, and highlights the distinction of propensity and cooperativity of 3-body interaction. Based on the geometric model, and what can be inferred from statistical analysis of such a model, we find that hydrophobic interactions and hydrogen-bonding interactions make nonadditive contributions to protein stability, but the nonadditive nature depends on whether such interactions are located in the protein interior or on the protein surface. When located in the interior, many hydrophobic interactions such as those involving alkyl residues are anticooperative. Salt-bridge and regular hydrogen-bonding interactions, such as those involving ionizable residues and polar residues, are cooperative. When located on the protein surface, these salt-bridge and regular hydrogen-bonding interactions are anticooperative, and hydrophobic interactions involving alkyl residues become cooperative. We show with examples that incorporating 3-body interactions improves discrimination of protein native structures against decoy conformations. In addition, analysis of cooperative 3-body interaction may reveal spatial motifs that can suggest specific protein functions.     

Towards understanding the crosstalk between protein post‐translational modifications: Homo‐ and heterotypic PTM pair distances on protein surfaces are not random

Post‐translational modifications (PTMs) represent an important regulatory layer influencing the structure and function of proteins. With broader availability of experimental information on the occurrences of different PTM types, the investigation of a potential “crosstalk” between different PTM types and combinatorial effects have moved into the research focus. Hypothesizing that relevant interferences between different PTM types and sites may become apparent when investigating their mutual physical distances, we performed a systematic survey of pairwise homo‐ and heterotypic distances of seven frequent PTM types considering their sequence and spatial distances in resolved protein structures. We found that actual PTM site distance distributions differ from random distributions with most PTM type pairs exhibiting larger than expected distances with the exception of homotypic phosphorylation site distances and distances between phosphorylation and ubiquitination sites that were found to be closer than expected by chance. Random reference distributions considering canonical acceptor amino acid residues only were found to be shifted to larger distances compared to distances between any amino acid residue type indicating an underlying tendency of PTM‐amenable residue types to be further apart than randomly expected. Distance distributions based on sequence separations were found largely consistent with their spatial counterparts suggesting a primary role of sequence‐based pairwise PTM‐location encoding rather than folding‐mediated effects. Our analysis provides a systematic and comprehensive overview of the characteristics of pairwise PTM site distances on proteins and reveals that, predominantly, PTM sites tend to avoid close proximity with the potential implication that an independent attachment or removal of PTMs remains possible. Proteins 2016; 85:78–92. © 2016 Wiley Periodicals, Inc.     

Interpretable pairwise distillations for generative protein sequence models

Many different types of generative models for protein sequences have been proposed in literature. Their uses include the prediction of mutational effects, protein design and the prediction of structural properties. Neural network (NN) architectures have shown great performances, commonly attributed to the capacity to extract non-trivial higher-order interactions from the data. In this work, we analyze two different NN models and assess how close they are to simple pairwise distributions, which have been used in the past for similar problems. We present an approach for extracting pairwise models from more complex ones using an energy-based modeling framework. We show that for the tested models the extracted pairwise models can replicate the energies of the original models and are also close in performance in tasks like mutational effect prediction. In addition, we show that even simpler, factorized models often come close in performance to the original models.     

Long- and short-range interactions in native protein structures are consistent/minimally frustrated in sequence space

We show that long- and short-range interactions in almost all protein native structures are actually consistent with each other for coarse-grained energy scales; specifically we mean the long-range inter-residue contact energies and the short-range secondary structure energies based on peptide dihedral angles, which are potentials of mean force evaluated from residue distributions observed in protein native structures. This consistency is observed at equilibrium in sequence space rather than in conformational space. Statistical ensembles of sequences are generated by exchanging residues for each of 797 protein native structures with the Metropolis method. It is shown that adding the other category of interaction to either the short- or long-range interactions decreases the means and variances of those energies for essentially all protein native structures, indicating that both interactions consistently work by more-or-less restricting sequence spaces available to one of the interactions. In addition to this consistency, independence by these interaction classes is also indicated by the fact that there are almost no correlations between them when equilibrated using both interactions and significant but small, positive correlations at equilibrium using only one of the interactions. Evidence is provided that protein native sequences can be regarded approximately as samples from the statistical ensembles of sequences with these energy scales and that all proteins have the same effective conformational temperature. Designing protein structures and sequences to be consistent and minimally frustrated among the various interactions is a most effective way to increase protein stability and foldability.     

Interspecific interactions and range limits: contrasts among interaction types

There is a great deal of interest in the effects of biotic interactions on geographic distributions. Nature contains many different types of biotic interactions (notably mutualism, commensalism, predation, amensalism, and competition), and it is difficult to compare the effects of multiple interaction types on species’ distributions. To resolve this problem, we analyze a general, flexible model of pairwise biotic interactions that can describe all interaction types. In the absence of strong positive feedback, a species’ ability to be present depends on its ability to increase in numbers when it is rare and the species it is interacting with is at equilibrium. This insight leads to counterintuitive conclusions. Notably, we often predict the same range limit when the focal species experiences competition, predation, or amensalism. Similarly, we often predict the same range margin or when the species experiences mutualism, commensalism, or benefits from prey. In the presence of strong positive density-dependent feedback, different species interactions produce different range limits in our model. In all cases, the abiotic environment can indirectly influence the impact of biotic interactions on range limits. We illustrate the implications of this observation by analyzing a stress gradient where biotic interactions are harmful in benign environments but beneficial in stressful environments. Our results emphasize the need to consider the effects of all biotic interactions on species’ range limits and provide a systematic comparison of when biotic interactions affect distributions.     

TOUCHSTONEX: protein structure prediction with sparse NMR data

TOUCHSTONEX, a new method for folding proteins that uses a small number of long-range contact restraints derived from NMR experimental NOE (nuclear Overhauser enhancement) data, is described. The method employs a new lattice-based, reduced model of proteins that explicitly represents C(alpha), C(beta), and the sidechain centers of mass. The force field consists of knowledge-based terms to produce protein-like behavior, including various short-range interactions, hydrogen bonding, and one-body, pairwise, and multibody long-range interactions. Contact restraints were incorporated into the force field as an NOE-specific pairwise potential. We evaluated the algorithm using a set of 125 proteins of various secondary structure types and lengths up to 174 residues. Using N/8 simulated, long-range sidechain contact restraints, where N is the number of residues, 108 proteins were folded to a C(alpha)-root-mean-square deviation (RMSD) from native below 6.5 A. The average RMSD of the lowest RMSD structures for all 125 proteins (folded and unfolded) was 4.4 A. The algorithm was also applied to limited experimental NOE data generated for three proteins. Using very few experimental sidechain contact restraints, and a small number of sidechain-main chain and main chain-main chain contact restraints, we folded all three proteins to low-to-medium resolution structures. The algorithm can be applied to the NMR structure determination process or other experimental methods that can provide tertiary restraint information, especially in the early stage of structure determination, when only limited data are available.     

An atomic environment potential for use in protein structure prediction

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

Helix-helix packing and interfacial pairwise interactions of residues in membrane proteins

Helix-helix packing plays a critical role in maintaining the tertiary structures of helical membrane proteins. By examining the overall distribution of voids and pockets in the transmembrane (TM) regions of helical membrane proteins, we found that bacteriorhodopsin and halorhodopsin are the most tightly packed, whereas mechanosensitive channel is the least tightly packed. Large residues F, W, and H have the highest propensity to be in a TM void or a pocket, whereas small residues such as S, G, A, and T are least likely to be found in a void or a pocket. The coordination number for non-bonded interactions for each of the residue types is found to correlate with the size of the residue. To assess specific interhelical interactions between residues, we have developed a new computational method to characterize nearest neighboring atoms that are in physical contact. Using an atom-based probabilistic model, we estimate the membrane helical interfacial pairwise (MHIP) propensity. We found that there are many residue pairs that have high propensity for interhelical interactions, but disulfide bonds are rarely found in the TM regions. The high propensity pairs include residue pairs between an aromatic residue and a basic residue (W-R, W-H, and Y-K). In addition, many residue pairs have high propensity to form interhelical polar-polar atomic contacts, for example, residue pairs between two ionizable residues, between one ionizable residue and one N or Q. Soluble proteins do not share this pattern of diverse polar-polar interhelical interaction. Exploratory analysis by clustering of the MHIP values suggests that residues similar in side-chain branchness, cyclic structures, and size tend to have correlated behavior in participating interhelical interactions. A chi-square test rejects the null hypothesis that membrane protein and soluble protein have the same distribution of interhelical pairwise propensity. This observation may help us to understand the folding mechanism of membrane proteins.     

Quantitative organization of the known protein x-ray structures. I. Methods and short-length-scale results

We address herein the problem of delineating the relationships between the known protein structures. In order to study this problem, methods have been developed to represent arbitrarily sized fragments of biopolymer backbone, and to compare distributions of such fragments. These methods are applied to a classification of 123 structures representing the entire set of known x-ray structures. The resulting data are analyzed (on the four-C alpha length scale) to determine both the large-scale organization of the set of known structures (i.e., the relationships between large groups of structures, each comprised of proteins that are structurally related) and its local structure (i.e., the quantitative degree of similarity between any two specific structures). It is shown that the set of structures forms a continuum of structural types, ranging from all-helical to all-sheet/barrel proteins. It is further demonstrated that the density of protein structures is not uniform across this continuum, but rather that structures cluster in certain regions, separated by regions of lower population. The properties of the various regions of the structural space are determined. The existence is demonstrated of strong quantitative correlations between the contents of different types of four-C alpha fragments within protein structures, which imply significant constraints on the types of architecture that can occur in proteins. Analysis of the distribution of structures demonstrates some hitherto unsuspected similarities and suggests that, in some circumstances, neither structural similarity nor sequence homology may be necessary conditions for evolutionary relationship between proteins. It is also suggested that these unsuspected similarities may imply similar folding mechanisms for structures of apparently different global architecture. Cases are also noted in which apparently similar structures may fold by different mechanisms. The connection between structure and dynamic properties is discussed, and a possible role of dynamics in the evolution of protein structures is suggested. The sensitivity of the methods presented herein to anomalies of structure refinement is demonstrated. It is suggested that the present results provide a framework for analyzing experimental results on structural similarity obtained using vibrational circular dichroism spectra, which are sensitive to local backbone structure.     

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.     

Higher-order interhelical spatial interactions in membrane proteins

Higher-order interactions are important for protein folding and assembly. We introduce the concept of interhelical three-body interactions as derived from Delaunay triangulation and alpha shapes of protein structures. In addition to glycophorin A, where triplets are strongly correlated with protein stability, we found that tight interhelical triplet interactions exist extensively in other membrane proteins, where many types of triplets occur far more frequently than in soluble proteins. We developed a probabilistic model for estimating the value of membrane helical interaction triplet (MHIT) propensity. Because the number of known structures of membrane proteins is limited, we developed a bootstrap method for determining the 95% confidence intervals of estimated MHIT values. We identified triplets that have high propensity for interhelical interactions and are unique to membrane proteins, e.g. AGF, AGG, GLL, GFF and others. A significant fraction (32%) of triplet types contains triplets that may be involved in interhelical hydrogen bond interactions, suggesting the prevalent and important roles of H-bond in the assembly of TM helices. There are several well-defined spatial conformations for triplet interactions on helices with similar parallel or antiparallel orientations and with similar right-handed or left-handed crossing angles. Often, they contain small residues and correspond to the regions of the closest contact between helices. Sequence motifs such as GG4 and AG4 can be part of the three-body interactions that have similar conformations, which in turn can be part of a higher-order cooperative four residue spatial motif observed in helical pairs from different proteins. In many cases, spatial motifs such as serine zipper and polar clamp are part of triplet interactions. On the basis of the analysis of the archaeal rhodopsin family of proteins, tightly packed triplet interactions can be achieved with several different choices of amino acid residues.     

The "random-coil" state of proteins: comparison of database statistics and molecular simulations.

This study presents a comparison of two models of the random-coil state, one based on statistical distributions from the structural database and the other based on molecular dynamics simulations. The database model relies on the assumption that the random- or statistical-coil state of a particular residue can be described by its conformational distribution in a sufficiently diverse subset of protein structures. The molecular dynamics model is based on distributions from molecular simulations carried out on "dipeptide" models (single residues with N-terminal acetyl and C-terminal N'-methyl amide blocking groups). A comparison of the two models for the residues Ala, Asn, Asp, Gly, and Val indicates that the database distributions are greatly influenced by long-range interactions and dominated by specific recognizable elements of protein structure. In contrast, the limited structural scope of the dipeptide models presents the extreme case of a peptide under the influence of only short-range interactions. The models were evaluated by a comparison of scalar coupling constants calculated from the conformational distributions and compared with experimentally values determined for unstructured peptides. Although the models gave different distributions, there was similar agreement with experiment. This comparison emphasizes the differences and limitations in each model and highlights the difficulty in presenting an accurate picture of the random-coil state. Proteins 1999;36:407- 418.     

Identifying sequence-structure pairs undetected by sequence alignments

We examine how effectively simple potential functions previously developed can identify compatibilities between sequences and structures of proteins for database searches. The potential function consists of pairwise contact energies, repulsive packing potentials of residues for overly dense arrangement and short-range potentials for secondary structures, all of which were estimated from statistical preferences observed in known protein structures. Each potential energy term was modified to represent compatibilities between sequences and structures for globular proteins. Pairwise contact interactions in a sequence-structure alignment are evaluated in a mean field approximation on the basis of probabilities of site pairs to be aligned. Gap penalties are assumed to be proportional to the number of contacts at each residue position, and as a result gaps will be more frequently placed on protein surfaces than in cores. In addition to minimum energy alignments, we use probability alignments made by successively aligning site pairs in order by pairwise alignment probabilities. The results show that the present energy function and alignment method can detect well both folds compatible with a given sequence and, inversely, sequences compatible with a given fold, and yield mostly similar alignments for these two types of sequence and structure pairs. Probability alignments consisting of most reliable site pairs only can yield extremely small root mean square deviations, and including less reliable pairs increases the deviations. Also, it is observed that secondary structure potentials are usefully complementary to yield improved alignments with this method. Remarkably, by this method some individual sequence-structure pairs are detected having only 5-20% sequence identity.     

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.     

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

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

Novel protein folds and their nonsequential structural analogs

Newly determined protein structures are classified to belong to a new fold, if the structures are sufficiently dissimilar from all other so far known protein structures. To analyze structural similarities of proteins, structure alignment tools are used. We demonstrate that the usage of nonsequential structure alignment tools, which neglect the polypeptide chain connectivity, can yield structure alignments with significant similarities between proteins of known three-dimensional structure and newly determined protein structures that possess a new fold. The recently introduced protein structure alignment tool, GANGSTA, is specialized to perform nonsequential alignments with proper assignment of the secondary structure types by focusing on helices and strands only. In the new version, GANGSTA+, the underlying algorithms were completely redesigned, yielding enhanced quality of structure alignments, offering alignment against a larger database of protein structures, and being more efficient. We applied DaliLite, TM-align, and GANGSTA+ on three protein crystal structures considered to be novel folds. Applying GANGSTA+ to these novel folds, we find proteins in the ASTRAL40 database, which possess significant structural similarities, albeit the alignments are nonsequential and in some cases involve secondary structure elements aligned in reverse orientation. A web server is available at http://agknapp.chemie.fu-berlin.de/gplus for pairwise alignment, visualization, and database comparison.     

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.     

Interaction between bound water molecules and local protein structures: A statistical analysis of the hydrogen bond structures around bound water molecules

Water molecules play an important role in protein folding and protein interactions through their structural association with proteins. Examples of such structural association can be found in protein crystal structures, and can often explain protein functionality in the context of structure. We herein report the systematic analysis of the local structures of proteins interacting with water molecules, and the characterization of their geometric features. We first examined the interaction of water molecules with a large local interaction environment by comparing the preference of water molecules in three regions, namely, the protein–protein interaction (PPI) interfaces, the crystal contact (CC) interfaces, and the non‐interfacial regions. High preference of water molecules to the PPI and CC interfaces was found. In addition, the bound water on the PPI interface was more favorably associated with the complex interaction structure, implying that such water‐mediated structures may participate in the shaping of the PPI interface. The pairwise water‐mediated interaction was then investigated, and the water‐mediated residue–residue interaction potential was derived. Subsequently, the types of polar atoms surrounding the water molecules were analyzed, and the preference of the hydrogen bond acceptor was observed. Furthermore, the geometries of the structures interacting with water were analyzed, and it was found that the major structure on the protein surface exhibited planar geometry rather than tetrahedral geometry. Several previously undiscovered characteristics of water–protein interactions were unfolded in this study, and are expected to lead to a better understanding of protein structure and function. Proteins 2016; 84:43–51. © 2015 Wiley Periodicals, Inc.     

Inferring ideal amino acid interaction forms from statistical protein contact potentials

We have analyzed 29 different published matrices of protein pairwise contact potentials (CPs) between amino acids derived from different sets of proteins, either crystallographic structures taken from the Protein Data Bank (PDB) or computer-generated decoys. Each of the CPs is similar to 1 of the 2 matrices derived in the work of Miyazawa and Jernigan (Proteins 1999;34:49-68). The CP matrices of the first class can be approximated with a correlation of order 0.9 by the formula e(ij) = h(i) + h(j), 1 相似文献