Folding and stability of helical bundle proteins from coarse‐grained models

We develop a coarse‐grained model where solvent is considered implicitly, electrostatics are included as short‐range interactions, and side‐chains are coarse‐grained to a single bead. The model depends on three main parameters: hydrophobic, electrostatic, and side‐chain hydrogen bond strength. The parameters are determined by considering three level of approximations and characterizing the folding for three selected proteins (training set). Nine additional proteins (containing up to 126 residues) as well as mutated versions (test set) are folded with the given parameters. In all folding simulations, the initial state is a random coil configuration. Besides the native state, some proteins fold into an additional state differing in the topology (structure of the helical bundle). We discuss the stability of the native states, and compare the dynamics of our model to all atom molecular dynamics simulations as well as some general properties on the interactions governing folding dynamics. Proteins 2013; 81:1200–1211. © 2013 Wiley Periodicals, Inc.     

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.     

A distance‐dependent atomic knowledge‐based potential and force for discrimination of native structures from decoys

The purpose of this article is to introduce a novel model for discriminating correctly folded proteins from well designed decoy structures using mechanical interatomic forces. In our model, we consider a protein as a collection of springs and the force imposed to each atom is calculated. A potential function is obtained from statistical contact preferences within known protein structures. Combining this function with the spring equation, the interatomic forces are calculated. Finally, we consider a structure and define a score function on the 3D structure of a protein. We compare the force imposed to each atom of a protein with the corresponding atom in the other structures. We then assign larger scores to those atoms with lower forces. The total score is the sum of partial scores of atoms. The optimal structure is assumed to be the one with the highest score in the data set. To evaluate the performance of our model, we apply it on several decoy sets. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

PRIMO/PRIMONA: A coarse‐grained model for proteins and nucleic acids that preserves near‐atomistic accuracy

The new coarse graining model PRIMO/PRIMONA for proteins and nucleic acids is proposed. This model combines one to several heavy atoms into coarse‐grained sites that are chosen to allow an analytical, high‐resolution reconstruction of all‐atom models based on molecular bonding geometry constraints. The accuracy of proposed reconstruction method in terms of structure and energetics is tested and compared with other popular reconstruction methods for a variety of protein and nucleic acid test sets. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Conserved buried water molecules enable the β‐trefoil architecture

Available high‐resolution crystal structures for the family of β‐trefoil proteins in the structural databank were queried for buried waters. Such waters were classified as either: (a) unique to a particular domain, family, or superfamily or (b) conserved among all β‐trefoil folds. Three buried waters conserved among all β‐trefoil folds were identified. These waters are related by the threefold rotational pseudosymmetry characteristic of this protein architecture (representing three instances of an identical structural environment within each repeating trefoil‐fold motif). The structural properties of this buried water are remarkable and include: residing in a cavity space no larger than a single water molecule, exhibiting a positional uncertainty (i.e., normalized B‐factor) substantially lower than the average Cα atom, providing essentially ideal H‐bonding geometry with three solvent‐inaccessible main chain groups, simultaneously serving as a bridging H‐bond for three different β‐strands at a point of secondary structure divergence, and orienting conserved hydrophobic side chains to form a nascent core‐packing group. Other published work supports an interpretation that these interactions are key to the formation of an efficient folding nucleus and folded thermostability. The fundamental threefold symmetric structural element of the β‐trefoil fold is therefore, surprisingly, a buried water molecule.     

A generalized knowledge‐based discriminatory function for biomolecular interactions

Several novel and established knowledge‐based discriminatory function formulations and reference state derivations have been evaluated to identify parameter sets capable of distinguishing native and near‐native biomolecular interactions from incorrect ones. We developed the r·m·r function, a novel atomic level radial distribution function with mean reference state that averages over all pairwise atom types from a reduced atom type composition, using experimentally determined intermolecular complexes in the Cambridge Structural Database (CSD) and the Protein Data Bank (PDB) as the information sources. We demonstrate that r·m·r had the best discriminatory accuracy and power for protein‐small molecule and protein‐DNA interactions, regardless of whether the native complex was included or excluded, from the test set. The superior performance of the r·m·r discriminatory function compared with seventeen alternative functions evaluated on publicly available test sets for protein‐small molecule and protein‐DNA interactions indicated that the function was not over optimized through back testing on a single class of biomolecular interactions. The initial success of the reduced composition and superior performance with the CSD as the distribution set over the PDB implies that further improvements and generality of the function are possible by deriving probabilities from subsets of the CSD, using structures that consist of only the atom types to be considered for given biomolecular interactions. The method is available as a web server module at http://protinfo.compbio.washington.edu . Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Improving the orientation‐dependent statistical potential using a reference state

Statistical potentials are frequently engaged in the protein structural prediction and protein folding for conformational evaluation. Theoretically, to describe the many‐body effect, pairwise interaction between two atom groups should be corrected by their relative geometric orientation. The potential functions developed by this means are called orientation‐dependent statistical potentials and have exhibited substantially improved performance. However, none of the currently available orientation‐dependent statistical potentials use any reference state, which has been proven to greatly enhance the power of distance‐dependent statistical potentials in numerous previous studies. In this work, we designed a reasonable reference state for the orientation‐dependent statistical potentials: using the average geometric relationship between atom pairs in known structures by neglecting their residue identities. The statistical potential developed using this reference state (called ORDER_AVE) prevails most available rival potentials in a series of tests on the decoy sets, although the information of side chain atoms (except the β‐carbon) is absent in its construction. Proteins 2014; 82:2383–2393. © 2014 Wiley Periodicals, Inc.     

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.     

Sequence determinants of thermodynamic stability in a WW domain—An all‐β‐sheet protein

The stabilities of 66 sequence variants of the human Pin1 WW domain have been determined by equilibrium thermal denaturation experiments. All 34 residues composing the hPin1 WW three‐stranded β‐sheet structure could be replaced one at a time with at least one different natural or non‐natural amino acid residue without leading to an unfolded protein. Alanine substitutions at only four positions within the hPin1 WW domain lead to a partially or completely unfolded protein—in the absence of a physiological ligand. The side chains of these four residues form a conserved, partially solvent‐inaccessible, continuous hydrophobic minicore comprising the N‐ and C‐termini. Ala mutations at five other residues, three of which constitute the ligand binding patch on the concave side of the β‐sheet, significantly destabilize the hPin1 WW domain without leading to an unfolded protein. The remaining mutations affect protein stability only slightly, suggesting that only a small subset of side chain interactions within the hPin1 WW domain are mandatory for acquiring and maintaining a stable, cooperatively folded β‐sheet structure.     

All‐atom chain‐building by optimizing MODELLER energy function using conformational space annealing

We have investigated the effect of rigorous optimization of the MODELLER energy function for possible improvement in protein all‐atom chain‐building. For this we applied the global optimization method called conformational space annealing (CSA) to the standard MODELLER procedure to achieve better energy optimization than what MODELLER provides. The method, which we call MODELLERCSA , is tested on two benchmark sets. The first is the 298 proteins taken from the HOMSTRAD multiple alignment set. By simply optimizing the MODELLER energy function, we observe significant improvement in side‐chain modeling, where MODELLERCSA provides about 10.7% (14.5%) improvement for χ₁ (χ₁ + χ₂) accuracy compared to the standard MODELLER modeling. The improvement of backbone accuracy by MODELLERCSA is shown to be less prominent, and a similar improvement can be achieved by simply generating many standard MODELLER models and selecting lowest energy models. However, the level of side‐chain modeling accuracy by MODELLERCSA could not be matched either by extensive MODELLER strategies, side‐chain remodeling by SCWRL3, or copying unmutated rotamers. The identical procedure was successfully applied to 100 CASP7 template base modeling domains during the prediction season in a blind fashion, and the results are included here for comparison. From this study, we observe a good correlation between the MODELLER energy and the side‐chain accuracy. Our findings indicate that, when a good alignment between a target protein and its templates is provided, thorough optimization of the MODELLER energy function leads to accurate all‐atom models. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

A systematic analysis of scoring functions in rigid‐body protein docking: The delicate balance between the predictive rate improvement and the risk of overtraining

Protein‐protein interactions play fundamental roles in biological processes including signaling, metabolism, and trafficking. While the structure of a protein complex reveals crucial details about the interaction, it is often difficult to acquire this information experimentally. As the number of interactions discovered increases faster than they can be characterized, protein‐protein docking calculations may be able to reduce this disparity by providing models of the interacting proteins. Rigid‐body docking is a widely used docking approach, and is often capable of generating a pool of models within which a near‐native structure can be found. These models need to be scored in order to select the acceptable ones from the set of poses. Recently, more than 100 scoring functions from the CCharPPI server were evaluated for this task using decoy structures generated with SwarmDock. Here, we extend this analysis to identify the predictive success rates of the scoring functions on decoys from three rigid‐body docking programs, ZDOCK, FTDock, and SDOCK, allowing us to assess the transferability of the functions. We also apply set‐theoretic measure to test whether the scoring functions are capable of identifying near‐native poses within different subsets of the benchmark. This information can provide guides for the use of the most efficient scoring function for each docking method, as well as instruct future scoring functions development efforts. Proteins 2017; 85:1287–1297. © 2017 Wiley Periodicals, Inc.     

Template‐free protein structure prediction and quality assessment with an all‐atom free‐energy model

Biophysical forcefields have contributed less than originally anticipated to recent progress in protein structure prediction. Here, we have investigated the selectivity of a recently developed all‐atom free‐energy forcefield for protein structure prediction and quality assessment (QA). Using a heuristic method, but excluding homology, we generated decoy‐sets for all targets of the CASP7 protein structure prediction assessment with <150 amino acids. The decoys in each set were then ranked by energy in short relaxation simulations and the best low‐energy cluster was submitted as a prediction. For four of nine template‐free targets, this approach generated high‐ranking predictions within the top 10 models submitted in CASP7 for the respective targets. For these targets, our de‐novo predictions had an average GDT_S score of 42.81, significantly above the average of all groups. The refinement protocol has difficulty for oligomeric targets and when no near‐native decoys are generated in the decoy library. For targets with high‐quality decoy sets the refinement approach was highly selective. Motivated by this observation, we rescored all server submissions up to 200 amino acids using a similar refinement protocol, but using no clustering, in a QA exercise. We found an excellent correlation between the best server models and those with the lowest energy in the forcefield. The free‐energy refinement protocol may thus be an efficient tool for relative QA and protein structure prediction. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Osmolytes modulate conformational exchange in solvent‐exposed regions of membrane proteins

Site‐directed spin labeling (SDSL) was used to investigate local structure and conformational exchange in two bacterial outer‐membrane TonB‐dependent transporters, BtuB and FecA. Protecting osmolytes, such as polyethylene glycols (PEGs) are known to modulate a substrate‐dependent conformational equilibrium in the energy coupling motif (Ton box) of BtuB. Here, we demonstrate that a segment that is N‐terminal to the Ton box in BtuB, is in conformational exchange between ordered and disordered states with or without substrate. Protecting osmolytes shift this equilibrium to favor the more ordered, folded state. However, a segment of BtuB that is C‐terminal to the Ton box that is not solvent exposed is insensitive to PEGs. Protecting osmolytes also modulate a conformational equilibrium in the Ton box of FecA, with larger molecular weight PEGs producing the largest shifts in the conformational free energy. These data indicate that solvent‐exposed regions of these transporters undergo conformational exchange and that regions of these transporters that are involved in protein–protein interactions sample multiple conformational substates. The sensitivity to solute provides an explanation for differences seen between two high‐resolution structures of BtuB, which each likely represent one conformation from a subset of states that are normally sampled by the protein. This work also illustrates how SDSL and osmolytes may be used to characterize and quantitate conformational equilibria in membrane proteins.     

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.     

The role of atomic level steric effects and attractive forces in protein folding

Protein folding into tertiary structures is controlled by an interplay of attractive contact interactions and steric effects. We investigate the balance between these contributions using structure‐based models using an all‐atom representation of the structure combined with a coarse‐grained contact potential. Tertiary contact interactions between atoms are collected into a single broad attractive well between the C^β atoms between each residue pair in a native contact. Through the width of these contact potentials we control their tolerance for deviations from the ideal structure and the spatial range of attractive interactions. In the compact native state dominant packing constraints limit the effects of a coarse‐grained contact potential. During folding, however, the broad attractive potentials allow an early collapse that starts before the native local structure is completely adopted. As a consequence the folding transition is broadened and the free energy barrier is decreased. Eventually two‐state folding behavior is lost completely for systems with very broad attractive potentials. The stabilization of native‐like residue interactions in non‐perfect geometries early in the folding process frequently leads to structural traps. Global mirror images are a notable example. These traps are penalized by the details of the repulsive interactions only after further collapse. Successful folding to the native state requires simultaneous guidance from both attractive and repulsive interactions. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Structure refinement of protein model decoys requires accurate side‐chain placement

In this study, the application of temperature‐based replica‐exchange (T‐ReX) simulations for structure refinement of decoys taken from the I‐TASSER dataset was examined. A set of eight nonredundant proteins was investigated using self‐guided Langevin dynamics (SGLD) with a generalized Born implicit solvent model to sample conformational space. For two of the protein test cases, a comparison of the SGLD/T‐ReX method with that of a hybrid explicit/implicit solvent molecular dynamics T‐ReX simulation model is provided. Additionally, the effect of side‐chain placement among the starting decoy structures, using alternative rotamer conformations taken from the SCWRL4 modeling program, was investigated. The simulation results showed that, despite having near‐native backbone conformations among the starting decoys, the determinant of their refinement is side‐chain packing to a level that satisfies a minimum threshold of native contacts to allow efficient excursions toward the downhill refinement regime on the energy landscape. By repacking using SCWRL4 and by applying the RWplus statistical potential for structure identification, the SGLD/T‐ReX simulations achieved refinement to an average of 38% increase in the number of native contacts relative to the original I‐TASSER decoy sets and a 25% reduction in values of C_α root‐mean‐square deviation. The hybrid model succeeded in obtaining a sharper funnel to low‐energy states for a modeled target than the implicit solvent SGLD model; yet, structure identification remained roughly the same. Without meeting a threshold of near‐native packing of side chains, the T‐ReX simulations degrade the accuracy of the decoys, and subsequently, refinement becomes tantamount to the protein folding problem. Proteins 2013. 2012 Published by Wiley Periodicals, Inc.     

On the satisfaction of backbone‐carbonyl lone pairs of electrons in protein structures

Protein structures are stabilized by a variety of noncovalent interactions (NCIs), including the hydrophobic effect, hydrogen bonds, electrostatic forces and van der Waals’ interactions. Our knowledge of the contributions of NCIs, and the interplay between them remains incomplete. This has implications for computational modeling of NCIs, and our ability to understand and predict protein structure, stability, and function. One consideration is the satisfaction of the full potential for NCIs made by backbone atoms. Most commonly, backbone‐carbonyl oxygen atoms located within α‐helices and β‐sheets are depicted as making a single hydrogen bond. However, there are two lone pairs of electrons to be satisfied for each of these atoms. To explore this, we used operational geometric definitions to generate an inventory of NCIs for backbone‐carbonyl oxygen atoms from a set of high‐resolution protein structures and associated molecular‐dynamics simulations in water. We included more‐recently appreciated, but weaker NCIs in our analysis, such as n→π* interactions, Cα‐H bonds and methyl‐H bonds. The data demonstrate balanced, dynamic systems for all proteins, with most backbone‐carbonyl oxygen atoms being satisfied by two NCIs most of the time. Combinations of NCIs made may correlate with secondary structure type, though in subtly different ways from traditional models of α‐ and β‐structure. In addition, we find examples of under‐ and over‐satisfied carbonyl‐oxygen atoms, and we identify both sequence‐dependent and sequence‐independent secondary‐structural motifs in which these reside. Our analysis provides a more‐detailed understanding of these contributors to protein structure and stability, which will be of use in protein modeling, engineering and design.