PIE—Efficient filters and coarse grained potentials for unbound protein–protein docking

Identifying correct binding modes in a large set of models is an important step in protein–protein docking. We identified protein docking filter based on overlap area that significantly reduces the number of candidate structures that require detailed examination. We also developed potentials based on residue contacts and overlap areas using a comprehensive learning set of 640 two‐chain protein complexes with mathematical programming. Our potential showed substantially better recognition capacity compared to other publicly accessible protein docking potentials in discriminating between native and nonnative binding modes on a large test set of 84 complexes independent of our training set. We were able to rank a near‐native model on the top in 43 cases and within top 10 in 51 cases. We also report an atomic potential that ranks a near‐native model on the top in 46 cases and within top 10 in 58 cases. Our filter+potential is well suited for selecting a small set of models to be refined to atomic resolution. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Multi-LZerD: multiple protein docking for asymmetric complexes

The tertiary structures of protein complexes provide a crucial insight about the molecular mechanisms that regulate their functions and assembly. However, solving protein complex structures by experimental methods is often more difficult than single protein structures. Here, we have developed a novel computational multiple protein docking algorithm, Multi‐LZerD, that builds models of multimeric complexes by effectively reusing pairwise docking predictions of component proteins. A genetic algorithm is applied to explore the conformational space followed by a structure refinement procedure. Benchmark on eleven hetero‐multimeric complexes resulted in near‐native conformations for all but one of them (a root mean square deviation smaller than 2.5Å). We also show that our method copes with unbound docking cases well, outperforming the methodology that can be directly compared with our approach. Multi‐LZerD was able to predict near‐native structures for multimeric complexes of various topologies.Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Understanding on the residue contact network using the log‐normal cluster model and the multilevel wheel diagram

Residue clusters play essential role in stabilizing protein structures in the form of complex networks. We show that the cluster sizes in a native protein follow the log‐normal distribution for a dataset consisting of 424 proteins. To our knowledge, this is the first time of such fitting for the native structures. Based on log‐normal model, the asymptotically increasing mean cluster sizes produce a critical protein chain length of about 200 amino acids, beyond which length most globular proteins have nearly the same mean cluster sizes. This suggests that the larger proteins use a different packing mechanism than the smaller proteins. We confirmed the scale‐free property of the residue contact network for most of the protein structures in the dataset, although the violations were observed for the tightly packed proteins. Residue cluster network wheel (RCNW) is proposed to visualize the relationship between the multiple properties of the residue network such as the cluster size, the residue types and contacts, and the flexibility of the residue. We noticed that the residues with large cluster size have smaller Cα displacement measured using the normal mode analysis. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 904–916, 2010.     

A reduced protein model with accurate native-structure identification ability

A protein model that is simple enough to be used in protein-folding simulations but accurate enough to identify a protein native fold is described. Its geometry consists of describing the residues by one, two, or three pseudoatoms, depending on the residue size. Its energy is given by a pairwise, knowledge-based potential obtained for all the pseudoatoms as a function of their relative distance. The pseudoatomic potential is also a function of the primary chain separation and residue order. The model is tested by gapless threading on a large, representative set of known protein and decoy structures obtained from the "Decoys 'R' Us" database. It is also tested by threading on gapped decoys generated for proteins with many homologs. The gapless threading tests show near 98% native-structure recognition as the lowest energy structure and almost 100% as one of the three lowest energy structures for over 2200 test proteins. In decoy threading tests, the model recognized the majority of the native structures. It is also able to recognize native structures among gapped decoys, in spite of close structural similarities. The results indicate that the pseudoatomic model has native recognition ability similar to comparable atomic-based models but much better than equivalent residue-based models.     

Burial of nonpolar surface area and thermodynamic stabilization of globins as a function of chain elongation

Proteins are biosynthesized from N to C terminus before they depart from the ribosome and reach their bioactive state in the cell. At present, very little is known about the evolution of conformation and the free energy of the nascent protein with chain elongation. These parameters critically affect the extent of folding during ribosome‐assisted biosynthesis. Here, we address the impact of vectorial amino acid addition on the burial of nonpolar surface area and on the free energy of native‐like structure formation in the absence of the ribosomal machinery. We focus on computational predictions on proteins bearing the globin fold, which is known to encompass the 3/3, 2/2, and archaeal subclasses. We find that the burial of nonpolar surface increases progressively with chain elongation, leading to native‐like conformations upon addition of the last C‐terminal residues, corresponding to incorporation of the last two helices. Additionally, the predicted folding entropy for generating native‐like structures becomes less unfavorable at nearly complete chain lengths, suggesting a link between the late burial of nonpolar surface and water release. Finally, the predicted folding free energy takes a progressive favorable dip toward more negative values, as the chain gets longer. These results suggest that thermodynamic stabilization of the native structure of newly synthesized globins during translation in the cell is significantly enhanced as the chain elongates. This is especially true upon departure of the last C‐terminal residues from the ribosomal tunnel, which hosts ca., 30–40 amino acids. Hence, we propose that release from the ribosome is a crucial step in the life of single‐domain proteins in the cell. Proteins 2014; 82:2318–2331. © 2014 Wiley Periodicals, Inc.     

SVR_CAF: An integrated score function for detecting native protein structures among decoys

An accurate score function for detecting the most native‐like models among a huge number of decoy sets is essential to the protein structure prediction. In this work, we developed a novel integrated score function (SVR_CAF) to discriminate native structures from decoys, as well as to rank near‐native structures and select best decoys when native structures are absent. SVR_CAF is a machine learning score, which incorporates the contact energy based score ( C E_score), amino acid network based score ( A AN_score), and the fast Fourier transform based score ( F FT_score). The score function was evaluated with four decoy sets for its discriminative ability and it shows higher overall performance than the state‐of‐the‐art score functions. Proteins 2014; 82:556–564. © 2013 Wiley Periodicals, Inc.     

3Drefine: Consistent protein structure refinement by optimizing hydrogen bonding network and atomic‐level energy minimization

One of the major limitations of computational protein structure prediction is the deviation of predicted models from their experimentally derived true, native structures. The limitations often hinder the possibility of applying computational protein structure prediction methods in biochemical assignment and drug design that are very sensitive to structural details. Refinement of these low‐resolution predicted models to high‐resolution structures close to the native state, however, has proven to be extremely challenging. Thus, protein structure refinement remains a largely unsolved problem. Critical assessment of techniques for protein structure prediction (CASP) specifically indicated that most predictors participating in the refinement category still did not consistently improve model quality. Here, we propose a two‐step refinement protocol, called 3Drefine, to consistently bring the initial model closer to the native structure. The first step is based on optimization of hydrogen bonding (HB) network and the second step applies atomic‐level energy minimization on the optimized model using a composite physics and knowledge‐based force fields. The approach has been evaluated on the CASP benchmark data and it exhibits consistent improvement over the initial structure in both global and local structural quality measures. 3Drefine method is also computationally inexpensive, consuming only few minutes of CPU time to refine a protein of typical length (300 residues). 3Drefine web server is freely available at http://sysbio.rnet.missouri.edu/3Drefine/ . Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Benchmarking a computational design method for the incorporation of metal ion‐binding sites at symmetric protein interfaces

The design of novel metal‐ion binding sites along symmetric axes in protein oligomers could provide new avenues for metalloenzyme design, construction of protein‐based nanomaterials and novel ion transport systems. Here, we describe a computational design method, symmetric protein recursive ion‐cofactor sampling (SyPRIS), for locating constellations of backbone positions within oligomeric protein structures that are capable of supporting desired symmetrically coordinated metal ion(s) chelated by sidechains (chelant model). Using SyPRIS on a curated benchmark set of protein structures with symmetric metal binding sites, we found high recovery of native metal coordinating rotamers: in 65 of the 67 (97.0%) cases, native rotamers featured in the best scoring model while in the remaining cases native rotamers were found within the top three scoring models. In a second test, chelant models were crossmatched against protein structures with identical cyclic symmetry. In addition to recovering all native placements, 10.4% (8939/86013) of the non‐native placements, had acceptable geometric compatibility scores. Discrimination between native and non‐native metal site placements was further enhanced upon constrained energy minimization using the Rosetta energy function. Upon sequence design of the surrounding first‐shell residues, we found further stabilization of native placements and a small but significant (1.7%) number of non‐native placement‐based sites with favorable Rosetta energies, indicating their designability in existing protein interfaces. The generality of the SyPRIS approach allows design of novel symmetric metal sites including with non‐natural amino acid sidechains, and should enable the predictive incorporation of a variety of metal‐containing cofactors at symmetric protein interfaces.     

On real-valued SDE and nonnegative-valued SDE population models with demographic variability

Population dynamics with demographic variability is frequently studied using discrete random variables with continuous-time Markov chain (CTMC) models. An approximation of a CTMC model using continuous random variables can be derived in a straightforward manner by applying standard methods based on the reaction rates in the CTMC model. This leads to a system of Itô stochastic differential equations (SDEs) which generally have the form \( d \mathbf {y} = \varvec{\mu } \, dt + G \, d \mathbf {W},\) where \(\mathbf {y}\) is the population vector of random variables, \(\varvec{\mu }\) is the drift vector, and G is the diffusion matrix. In some problems, the derived SDE model may not have real-valued or nonnegative solutions for all time. For such problems, the SDE model may be declared infeasible. In this investigation, new systems of SDEs are derived with real-valued solutions and with nonnegative solutions. To derive real-valued SDE models, reaction rates are assumed to be nonnegative for all time with negative reaction rates assigned probability zero. This biologically realistic assumption leads to the derivation of real-valued SDE population models. However, small but negative values may still arise for a real-valued SDE model. This is due to the magnitudes of certain problem-dependent diffusion coefficients when population sizes are near zero. A slight modification of the diffusion coefficients when population sizes are near zero ensures that a real-valued SDE model has a nonnegative solution, yet maintains the integrity of the SDE model when sizes are not near zero. Several population dynamic problems are examined to illustrate the methodology.

     

A global machine learning based scoring function for protein structure prediction

We present a knowledge‐based function to score protein decoys based on their similarity to native structure. A set of features is constructed to describe the structure and sequence of the entire protein chain. Furthermore, a qualitative relationship is established between the calculated features and the underlying electromagnetic interaction that dominates this scale. The features we use are associated with residue–residue distances, residue–solvent distances, pairwise knowledge‐based potentials and a four‐body potential. In addition, we introduce a new target to be predicted, the fitness score, which measures the similarity of a model to the native structure. This new approach enables us to obtain information both from decoys and from native structures. It is also devoid of previous problems associated with knowledge‐based potentials. These features were obtained for a large set of native and decoy structures and a back‐propagating neural network was trained to predict the fitness score. Overall this new scoring potential proved to be superior to the knowledge‐based scoring functions used as its inputs. In particular, in the latest CASP (CASP10) experiment our method was ranked third for all targets, and second for freely modeled hard targets among about 200 groups for top model prediction. Ours was the only method ranked in the top three for all targets and for hard targets. This shows that initial results from the novel approach are able to capture details that were missed by a broad spectrum of protein structure prediction approaches. Source codes and executable from this work are freely available at http://mathmed.org /#Software and http://mamiris.com/ . Proteins 2014; 82:752–759. © 2013 Wiley Periodicals, Inc.     

Predicted residue–residue contacts can help the scoring of 3D models

During the 7th Critical Assessment of Protein Structure Prediction (CASP7) experiment, it was suggested that the real value of predicted residue–residue contacts might lie in the scoring of 3D model structures. Here, we have carried out a detailed reassessment of the contact predictions made during the recent CASP8 experiment to determine whether predicted contacts might aid in the selection of close‐to‐native structures or be a useful tool for scoring 3D structural models. We used the contacts predicted by the CASP8 residue–residue contact prediction groups to select models for each target domain submitted to the experiment. We found that the information contained in the predicted residue–residue contacts would probably have helped in the selection of 3D models in the free modeling regime and over the harder comparative modeling targets. Indeed, in many cases, the models selected using just the predicted contacts had better GDT‐TS scores than all but the best 3D prediction groups. Despite the well‐known low accuracy of residue–residue contact predictions, it is clear that the predictive power of contacts can be useful in 3D model prediction strategies. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Extracting knowledge from protein structure geometry

Protein structure prediction techniques proceed in two steps, namely the generation of many structural models for the protein of interest, followed by an evaluation of all these models to identify those that are native‐like. In theory, the second step is easy, as native structures correspond to minima of their free energy surfaces. It is well known however that the situation is more complicated as the current force fields used for molecular simulations fail to recognize native states from misfolded structures. In an attempt to solve this problem, we follow an alternate approach and derive a new potential from geometric knowledge extracted from native and misfolded conformers of protein structures. This new potential, Metric Protein Potential (MPP), has two main features that are key to its success. Firstly, it is composite in that it includes local and nonlocal geometric information on proteins. At the short range level, it captures and quantifies the mapping between the sequences and structures of short (7‐mer) fragments of protein backbones through the introduction of a new local energy term. The local energy term is then augmented with a nonlocal residue‐based pairwise potential, and a solvent potential. Secondly, it is optimized to yield a maximized correlation between the energy of a structural model and its root mean square (RMS) to the native structure of the corresponding protein. We have shown that MPP yields high correlation values between RMS and energy and that it is able to retrieve the native structure of a protein from a set of high‐resolution decoys. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Protein-protein docking with multiple residue conformations and residue substitutions

The protein docking problem has two major aspects: sampling conformations and orientations, and scoring them for fit. To investigate the extent to which the protein docking problem may be attributed to the sampling of ligand side‐chain conformations, multiple conformations of multiple residues were calculated for the uncomplexed (unbound) structures of protein ligands. These ligand conformations were docked into both the complexed (bound) and unbound conformations of the cognate receptors, and their energies were evaluated using an atomistic potential function. The following questions were considered: (1) does the ensemble of precalculated ligand conformations contain a structure similar to the bound form of the ligand? (2) Can the large number of conformations that are calculated be efficiently docked into the receptors? (3) Can near‐native complexes be distinguished from non‐native complexes? Results from seven test systems suggest that the precalculated ensembles do include side‐chain conformations similar to those adopted in the experimental complexes. By assuming additivity among the side chains, the ensemble can be docked in less than 12 h on a desktop computer. These multiconformer dockings produce near‐native complexes and also non‐native complexes. When docked against the bound conformations of the receptors, the near‐native complexes of the unbound ligand were always distinguishable from the non‐native complexes. When docked against the unbound conformations of the receptors, the near‐native dockings could usually, but not always, be distinguished from the non‐native complexes. In every case, docking the unbound ligands with flexible side chains led to better energies and a better distinction between near‐native and non‐native fits. An extension of this algorithm allowed for docking multiple residue substitutions (mutants) in addition to multiple conformations. The rankings of the docked mutant proteins correlated with experimental binding affinities. These results suggest that sampling multiple residue conformations and residue substitutions of the unbound ligand contributes to, but does not fully provide, a solution to the protein docking problem. Conformational sampling allows a classical atomistic scoring function to be used; such a function may contribute to better selectivity between near‐native and non‐native complexes. Allowing for receptor flexibility may further extend these results.     

A novel method for predicting and using distance constraints of high accuracy for refining protein structure prediction

The principal bottleneck in protein structure prediction is the refinement of models from lower accuracies to the resolution observed by experiment. We developed a novel constraints‐based refinement method that identifies a high number of accurate input constraints from initial models and rebuilds them using restrained torsion angle dynamics (rTAD). We previously created a Bayesian statistics‐based residue‐specific all‐atom probability discriminatory function (RAPDF) to discriminate native‐like models by measuring the probability of accuracy for atom type distances within a given model. Here, we exploit RAPDF to score (i.e., filter) constraints from initial predictions that may or may not be close to a native‐like state, obtain consensus of top scoring constraints amongst five initial models, and compile sets with no redundant residue pair constraints. We find that this method consistently produces a large and highly accurate set of distance constraints from which to build refinement models. We further optimize the balance between accuracy and coverage of constraints by producing multiple structure sets using different constraint distance cutoffs, and note that the cutoff governs spatially near versus distant effects in model generation. This complete procedure of deriving distance constraints for rTAD simulations improves the quality of initial predictions significantly in all cases evaluated by us. Our procedure represents a significant step in solving the protein structure prediction and refinement problem, by enabling the use of consensus constraints, RAPDF, and rTAD for protein structure modeling and refinement. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

CONFOLD: Residue‐residue contact‐guided ab initio protein folding

Predicted protein residue–residue contacts can be used to build three‐dimensional models and consequently to predict protein folds from scratch. A considerable amount of effort is currently being spent to improve contact prediction accuracy, whereas few methods are available to construct protein tertiary structures from predicted contacts. Here, we present an ab initio protein folding method to build three‐dimensional models using predicted contacts and secondary structures. Our method first translates contacts and secondary structures into distance, dihedral angle, and hydrogen bond restraints according to a set of new conversion rules, and then provides these restraints as input for a distance geometry algorithm to build tertiary structure models. The initially reconstructed models are used to regenerate a set of physically realistic contact restraints and detect secondary structure patterns, which are then used to reconstruct final structural models. This unique two‐stage modeling approach of integrating contacts and secondary structures improves the quality and accuracy of structural models and in particular generates better β‐sheets than other algorithms. We validate our method on two standard benchmark datasets using true contacts and secondary structures. Our method improves TM‐score of reconstructed protein models by 45% and 42% over the existing method on the two datasets, respectively. On the dataset for benchmarking reconstructions methods with predicted contacts and secondary structures, the average TM‐score of best models reconstructed by our method is 0.59, 5.5% higher than the existing method. The CONFOLD web server is available at http://protein.rnet.missouri.edu/confold/ . Proteins 2015; 83:1436–1449. © 2015 Wiley Periodicals, Inc.     

Structural characterization of proteins using residue environments

A primary challenge for structural genomics is the automated functional characterization of protein structures. We have developed a sequence-independent method called S-BLEST (Structure-Based Local Environment Search Tool) for the annotation of previously uncharacterized protein structures. S-BLEST encodes the local environment of an amino acid as a vector of structural property values. It has been applied to all amino acids in a nonredundant database of protein structures to generate a searchable structural resource. Given a query amino acid from an experimentally determined or modeled structure, S-BLEST quickly identifies similar amino acid environments using a K-nearest neighbor search. In addition, the method gives an estimation of the statistical significance of each result. We validated S-BLEST on X-ray crystal structures from the ASTRAL 40 nonredundant dataset. We then applied it to 86 crystallographically determined proteins in the protein data bank (PDB) with unknown function and with no significant sequence neighbors in the PDB. S-BLEST was able to associate 20 proteins with at least one local structural neighbor and identify the amino acid environments that are most similar between those neighbors.     

VoroMQA: Assessment of protein structure quality using interatomic contact areas

In the absence of experimentally determined protein structure many biological questions can be addressed using computational structural models. However, the utility of protein structural models depends on their quality. Therefore, the estimation of the quality of predicted structures is an important problem. One of the approaches to this problem is the use of knowledge‐based statistical potentials. Such methods typically rely on the statistics of distances and angles of residue‐residue or atom‐atom interactions collected from experimentally determined structures. Here, we present VoroMQA (Voronoi tessellation‐based Model Quality Assessment), a new method for the estimation of protein structure quality. Our method combines the idea of statistical potentials with the use of interatomic contact areas instead of distances. Contact areas, derived using Voronoi tessellation of protein structure, are used to describe and seamlessly integrate both explicit interactions between protein atoms and implicit interactions of protein atoms with solvent. VoroMQA produces scores at atomic, residue, and global levels, all in the fixed range from 0 to 1. The method was tested on the CASP data and compared to several other single‐model quality assessment methods. VoroMQA showed strong performance in the recognition of the native structure and in the structural model selection tests, thus demonstrating the efficacy of interatomic contact areas in estimating protein structure quality. The software implementation of VoroMQA is freely available as a standalone application and as a web server at http://bioinformatics.lt/software/voromqa . Proteins 2017; 85:1131–1145. © 2017 Wiley Periodicals, Inc.     

Design and structure of two new protein cages illustrate successes and ongoing challenges in protein engineering

In recent years, new protein engineering methods have produced more than a dozen symmetric, self‐assembling protein cages whose structures have been validated to match their design models with near‐atomic accuracy. However, many protein cage designs that are tested in the lab do not form the desired assembly, and improving the success rate of design has been a point of recent emphasis. Here we present two protein structures solved by X‐ray crystallography of designed protein oligomers that form two‐component cages with tetrahedral symmetry. To improve on the past tendency toward poorly soluble protein, we used a computational protocol that favors the formation of hydrogen‐bonding networks over exclusively hydrophobic interactions to stabilize the designed protein–protein interfaces. Preliminary characterization showed highly soluble expression, and solution studies indicated successful cage formation by both designed proteins. For one of the designs, a crystal structure confirmed at high resolution that the intended tetrahedral cage was formed, though several flipped amino acid side chain rotamers resulted in an interface that deviates from the precise hydrogen‐bonding pattern that was intended. A structure of the other designed cage showed that, under the conditions where crystals were obtained, a noncage structure was formed wherein a porous 3D protein network in space group I2₁3 is generated by an off‐target twofold homomeric interface. These results illustrate some of the ongoing challenges of developing computational methods for polar interface design, and add two potentially valuable new entries to the growing list of engineered protein materials for downstream applications.