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.     

Efficient identification of near‐native conformations in ab initio protein structure prediction using structural profiles

One of the major bottlenecks in many ab initio protein structure prediction methods is currently the selection of a small number of candidate structures for high‐resolution refinement from large sets of low‐resolution decoys. This step often includes a scoring by low‐resolution energy functions and a clustering of conformations by their pairwise root mean square deviations (RMSDs). As an efficient selection is crucial to reduce the overall computational cost of the predictions, any improvement in this direction can increase the overall performance of the predictions and the range of protein structures that can be predicted. We show here that the use of structural profiles, which can be predicted with good accuracy from the amino acid sequences of proteins, provides an efficient means to identify good candidate structures. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Selecting near-native protein structures from ab initio models using ensemble clustering

Background: Ab initio protein structure prediction is to predict the tertiary structure of a protein from its amino acid sequence alone. As an important topic in bioinformatics, considerable efforts have been made on designing the ab initio methods. Unfortunately, lacking of a perfect energy function, it is a difficult task to select a good near-native structure from the predicted decoy structures in the last step. Methods: Here we propose an ensemble clustering method based on k-medoids to deal with this problem. The k-medoids method is run many times to generate clustering ensembles, and then a voting method is used to combine the clustering results. A confidence score is defined to select the final near-native model, considering both the cluster size and the cluster similarity. Results: We have applied the method to 54 single-domain targets in CASP-11. For about 70.4% of these targets, the proposed method can select better near-native structures compared to the SPICKER method used by the I-TASSER server. Conclusions: The experiments show that, the proposed method is effective in selecting the near-native structure from decoy sets for different targets in terms of the similarity between the selected structure and the native structure.     

A permissive secondary structure-guided superposition tool for clustering of protein fragments toward protein structure prediction via fragment assembly

MOTIVATION: Secondary-Structure Guided Superposition tool (SSGS) is a permissive secondary structure-based algorithm for matching of protein structures and in particular their fragments. The algorithm was developed towards protein structure prediction via fragment assembly. RESULTS: In a fragment-based structural prediction scheme, a protein sequence is cut into building blocks (BBs). The BBs are assembled to predict their relative 3D arrangement. Finally, the assemblies are refined. To implement this prediction scheme, a clustered structural library representing sequence patterns for protein fragments is essential. To create a library, BBs generated by cutting proteins from the PDB are compared and structurally similar BBs are clustered. To allow structural comparison and clustering of the BBs, which are often relatively short with flexible loops, we have devised SSGS. SSGS maintains high similarity between cluster members and is highly efficient. When it comes to comparing BBs for clustering purposes, the algorithm obtains better results than other, non-secondary structure guided protein superimposition algorithms.     

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.     

Conserved residue clustering and protein structure prediction

Protein residues that are critical for structure and function are expected to be conserved throughout evolution. Here, we investigate the extent to which these conserved residues are clustered in three-dimensional protein structures. In 92% of the proteins in a data set of 79 proteins, the most conserved positions in multiple sequence alignments are significantly more clustered than randomly selected sets of positions. The comparison to random subsets is not necessarily appropriate, however, because the signal could be the result of differences in the amino acid composition of sets of conserved residues compared to random subsets (hydrophobic residues tend to be close together in the protein core), or differences in sequence separation of the residues in the different sets. In order to overcome these limits, we compare the degree of clustering of the conserved positions on the native structure and on alternative conformations generated by the de novo structure prediction method Rosetta. For 65% of the 79 proteins, the conserved residues are significantly more clustered in the native structure than in the alternative conformations, indicating that the clustering of conserved residues in protein structures goes beyond that expected purely from sequence locality and composition effects. The differences in the spatial distribution of conserved residues can be utilized in de novo protein structure prediction: We find that for 79% of the proteins, selection of the Rosetta generated conformations with the greatest clustering of the conserved residues significantly enriches the fraction of close-to-native structures.     

Automatic classification of protein structures relying on similarities between alignments

ABSTRACT: BACKGROUND: Identification of protein structural cores requires isolation of sets of proteins all sharing a same subset of structural motifs. In the context of ever growing number of available 3D protein structures, standard and automatic clustering algorithms require adaptations so as to allow for efficient identification of such sets of proteins. RESULTS: When considering a pair of 3D structures, they are stated as similar or not according to the local similarities of their matching substructures in a structural alignment. This binary relation can be represented in a graph of similarities where a node represents a 3D protein structure and an edge states that two 3D protein structures are similar. Therefore, the classification of proteins into structural families can be viewed as graph clustering task. Unfortunately, because such a graph encodes only pairwise similarity information, clustering algorithms may group in the same cluster a subset of 3D structures that do not share a common substructure. To overcome this drawback we first define a ternary similarity on a triple of 3D structures as a constraint to be satisfied by the graph of similarities. Such a ternary constraint takes into account similarities between pairwise alignments, so as to ensure that the three involved protein structures do have some common substructure. We propose hereunder a modification algorithm that eliminates edges from the original graph of similarities and outputs a reduced graph in which no ternary constraints are violated. Our proposition is then first to build a graph of similarities, then to reduce the graph according to the modification algorithm, and finally to apply to the reduced graph a standard graph clustering algorithm. We applied this method to ASTRAL-40 non-redundant protein domains, identifying significant pairwise similarities with Yakusa, a program devised for rapid 3D structure alignments. CONCLUSIONS: We show that filtering similarities prior to standard graph based clustering process by applying ternary similarity constraints i) improves the separation of proteins of different classes and consequently ii) improves the classification quality of standard graph based clustering algorithms according to the reference classification SCOP.     

Some fundamental aspects of building protein structures from fragment libraries

We have investigated some of the basic principles that influence generation of protein structures using a fragment-based, random insertion method. We tested buildup methods and fragment library quality for accuracy in constructing a set of known structures. The parameters most influential in the construction procedure are bond and torsion angles with minor inaccuracies in bond angles alone causing >6 A CalphaRMSD for a 150-residue protein. Idealization to a standard set of values corrects this problem, but changes the torsion angles and does not work for every structure. Alternatively, we found using Cartesian coordinates instead of torsion angles did not reduce performance and can potentially increase speed and accuracy. Under conditions simulating ab initio structure prediction, fragment library quality can be suboptimal and still produce near-native structures. Using various clustering criteria, we created a number of libraries and used them to predict a set of native structures based on nonnative fragments. Local CalphaRMSD fit of fragments, library size, and takeoff/landing angle criteria weakly influence the accuracy of the models. Based on a fragment's minimal perturbation upon insertion into a known structure, a seminative fragment library was created that produced more accurate structures with fragments that were less similar to native fragments than the other sets. These results suggest that fragments need only contain native-like subsections, which when correctly overlapped, can recreate a native-like model. For fragment-based, random insertion methods used in protein structure prediction and design, our findings help to define the parameters this method needs to generate near-native structures.     

Local structure prediction with local structure-based sequence profiles

MOTIVATION: A large body of experimental and theoretical evidence suggests that local structural determinants are frequently encoded in short segments of protein sequence. Although the local structural information, once recognized, is particularly useful in protein structural and functional analyses, it remains a difficult problem to identify embedded local structural codes based solely on sequence information. RESULTS: In this paper, we describe a local structure prediction method aiming at predicting the backbone structures of nine-residue sequence segments. Two elements are the keys for this local structure prediction procedure. The first key element is the LSBSP1 database, which contains a large number of non-redundant local structure-based sequence profiles for nine-residue structure segments. The second key element is the consensus approach, which identifies a consensus structure from a set of hit structures. The local structure prediction procedure starts by matching a query sequence segment of nine consecutive amino acid residues to all the sequence profiles in the local structure-based sequence profile database (LSBSP1). The consensus structure, which is at the center of the largest structural cluster of the hit structures, is predicted to be the native state structure adopted by the query sequence segment. This local structure prediction method is assessed with a large set of random test protein structures that have not been used in constructing the LSBSP1 database. The benchmark results indicate that the prediction capacities of the novel local structure prediction procedure exceed the prediction capacities of the local backbone structure prediction methods based on the I-sites library by a significant margin. AVAILABILITY: All the computational and assessment procedures have been implemented in the integrated computational system PrISM.1 (Protein Informatics System for Modeling). The system and associated databases for LINUX systems can be downloaded from the website: http://www.columbia.edu/~ay1/.     

Selecting High Quality Protein Structures from Diverse Conformational Ensembles

Protein structure prediction encompasses two major challenges: 1), the generation of a large ensemble of high resolution structures for a given amino-acid sequence; and 2), the identification of the structure closest to the native structure for a blind prediction. In this article, we address the second challenge, by proposing what is, to our knowledge, a novel iterative traveling-salesman problem-based clustering method to identify the structures of a protein, in a given ensemble, which are closest to the native structure. The method consists of an iterative procedure, which aims at eliminating clusters of structures at each iteration, which are unlikely to be of similar fold to the native, based on a statistical analysis of cluster density and average spherical radius. The method, denoted as ICON, has been tested on four data sets: 1), 1400 proteins with high resolution decoys; 2), medium-to-low resolution decoys from Decoys ‘R’ Us; 3), medium-to-low resolution decoys from the first-principles approach, ASTRO-FOLD; and 4), selected targets from CASP8. The extensive tests demonstrate that ICON can identify high-quality structures in each ensemble, regardless of the resolution of conformers. In a total of 1454 proteins, with an average of 1051 conformers per protein, the conformers selected by ICON are, on an average, in the top 3.5% of the conformers in the ensemble.     

Clustering 100,000 protein structure decoys in minutes

Ab initio protein structure prediction methods first generate large sets of structural conformations as candidates (called decoys), and then select the most representative decoys through clustering techniques. Classical clustering methods are inefficient due to the pairwise distance calculation, and thus become infeasible when the number of decoys is large. In addition, the existing clustering approaches suffer from the arbitrariness in determining a distance threshold for proteins within a cluster: a small distance threshold leads to many small clusters, while a large distance threshold results in the merging of several independent clusters into one cluster. In this paper, we propose an efficient clustering method through fast estimating cluster centroids and efficient pruning rotation spaces. The number of clusters is automatically detected by information distance criteria. A package named ONION, which can be downloaded freely, is implemented accordingly. Experimental results on benchmark data sets suggest that ONION is 14 times faster than existing tools, and ONION obtains better selections for 31 targets, and worse selection for 19 targets compared to SPICKER’s selections. On an average PC, ONION can cluster 100,000 decoys in around 12 minutes.     

Protein structural motif prediction in multidimensional phi-psi space leads to improved secondary structure prediction.

A significant step towards establishing the structure and function of a protein is the prediction of the local conformation of the polypeptide chain. In this article, we present systems for the prediction of three new alphabets of local structural motifs. The motifs are built by applying multidimensional scaling (MDS) and clustering to pair-wise angular distances for multiple phi-psi angle values collected from high-resolution protein structures. The predictive systems, based on ensembles of bidirectional recurrent neural network architectures, and trained on a large non-redundant set of protein structures, achieve 72%, 66%, and 60% correct motif prediction on an independent test set for di-peptides (six classes), tri-peptides (eight classes) and tetra-peptides (14 classes), respectively, 28-30% above baseline statistical predictors. We then build a further system, based on ensembles of two-layered bidirectional recurrent neural networks, to map structural motif predictions into a traditional 3-class (helix, strand, coil) secondary structure. This system achieves 79.5% correct prediction using the "hard" CASP 3-class assignment, and 81.4% with a more lenient assignment, outperforming a sophisticated state-of-the-art predictor (Porter) trained in the same experimental conditions. The structural motif predictor is publicly available at: http://distill.ucd.ie/porter+/.     

In quest of an empirical potential for protein structure prediction

Key to successful protein structure prediction is a potential that recognizes the native state from misfolded structures. Recent advances in empirical potentials based on known protein structures include improved reference states for assessing random interactions, sidechain-orientation-dependent pair potentials, potentials for describing secondary or supersecondary structural preferences and, most importantly, optimization protocols that sculpt the energy landscape to enhance the correlation between native-like features and the energy. Improved clustering algorithms that select native-like structures on the basis of cluster density also resulted in greater prediction accuracy. For template-based modeling, these advances allowed improvement in predicted structures relative to their initial template alignments over a wide range of target-template homology. This represents significant progress and suggests applications to proteome-scale structure prediction.     

Restricted mobility of side chains on concave surfaces of solenoid proteins may impart heightened potential for intermolecular interactions

Significant progress has been made in the determination of the protein structures with their number today passing over a hundred thousand structures. The next challenge is the understanding and prediction of protein–protein and protein–ligand interactions. In this work we address this problem by analyzing curved solenoid proteins. Many of these proteins are considered as “hub molecules” for their high potential to interact with many different molecules and to be a scaffold for multisubunit protein machineries. Our analysis of these structures through molecular dynamics simulations reveals that the mobility of the side‐chains on the concave surfaces of the solenoids is lower than on the convex ones. This result provides an explanation to the observed preferential binding of the ligands, including small and flexible ligands, to the concave surface of the curved solenoid proteins. The relationship between the landscapes and dynamic properties of the protein surfaces can be further generalized to the other types of protein structures and eventually used in the computer algorithms, allowing prediction of protein–ligand interactions by analysis of protein surfaces . Proteins 2015; 83:1654–1664. © 2015 Wiley Periodicals, Inc.     

Protein docking using surface matching and supervised machine learning

Computational prediction of protein complex structures through docking offers a means to gain a mechanistic understanding of protein interactions that mediate biological processes. This is particularly important as the number of experimentally determined structures of isolated proteins exceeds the number of structures of complexes. A comprehensive docking procedure is described in which efficient sampling of conformations is achieved by matching surface normal vectors, fast filtering for shape complementarity, clustering by RMSD, and scoring the docked conformations using a supervised machine learning approach. Contacting residue pair frequencies, residue propensities, evolutionary conservation, and shape complementarity score for each docking conformation are used as input data to a Random Forest classifier. The performance of the Random Forest approach for selecting correctly docked conformations was assessed by cross-validation using a nonredundant benchmark set of X-ray structures for 93 heterodimer and 733 homodimer complexes. The single highest rank docking solution was the correct (near-native) structure for slightly more than one third of the complexes. Furthermore, the fraction of highly ranked correct structures was significantly higher than the overall fraction of correct structures, for almost all complexes. A detailed analysis of the difficult to predict complexes revealed that the majority of the homodimer cases were explained by incorrect oligomeric state annotation. Evolutionary conservation and shape complementarity score as well as both underrepresented and overrepresented residue types and residue pairs were found to make the largest contributions to the overall prediction accuracy. Finally, the method was also applied to docking unbound subunit structures from a previously published benchmark set.     

HCPM--program for hierarchical clustering of protein models

HCPM is a tool for clustering protein structures from comparative modeling, ab initio structure prediction, etc. A hierarchical clustering algorithm is designed and tested, and a heuristic is provided for an optimal cluster selection. The method has been successfully tested during the CASP6 experiment.     

A binary matrix factorization algorithm for protein complex prediction

BACKGROUND: Identifying biologically relevant protein complexes from a large protein-protein interaction (PPI) network, is essential to understand the organization of biological systems. However, high-throughput experimental techniques that can produce a large amount of PPIs are known to yield non-negligible rates of false-positives and false-negatives, making the protein complexes difficult to be identified. RESULTS: We propose a binary matrix factorization (BMF) algorithm under the Bayesian Ying-Yang (BYY) harmony learning, to detect protein complexes by clustering the proteins which share similar interactions through factorizing the binary adjacent matrix of a PPI network. The proposed BYY-BMF algorithm automatically determines the cluster number while this number is pre-given for most existing BMF algorithms. Also, BYY-BMF's clustering results does not depend on any parameters or thresholds, unlike the Markov Cluster Algorithm (MCL) that relies on a so-called inflation parameter. On synthetic PPI networks, the predictions evaluated by the known annotated complexes indicate that BYY-BMF is more robust than MCL for most cases. On real PPI networks from the MIPS and DIP databases, BYY-BMF obtains a better balanced prediction accuracies than MCL and a spectral analysis method, while MCL has its own advantages, e.g., with good separation values.     

β-sheet topology prediction with high precision and recall for β and mixed α/β proteins

The prediction of the correct β-sheet topology for pure β and mixed α/β proteins is a critical intermediate step toward the three dimensional protein structure prediction. The predicted beta sheet topology provides distance constraints between sequentially separated residues, which reduces the three dimensional search space for a protein structure prediction algorithm. Here, we present a novel mixed integer linear optimization based framework for the prediction of β-sheet topology in β and mixed α/β proteins. The objective is to maximize the total strand-to-strand contact potential of the protein. A large number of physical constraints are applied to provide biologically meaningful topology results. The formulation permits the creation of a rank-ordered list of preferred β-sheet arrangements. Finally, the generated topologies are re-ranked using a fully atomistic approach involving torsion angle dynamics and clustering. For a large, non-redundant data set of 2102 β and mixed α/β proteins with at least 3 strands taken from the PDB, the proposed approach provides the top 5 solutions with average precision and recall greater than 78%. Consistent results are obtained in the β-sheet topology prediction for blind targets provided during the CASP8 and CASP9 experiments, as well as for actual and predicted secondary structures. The β-sheet topology prediction algorithm, BeST, is available to the scientific community at http://selene.princeton.edu/BeST/.     

Generalized comparative modeling (GENECOMP): a combination of sequence comparison, threading, and lattice modeling for protein structure prediction and refinement

An improved generalized comparative modeling method, GENECOMP, for the refinement of threading models is developed and validated on the Fischer database of 68 probe-template pairs, a standard benchmark used to evaluate threading approaches. The basic idea is to perform ab initio folding using a lattice protein model, SICHO, near the template provided by the new threading algorithm PROSPECTOR. PROSPECTOR also provides predicted contacts and secondary structure for the template-aligned regions, and possibly for the unaligned regions by garnering additional information from other top-scoring threaded structures. Since the lowest-energy structure generated by the simulations is not necessarily the best structure, we employed two structure-selection protocols: distance geometry and clustering. In general, clustering is found to generate somewhat better quality structures in 38 of 68 cases. When applied to the Fischer database, the protocol does no harm and in a significant number of cases improves upon the initial threading model, sometimes dramatically. The procedure is readily automated and can be implemented on a genomic scale.     

ProtoNet: hierarchical classification of the protein space

The ProtoNet site provides an automatic hierarchical clustering of the SWISS-PROT protein database. The clustering is based on an all-against-all BLAST similarity search. The similarities' E-score is used to perform a continuous bottom-up clustering process by applying alternative rules for merging clusters. The outcome of this clustering process is a classification of the input proteins into a hierarchy of clusters of varying degrees of granularity. ProtoNet (version 1.3) is accessible in the form of an interactive web site at http://www.protonet.cs.huji.ac.il. ProtoNet provides navigation tools for monitoring the clustering process with a vertical and horizontal view. Each cluster at any level of the hierarchy is assigned with a statistical index, indicating the level of purity based on biological keywords such as those provided by SWISS-PROT and InterPro. ProtoNet can be used for function prediction, for defining superfamilies and subfamilies and for large-scale protein annotation purposes.