Contact prediction for beta and alpha‐beta proteins using integer linear optimization and its impact on the first principles 3D structure prediction method ASTRO‐FOLD

An integer linear optimization model is presented to predict residue contacts in β, α + β, and α/β proteins. The total energy of a protein is expressed as sum of a C^α? C^α distance dependent contact energy contribution and a hydrophobic contribution. The model selects contact that assign lowest energy to the protein structure as satisfying a set of constraints that are included to enforce certain physically observed topological information. A new method based on hydrophobicity is proposed to find the β‐sheet alignments. These β‐sheet alignments are used as constraints for contacts between residues of β‐sheets. This model was tested on three independent protein test sets and CASP8 test proteins consisting of β, α + β, α/β proteins and it was found to perform very well. The average accuracy of the predictions (separated by at least six residues) was ～61%. The average true positive and false positive distances were also calculated for each of the test sets and they are 7.58 Å and 15.88 Å, respectively. Residue contact prediction can be directly used to facilitate the protein tertiary structure prediction. This proposed residue contact prediction model is incorporated into the first principles protein tertiary structure prediction approach, ASTRO‐FOLD. The effectiveness of the contact prediction model was further demonstrated by the improvement in the quality of the protein structure ensemble generated using the predicted residue contacts for a test set of 10 proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

CNNcon: Improved Protein Contact Maps Prediction Using Cascaded Neural Networks

Backgrounds

Despite continuing progress in X-ray crystallography and high-field NMR spectroscopy for determination of three-dimensional protein structures, the number of unsolved and newly discovered sequences grows much faster than that of determined structures. Protein modeling methods can possibly bridge this huge sequence-structure gap with the development of computational science. A grand challenging problem is to predict three-dimensional protein structure from its primary structure (residues sequence) alone. However, predicting residue contact maps is a crucial and promising intermediate step towards final three-dimensional structure prediction. Better predictions of local and non-local contacts between residues can transform protein sequence alignment to structure alignment, which can finally improve template based three-dimensional protein structure predictors greatly.

Methods

CNNcon, an improved multiple neural networks based contact map predictor using six sub-networks and one final cascade-network, was developed in this paper. Both the sub-networks and the final cascade-network were trained and tested with their corresponding data sets. While for testing, the target protein was first coded and then input to its corresponding sub-networks for prediction. After that, the intermediate results were input to the cascade-network to finish the final prediction.

Results

The CNNcon can accurately predict 58.86% in average of contacts at a distance cutoff of 8 Å for proteins with lengths ranging from 51 to 450. The comparison results show that the present method performs better than the compared state-of-the-art predictors. Particularly, the prediction accuracy keeps steady with the increase of protein sequence length. It indicates that the CNNcon overcomes the thin density problem, with which other current predictors have trouble. This advantage makes the method valuable to the prediction of long length proteins. As a result, the effective prediction of long length proteins could be possible by the CNNcon.     

Prediction of helix-helix contacts and interacting helices in polytopic membrane proteins using neural networks

Despite rapidly increasing numbers of available 3D structures, membrane proteins still account for less than 1% of all structures in the Protein Data Bank. Recent high-resolution structures indicate a clearly broader structural diversity of membrane proteins than initially anticipated, motivating the development of reliable structure prediction methods specifically tailored for this class of molecules. One important prediction target capturing all major aspects of a protein's 3D structure is its contact map. Our analysis shows that computational methods trained to predict residue contacts in globular proteins perform poorly when applied to membrane proteins. We have recently published a method to identify interacting alpha-helices in membrane proteins based on the analysis of coevolving residues in predicted transmembrane regions. Here, we present a substantially improved algorithm for the same problem, which uses a newly developed neural network approach to predict helix-helix contacts. In addition to the input features commonly used for contact prediction of soluble proteins, such as windowed residue profiles and residue distance in the sequence, our network also incorporates features that apply to membrane proteins only, such as residue position within the transmembrane segment and its orientation toward the lipophilic environment. The obtained neural network can predict contacts between residues in transmembrane segments with nearly 26% accuracy. It is therefore the first published contact predictor developed specifically for membrane proteins performing with equal accuracy to state-of-the-art contact predictors available for soluble proteins. The predicted helix-helix contacts were employed in a second step to identify interacting helices. For our dataset consisting of 62 membrane proteins of solved structure, we gained an accuracy of 78.1%. Because the reliable prediction of helix interaction patterns is an important step in the classification and prediction of membrane protein folds, our method will be a helpful tool in compiling a structural census of membrane proteins.     

Combining Evolutionary Information and an Iterative Sampling Strategy for Accurate Protein Structure Prediction

Recent work has shown that the accuracy of ab initio structure prediction can be significantly improved by integrating evolutionary information in form of intra-protein residue-residue contacts. Following this seminal result, much effort is put into the improvement of contact predictions. However, there is also a substantial need to develop structure prediction protocols tailored to the type of restraints gained by contact predictions. Here, we present a structure prediction protocol that combines evolutionary information with the resolution-adapted structural recombination approach of Rosetta, called RASREC. Compared to the classic Rosetta ab initio protocol, RASREC achieves improved sampling, better convergence and higher robustness against incorrect distance restraints, making it the ideal sampling strategy for the stated problem. To demonstrate the accuracy of our protocol, we tested the approach on a diverse set of 28 globular proteins. Our method is able to converge for 26 out of the 28 targets and improves the average TM-score of the entire benchmark set from 0.55 to 0.72 when compared to the top ranked models obtained by the EVFold web server using identical contact predictions. Using a smaller benchmark, we furthermore show that the prediction accuracy of our method is only slightly reduced when the contact prediction accuracy is comparatively low. This observation is of special interest for protein sequences that only have a limited number of homologs.     

Towards accurate residue-residue hydrophobic contact prediction for alpha helical proteins via integer linear optimization

A new optimization-based method is presented to predict the hydrophobic residue contacts in alpha-helical proteins. The proposed approach uses a high resolution distance dependent force field to calculate the interaction energy between different residues of a protein. The formulation predicts the hydrophobic contacts by minimizing the sum of these contact energies. These residue contacts are highly useful in narrowing down the conformational space searched by protein structure prediction algorithms. The proposed algorithm also offers the algorithmic advantage of producing a rank ordered list of the best contact sets. This model was tested on four independent alpha-helical protein test sets and was found to perform very well. The average accuracy of the predictions (separated by at least six residues) obtained using the presented method was approximately 66% for single domain proteins. The average true positive and false positive distances were also calculated for each protein test set and they are 8.87 and 14.67 A, respectively.     

A pair-to-pair amino acids substitution matrix and its applications for protein structure prediction

We present a new structurally derived pair-to-pair substitution matrix (P2PMAT). This matrix is constructed from a very large amount of integrated high quality multiple sequence alignments (Blocks) and protein structures. It evaluates the likelihoods of all 160,000 pair-to-pair substitutions. P2PMAT matrix implicitly accounts for evolutionary conservation, correlated mutations, and residue-residue contact potentials. The usefulness of the matrix for structural predictions is shown in this article. Predicting protein residue-residue contacts from sequence information alone, by our method (P2PConPred) is particularly accurate in the protein cores, where it performs better than other basic contact prediction methods (increasing accuracy by 25-60%). The method mean accuracy for protein cores is 24% for 59 diverse families and 34% for a subset of proteins shorter than 100 residues. This is above the level that was recently shown to be sufficient to significantly improve ab initio protein structure prediction. We also demonstrate the ability of our approach to identify native structures within large sets of (300-2000) protein decoys. On the basis of evolutionary information alone our method ranks the native structure in the top 0.3% of the decoys in 4/10 of the sets, and in 8/10 of sets the native structure is ranked in the top 10% of the decoys. The method can, thus, be used to assist filtering wrong models, complementing traditional scoring functions.     

PROFcon: novel prediction of long-range contacts

MOTIVATION: Despite the continuing advance in the experimental determination of protein structures, the gap between the number of known protein sequences and structures continues to increase. Prediction methods can bridge this sequence-structure gap only partially. Better predictions of non-local contacts between residues could improve comparative modeling, fold recognition and could assist in the experimental structure determination. RESULTS: Here, we introduced PROFcon, a novel contact prediction method that combines information from alignments, from predictions of secondary structure and solvent accessibility, from the region between two residues and from the average properties of the entire protein. In contrast to some other methods, PROFcon predicted short and long proteins at similar levels of accuracy. As expected, PROFcon was clearly less accurate when tested on sparse evolutionary profiles, that is, on families with few homologs. Prediction accuracy was highest for proteins belonging to the SCOP alpha/beta class. PROFcon compared favorably with state-of-the-art prediction methods at the CASP6 meeting. While the performance may still be perceived as low, our method clearly pushed the mark higher. Furthermore, predictions are already accurate enough to seed predictions of global features of protein structure.     

Effect of using suboptimal alignments in template-based protein structure prediction

Computational protein structure prediction remains a challenging task in protein bioinformatics. In the recent years, the importance of template-based structure prediction is increasing because of the growing number of protein structures solved by the structural genomics projects. To capitalize the significant efforts and investments paid on the structural genomics projects, it is urgent to establish effective ways to use the solved structures as templates by developing methods for exploiting remotely related proteins that cannot be simply identified by homology. In this work, we examine the effect of using suboptimal alignments in template-based protein structure prediction. We showed that suboptimal alignments are often more accurate than the optimal one, and such accurate suboptimal alignments can occur even at a very low rank of the alignment score. Suboptimal alignments contain a significant number of correct amino acid residue contacts. Moreover, suboptimal alignments can improve template-based models when used as input to Modeller. Finally, we use suboptimal alignments for handling a contact potential in a probabilistic way in a threading program, SUPRB. The probabilistic contacts strategy outperforms the partly thawed approach, which only uses the optimal alignment in defining residue contacts, and also the re-ranking strategy, which uses the contact potential in re-ranking alignments. The comparison with existing methods in the template-recognition test shows that SUPRB is very competitive and outperforms existing methods.     

Limitations of Ab Initio Predictions of Peptide Binding to MHC Class II Molecules

Successful predictions of peptide MHC binding typically require a large set of binding data for the specific MHC molecule that is examined. Structure based prediction methods promise to circumvent this requirement by evaluating the physical contacts a peptide can make with an MHC molecule based on the highly conserved 3D structure of peptide:MHC complexes. While several such methods have been described before, most are not publicly available and have not been independently tested for their performance. We here implemented and evaluated three prediction methods for MHC class II molecules: statistical potentials derived from the analysis of known protein structures; energetic evaluation of different peptide snapshots in a molecular dynamics simulation; and direct analysis of contacts made in known 3D structures of peptide:MHC complexes. These methods are ab initio in that they require structural data of the MHC molecule examined, but no specific peptide:MHC binding data. Moreover, these methods retain the ability to make predictions in a sufficiently short time scale to be useful in a real world application, such as screening a whole proteome for candidate binding peptides. A rigorous evaluation of each methods prediction performance showed that these are significantly better than random, but still substantially lower than the best performing sequence based class II prediction methods available. While the approaches presented here were developed independently, we have chosen to present our results together in order to support the notion that generating structure based predictions of peptide:MHC binding without using binding data is unlikely to give satisfactory results.     

Combining Physicochemical and Evolutionary Information for Protein Contact Prediction

We introduce a novel contact prediction method that achieves high prediction accuracy by combining evolutionary and physicochemical information about native contacts. We obtain evolutionary information from multiple-sequence alignments and physicochemical information from predicted ab initio protein structures. These structures represent low-energy states in an energy landscape and thus capture the physicochemical information encoded in the energy function. Such low-energy structures are likely to contain native contacts, even if their overall fold is not native. To differentiate native from non-native contacts in those structures, we develop a graph-based representation of the structural context of contacts. We then use this representation to train an support vector machine classifier to identify most likely native contacts in otherwise non-native structures. The resulting contact predictions are highly accurate. As a result of combining two sources of information—evolutionary and physicochemical—we maintain prediction accuracy even when only few sequence homologs are present. We show that the predicted contacts help to improve ab initio structure prediction. A web service is available at http://compbio.robotics.tu-berlin.de/epc-map/.     

Exploring the effects of sparse restraints on protein structure prediction

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter‐residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse‐grained structure‐based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary‐structural information, a small fraction of the native contact map (5%‐10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ‐proteins. However, this distinction reduces for β‐proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure‐based models can be used to understand the efficacy of structure‐prediction restraints and could, in future, be tuned to include specific force‐field interactions, secondary structure errors and noise in the sparse maps.     

Accurate Prediction of Protein Catalytic Residues by Side Chain Orientation and Residue Contact Density

Prediction of protein catalytic residues provides useful information for the studies of protein functions. Most of the existing methods combine both structure and sequence information but heavily rely on sequence conservation from multiple sequence alignments. The contribution of structure information is usually less than that of sequence conservation in existing methods. We found a novel structure feature, residue side chain orientation, which is the first structure-based feature that achieves prediction results comparable to that of evolutionary sequence conservation. We developed a structure-based method, Enzyme Catalytic residue SIde-chain Arrangement (EXIA), which is based on residue side chain orientations and backbone flexibility of protein structure. The prediction that uses EXIA outperforms existing structure-based features. The prediction quality of combing EXIA and sequence conservation exceeds that of the state-of-the-art prediction methods. EXIA is designed to predict catalytic residues from single protein structure without needing sequence or structure alignments. It provides invaluable information when there is no sufficient or reliable homology information for target protein. We found that catalytic residues have very special side chain orientation and designed the EXIA method based on the newly discovered feature. It was also found that EXIA performs well for a dataset of enzymes without any bounded ligand in their crystallographic structures.     

Statistical mechanical treatment of α-helices and extended structures in proteins with inclusion of short- and medium-range interactions

A statistical mechanical model of protein conformation with medium-range interactions between theith and (i+k)^th residues (k<-4) is presented. Two two-state models, an α-helix-coil and an extended-structure-coil model, are formulated using the same form of the partition function, but the two models are applied independently to predict the locations of α-helical, extended, and coil segments; in the relatively few cases (<2%) where the predictions from the two models are in conflict, the prediction is scored as an incorrect one. Two independent sets of statistical weights (one set for each model) are derived to describe the interactions between the 20 amino acid residues for each range of interactionk; they are evaluated by minimizing an objective function so that the probability profiles for the α-helix or extended structure, respectively, in proteins computed from these statistical weights correlate optimally with the experimentally observed native conformations of these proteins. Examination of the resulting statistical weights shows that those for the interactions between hydrophobic residues and between a hydrophobic and a hydrophilic residue have reasonable magnitudes compared to what would be expected from the spatial arrangements of the side chains in the α-helix and the extended structure, and that those for the α-helix-coil model correlate well with experimentally determined values of the Zimm-Bragg parameterss and σ of the helix-coil transition theory. From the point of view of a method to predict the conformational states (i.e., α-helix, extended structure, and coil) of each residue, the statistical weights (as inall empirical prediction schemes) depend very much on the proteins used for the data base, since the presently available set of proteins of known structure is still too small for very high predictability; as a result, the correctness of the prediction is not very good for proteins not included in the data base. However, the correctness of the prediction, at least for the 37 proteins utilized as the data base in this study, is 91% and 87% for the α-helix-coil and the extended-structure-coil models, respectively; further, 79% of all the residues are predicted correctly when both the α-helix-coil and extended-structure-coil models are applied independently.     

Evaluation of residue-residue contact prediction methods: From retrospective to prospective

Sequence-based residue contact prediction plays a crucial role in protein structure reconstruction. In recent years, the combination of evolutionary coupling analysis (ECA) and deep learning (DL) techniques has made tremendous progress for residue contact prediction, thus a comprehensive assessment of current methods based on a large-scale benchmark data set is very needed. In this study, we evaluate 18 contact predictors on 610 non-redundant proteins and 32 CASP13 targets according to a wide range of perspectives. The results show that different methods have different application scenarios: (1) DL methods based on multi-categories of inputs and large training sets are the best choices for low-contact-density proteins such as the intrinsically disordered ones and proteins with shallow multi-sequence alignments (MSAs). (2) With at least 5L (L is sequence length) effective sequences in the MSA, all the methods show the best performance, and methods that rely only on MSA as input can reach comparable achievements as methods that adopt multi-source inputs. (3) For top L/5 and L/2 predictions, DL methods can predict more hydrophobic interactions while ECA methods predict more salt bridges and disulfide bonds. (4) ECA methods can detect more secondary structure interactions, while DL methods can accurately excavate more contact patterns and prune isolated false positives. In general, multi-input DL methods with large training sets dominate current approaches with the best overall performance. Despite the great success of current DL methods must be stated the fact that there is still much room left for further improvement: (1) With shallow MSAs, the performance will be greatly affected. (2) Current methods show lower precisions for inter-domain compared with intra-domain contact predictions, as well as very high imbalances in precisions between intra-domains. (3) Strong prediction similarities between DL methods indicating more feature types and diversified models need to be developed. (4) The runtime of most methods can be further optimized.     

Modeling ensembles of transmembrane beta-barrel proteins

Transmembrane beta-barrel (TMB) proteins are embedded in the outer membrane of gram-negative bacteria, mitochondria, and chloroplasts. Despite their importance, very few nonhomologous TMB structures have been determined by X-ray diffraction because of the experimental difficulty encountered in crystallizing transmembrane proteins. We introduce the program partiFold to investigate the folding landscape of TMBs. By computing the Boltzmann partition function, partiFold estimates inter-beta-strand residue interaction probabilities, predicts contacts and per-residue X-ray crystal structure B-values, and samples conformations from the Boltzmann low energy ensemble. This broad range of predictive capabilities is achieved using a single, parameterizable grammatical model to describe potential beta-barrel supersecondary structures, combined with a novel energy function of stacked amino acid pair statistical potentials. PartiFold outperforms existing programs for inter-beta-strand residue contact prediction on TMB proteins, offering both higher average predictive accuracy as well as more consistent results. Moreover, the integration of these contact probabilities inside a stochastic contact map can be used to infer a more meaningful picture of the TMB folding landscape, which cannot be achieved with other methods. Partifold's predictions of B-values are competitive with recent methods specifically designed for this problem. Finally, we show that sampling TMBs from the Boltzmann ensemble matches the X-ray crystal structure better than single structure prediction methods. A webserver running partiFold is available at http://partiFold.csail.mit.edu/.     

Deep learning methods for 3D structural proteome and interactome modeling

Bolstered by recent methodological and hardware advances, deep learning has increasingly been applied to biological problems and structural proteomics. Such approaches have achieved remarkable improvements over traditional machine learning methods in tasks ranging from protein contact map prediction to protein folding, prediction of protein–protein interaction interfaces, and characterization of protein–drug binding pockets. In particular, emergence of ab initio protein structure prediction methods including AlphaFold2 has revolutionized protein structural modeling. From a protein function perspective, numerous deep learning methods have facilitated deconvolution of the exact amino acid residues and protein surface regions responsible for binding other proteins or small molecule drugs. In this review, we provide a comprehensive overview of recent deep learning methods applied in structural proteomics.     

CAB-Align: A Flexible Protein Structure Alignment Method Based on the Residue-Residue Contact Area

Proteins are flexible, and this flexibility has an essential functional role. Flexibility can be observed in loop regions, rearrangements between secondary structure elements, and conformational changes between entire domains. However, most protein structure alignment methods treat protein structures as rigid bodies. Thus, these methods fail to identify the equivalences of residue pairs in regions with flexibility. In this study, we considered that the evolutionary relationship between proteins corresponds directly to the residue–residue physical contacts rather than the three-dimensional (3D) coordinates of proteins. Thus, we developed a new protein structure alignment method, contact area-based alignment (CAB-align), which uses the residue–residue contact area to identify regions of similarity. The main purpose of CAB-align is to identify homologous relationships at the residue level between related protein structures. The CAB-align procedure comprises two main steps: First, a rigid-body alignment method based on local and global 3D structure superposition is employed to generate a sufficient number of initial alignments. Then, iterative dynamic programming is executed to find the optimal alignment. We evaluated the performance and advantages of CAB-align based on four main points: (1) agreement with the gold standard alignment, (2) alignment quality based on an evolutionary relationship without 3D coordinate superposition, (3) consistency of the multiple alignments, and (4) classification agreement with the gold standard classification. Comparisons of CAB-align with other state-of-the-art protein structure alignment methods (TM-align, FATCAT, and DaliLite) using our benchmark dataset showed that CAB-align performed robustly in obtaining high-quality alignments and generating consistent multiple alignments with high coverage and accuracy rates, and it performed extremely well when discriminating between homologous and nonhomologous pairs of proteins in both single and multi-domain comparisons. The CAB-align software is freely available to academic users as stand-alone software at http://www.pharm.kitasato-u.ac.jp/bmd/bmd/Publications.html.     

Bayesian Markov Random Field Analysis for Protein Function Prediction Based on Network Data

Inference of protein functions is one of the most important aims of modern biology. To fully exploit the large volumes of genomic data typically produced in modern-day genomic experiments, automated computational methods for protein function prediction are urgently needed. Established methods use sequence or structure similarity to infer functions but those types of data do not suffice to determine the biological context in which proteins act. Current high-throughput biological experiments produce large amounts of data on the interactions between proteins. Such data can be used to infer interaction networks and to predict the biological process that the protein is involved in. Here, we develop a probabilistic approach for protein function prediction using network data, such as protein-protein interaction measurements. We take a Bayesian approach to an existing Markov Random Field method by performing simultaneous estimation of the model parameters and prediction of protein functions. We use an adaptive Markov Chain Monte Carlo algorithm that leads to more accurate parameter estimates and consequently to improved prediction performance compared to the standard Markov Random Fields method. We tested our method using a high quality S.cereviciae validation network with 1622 proteins against 90 Gene Ontology terms of different levels of abstraction. Compared to three other protein function prediction methods, our approach shows very good prediction performance. Our method can be directly applied to protein-protein interaction or coexpression networks, but also can be extended to use multiple data sources. We apply our method to physical protein interaction data from S. cerevisiae and provide novel predictions, using 340 Gene Ontology terms, for 1170 unannotated proteins and we evaluate the predictions using the available literature.     

Alpha-helical topology prediction and generation of distance restraints in membrane proteins

The field of protein structure prediction has seen significant advances in recent years. Researchers have followed a multitude of approaches, including methods based on comparative modeling, fold recognition and threading, and first-principles techniques. It is noteworthy that the structure prediction of membrane proteins is comparatively less studied by researchers in the field. A membrane protein is characterized by a protein structure that extends into or through the lipid-lipid bilayer of a cell. The structure is influenced by the combination of the hydrophobic bilayer region, the direct interaction with the bilayer, and the aqueous external environment. Due to the difficulty in obtaining reliable experimental structures, accurate computational prediction of membrane proteins is of paramount importance. An optimization model has been developed to predict the interhelical interactions in α-helical membrane proteins. A database of α-helical membrane proteins of known structure and limited sequence identity can be constructed to develop interaction probabilities. By then maximizing the occurrence of highly probable pairwise or three-residue interactions, realistic contacts can be predicted by imposing a number of geometrical constraints. The development of these low distance contacts can provide additional distance restraints for first principles-based approaches to the tertiary structure prediction problem. The proposed approach is shown to successfully predict interhelical contacts in several membrane protein systems, including bovine rhodopsin and the recently released human β2 adrenergic receptor protein structure.