Contact prediction using mutual information and neural nets

Enhancing coevolutionary signals in protein-protein interaction prediction through clade-wise alignment integration

Protein-protein interactions (PPIs) play essential roles in most biological processes. The binding interfaces between interacting proteins impose evolutionary constraints that have successfully been employed to predict PPIs from multiple sequence alignments (MSAs). To construct MSAs, critical choices have to be made: how to ensure the reliable identification of orthologs, and how to optimally balance the need for large alignments versus sufficient alignment quality. Here, we propose a divide-and-conquer strategy for MSA generation: instead of building a single, large alignment for each protein, multiple distinct alignments are constructed under distinct clades in the tree of life. Coevolutionary signals are searched separately within these clades, and are only subsequently integrated using machine learning techniques. We find that this strategy markedly improves overall prediction performance, concomitant with better alignment quality. Using the popular DCA algorithm to systematically search pairs of such alignments, a genome-wide all-against-all interaction scan in a bacterial genome is demonstrated. Given the recent successes of AlphaFold in predicting direct PPIs at atomic detail, a discover-and-refine approach is proposed: our method could provide a fast and accurate strategy for pre-screening the entire genome, submitting to AlphaFold only promising interaction candidates-thus reducing false positives as well as computation time.

New Labeling Methods for Deep Learning Real-Valued Inter-Residue Distance Prediction

BACKGROUND

Much of the recent success in protein structure prediction has been a result of accurate protein contact prediction-a binary classification problem. Dozens of methods, built from various types of machine learning and deep learning algorithms, have been published over the last two decades for predicting contacts. Recently, many groups, including Google DeepMind, have demonstrated that reformulating the problem as a multi-class classification problem is a more promising direction to pursue. As an alternative approach, we recently proposed real-valued distance predictions, formulating the problem as a regression problem. The nuances of protein 3D structures make this formulation appropriate, allowing predictions to reflect inter-residue distances in nature. Despite these promises, the accurate prediction of real-valued distances remains relatively unexplored; possibly due to classification being better suited to machine and deep learning algorithms.

METHODS

Can regression methods be designed to predict real-valued distances as precise as binary contacts? To investigate this, we propose multiple novel methods of input label engineering, which is different from feature engineering, with the goal of optimizing the distribution of distances to cater to the loss function of the deep-learning model. Since an important utility of predicted contacts or distances is to build three-dimensional models, we also tested if predicted distances can reconstruct more accurate models than contacts.

RESULTS

Our results demonstrate, for the first time, that deep learning methods for real-valued protein distance prediction can deliver distances as precise as binary classification methods. When using an optimal distance transformation function on the standard PSICOV dataset consisting of 150 representative proteins, the precision of 'top-all' long-range contacts improves from 60.9% to 61.4% when predicting real-valued distances instead of contacts. When building three-dimensional models we observed an average TM-score increase from 0.61 to 0.72, highlighting the advantage of predicting real-valued distances.

Mutations in transmembrane proteins: diseases, evolutionary insights, prediction and comparison with globular proteins

Membrane proteins are unique in that they interact with lipid bilayers, making them indispensable for transporting molecules and relaying signals between and across cells. Due to the significance of the protein's functions, mutations often have profound effects on the fitness of the host. This is apparent both from experimental studies, which implicated numerous missense variants in diseases, as well as from evolutionary signals that allow elucidating the physicochemical constraints that intermembrane and aqueous environments bring. In this review, we report on the current state of knowledge acquired on missense variants (referred to as to single amino acid variants) affecting membrane proteins as well as the insights that can be extrapolated from data already available. This includes an overview of the annotations for membrane protein variants that have been collated within databases dedicated to the topic, bioinformatics approaches that leverage evolutionary information in order to shed light on previously uncharacterized membrane protein structures or interaction interfaces, tools for predicting the effects of mutations tailored specifically towards the characteristics of membrane proteins as well as two clinically relevant case studies explaining the implications of mutated membrane proteins in cancer and cardiomyopathy.

Assessing the accuracy of contact predictions in CASP13

The accuracy of sequence-based tertiary contact predictions was assessed in a blind prediction experiment at the CASP13 meeting. After 4 years of significant improvements in prediction accuracy, another dramatic advance has taken place since CASP12 was held 2 years ago. The precision of predicting the top L/5 contacts in the free modeling category, where L is the corresponding length of the protein in residues, has exceeded 70%. As a comparison, the best-performing group at CASP12 with a 47% precision would have finished below the top 1/3 of the CASP13 groups. Extensively trained deep neural network approaches dominate the top performing algorithms, which appear to efficiently integrate information on coevolving residues and interacting fragments or possibly utilize memories of sequence similarities and sometimes can deliver accurate results even in the absence of virtually any target specific evolutionary information. If the current performance is evaluated by F-score on L contacts, it stands around 24% right now, which, despite the tremendous impact and advance in improving its utility for structure modeling, also suggests that there is much room left for further improvement.

Protein Inter-Residue Contacts Prediction: Methods, Performances and Applications

Background:

Protein inter-residue contacts prediction play an important role in the field of protein structure and function research. As a low-dimensional representation of protein tertiary structure, protein inter-residue contacts could greatly help de novo protein structure prediction methods to reduce the conformational search space. Over the past two decades, various methods have been developed for protein inter-residue contacts prediction.

Objective:

We provide a comprehensive and systematic review of protein inter-residue contacts prediction methods.

Results:

Protein inter-residue contacts prediction methods are roughly classified into five categories: correlated mutations methods, machine-learning methods, fusion methods, templatebased methods and 3D model-based methods. In this paper, firstly we describe the common definition of protein inter-residue contacts and show the typical application of protein inter-residue contacts. Then, we present a comprehensive review of the three main categories for protein interresidue contacts prediction: correlated mutations methods, machine-learning methods and fusion methods. Besides, we analyze the constraints for each category. Furthermore, we compare several representative methods on the CASP11 dataset and discuss performances of these methods in detail.

Conclusion:

Correlated mutations methods achieve better performances for long-range contacts, while the machine-learning method performs well for short-range contacts. Fusion methods could take advantage of the machine-learning and correlated mutations methods. Employing more effective fusion strategy could be helpful to further improve the performances of fusion methods.

A large-scale comparative assessment of methods for residue-residue contact prediction

Sequence-based prediction of residue-residue contact in proteins becomes increasingly more important for improving protein structure prediction in the big data era. In this study, we performed a large-scale comparative assessment of 15 locally installed contact predictors. To assess these methods, we collected a big data set consisting of 680 nonredundant proteins covering different structural classes and target difficulties. We investigated a wide range of factors that may influence the precision of contact prediction, including target difficulty, structural class, the alignment depth and distribution of contact pairs in a protein structure. We found that: (1) the machine learning-based methods outperform the direct-coupling-based methods for short-range contact prediction, while the latter are significantly better for long-range contact prediction. The consensus-based methods, which combine machine learning and direct-coupling methods, perform the best. (2) The target difficulty does not have clear influence on the machine learning-based methods, while it does affect the direct-coupling and consensus-based methods significantly. (3) The alignment depth has relatively weak effect on the machine learning-based methods. However, for the direct-coupling-based methods and consensus-based methods, the predicted contacts for targets with deeper alignment tend to be more accurate. (4) All methods perform relatively better on β and α + β proteins than on α proteins. (5) Residues buried in the core of protein structure are more prone to be in contact than residues on the surface (22 versus 6%). We believe these are useful results for guiding future development of new approach to contact prediction.

NeBcon: protein contact map prediction using neural network training coupled with naïve Bayes classifiers

Motivation

Recent CASP experiments have witnessed exciting progress on folding large-size non-humongous proteins with the assistance of co-evolution based contact predictions. The success is however anecdotal due to the requirement of the contact prediction methods for the high volume of sequence homologs that are not available to most of the non-humongous protein targets. Development of efficient methods that can generate balanced and reliable contact maps for different type of protein targets is essential to enhance the success rate of the ab initio protein structure prediction.

Results

We developed a new pipeline, NeBcon, which uses the naïve Bayes classifier (NBC) theorem to combine eight state of the art contact methods that are built from co-evolution and machine learning approaches. The posterior probabilities of the NBC model are then trained with intrinsic structural features through neural network learning for the final contact map prediction. NeBcon was tested on 98 non-redundant proteins, which improves the accuracy of the best co-evolution based meta-server predictor by 22%; the magnitude of the improvement increases to 45% for the hard targets that lack sequence and structural homologs in the databases. Detailed data analysis showed that the major contribution to the improvement is due to the optimized NBC combination of the complementary information from both co-evolution and machine learning predictions. The neural network training also helps to improve the coupling of the NBC posterior probability and the intrinsic structural features, which were found particularly important for the proteins that do not have sufficient number of homologous sequences to derive reliable co-evolution profiles.

Availiablity and Implementation

On-line server and standalone package of the program are available at http://zhanglab.ccmb.med.umich.edu/NeBcon/ .

Contact

zhng@umich.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

RRCRank: a fusion method using rank strategy for residue-residue contact prediction

Background

In structural biology area, protein residue-residue contacts play a crucial role in protein structure prediction. Some researchers have found that the predicted residue-residue contacts could effectively constrain the conformational search space, which is significant for de novo protein structure prediction. In the last few decades, related researchers have developed various methods to predict residue-residue contacts, especially, significant performance has been achieved by using fusion methods in recent years. In this work, a novel fusion method based on rank strategy has been proposed to predict contacts. Unlike the traditional regression or classification strategies, the contact prediction task is regarded as a ranking task. First, two kinds of features are extracted from correlated mutations methods and ensemble machine-learning classifiers, and then the proposed method uses the learning-to-rank algorithm to predict contact probability of each residue pair.

Results

First, we perform two benchmark tests for the proposed fusion method (RRCRank) on CASP11 dataset and CASP12 dataset respectively. The test results show that the RRCRank method outperforms other well-developed methods, especially for medium and short range contacts. Second, in order to verify the superiority of ranking strategy, we predict contacts by using the traditional regression and classification strategies based on the same features as ranking strategy. Compared with these two traditional strategies, the proposed ranking strategy shows better performance for three contact types, in particular for long range contacts. Third, the proposed RRCRank has been compared with several state-of-the-art methods in CASP11 and CASP12. The results show that the RRCRank could achieve comparable prediction precisions and is better than three methods in most assessment metrics.

Conclusions

The learning-to-rank algorithm is introduced to develop a novel rank-based method for the residue-residue contact prediction of proteins, which achieves state-of-the-art performance based on the extensive assessment.

Electronic supplementary material

The online version of this article (10.1186/s12859-017-1811-9) contains supplementary material, which is available to authorized users.

Co-evolution techniques are reshaping the way we do structural bioinformatics

Co-evolution techniques were originally conceived to assist in protein structure prediction by inferring pairs of residues that share spatial proximity. However, the functional relationships that can be extrapolated from co-evolution have also proven to be useful in a wide array of structural bioinformatics applications. These techniques are a powerful way to extract structural and functional information in a sequence-rich world.

Applications of contact predictions to structural biology

Evolutionary pressure on residue interactions, intramolecular or intermolecular, that are important for protein structure or function can lead to covariance between the two positions. Recent methodological advances allow much more accurate contact predictions to be derived from this evolutionary covariance signal. The practical application of contact predictions has largely been confined to structural bioinformatics, yet, as this work seeks to demonstrate, the data can be of enormous value to the structural biologist working in X-ray crystallo-graphy, cryo-EM or NMR. Integrative structural bioinformatics packages such as Rosetta can already exploit contact predictions in a variety of ways. The contribution of contact predictions begins at construct design, where structural domains may need to be expressed separately and contact predictions can help to predict domain limits. Structure solution by molecular replacement (MR) benefits from contact predictions in diverse ways: in difficult cases, more accurate search models can be constructed using ab initio modelling when predictions are available, while intermolecular contact predictions can allow the construction of larger, oligomeric search models. Furthermore, MR using supersecondary motifs or large-scale screens against the PDB can exploit information, such as the parallel or antiparallel nature of any β-strand pairing in the target, that can be inferred from contact predictions. Contact information will be particularly valuable in the determination of lower resolution structures by helping to assign sequence register. In large complexes, contact information may allow the identity of a protein responsible for a certain region of density to be determined and then assist in the orientation of an available model within that density. In NMR, predicted contacts can provide long-range information to extend the upper size limit of the technique in a manner analogous but complementary to experimental methods. Finally, predicted contacts can distinguish between biologically relevant interfaces and mere lattice contacts in a final crystal structure, and have potential in the identification of functionally important regions and in foreseeing the consequences of mutations.

Deep learning for computational chemistry

The rise and fall of artificial neural networks is well documented in the scientific literature of both computer science and computational chemistry. Yet almost two decades later, we are now seeing a resurgence of interest in deep learning, a machine learning algorithm based on multilayer neural networks. Within the last few years, we have seen the transformative impact of deep learning in many domains, particularly in speech recognition and computer vision, to the extent that the majority of expert practitioners in those field are now regularly eschewing prior established models in favor of deep learning models. In this review, we provide an introductory overview into the theory of deep neural networks and their unique properties that distinguish them from traditional machine learning algorithms used in cheminformatics. By providing an overview of the variety of emerging applications of deep neural networks, we highlight its ubiquity and broad applicability to a wide range of challenges in the field, including quantitative structure activity relationship, virtual screening, protein structure prediction, quantum chemistry, materials design, and property prediction. In reviewing the performance of deep neural networks, we observed a consistent outperformance against non-neural networks state-of-the-art models across disparate research topics, and deep neural network-based models often exceeded the "glass ceiling" expectations of their respective tasks. Coupled with the maturity of GPU-accelerated computing for training deep neural networks and the exponential growth of chemical data on which to train these networks on, we anticipate that deep learning algorithms will be a valuable tool for computational chemistry. © 2017 Wiley Periodicals, Inc.

Identification of Position-Specific Correlations between DNA-Binding Domains and Their Binding Sites. Application to the MerR Family of Transcription Factors

The large and increasing volume of genomic data analyzed by comparative methods provides information about transcription factors and their binding sites that, in turn, enables statistical analysis of correlations between factors and sites, uncovering mechanisms and evolution of specific protein-DNA recognition. Here we present an online tool, Prot-DNA-Korr, designed to identify and analyze crucial protein-DNA pairs of positions in a family of transcription factors. Correlations are identified by analysis of mutual information between columns of protein and DNA alignments. The algorithm reduces the effects of common phylogenetic history and of abundance of closely related proteins and binding sites. We apply it to five closely related subfamilies of the MerR family of bacterial transcription factors that regulate heavy metal resistance systems. We validate the approach using known 3D structures of MerR-family proteins in complexes with their cognate DNA binding sites and demonstrate that a significant fraction of correlated positions indeed form specific side-chain-to-base contacts. The joint distribution of amino acids and nucleotides hence may be used to predict changes of specificity for point mutations in transcription factors.

Protein Residue Contacts and Prediction Methods

In the field of computational structural proteomics, contact predictions have shown new prospects of solving the longstanding problem of ab initio protein structure prediction. In the last few years, application of deep learning algorithms and availability of large protein sequence databases, combined with improvement in methods that derive contacts from multiple sequence alignments, have shown a huge increase in the precision of contact prediction. In addition, these predicted contacts have also been used to build three-dimensional models from scratch.In this chapter, we briefly discuss many elements of protein residue-residue contacts and the methods available for prediction, focusing on a state-of-the-art contact prediction tool, DNcon. Illustrating with a case study, we describe how DNcon can be used to make ab initio contact predictions for a given protein sequence and discuss how the predicted contacts may be analyzed and evaluated.

Protein contact prediction by integrating joint evolutionary coupling analysis and supervised learning

MOTIVATION

Protein contact prediction is important for protein structure and functional study. Both evolutionary coupling (EC) analysis and supervised machine learning methods have been developed, making use of different information sources. However, contact prediction is still challenging especially for proteins without a large number of sequence homologs.

RESULTS

This article presents a group graphical lasso (GGL) method for contact prediction that integrates joint multi-family EC analysis and supervised learning to improve accuracy on proteins without many sequence homologs. Different from existing single-family EC analysis that uses residue coevolution information in only the target protein family, our joint EC analysis uses residue coevolution in both the target family and its related families, which may have divergent sequences but similar folds. To implement this, we model a set of related protein families using Gaussian graphical models and then coestimate their parameters by maximum-likelihood, subject to the constraint that these parameters shall be similar to some degree. Our GGL method can also integrate supervised learning methods to further improve accuracy. Experiments show that our method outperforms existing methods on proteins without thousands of sequence homologs, and that our method performs better on both conserved and family-specific contacts.

AVAILABILITY AND IMPLEMENTATION

See http://raptorx.uchicago.edu/ContactMap/ for a web server implementing the method.

CONTACT

j3xu@ttic.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Enhancement of E. coli acyl-CoA synthetase FadD activity on medium chain fatty acids

FadD catalyses the first step in E. coli beta-oxidation, the activation of free fatty acids into acyl-CoA thioesters. This activation makes fatty acids competent for catabolism and reduction into derivatives like alcohols and alkanes. Alcohols and alkanes derived from medium chain fatty acids (MCFAs, 6-12 carbons) are potential biofuels; however, FadD has low activity on MCFAs. Herein, we generate mutations in fadD that enhance its acyl-CoA synthetase activity on MCFAs. Homology modeling reveals that these mutations cluster on a face of FadD from which the co-product, AMP, is expected to exit. Using FadD homology models, we design additional FadD mutations that enhance E. coli growth rate on octanoate and provide evidence for a model wherein FadD activity on octanoate can be enhanced by aiding product exit. These studies provide FadD mutants useful for producing MCFA derivatives and a rationale to alter the substrate specificity of adenylating enzymes.

Toward an accurate prediction of inter-residue distances in proteins using 2D recursive neural networks

Background

Protein inter-residue contact maps provide a translation and rotation invariant topological representation of a protein. They can be used as an intermediary step in protein structure predictions. However, the prediction of contact maps represents an unbalanced problem as far fewer examples of contacts than non-contacts exist in a protein structure.

In this study we explore the possibility of completely eliminating the unbalanced nature of the contact map prediction problem by predicting real-value distances between residues. Predicting full inter-residue distance maps and applying them in protein structure predictions has been relatively unexplored in the past.

Results

We initially demonstrate that the use of native-like distance maps is able to reproduce 3D structures almost identical to the targets, giving an average RMSD of 0.5Å. In addition, the corrupted physical maps with an introduced random error of ±6Å are able to reconstruct the targets within an average RMSD of 2Å.

After demonstrating the reconstruction potential of distance maps, we develop two classes of predictors using two-dimensional recursive neural networks: an ab initio predictor that relies only on the protein sequence and evolutionary information, and a template-based predictor in which additional structural homology information is provided. We find that the ab initio predictor is able to reproduce distances with an RMSD of 6Å, regardless of the evolutionary content provided. Furthermore, we show that the template-based predictor exploits both sequence and structure information even in cases of dubious homology and outperforms the best template hit with a clear margin of up to 3.7Å.

Lastly, we demonstrate the ability of the two predictors to reconstruct the CASP9 targets shorter than 200 residues producing the results similar to the state of the machine learning art approach implemented in the Distill server.

Conclusions

The methodology presented here, if complemented by more complex reconstruction protocols, can represent a possible path to improve machine learning algorithms for 3D protein structure prediction. Moreover, it can be used as an intermediary step in protein structure predictions either on its own or complemented by NMR restraints.

Evaluation of residue-residue contact prediction in CASP10

We present the results of the assessment of the intramolecular residue-residue contact predictions from 26 prediction groups participating in the 10th round of the CASP experiment. The most recently developed direct coupling analysis methods did not take part in the experiment likely because they require a very deep sequence alignment not available for any of the 114 CASP10 targets. The performance of contact prediction methods was evaluated with the measures used in previous CASPs (i.e., prediction accuracy and the difference between the distribution of the predicted contacts and that of all pairs of residues in the target protein), as well as new measures, such as the Matthews correlation coefficient, the area under the precision-recall curve and the ranks of the first correctly and incorrectly predicted contact. We also evaluated the ability to detect interdomain contacts and tested whether the difficulty of predicting contacts depends upon the protein length and the depth of the family sequence alignment. The analyses were carried out on the target domains for which structural homologs did not exist or were difficult to identify. The evaluation was performed for all types of contacts (short, medium, and long-range), with emphasis placed on long-range contacts, i.e. those involving residues separated by at least 24 residues along the sequence. The assessment suggests that the best CASP10 contact prediction methods perform at approximately the same level, and comparably to those participating in CASP9.

Chemical genomics approach for GPCR-ligand interaction prediction and extraction of ligand binding determinants

Chemical genomics research has revealed that G-protein coupled receptors (GPCRs) interact with a variety of ligands and that a large number of ligands are known to bind GPCRs even with low transmembrane (TM) sequence similarity. It is crucial to extract informative binding region propensities from large quantities of bioactivity data. To address this issue, we propose a machine learning approach that enables identification of both chemical substructures and amino acid properties that are associated with ligand binding, which can be applied to virtual ligand screening on a GPCR-wide scale. We also address the question of how to select plausible negative noninteraction pairs based on a statistical approach in order to develop reliable prediction models for GPCR-ligand interactions. The key interaction sites estimated by our approach can be of great use not only for screening of active compounds but also for modification of active compounds with the aim of improving activity or selectivity.

Effective inter-residue contact definitions for accurate protein fold recognition

BACKGROUND

Effective encoding of residue contact information is crucial for protein structure prediction since it has a unique role to capture long-range residue interactions compared to other commonly used scoring terms. The residue contact information can be incorporated in structure prediction in several different ways: It can be incorporated as statistical potentials or it can be also used as constraints in ab initio structure prediction. To seek the most effective definition of residue contacts for template-based protein structure prediction, we evaluated 45 different contact definitions, varying bases of contacts and distance cutoffs, in terms of their ability to identify proteins of the same fold.

RESULTS

We found that overall the residue contact pattern can distinguish protein folds best when contacts are defined for residue pairs whose Cβ atoms are at 7.0 Å or closer to each other. Lower fold recognition accuracy was observed when inaccurate threading alignments were used to identify common residue contacts between protein pairs. In the case of threading, alignment accuracy strongly influences the fraction of common contacts identified among proteins of the same fold, which eventually affects the fold recognition accuracy. The largest deterioration of the fold recognition was observed for β-class proteins when the threading methods were used because the average alignment accuracy was worst for this fold class. When results of fold recognition were examined for individual proteins, we found that the effective contact definition depends on the fold of the proteins. A larger distance cutoff is often advantageous for capturing spatial arrangement of the secondary structures which are not physically in contact. For capturing contacts between neighboring β strands, considering the distance between Cα atoms is better than the Cβ-based distance because the side-chain of interacting residues on β strands sometimes point to opposite directions.

CONCLUSION

Residue contacts defined by Cβ-Cβ distance of 7.0 Å work best overall among tested to identify proteins of the same fold. We also found that effective contact definitions differ from fold to fold, suggesting that using different residue contact definition specific for each template will lead to improvement of the performance of threading.

Toward optimal fragment generations for ab initio protein structure assembly

Fragment assembly using structural motifs excised from other solved proteins has shown to be an efficient method for ab initio protein-structure prediction. However, how to construct accurate fragments, how to derive optimal restraints from fragments, and what the best fragment length is are the basic issues yet to be systematically examined. In this work, we developed a gapless-threading method to generate position-specific structure fragments. Distance profiles and torsion angle pairs are then derived from the fragments by statistical consistency analysis, which achieved comparable accuracy with the machine-learning-based methods although the fragments were taken from unrelated proteins. When measured by both accuracies of the derived distance profiles and torsion angle pairs, we come to a consistent conclusion that the optimal fragment length for structural assembly is around 10, and at least 100 fragments at each location are needed to achieve optimal structure assembly. The distant profiles and torsion angle pairs as derived by the fragments have been successfully used in QUARK for ab initio protein structure assembly and are provided by the QUARK online server at http://zhanglab.ccmb. med.umich.edu/QUARK/.

Deep architectures for protein contact map prediction

MOTIVATION

Residue-residue contact prediction is important for protein structure prediction and other applications. However, the accuracy of current contact predictors often barely exceeds 20% on long-range contacts, falling short of the level required for ab initio structure prediction.

RESULTS

Here, we develop a novel machine learning approach for contact map prediction using three steps of increasing resolution. First, we use 2D recursive neural networks to predict coarse contacts and orientations between secondary structure elements. Second, we use an energy-based method to align secondary structure elements and predict contact probabilities between residues in contacting alpha-helices or strands. Third, we use a deep neural network architecture to organize and progressively refine the prediction of contacts, integrating information over both space and time. We train the architecture on a large set of non-redundant proteins and test it on a large set of non-homologous domains, as well as on the set of protein domains used for contact prediction in the two most recent CASP8 and CASP9 experiments. For long-range contacts, the accuracy of the new CMAPpro predictor is close to 30%, a significant increase over existing approaches.

AVAILABILITY

CMAPpro is available as part of the SCRATCH suite at http://scratch.proteomics.ics.uci.edu/.

CONTACT

pfbaldi@uci.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Contact map prediction using a large-scale ensemble of rule sets and the fusion of multiple predicted structural features

MOTIVATION

The prediction of a protein's contact map has become in recent years, a crucial stepping stone for the prediction of the complete 3D structure of a protein. In this article, we describe a methodology for this problem that was shown to be successful in CASP8 and CASP9. The methodology is based on (i) the fusion of the prediction of a variety of structural aspects of protein residues, (ii) an ensemble strategy used to facilitate the training process and (iii) a rule-based machine learning system from which we can extract human-readable explanations of the predictor and derive useful information about the contact map representation.

RESULTS

The main part of the evaluation is the comparison against the sequence-based contact prediction methods from CASP9, where our method presented the best rank in five out of the six evaluated metrics. We also assess the impact of the size of the ensemble used in our predictor to show the trade-off between performance and training time of our method. Finally, we also study the rule sets generated by our machine learning system. From this analysis, we are able to estimate the contribution of the attributes in our representation and how these interact to derive contact predictions.

AVAILABILITY

http://icos.cs.nott.ac.uk/servers/psp.html.

CONTACT

natalio.krasnogor@nottingham.ac.uk

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Mapping the mutual information network of enzymatic families in the protein structure to unveil functional features

Amino acids committed to a particular function correlate tightly along evolution and tend to form clusters in the 3D structure of the protein. Consequently, a protein can be seen as a network of co-evolving clusters of residues. The goal of this work is two-fold: first, we have combined mutual information and structural data to describe the amino acid networks within a protein and their interactions. Second, we have investigated how this information can be used to improve methods of prediction of functional residues by reducing the search space. As a main result, we found that clusters of co-evolving residues related to the catalytic site of an enzyme have distinguishable topological properties in the network. We also observed that these clusters usually evolve independently, which could be related to a fail-safe mechanism. Finally, we discovered a significant enrichment of functional residues (e.g. metal binding, susceptibility to detrimental mutations) in the clusters, which could be the foundation of new prediction tools.

Integrated analysis of residue coevolution and protein structure in ABC transporters

Intraprotein side chain contacts can couple the evolutionary process of amino acid substitution at one position to that at another. This coupling, known as residue coevolution, may vary in strength. Conserved contacts thus not only define 3-dimensional protein structure, but also indicate which residue-residue interactions are crucial to a protein's function. Therefore, prediction of strongly coevolving residue-pairs helps clarify molecular mechanisms underlying function. Previously, various coevolution detectors have been employed separately to predict these pairs purely from multiple sequence alignments, while disregarding available structural information. This study introduces an integrative framework that improves the accuracy of such predictions, relative to previous approaches, by combining multiple coevolution detectors and incorporating structural contact information. This framework is applied to the ABC-B and ABC-C transporter families, which include the drug exporter P-glycoprotein involved in multidrug resistance of cancer cells, as well as the CFTR chloride channel linked to cystic fibrosis disease. The predicted coevolving pairs are further analyzed based on conformational changes inferred from outward- and inward-facing transporter structures. The analysis suggests that some pairs coevolved to directly regulate conformational changes of the alternating-access transport mechanism, while others to stabilize rigid-body-like components of the protein structure. Moreover, some identified pairs correspond to residues previously implicated in cystic fibrosis.

The MULTICOM toolbox for protein structure prediction

Background

As genome sequencing is becoming routine in biomedical research, the total number of protein sequences is increasing exponentially, recently reaching over 108 million. However, only a tiny portion of these proteins (i.e. ~75,000 or < 0.07%) have solved tertiary structures determined by experimental techniques. The gap between protein sequence and structure continues to enlarge rapidly as the throughput of genome sequencing techniques is much higher than that of protein structure determination techniques. Computational software tools for predicting protein structure and structural features from protein sequences are crucial to make use of this vast repository of protein resources.

Results

To meet the need, we have developed a comprehensive MULTICOM toolbox consisting of a set of protein structure and structural feature prediction tools. These tools include secondary structure prediction, solvent accessibility prediction, disorder region prediction, domain boundary prediction, contact map prediction, disulfide bond prediction, beta-sheet topology prediction, fold recognition, multiple template combination and alignment, template-based tertiary structure modeling, protein model quality assessment, and mutation stability prediction.

Conclusions

These tools have been rigorously tested by many users in the last several years and/or during the last three rounds of the Critical Assessment of Techniques for Protein Structure Prediction (CASP7-9) from 2006 to 2010, achieving state-of-the-art or near performance. In order to facilitate bioinformatics research and technological development in the field, we have made the MULTICOM toolbox freely available as web services and/or software packages for academic use and scientific research. It is available at http://sysbio.rnet.missouri.edu/multicom_toolbox/.

Ab initio protein structure assembly using continuous structure fragments and optimized knowledge-based force field

Ab initio protein folding is one of the major unsolved problems in computational biology owing to the difficulties in force field design and conformational search. We developed a novel program, QUARK, for template-free protein structure prediction. Query sequences are first broken into fragments of 1-20 residues where multiple fragment structures are retrieved at each position from unrelated experimental structures. Full-length structure models are then assembled from fragments using replica-exchange Monte Carlo simulations, which are guided by a composite knowledge-based force field. A number of novel energy terms and Monte Carlo movements are introduced and the particular contributions to enhancing the efficiency of both force field and search engine are analyzed in detail. QUARK prediction procedure is depicted and tested on the structure modeling of 145 nonhomologous proteins. Although no global templates are used and all fragments from experimental structures with template modeling score >0.5 are excluded, QUARK can successfully construct 3D models of correct folds in one-third cases of short proteins up to 100 residues. In the ninth community-wide Critical Assessment of protein Structure Prediction experiment, QUARK server outperformed the second and third best servers by 18 and 47% based on the cumulative Z-score of global distance test-total scores in the FM category. Although ab initio protein folding remains a significant challenge, these data demonstrate new progress toward the solution of the most important problem in the field.

Improving protein structure prediction using multiple sequence-based contact predictions

Although residue-residue contact maps dictate the topology of proteins, sequence-based ab initio contact predictions have been found little use in actual structure prediction due to the low accuracy. We developed a composite set of nine SVM-based contact predictors that are used in I-TASSER simulation in combination with sparse template contact restraints. When testing the strategy on 273 nonhomologous targets, remarkable improvements of I-TASSER models were observed for both easy and hard targets, with p value by Student's t test<0.00001 and 0.001, respectively. In several cases, template modeling score increases by >30%, which essentially converts "nonfoldable" targets into "foldable" ones. In CASP9, I-TASSER employed ab initio contact predictions, and generated models for 26 FM targets with a GDT-score 16% and 44% higher than the second and third best servers from other groups, respectively. These findings demonstrate a new avenue to improve the accuracy of protein structure prediction especially for free-modeling targets.

Enhanced Inter-helical Residue Contact Prediction in Transmembrane Proteins

In this paper, based on a recent work by McAllister and Floudas who developed a mathematical optimization model to predict the contacts in transmembrane alpha-helical proteins from a limited protein data set [1], we have enhanced this method by 1) building a more comprehensive data set for transmembrane alpha-helical proteins and this enhanced data set is then used to construct the probability sets, MIN-1N and MIN-2N, for residue contact prediction, 2) enhancing the mathematical model via modifications of several important physical constraints and 3) applying a new blind contact prediction scheme on different protein sets proposed from analyzing the contact prediction on 65 proteins from Fuchs et al. [2]. The blind contact prediction scheme has been tested on two different membrane protein sets. Firstly it is applied to five carefully selected proteins from the training set. The contact prediction of these five proteins uses probability sets built by excluding the target protein from the training set, and an average accuracy of 56% was obtained. Secondly, it is applied to six independent membrane proteins with complicated topologies, and the prediction accuracies are 73% for 2ZY9A, 21% for 3KCUA, 46% for 2W1PA, 64% for 3CN5A, 77% for 3IXZA and 83% for 3K3FA. The average prediction accuracy for the six proteins is 60.7%. The proposed approach is also compared with a support vector machine method (TMhit [3]) and it is shown that it exhibits better prediction accuracy.

Evaluation of residue-residue contact predictions in CASP9

This work presents the results of the assessment of the intramolecular residue-residue contact predictions submitted to CASP9. The methodology for the assessment does not differ from that used in previous CASPs, with two basic evaluation measures being the precision in recognizing contacts and the difference between the distribution of distances in the subset of predicted contact pairs versus all pairs of residues in the structure. The emphasis is placed on the prediction of long-range contacts (i.e., contacts between residues separated by at least 24 residues along sequence) in target proteins that cannot be easily modeled by homology. Although there is considerable activity in the field, the current analysis reports no discernable progress since CASP8.

Application of information theory to feature selection in protein docking

In the era of structural genomics, the prediction of protein interactions using docking algorithms is an important goal. The success of this method critically relies on the identification of good docking solutions among a vast excess of false solutions. We have adapted the concept of mutual information (MI) from information theory to achieve a fast and quantitative screening of different structural features with respect to their ability to discriminate between physiological and nonphysiological protein interfaces. The strategy includes the discretization of each structural feature into distinct value ranges to optimize its mutual information. We have selected 11 structural features and two datasets to demonstrate that the MI is dimensionless and can be directly compared for diverse structural features and between datasets of different sizes. Conversion of the MI values into a simple scoring function revealed that those features with a higher MI are actually more powerful for the identification of good docking solutions. Thus, an MI-based approach allows the rapid screening of structural features with respect to their information content and should therefore be helpful for the design of improved scoring functions in future. In addition, the concept presented here may also be adapted to related areas that require feature selection for biomolecules or organic ligands.

Identification of missense mutation (I12T) in the BSND gene and bioinformatics analysis

Nonsyndromic hearing loss is a paradigm of genetic heterogeneity with 85 loci and 39 nuclear disease genes reported so far. Mutations of BSND have been shown to cause Bartter syndrome type IV, characterized by significant renal abnormalities and deafness and nonsyndromic nearing loss. We studied a Pakistani consanguineous family. Clinical examinations of affected individuals did not reveal the presence of any associated signs, which are hallmarks of the Bartter syndrome type IV. Linkage analysis identified an area of 18.36 Mb shared by all affected individuals between markers D1S2706 and D1S1596. A maximum two-point LOD score of 2.55 with markers D1S2700 and multipoint LOD score of 3.42 with marker D1S1661 were obtained. BSND mutation, that is, p.I12T, cosegregated in all extant members of our pedigree. BSND mutations can cause nonsyndromic hearing loss, and it is a second report for this mutation. The respected protein, that is, BSND, was first modeled, and then, the identified mutation was further analyzed by using different bioinformatics tools; finally, this protein and its mutant was docked with CLCNKB and REN, interactions of BSND, respectively.

Computational approaches to therapeutic peptide discovery

The development of peptides with therapeutic activities can be based on naturally occurring peptides or alternatively on de novo design. The discovery of natural peptides is often a matter of serendipity. In part, this is because natural peptides are typically proteolytically cleaved out from precursor proteins, a feature that averts the direct benefits of the genomic revolution. The first part of this review describes attempts to create a more systematic identification of natural peptides relying on a two step process. In the initial step, an in silico peptidome is predicted through the use of machine learning. Then, various computational biology tools are tailored to focus on peptides predicted to have the desired biological activity; for example, activating a GPCR or modulating the cellular arm of the immune system. The second part of the review is devoted to de novo peptide design and focuses on arguably the simplest scenario in which the designed peptide corresponds to a contiguous protein subsequence. Amongst these peptides, those corresponding to helical segments are prominent, mainly due to their relative ability to fold independently. Inspired by the clinical success of viral entry inhibitors, which are peptides corresponding to helical segments in viral envelope proteins, a computational tool for the identification of intramolecular helix-helix interactions was developed. Using this approach, peptides having anti-cancer, anti-angiogenic, and anti-inflammatory activities have been recently rationally designed and biologically characterized.

Molecular model of hexokinase binding to the outer mitochondrial membrane porin (VDAC1): Implication for the design of new cancer therapies

A key feature of many cancers is the capacity and the propensity to metabolize glucose to lactic acid at a very high rate even in the presence of oxygen. This characteristic was first discovered in 1924 by Otto Heinrich Warburg. Hexokinase, the first enzyme in the glycolytic pathway, not only improves the cell's energy supply in malignant cells, but also protects cancer cells against apoptosis through direct interaction with mitochondria and with the Voltage Dependent Anion Channel 1 (VDAC1). The rupture of HK:VDAC1 protein complex provides a therapeutic opportunity, as this association appears to protect tumor cells from mitochondrial outer membrane permeabilization, an event that marks the point of no return in multiple pathways leading to cell death. In the absence of a crystallographic structure and in order to perform an in silico screening of possible small molecules able to inhibit the protein association, we are presenting a computational model of HK-I:VDAC1 complex. It appears as evident how the first 15 N-terminal residues of HK-I interact with the inner part of the barrel of VDAC1 and not with the outside walls, within the mitochondrial membrane as previously believed. This finding is in agreement with the existence of a secondary ATP binding site in the same N-terminal region of HK-I which seems to have a crucial role in HK-I interaction with VDAC1. This evidence appears to be in accord also with the high levels of ATP that are found in cancer cells. Eventually such arrangements may contribute to stabilize the tertiary structure of VDAC1 while shielding from pro-apoptotic factor binding, protecting in a synergic way the tumoral cell from programmed death.

Exposing the co-adaptive potential of protein-protein interfaces through computational sequence design

MOTIVATION

In nature, protein-protein interactions are constantly evolving under various selective pressures. Nonetheless, it is expected that crucial interactions are maintained through compensatory mutations between interacting proteins. Thus, many studies have used evolutionary sequence data to extract such occurrences of correlated mutation. However, this research is confounded by other evolutionary pressures that contribute to sequence covariance, such as common ancestry.

RESULTS

Here, we focus exclusively on the compensatory mutations deriving from physical protein interactions, by performing large-scale computational mutagenesis experiments for >260 protein-protein interfaces. We investigate the potential for co-adaptability present in protein pairs that are always found together in nature (obligate) and those that are occasionally in complex (transient). By modeling each complex both in bound and unbound forms, we find that naturally transient complexes possess greater relative capacity for correlated mutation than obligate complexes, even when differences in interface size are taken into account.

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.

Identifying and seeing beyond multiple sequence alignment errors using intra-molecular protein covariation

Background

There is currently no way to verify the quality of a multiple sequence alignment that is independent of the assumptions used to build it. Sequence alignments are typically evaluated by a number of established criteria: sequence conservation, the number of aligned residues, the frequency of gaps, and the probable correct gap placement. Covariation analysis is used to find putatively important residue pairs in a sequence alignment. Different alignments of the same protein family give different results demonstrating that covariation depends on the quality of the sequence alignment. We thus hypothesized that current criteria are insufficient to build alignments for use with covariation analyses.

Methodology/Principal Findings

We show that current criteria are insufficient to build alignments for use with covariation analyses as systematic sequence alignment errors are present even in hand-curated structure-based alignment datasets like those from the Conserved Domain Database. We show that current non-parametric covariation statistics are sensitive to sequence misalignments and that this sensitivity can be used to identify systematic alignment errors. We demonstrate that removing alignment errors due to 1) improper structure alignment, 2) the presence of paralogous sequences, and 3) partial or otherwise erroneous sequences, improves contact prediction by covariation analysis. Finally we describe two non-parametric covariation statistics that are less sensitive to sequence alignment errors than those described previously in the literature.

Conclusions/Significance

Protein alignments with errors lead to false positive and false negative conclusions (incorrect assignment of covariation and conservation, respectively). Covariation analysis can provide a verification step, independent of traditional criteria, to identify systematic misalignments in protein alignments. Two non-parametric statistics are shown to be somewhat insensitive to misalignment errors, providing increased confidence in contact prediction when analyzing alignments with erroneous regions because of an emphasis on they emphasize pairwise covariation over group covariation.

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 beta, alpha + beta, and alpha/beta proteins. The total energy of a protein is expressed as sum of a C(alpha)-C(alpha) 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 beta-sheet alignments. These beta-sheet alignments are used as constraints for contacts between residues of beta-sheets. This model was tested on three independent protein test sets and CASP8 test proteins consisting of beta, alpha + beta, alpha/beta proteins and it was found to perform very well. The average accuracy of the predictions (separated by at least six residues) was approximately 61%. The average true positive and false positive distances were also calculated for each of the test sets and they are 7.58 A and 15.88 A, 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.

BCL::contact-low confidence fold recognition hits boost protein contact prediction and de novo structure determination

Knowledge of all residue-residue contacts within a protein allows determination of the protein fold. Accurate prediction of even a subset of long-range contacts (contacts between amino acids far apart in sequence) can be instrumental for determining tertiary structure. Here we present BCL::Contact, a novel contact prediction method that utilizes artificial neural networks (ANNs) and specializes in the prediction of medium to long-range contacts. BCL::Contact comes in two modes: sequence-based and structure-based. The sequence-based mode uses only sequence information and has individual ANNs specialized for helix-helix, helix-strand, strand-helix, strand-strand, and sheet-sheet contacts. The structure-based mode combines results from 32-fold recognition methods with sequence information to a consensus prediction. The two methods were presented in the 6(th) and 7(th) Critical Assessment of Techniques for Protein Structure Prediction (CASP) experiments. The present work focuses on elucidating the impact of fold recognition results onto contact prediction via a direct comparison of both methods on a joined benchmark set of proteins. The sequence-based mode predicted contacts with 42% accuracy (7% false positive rate), while the structure-based mode achieved 45% accuracy (2% false positive rate). Predictions by both modes of BCL::Contact were supplied as input to the protein tertiary structure prediction program Rosetta for a benchmark of 17 proteins with no close sequence homologs in the protein data bank (PDB). Rosetta created higher accuracy models, signified by an improvement of 1.3 A on average root mean square deviation (RMSD), when driven by the predicted contacts. Further, filtering Rosetta models by agreement with the predicted contacts enriches for native-like fold topologies.

Linear predictive coding representation of correlated mutation for protein sequence alignment

Background

Although both conservation and correlated mutation (CM) are important information reflecting the different sorts of context in multiple sequence alignment, most of alignment methods use sequence profiles that only represent conservation. There is no general way to represent correlated mutation and incorporate it with sequence alignment yet.

Methods

We develop a novel method, CM profile, to represent correlated mutation as the spectral feature derived by using linear predictive coding where correlated mutations among different positions are represented by a fixed number of values. We combine CM profile with conventional sequence profile to improve alignment quality.

Results

For distantly related protein pairs, using CM profile improves the profile-profile alignment with or without predicted secondary structure. Especially, at superfamily level, combining CM profile with sequence profile improves profile-profile alignment by 9.5% while predicted secondary structure does by 6.0%. More significantly, using both of them improves profile-profile alignment by 13.9%. We also exemplify the effectiveness of CM profile by demonstrating that the resulting alignment preserves share coevolution and contacts.

Conclusions

In this work, we introduce a novel method, CM profile, which represents correlated mutation information as paralleled form, and apply it to the protein sequence alignment problem. When combined with conventional sequence profile, CM profile improves alignment quality significantly better than predicted secondary structure information, which should be beneficial for target-template alignment in protein structure prediction. Because of the generality of CM profile, it can be used for other bioinformatics applications in the same way of using sequence profile.

Assessment of domain boundary predictions and the prediction of intramolecular contacts in CASP8

This article details the assessment process and evaluation results for two categories in the 8th Critical Assessment of Protein Structure Prediction experiment (CASP8). The domain prediction category was evaluated with a range of scores including the Normalized Domain Overlap score and a domain boundary distance measure. Residue-residue contact predictions were evaluated with standard CASP measures, prediction accuracy, and Xd. In the domain boundary prediction category, prediction methods still make reliable predictions for targets that have structural templates, but continue to struggle to make good predictions for the few ab initio targets in CASP. There was little indication of improvement in the domain prediction category. The contact prediction category demonstrated that there was renewed interest among predictors and despite the small sample size the results suggested that there had been an increase in prediction accuracy. In contrast to CASP7 contact specialists predicted contacts more accurately than the majority of tertiary structure predictors. Despite this small success, the lack of free modeling targets makes it unlikely that either category will be included in their present form in CASP9.

Reducing phylogenetic bias in correlated mutation analysis

Correlated mutation analysis (CMA) is a sequence-based approach for ab initio protein contact map prediction. The basis of this approach is the observed correlation between mutations in interacting amino acid residues. These correlations are often estimated by either calculating the Pearson's correlation coefficient (PCC) or the mutual information (MI) between columns in a multiple sequence alignment (MSA) of the protein of interest and its homologs. A major challenge of CMA is to filter out the background noise originating from phylogenetic relatedness between sequences included in the MSA. Recently, a procedure to reduce this background noise was demonstrated to improve an MI-based predictor. Herein, we tested whether a similar approach can also improve the performance of the classical PCC-based method. Indeed, performance improvements were achieved for all four major SCOP classes. Furthermore, the results reveal that the improved PCC-based method is superior to MI-based methods for proteins having MSAs of up to 100 sequences.

Protein secondary structure prediction

While the prediction of a native protein structure from sequence continues to remain a challenging problem, over the past decades computational methods have become quite successful in exploiting the mechanisms behind secondary structure formation. The great effort expended in this area has resulted in the development of a vast number of secondary structure prediction methods. Especially the combination of well-optimized/sensitive machine-learning algorithms and inclusion of homologous sequence information has led to increased prediction accuracies of up to 80%. In this chapter, we will first introduce some basic notions and provide a brief history of secondary structure prediction advances. Then a comprehensive overview of state-of-the-art prediction methods will be given. Finally, we will discuss open questions and challenges in this field and provide some practical recommendations for the user.

Disentangling direct from indirect co-evolution of residues in protein alignments

Predicting protein structure from primary sequence is one of the ultimate challenges in computational biology. Given the large amount of available sequence data, the analysis of co-evolution, i.e., statistical dependency, between columns in multiple alignments of protein domain sequences remains one of the most promising avenues for predicting residues that are contacting in the structure. A key impediment to this approach is that strong statistical dependencies are also observed for many residue pairs that are distal in the structure. Using a comprehensive analysis of protein domains with available three-dimensional structures we show that co-evolving contacts very commonly form chains that percolate through the protein structure, inducing indirect statistical dependencies between many distal pairs of residues. We characterize the distributions of length and spatial distance traveled by these co-evolving contact chains and show that they explain a large fraction of observed statistical dependencies between structurally distal pairs. We adapt a recently developed Bayesian network model into a rigorous procedure for disentangling direct from indirect statistical dependencies, and we demonstrate that this method not only successfully accomplishes this task, but also allows contacts with weak statistical dependency to be detected. To illustrate how additional information can be incorporated into our method, we incorporate a phylogenetic correction, and we develop an informative prior that takes into account that the probability for a pair of residues to contact depends strongly on their primary-sequence distance and the amount of conservation that the corresponding columns in the multiple alignment exhibit. We show that our model including these extensions dramatically improves the accuracy of contact prediction from multiple sequence alignments.