BCov: a method for predicting β-sheet topology using sparse inverse covariance estimation and integer programming

SSA: Subset sum approach to protein β-sheet structure prediction

The three-dimensional structures of proteins provide their functions and incorrect folding of its β-strands can be the cause of many diseases. There are two major approaches for determining protein structures: computational prediction and experimental methods that employ technologies such as Cryo-electron microscopy. Due to experimental methods's high costs, extended wait times for its lengthy processes, and incompleteness of results, computational prediction is an attractive alternative. As the focus of the present paper, β-sheet structure prediction is a major portion of overall protein structure prediction. Prediction of other substructures, such as α-helices, is simpler with lower computational time complexities. Brute force methods are the most common approach and dynamic programming is also utilized to generate all possible conformations. The current study introduces the Subset Sum Approach (SSA) for the direct search space generation method, which is shown to outperform the dynamic programming approach in terms of both time and space. For the first time, the present work has calculated both the state space cardinality of the dynamic programming approach and the search space cardinality of the general brute force approaches. In regard to a set of pruning rules, SSA has demonstrated higher efficiency with respect to both time and accuracy in comparison to state-of-the-art methods.

RDb2C2: an improved method to identify the residue-residue pairing in β strands

Background

Despite the great advance of protein structure prediction, accurate prediction of the structures of mainly β proteins is still highly challenging, but could be assisted by the knowledge of residue-residue pairing in β strands. Previously, we proposed a ridge-detection-based algorithm RDb₂C that adopted a multi-stage random forest framework to predict the β-β pairing given the amino acid sequence of a protein.

Results

In this work, we developed a second version of this algorithm, RDb₂C2, by employing the residual neural network to further enhance the prediction accuracy. In the benchmark test, this new algorithm improves the F1-score by > 10 percentage points, reaching impressively high values of ~ 72% and ~ 73% in the BetaSheet916 and BetaSheet1452 sets, respectively.

Conclusion

Our new method promotes the prediction accuracy of β-β pairing to a new level and the prediction results could better assist the structure modeling of mainly β proteins. We prepared an online server of RDb₂C2 at http://structpred.life.tsinghua.edu.cn/rdb2c2.html.

ISSEC: inferring contacts among protein secondary structure elements using deep object detection

BACKGROUND

The formation of contacts among protein secondary structure elements (SSEs) is an important step in protein folding as it determines topology of protein tertiary structure; hence, inferring inter-SSE contacts is crucial to protein structure prediction. One of the existing strategies infers inter-SSE contacts directly from the predicted possibilities of inter-residue contacts without any preprocessing, and thus suffers from the excessive noises existing in the predicted inter-residue contacts. Another strategy defines SSEs based on protein secondary structure prediction first, and then judges whether each candidate SSE pair could form contact or not. However, it is difficult to accurately determine boundary of SSEs due to the errors in secondary structure prediction. The incorrectly-deduced SSEs definitely hinder subsequent prediction of the contacts among them.

RESULTS

We here report an accurate approach to infer the inter-SSE contacts (thus called as ISSEC) using the deep object detection technique. The design of ISSEC is based on the observation that, in the inter-residue contact map, the contacting SSEs usually form rectangle regions with characteristic patterns. Therefore, ISSEC infers inter-SSE contacts through detecting such rectangle regions. Unlike the existing approach directly using the predicted probabilities of inter-residue contact, ISSEC applies the deep convolution technique to extract high-level features from the inter-residue contacts. More importantly, ISSEC does not rely on the pre-defined SSEs. Instead, ISSEC enumerates multiple candidate rectangle regions in the predicted inter-residue contact map, and for each region, ISSEC calculates a confidence score to measure whether it has characteristic patterns or not. ISSEC employs greedy strategy to select non-overlapping regions with high confidence score, and finally infers inter-SSE contacts according to these regions.

CONCLUSIONS

Comprehensive experimental results suggested that ISSEC outperformed the state-of-the-art approaches in predicting inter-SSE contacts. We further demonstrated the successful applications of ISSEC to improve prediction of both inter-residue contacts and tertiary structure as well.

Enhancement of Protein β-Sheet Topology Prediction Using Maximum Weight Disjoint Path Cover

Predicting β-sheet topology (β-topology) is one of the most critical intermediate steps towards protein structure and function prediction. The β-topology prediction problem is defined as the determination of the optimal arrangement of β-strand interactions within protein β-sheets. Significant efforts have been made to predict β-topologies. However, due to the inaccurate determination of interactions among β-strands and the huge topological space of proteins with a large number of β-strands, more efficient methods are required to improve both the accuracy and speed of β-topology prediction. In order to attain higher accuracy, the current paper introduces a bidirectional strand-strand interaction graph and considers all possible orientations (parallel and antiparallel) and orders of β-strand pairwise interactions. For the first time, the β-topology prediction is transformed into a maximum weight disjoint path cover solution by conserving all potential topologies. Moreover, to manage the computation time, a set of candidate β-sheets is generated and an optimization process is applied to select a subset of maximum score disjoint β-sheets as a predicted β-topology. The proposed method is comprehensively compared with state-of-the-art methods. The experimental results on the BetaSheet916 and BetaSheet1452 datasets reveal that the current study's approach enhances performance measurements as well as reduces the runtime.

BetaDL: A protein beta-sheet predictor utilizing a deep learning model and independent set solution

The sequence-based prediction of beta-residue contacts and beta-sheet structures contain key information for protein structure prediction. However, the determination of beta-sheet structures poses numerous challenges due to long-range beta-residue interactions and the huge number of possible beta-sheet structures. Recently gaining attention has been the prediction of residue contacts based on deep learning models whose results have led to improvement in protein structure prediction. In addition, to reduce the computational complexity of determining beta-sheet structures, it has been suggested that this problem be transformed into graph-based solutions. Consequently, the current work proposes BetaDL, a combination of a deep learning and a graph-based beta-sheet structure predictor. BetaDL adopts deep learning models to capture beta-residue contacts and improve beta-sheet structure predictions. In addition, a graph-based approach is presented to model the beta-sheets conformational space and a new score function is introduced to evaluate beta-sheets. Furthermore, the present study demonstrates that the beta-sheet structure can be predicted within an acceptable computational time by the utilization of a heuristic maximum weight independent set solution. When compared to state-of-the-art methods, experimental results from BetaSheet916 and BetaSheet1452 datasets indicate that BetaDL improves the accuracy of beta-residue contact and beta-sheet structure prediction. Using BetaDL, beta-sheet structures are predicted with a 4% and 6% improvement in the F1-score at the residue and strand levels, respectively. BetaDL's source code and data are available at http://kerg.um.ac.ir/index.php/datasets/#BetaDL.

ccPDB 2.0: an updated version of datasets created and compiled from Protein Data Bank

ccPDB 2.0 (http://webs.iiitd.edu.in/raghava/ccpdb) is an updated version of the manually curated database ccPDB that maintains datasets required for developing methods to predict the structure and function of proteins. The number of datasets compiled from literature increased from 45 to 141 in ccPDB 2.0. Similarly, the number of protein structures used for creating datasets also increased from ~74 000 to ~137 000 (PDB March 2018 release). ccPDB 2.0 provides the same web services and flexible tools which were present in the previous version of the database. In the updated version, links of the number of methods developed in the past few years have also been incorporated. This updated resource is built on responsive templates which is compatible with smartphones (mobile, iPhone, iPad, tablets etc.) and large screen gadgets. In summary, ccPDB 2.0 is a user-friendly web-based platform that provides comprehensive as well as updated information about datasets.

Identification of residue pairing in interacting β-strands from a predicted residue contact map

Background

Despite the rapid progress of protein residue contact prediction, predicted residue contact maps frequently contain many errors. However, information of residue pairing in β strands could be extracted from a noisy contact map, due to the presence of characteristic contact patterns in β-β interactions. This information may benefit the tertiary structure prediction of mainly β proteins. In this work, we propose a novel ridge-detection-based β-β contact predictor to identify residue pairing in β strands from any predicted residue contact map.

Results

Our algorithm RDb₂C adopts ridge detection, a well-developed technique in computer image processing, to capture consecutive residue contacts, and then utilizes a novel multi-stage random forest framework to integrate the ridge information and additional features for prediction. Starting from the predicted contact map of CCMpred, RDb₂C remarkably outperforms all state-of-the-art methods on two conventional test sets of β proteins (BetaSheet916 and BetaSheet1452), and achieves F1-scores of ~ 62% and ~ 76% at the residue level and strand level, respectively. Taking the prediction of the more advanced RaptorX-Contact as input, RDb₂C achieves impressively higher performance, with F1-scores reaching ~ 76% and ~ 86% at the residue level and strand level, respectively. In a test of structural modeling using the top 1 L predicted contacts as constraints, for 61 mainly β proteins, the average TM-score achieves 0.442 when using the raw RaptorX-Contact prediction, but increases to 0.506 when using the improved prediction by RDb₂C.

Conclusion

Our method can significantly improve the prediction of β-β contacts from any predicted residue contact maps. Prediction results of our algorithm could be directly applied to effectively facilitate the practical structure prediction of mainly β proteins.

Availability

All source data and codes are available at http://166.111.152.91/Downloads.html or the GitHub address of https://github.com/wzmao/RDb2C.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2150-1) contains supplementary material, which is available to authorized users.

Protein β-sheet prediction using an efficient dynamic programming algorithm

Predicting the β-sheet structure of a protein is one of the most important intermediate steps towards the identification of its tertiary structure. However, it is regarded as the primary bottleneck due to the presence of non-local interactions between several discontinuous regions in β-sheets. To achieve reliable long-range interactions, a promising approach is to enumerate and rank all β-sheet conformations for a given protein and find the one with the highest score. The problem with this solution is that the search space of the problem grows exponentially with respect to the number of β-strands. Additionally, brute-force calculation in this conformational space leads to dealing with a combinatorial explosion problem with intractable computational complexity. The main contribution of this paper is to generate and search the space of the problem efficiently to reduce the time complexity of the problem. To achieve this, two tree structures, called sheet-tree and grouping-tree, are proposed. They model the search space by breaking it into sub-problems. Then, an advanced dynamic programming is proposed that stores the intermediate results, avoids repetitive calculation by repeatedly uses them efficiently in successive steps and reduces the space of the problem by removing those intermediate results that will no longer be required in later steps. As a consequence, the following contributions have been made. Firstly, more accurate β-sheet structures are found by searching all possible conformations, and secondly, the time complexity of the problem is reduced by searching the space of the problem efficiently which makes the proposed method applicable to predict β-sheet structures with high number of β-strands. Experimental results on the BetaSheet916 dataset showed significant improvements of the proposed method in both execution time and the prediction accuracy in comparison with the state-of-the-art β-sheet structure prediction methods Moreover, we investigate the effect of different contact map predictors on the performance of the proposed method using BetaSheet1452 dataset. The source code is available at http://www.conceptsgate.com/BetaTop.rar.

Efficient dynamic programming algorithm with prior knowledge for protein β-strand alignment

One of the main tasks towards the prediction of protein β-sheet structure is to predict the native alignment of β-strands. The alignment of two β-strands defines similar regions that may reflect functional, structural, or evolutionary relationships between them. Therefore, any improvement in β-strands alignment not only reduces the computational search space but also improves β-sheet structure prediction accuracy. To define the alignment scores, previous studies utilized predicted residue-residue contacts (contact maps). However, there are two serious problems using them. First, the precision of contact map prediction techniques, especially for long-range contacts (i.e., β-residues), is still not satisfactory. Second, the residue-residue contact predictors usually utilize general properties of amino acids and disregard the structural features of β-residues. In this paper, we consider β-structure information, which is estimated from protein β-sheet data sets, as alignment scores. However, the predicted contact maps are used as a prior knowledge about residues. They are used for strengthening or weakening the alignment scores in our algorithm. Thus, we can utilize both β-residues and β-structure information in alignment of β-strands. The structure of dynamic programming of the alignment algorithm is changed in order to work with our prior knowledge. Moreover, the Four Russians method is applied to the proposed alignment algorithm in order to reduce the time complexity of the problem. For evaluating the proposed method, we applied it to the state-of-the-art β-sheet structure prediction methods. The experimental results on the BetaSheet916 data set showed significant improvements in the execution time, the accuracy of β-strands' alignment and consequently β-sheet structure prediction accuracy. The results are available at http://conceptsgate.com/BetaSheet.

bbcontacts: prediction of β-strand pairing from direct coupling patterns

MOTIVATION

It has recently become possible to build reliable de novo models of proteins if a multiple sequence alignment (MSA) of at least 1000 homologous sequences can be built. Methods of global statistical network analysis can explain the observed correlations between columns in the MSA by a small set of directly coupled pairs of columns. Strong couplings are indicative of residue-residue contacts, and from the predicted contacts a structure can be computed. Here, we exploit the structural regularity of paired β-strands that leads to characteristic patterns in the noisy matrices of couplings. The β-β contacts should be detected more reliably than single contacts, reducing the required number of sequences in the MSAs.

RESULTS

bbcontacts predicts β-β contacts by detecting these characteristic patterns in the 2D map of coupling scores using two hidden Markov models (HMMs), one for parallel and one for antiparallel contacts. β-bulges are modelled as indel states. In contrast to existing methods, bbcontacts uses predicted instead of true secondary structure. On a standard set of 916 test proteins, 34% of which have MSAs with < 1000 sequences, bbcontacts achieves 50% precision for contacting β-β residue pairs at 50% recall using predicted secondary structure and 64% precision at 64% recall using true secondary structure, while existing tools achieve around 45% precision at 45% recall using true secondary structure.

AVAILABILITY AND IMPLEMENTATION

bbcontacts is open source software (GNU Affero GPL v3) available at https://bitbucket.org/soedinglab/bbcontacts .

An amino acid code for β-sheet packing structure

To understand the relationship between protein sequence and structure, this work extends the knob-socket model in an investigation of β-sheet packing. Over a comprehensive set of β-sheet folds, the contacts between residues were used to identify packing cliques: sets of residues that all contact each other. These packing cliques were then classified based on size and contact order. From this analysis, the two types of four-residue packing cliques necessary to describe β-sheet packing were characterized. Both occur between two adjacent hydrogen bonded β-strands. First, defining the secondary structure packing within β-sheets, the combined socket or XY:HG pocket consists of four residues i, i+2 on one strand and j, j+2 on the other. Second, characterizing the tertiary packing between β-sheets, the knob-socket XY:H+B consists of a three-residue XY:H socket (i, i+2 on one strand and j on the other) packed against a knob B residue (residue k distant in sequence). Depending on the packing depth of the knob B residue, two types of knob-sockets are found: side-chain and main-chain sockets. The amino acid composition of the pockets and knob-sockets reveal the sequence specificity of β-sheet packing. For β-sheet formation, the XY:HG pocket clearly shows sequence specificity of amino acids. For tertiary packing, the XY:H+B side-chain and main-chain sockets exhibit distinct amino acid preferences at each position. These relationships define an amino acid code for β-sheet structure and provide an intuitive topological mapping of β-sheet packing.