Contact-Assisted Threading in Low-Homology Protein Modeling

Abstract

The ability to successfully predict the three-dimensional structure of a protein from its amino acid sequence has made considerable progress in the recent past. The progress is propelled by the improved accuracy of deep learning-based inter-residue contact map predictors coupled with the rising growth of protein sequence databases. Contact map encodes interatomic interaction information that can be exploited for highly accurate prediction of protein structures via contact map threading even for the query proteins that are not amenable to direct homology modeling. As such, contact-assisted threading has garnered considerable research effort. In this chapter, we provide an overview of existing contact-assisted threading methods while highlighting the recent advances and discussing some of the current limitations and future prospects in the application of contact-assisted threading for improving the accuracy of low-homology protein modeling.

1. Introduction

The computational prediction of the three-dimensional (3D) structure of a protein from its amino acid sequence remains elusive [1–4]. Despite the encouraging recent progress in ab initio protein structure prediction [5–12], template-based modeling (TBM) [13] remains one of the most reliable approaches in protein structure prediction [14–21], especially when homologous templates are available in the Protein Data Bank (PDB) [22]. TBM approaches can be broadly classified into homology modeling and protein threading based on the degree of homology. Homology modeling or comparative modeling is the process of building a structure of a query protein from a homologous template with a high degree of sequence similarity [23], whereas threading or fold recognition corresponds to an advanced template identification strategy where only distant homologs are available in the PDB but are not easily identifiable [3, 24, 25]. The primary objective of threading is to recognize one or more templates that are consistent with the query sequence, that is, existing folds that might be potentially analogous to the query sequence. Since its inception at the beginning of the 1990s [3, 24], threading remains an active area of research. The general principle behind protein threading is that there exists a finite number of unique folds in nature and many proteins (~90% [14]) share the same folds [26, 27], even though their sequences differ, illustrating that in theory the structure of most proteins can be successfully predicted by threading a query protein sequence onto a library of structural templates [14].

Current threading strategies are based on various techniques ranging from dynamic programming to profile-profile comparison based on hidden Markov models to more advanced machine learning approaches [18, 21, 28–49]. Some of these methods use only sequence-based features, while others [14, 18, 19, 31] use sequence and structure-based features for calculating the fitness score between the query and template. With the recent advances in residue-residue contact prediction [50–61] driven by sequence coevolution and deep learning, predicted contact information has become an additional structural feature in protein threading, leading to the development of numerous contact-assisted threading methods in the last few years [16, 20, 62–65]. The usefulness of these cutting-edge contact-assisted threading methods are particularly noteworthy in low-homology (see Note 1) protein modeling scenarios [63, 64, 66]. Here, we provide an overview of existing contact-assisted threading methods, highlighting some of the recent advances in low-homology protein modeling. We also discuss some of the current limitations and future prospects in contact-assisted threading.

2. Materials

Most threading methods have certain aspects in common. Here, we provide a brief overview of the common methodologies used in threading.

2.1. Template Library

Template library is a collection of representative protein structures (aka templates) from the PDB. A query protein sequence is threaded (or aligned) across each template in the library. Therefore, in order to minimize the time to search the whole template library, it is a common practice to make the library nonredundant by considering a small fraction of representative templates from a group of highly similar templates [14].

2.2. Query and Template Feature Set

Threading approaches use different sequential and structural features for the query protein and the templates. Below, we briefly discuss various common features used in threading.

2.2.1. Sequence Profiles

Sequence profile contains the evolutionary information as well as the sequence diversity among homologous sequences of the query protein. A sequence profile is considered as a rich source of information in threading because homologous proteins tend to have similar sequence profiles. Programs such as PSI-BLAST [17] and HHblits [67] can be used to generate sequence profiles.

2.2.2. Secondary Structures

A protein’s local conformation may be defined in terms of its secondary structure and using the secondary structure as a feature in threading has attracted much attention since the early days of threading approaches. The secondary structure of a query protein can be predicted using secondary structure predictors such as PSIPRED [68], SPIDER3 [69], and RaptorX Property [70]. Most of these methods predict the likelihood of various secondary structure types. Most popular secondary structure predictors [16, 18, 71] use the three-class secondary structures (alpha helices, beta strands, and loop), even though some of the recent threading methods [72] use both three-class and eight-class secondary structure types. While the secondary structure of a query protein is typically predicted from its sequence information, the secondary structures of the template proteins are calculated directly from the PDB structures using programs such as DSSP [73] and STRIDE [74].

2.2.3. Solvent Accessibility

Solvent accessibility is related to the spatial organization and packing of residues and is therefore considered as an important feature for threading. Solvent accessibility can be categorized using binary classification (buried or exposed) or using a three-class classification (buried, intermediate, and exposed). While solvent accessibility predictors such as PSIPRED, SPIDER3, and RaptorX Property are typically used to predict the solvent accessibility of each residue in the query protein, DSSP and STRIDE can be used for calculating that of the template.

2.2.4. Backbone Dihedral Angles

A protein’s dihedral angle is the angle of the polypeptide backbone where two neighboring planes meet. The dihedral angles for the query protein can be predicted using predictors such as PSIPRED and SPIDER3.

2.2.5. Additional Features

In addition to these features, structure profiles, hydrophobicity, and amino acid substitution matrix such as BLOSUM are also considered as features for threading [71, 72]. Contact-assisted threading methods use the pairwise predicted (or native) contact information for a query (or template) protein because contact information is considered as a rich source of information for threading. Contact-assisted threading methods use contact information either implicitly such as in PROSPECT [46], PROSPECTOR [75, 76], and RAPTOR [14] or explicitly such as in EigenTHREADER [20], map_align [62], CEthreader [63], CATHER [64], ThreaderAI [65], and our in-house threading method [16].

2.3. Threading Performance Measure

Measuring the structural similarity between the predicted and the native protein 3D structure is critically important for objectively evaluating the performance of a threading method. Some most commonly used scores are the template modeling score (TM-score) [77], the root-mean-square deviation (RMSD) [78], the global distance test (GDT) [79], and the local distance difference test (lDDT) [80]. TM-score is one of the most widely used scoring metrics having scores in the range (0, 1) with higher scores indicating better similarities. A TM-score >0.5 typically indicates the correct overall fold [81].

3. Methods

3.1. Overview of Protein Threading

The goal of protein threading is to optimally align a query sequence to a known structural template [82]. This requires identifying the correct or best-fit template from a library of templates and the optimal query-template alignment from the space of all possible query-template alignments. The query-template alignment represents a correspondence between each query residue and the spatial positioning of the aligned template residues. Overall, protein threading can be mainly considered to involving three components: (1) a threading scoring function that evaluates the fitness of query-template alignments, (2) identification of the best-fit structural template from the library of templates, and (3) an optimal alignment of the query sequence to the template. In the following, we discuss each component in more details.

3.1.1. Threading Scoring Function

The scoring function plays an important role to quantitatively assess the fitness of query-template alignments [14]. The scoring function normally consists of the profile similarity score, the structural consistency score, and the gap penalty. The profile similarity score can be calculated by comparing the query and template profiles. It quantifies how the query is evolutionary related to the template. The structural consistency score contains two components: consistency of local structures such as secondary structure and solvent accessibility compatibility and consistency of global structures or pairwise interatomic interactions. Weights can be used in the scoring function to control the relative importance of different scoring terms.

3.1.2. Template Selection

Identifying the best-fit template inevitably requires using the alignment score of query-template alignments. The raw query-template alignment score cannot be directly used to rank templates due to the biases introduced by the protein length [14]. Both machine learning-based methods and Z-score are used to mitigate the bias. Several protein threading methods [40, 46, 83–85] use machine learning models such as the neural network for the template ranking by formulating the template selection as a classification problem, even though a majority of the threading methods [18, 63, 64] rely on Z-score for the template selection. Z-scores of the query-template pair are computed from the means and standard deviations of the scores of the query sequence with all templates of the template library. However, it cannot cancel out all the biases introduced by the protein length. A large protein appears to have a high Z-score. It is also difficult to interpret the Z-score, particularly when the scoring function is the weighted sum of different scoring terms [14].

3.1.3. Optimal Query-Template Alignment

The optimal query-template alignment is the alignment that optimally aligns residues in the query sequence homologous to residues in the template. It is often the case that a threading scoring function is effective in selecting the homologous template, but the query-template alignment is significantly weak [25, 86]. In such cases, the alignment may be suboptimal, which might result in less accurate template-based models built from such an alignment, that is, the sensitivity of query-template alignment directly affects the overall performance of template-based modeling.

3.2. Contact-Assisted Protein Threading

3.2.1. Residue-Residue Contact Map

A contact map of a protein is a binary, square, symmetric matrix with vertices corresponding to residues of the protein, and a contact edge indicates that the distance between a residue pair is smaller than a given threshold. Typically, this distance threshold is considered 8 Å between the C_α and C_β atoms of the residue pairs [16, 20]. Here, the set of contacts between residue pair (i, j) is defined as:

$$C(i,j)=\{\begin{array}{cc}1& \text{ if }{d}_{ij}\le 8Å\\ 0& \text{ otherwise }\end{array}$$ (1)

where d_ij is the distance between the residue pair (i, j). Figure 1 shows a representative protein 3D structure and its corresponding 2D residue-residue contact map.

Fig. 1.

A representative protein 3D structure and its corresponding 2D binary contact map. (a) 3D structure of a representative protein (PDB ID 1cc8A), (b) the corresponding 2D residue-residue contact map, considering C_α atoms and a distance threshold of 8 Å

3.2.2. Contact Map Alignment

Contact map alignment is a way of measuring the similarity between two contact maps. The maximum contact map overlap problem tries to evaluate the similarity of the two proteins by calculating the maximum overlap between their contact maps while preserving the ordering of residues of both sequences, leading to a pairwise sequence alignment as illustrated in Fig. 2. Since direct contact map alignment is computationally expensive [63], several approximation algorithms [62, 87–92] have been developed to address the contact map alignment problem including the eigendecomposition-based strategy, graphlet degree-based approach, and iterative double dynamic programming-based approach. Eigendecomposition decomposes a contact map into eigenvectors and corresponding eigenvalues. This approach compares two proteins by comparing their contact map eigenvectors, which can be performed in polynomial time. For example, approaches such as EIGAs [87], SABERTOOTH [89], and Al-Eigen [90] use the eigendecomposition to approximate contact maps using the top eigenvectors and use the global alignment of key eigenvectors to find the similarity between two contact maps. GR-Align [92] is a fast contact map alignment approach based on graphlet degree distribution. Moreover, [93] proposes a contact map alignment algorithm C-Align based on C_α atoms using dynamic programming. Recent methods such as map_align [62] employ iterative double dynamic programming to calculate contact map alignment, with the goal of optimizing the number of contact overlaps while minimizing the number of gaps.

Fig. 2.

Contact map alignment. (a) contact map of a representative protein (PDB ID 1cc8A), (b) contact map of another representative protein (PDB ID 1wvnA), (c) sequence alignment of 1cc8A and 1wvnA using Al-Eigen. In both cases, C_α atoms and the distance threshold of 8 Å are considered. (d) 1wvnA (in rainbow) is structurally superimposed on 1cc8A (in gray)

3.3. Overview of Existing Contact-Assisted Threading Methods

Table 1 shows several publicly available contact-assisted threading methods. These approaches can be broadly subdivided into two classes: (1) methods that implicitly use contact information via pairwise contact potential such as PROSPECT [46], PROSPECTOR [75, 76], and RAPTOR [14]; and (2) methods that explicitly use contact information via predicted residue-residue contacts including the current state-of-the-art contact-assisted threading methods such as EigenTHREADER [20], map_align [62], CEthreader [63], CATHER [64], ThreaderAI [65], and our in-house threading method [16]. We briefly discuss them below.

Table 1.

Selected publicly accessible threading methods that implicitly or explicitly use contact information

Name (reference)	Method	Availability
PROSPECT (Xu and coworkers [46])	Divide-and-conquer algorithm	http://compbio.ornl.gov/structure/prospect/
PROSPECTOR (Skolnick and coworkers [75, 76])	Hierarchical approach	http://bioinformatics.danforthceneter.org/services/threading.html
RAPTOR (Xu and coworkers [14])	Linear programming	http://www.cs.uwaterloo.ca/~j3xu/RAPTOR_form.htm
EigenTHREADER (Jones and coworkers [20])	Dynamic programming and eigendecomposition	http://bioinfadmin.cs.ucl.ac.uk/downloads/eigenTHREADER/
map_align (Baker and coworkers [62])	Iterative double dynamic programming	https://github.com/sokrypton/map_align
CEthreader (Zhang and coworkers [63])	Dynamic programming and eigendecomposition	https://zhanglab.ccmb.med.umich.edu/CEthreader/
CATHER (Yang and coworkers [64])	Iterative double dynamic programming	https://yanglab.nankai.edu.cn/CATHER/
ThreaderAI (Shen and coworkers [65])	Deep residual neural network and dynamic programming	https://github.com/ShenLab/ThreaderAI

3.3.1. Threading Methods That Implicitly Use Contact Information via Pairwise Contact Potential

PROSPECT (PROtein Structure Prediction and Evaluation Computer Toolkit) [46] is one of the earliest protein threading methods, which makes use of pairwise contact potential by introducing a contact term into its scoring function. This study considers that pairwise contact potentials are measured only between core secondary structures. The contact cutoff is set at 7 Å between the C_β atoms. Additionally, the method uses a divide-and-conquer algorithm for the alignment searching procedure. Another method, PROSPECTOR (PROtein Structure Predictor Employing Combined Threading to Optimize Results) [75, 76], uses a “partly thawed” technique to assess the contact potential based on the previous alignment iterations. RAPTOR (RApid Protein Threading by Operation Research technique) [14] is another protein threading method that introduces contact capacity score. It considers only contacts between two core residues where the spatial distance between C_α atoms is 7 Å with a sequence separation of 4. It addresses threading as a problem of wide-scale integer programming, relaxes it to a problem of linear programming, and uses a branch-and-bound approach to solve the integer program. However, the performance contribution of pairwise contact potential in the above methods is not significant compared to that of sequence profile, particularly for distantly related proteins. The underlying reason may be noisy contacts that do not hold any extra signal, yielding just modest improvement.

3.3.2. Threading Methods That Explicitly Use Contact Information via Predicted Residue-Residue Contacts

Recent successful applications of deep learning have resulted in significantly improved inter-residue contact prediction methods [53, 56, 60, 94]. As such, the newest contact-assisted threading methods have been explicitly integrating predicted residue-residue contact information to improve threading performance. EigenTHREADER [20], developed in 2017, extends Al-Eigen [90] to enable threading by predicting a protein’s contact map using classical neural network-based predictor MetaPSICOV [53] and then searching a library of templates’ contact maps. Despite the superior performance of EigenTHREADER over other profile-based threading methods for low-homology threading, it can be further improved by integrating other linear features such as sequence profiles along with inter-residue contact maps. map_align [62], developed in 2017, proposes an iterative double dynamic programming algorithm [95] that aligns contact maps, predicted by pure coevolutionary-based predictor GREMLIN [96], in combination with metagenomic sequences of microbial DNA [97]. The elevated performance of map_align can be attributed to the contribution of contact maps in low-homology threading. However, considering that the outcomes rely on the initial estimate of the similarity matrix, which is not always optimal, this approach does not necessarily guarantee optimal solutions. CEthreader [63] (Contact Eigenvector-based threader), developed in 2019, uses contact maps predicted from deep residual neural-network-based predictor ResPRE [94]. Similar to Al-Eigen, this work uses the eigendecom-position technique to approximate contact maps by the cross product of single-body eigenvectors. CEthreader introduces a dot-product scoring function by incorporating contact information along with secondary structures and sequence profiles to align contact eigenvectors and uses dynamic programming to generate the query-template alignments. However, the method can be further strengthened by considering negative eigenvalues in addition to positive eigenvalues, since the incorporation of both positive and negative eigenvalues restores the contact map. Another new contact-assisted threading algorithm CATHER [64] (contact-assisted THreadER), developed in 2020, uses both conventional sequential profiles and contact maps predicted by a deep learning-based method MapPred [98]. A very recent method ThreaderAI [65] integrates deep learning-based contact information with traditional sequential and structural features by formulating the task of threading as the classical computer vision’s classification problem. This work introduces a deep residual neural network to predict query-template alignments. Based on the reported results of the above methods, contact-assisted threading methods significantly outperform profile-based threading methods by a large margin, particularly for low-homology targets.

Our in-house threading method [16], developed in 2019, integrates the standard threading technique along with inter-residue contact information predicted by the state-of-the-art ultra-deep learning-based method RaptorX [56]. First, our method applies the standard threading technique to select the top templates based on the Z-score and then applies the contact map overlap score using Al-Eigen along with the Z-score to calculate the final score for selecting the best-fit template. Based on large-scale bench-marking results, this method outperforms profile-based threading method MUSTER as well as other contact-assisted threading methods EigenTHREADER and map_align.

3.4. Significance of Contact Maps Quality in Threading

While incorporating contact information into threading is highly effective, our recent study [99] shows the impact of diverse quality of contact maps on contact-assisted threading performance in that integrating high-quality contacts having the Matthews correlation coefficient (MCC) ≥0.5 results in improved threading performance for ~30% of the cases, while low-quality contacts having MCC <0.35 degrade the threading performance for 50% of the cases. The results reveal the reciprocal coupling between the quality of predicted contact maps and contact-assisted threading performance and indicate that the rapid advancement in contact prediction methods powered by deep learning can synergistically assist contact-assisted threading, leading to improved low-homology protein modeling.

3.5. Growth of Protein Sequence Databases and Its Implication in Threading

Since most contact map predictions, secondary structure predictions, and sequence profiles depend on the evolutionary signal derived from multiple sequence alignments (MSA) (see Note 2), the adequate number of homologous sequences is critical to the success of these approaches. This limitation can be largely overcome by taking advantage of the fast-paced growth of whole-genome sequence databases such as the nr database compiled by the National Center for Biotechnology Information (NCBI), UniRef [100], UniProt [101], Uniclust [102], as well as metagenome databases from the European Bioinformatics Institute (EBI) Meta-genomics [103, 104] and Metaclust [105]. For instance, with the addition of two billion metagenomic protein sequences, there is a significant increase in the number of families of unknown structures, which can now be reliably modeled by using the coevolutionary information [62]. A recent paper [106] demonstrates improved protein structure prediction through marine metagenomics for low-homology proteins, illustrating the potential usefulness of growing sequence databases on protein structure prediction. Two newest emerging sequence databases, BFD [107] and MGnify [108], may further enrich the evolutionary information. Recently, DeepMSA [109] method for generating multiple sequence alignment information shows the benefit of generating deep multiple sequence alignment by combining the multiple sequence databases for threading as well as contact predictions.

3.6. Discussion

The improved performance of contact-assisted threading methods is attributed to successfully integrating inter-residue contact information along with traditional linear and nonlinear threading features. Although contact-assisted threading approaches have witnessed promising progress so far, but there is still room for improvement with the advancement of deep learning-based inter-residue distance prediction [6, 7, 110–113] instead of binary contacts (see Note 3). A protein can be represented by a 2D inter-residue distance map, where a distance map is a square, symmetric matrix with vertices corresponding to residues of the protein and an edge indicates the distance between a residue pair. As distances carry more information than contacts [85], recent distance-based threading method DeepThreader [85] shows further improvement, particularly for low-homology threading, by outperforming existing contact-assisted threading approaches. Inspired by the promising results, CEthreader method is extended to distance-guided threading method DEthreader in the recently concluded 14th critical assessment of protein structure prediction (CASP14) experiment (see Note 4) by adding a distance map-based energy term in the threading scoring function. Similarly, CATHER has also replaced contacts with distances in CASP14. Our most recent threading method DisCovER [71] (distance- and orientation-based Covariational threadER) goes one step further by effectively integrating information from inter-residue distance and orientation along with the topological network neighborhood (see Note 5) of a query-template alignment. DisCovER shows the usefulness of incorporating inter-residue orientation along with distance information together with the neighborhood effect induced by the query-template alignment, leading to improved threading performance.

While no single-template threading method works well for all types of targets [13], multiple-template approaches as well as meta-approaches work better in protein structure prediction [41, 45, 66]. For instance, previous multiple-template approaches [45, 114–119] demonstrate their superior performance over the best single-template threading method by attaining better alignments. Moreover, meta-approaches [41, 66, 120] show promising results over individual approaches, particularly for distantly homologous proteins. In the case of meta-servers, there is a need to select the top model based on various scoring functions by scoring predicted 3D models using model quality assessment programs (MQAPs), including single-model [121–130] and consensus [131–134] methods. Furthermore, even when using the most advanced template-based modeling pipeline, predicted models often fail to reach near-native accuracy. Protein structure refinement methods [135–144] are needed to bring these moderately accurate predicted models closer to the native state.