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

Inter-Residue Distance Prediction From Duet Deep Learning Models

Residue distance prediction from the sequence is critical for many biological applications such as protein structure reconstruction, protein–protein interaction prediction, and protein design. However, prediction of fine-grained distances between residues with long sequence separations still remains challenging. In this study, we propose DuetDis, a method based on duet feature sets and deep residual network with squeeze-and-excitation (SE), for protein inter-residue distance prediction. DuetDis embraces the ability to learn and fuse features directly or indirectly extracted from the whole-genome/metagenomic databases and, therefore, minimize the information loss through ensembling models trained on different feature sets. We evaluate DuetDis and 11 widely used peer methods on a large-scale test set (610 proteins chains). The experimental results suggest that 1) prediction results from different feature sets show obvious differences; 2) ensembling different feature sets can improve the prediction performance; 3) high-quality multiple sequence alignment (MSA) used for both training and testing can greatly improve the prediction performance; and 4) DuetDis is more accurate than peer methods for the overall prediction, more reliable in terms of model prediction score, and more robust against shallow multiple sequence alignment (MSA).

COMTOP: Protein Residue-Residue Contact Prediction through Mixed Integer Linear Optimization

Protein contact prediction helps reconstruct the tertiary structure that greatly determines a protein’s function; therefore, contact prediction from the sequence is an important problem. Recently there has been exciting progress on this problem, but many of the existing methods are still low quality of prediction accuracy. In this paper, we present a new mixed integer linear programming (MILP)-based consensus method: a Consensus scheme based On a Mixed integer linear opTimization method for prOtein contact Prediction (COMTOP). The MILP-based consensus method combines the strengths of seven selected protein contact prediction methods, including CCMpred, EVfold, DeepCov, NNcon, PconsC4, plmDCA, and PSICOV, by optimizing the number of correctly predicted contacts and achieving a better prediction accuracy. The proposed hybrid protein residue–residue contact prediction scheme was tested in four independent test sets. For 239 highly non-redundant proteins, the method showed a prediction accuracy of 59.68%, 70.79%, 78.86%, 89.04%, 94.51%, and 97.35% for top-5L, top-3L, top-2L, top-L, top-L/2, and top-L/5 contacts, respectively. When tested on the CASP13 and CASP14 test sets, the proposed method obtained accuracies of 75.91% and 77.49% for top-L/5 predictions, respectively. COMTOP was further tested on 57 non-redundant α-helical transmembrane proteins and achieved prediction accuracies of 64.34% and 73.91% for top-L/2 and top-L/5 predictions, respectively. For all test datasets, the improvement of COMTOP in accuracy over the seven individual methods increased with the increasing number of predicted contacts. For example, COMTOP performed much better for large number of contact predictions (such as top-5L and top-3L) than for small number of contact predictions such as top-L/2 and top-L/5. The results and analysis demonstrate that COMTOP can significantly improve the performance of the individual methods; therefore, COMTOP is more robust against different types of test sets. COMTOP also showed better/comparable predictions when compared with the state-of-the-art predictors.

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

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

The amino acid sequence of a protein ultimately determines its tertiary structure, and the tertiary structure determines its function(s) and plays a key role in understanding biological processes and disease pathogenesis. Protein tertiary structure can be determined using experimental techniques such as cryo-electron microscopy, nuclear magnetic resonance and X-ray crystallography, which are very expensive and time-consuming. As an alternative, researchers are trying to use in silico methods to predict the 3D structures. Residue contact-assisted protein folding paves an avenue for sequence-based protein structure prediction and therefore has become one of the most challenging and promising problems in structural bioinformatics. Over the past years, contact prediction has undergone continuous evolution in techniques. Through a retrospective analysis of traditional machine learning /evolutionary coupling analysis methods/ consensus machine learning methods and a multi-perspective study on recently developed deep learning methods, we explore the most advanced contact predictors, pursue application scenarios for different methods, and seek prospective directions for further improvement. We anticipate that our study will serve as a practical and useful guide for the development of future approaches to contact prediction.

Protein modeling

Proteins are essential and versatile polymers consisting of sequenced amino acids that often possess an organized three-dimensional arrangement, (a result of their monomeric composition), which determines their biological role in cellular function. Proteins are involved in enzymatic catalysis; they participate in genetic information decoding and transmission processes, in cell recognition, in signaling, and transport of substances, in regulation of intra and extracellular conditions, and other functions.

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.

COMSAT: Residue contact prediction of transmembrane proteins based on support vector machines and mixed integer linear programming

In this article, we present COMSAT, a hybrid framework for residue contact prediction of transmembrane (TM) proteins, integrating a support vector machine (SVM) method and a mixed integer linear programming (MILP) method. COMSAT consists of two modules: COMSAT_SVM which is trained mainly on position-specific scoring matrix features, and COMSAT_MILP which is an ab initio method based on optimization models. Contacts predicted by the SVM model are ranked by SVM confidence scores, and a threshold is trained to improve the reliability of the predicted contacts. For TM proteins with no contacts above the threshold, COMSAT_MILP is used. The proposed hybrid contact prediction scheme was tested on two independent TM protein sets based on the contact definition of 14 Å between Cα-Cα atoms. First, using a rigorous leave-one-protein-out cross validation on the training set of 90 TM proteins, an accuracy of 66.8%, a coverage of 12.3%, a specificity of 99.3% and a Matthews' correlation coefficient (MCC) of 0.184 were obtained for residue pairs that are at least six amino acids apart. Second, when tested on a test set of 87 TM proteins, the proposed method showed a prediction accuracy of 64.5%, a coverage of 5.3%, a specificity of 99.4% and a MCC of 0.106. COMSAT shows satisfactory results when compared with 12 other state-of-the-art predictors, and is more robust in terms of prediction accuracy as the length and complexity of TM protein increase. COMSAT is freely accessible at http://hpcc.siat.ac.cn/COMSAT/.

WeFold: a coopetition for protein structure prediction

The protein structure prediction problem continues to elude scientists. Despite the introduction of many methods, only modest gains were made over the last decade for certain classes of prediction targets. To address this challenge, a social-media based worldwide collaborative effort, named WeFold, was undertaken by 13 labs. During the collaboration, the laboratories were simultaneously competing with each other. Here, we present the first attempt at "coopetition" in scientific research applied to the protein structure prediction and refinement problems. The coopetition was possible by allowing the participating labs to contribute different components of their protein structure prediction pipelines and create new hybrid pipelines that they tested during CASP10. This manuscript describes both successes and areas needing improvement as identified throughout the first WeFold experiment and discusses the efforts that are underway to advance this initiative. A footprint of all contributions and structures are publicly accessible at http://www.wefold.org.

Prediction of protein secondary structure using feature selection and analysis approach

The prediction of the secondary structure of a protein from its amino acid sequence is an important step towards the prediction of its three-dimensional structure. However, the accuracy of ab initio secondary structure prediction from sequence is about 80% currently, which is still far from satisfactory. In this study, we proposed a novel method that uses binomial distribution to optimize tetrapeptide structural words and increment of diversity with quadratic discriminant to perform prediction for protein three-state secondary structure. A benchmark dataset including 2,640 proteins with sequence identity of less than 25% was used to train and test the proposed method. The results indicate that overall accuracy of 87.8% was achieved in secondary structure prediction by using ten-fold cross-validation. Moreover, the accuracy of predicted secondary structures ranges from 84 to 89% at the level of residue. These results suggest that the feature selection technique can detect the optimized tetrapeptide structural words which affect the accuracy of predicted secondary structures.

Protein folding and de novo protein design for biotechnological applications

In the postgenomic era, the medical/biological fields are advancing faster than ever. However, before the power of full-genome sequencing can be fully realized, the connection between amino acid sequence and protein structure, known as the protein folding problem, needs to be elucidated. The protein folding problem remains elusive, with significant difficulties still arising when modeling amino acid sequences lacking an identifiable template. Understanding protein folding will allow for unforeseen advances in protein design; often referred to as the inverse protein folding problem. Despite challenges in protein folding, de novo protein design has recently demonstrated significant success via computational techniques. We review advances and challenges in protein structure prediction and de novo protein design, and highlight their interplay in successful biotechnological applications.

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

MOTIVATION

Prediction of protein residue contacts, even at the coarse-grain level, can help in finding solutions to the protein structure prediction problem. Unlike α-helices that are locally stabilized, β-sheets result from pairwise hydrogen bonding of two or more disjoint regions of the protein backbone. The problem of predicting contacts among β-strands in proteins has been addressed by several supervised computational approaches. Recently, prediction of residue contacts based on correlated mutations has been greatly improved and finally allows the prediction of 3D structures of the proteins.

RESULTS

In this article, we describe BCov, which is the first unsupervised method to predict the β-sheet topology starting from the protein sequence and its secondary structure. BCov takes advantage of the sparse inverse covariance estimation to define β-strand partner scores. Then an optimization based on integer programming is carried out to predict the β-sheet connectivity. When tested on the prediction of β-strand pairing, BCov scores with average values of Matthews Correlation Coefficient (MCC) and F1 equal to 0.56 and 0.61, respectively, on a non-redundant dataset of 916 protein chains known with atomic resolution. Our approach well compares with the state-of-the-art methods trained so far for this specific task.

AVAILABILITY AND IMPLEMENTATION

The method is freely available under General Public License at http://biocomp.unibo.it/savojard/bcov/bcov-1.0.tar.gz. The new dataset BetaSheet1452 can be downloaded at http://biocomp.unibo.it/savojard/bcov/BetaSheet1452.dat.

Protein WISDOM: a workbench for in silico de novo design of biomolecules

The aim of de novo protein design is to find the amino acid sequences that will fold into a desired 3-dimensional structure with improvements in specific properties, such as binding affinity, agonist or antagonist behavior, or stability, relative to the native sequence. Protein design lies at the center of current advances drug design and discovery. Not only does protein design provide predictions for potentially useful drug targets, but it also enhances our understanding of the protein folding process and protein-protein interactions. Experimental methods such as directed evolution have shown success in protein design. However, such methods are restricted by the limited sequence space that can be searched tractably. In contrast, computational design strategies allow for the screening of a much larger set of sequences covering a wide variety of properties and functionality. We have developed a range of computational de novo protein design methods capable of tackling several important areas of protein design. These include the design of monomeric proteins for increased stability and complexes for increased binding affinity. To disseminate these methods for broader use we present Protein WISDOM (http://www.proteinwisdom.org), a tool that provides automated methods for a variety of protein design problems. Structural templates are submitted to initialize the design process. The first stage of design is an optimization sequence selection stage that aims at improving stability through minimization of potential energy in the sequence space. Selected sequences are then run through a fold specificity stage and a binding affinity stage. A rank-ordered list of the sequences for each step of the process, along with relevant designed structures, provides the user with a comprehensive quantitative assessment of the design. Here we provide the details of each design method, as well as several notable experimental successes attained through the use of the methods.

Predicting protein β-sheet contacts using a maximum entropy-based correlated mutation measure

MOTIVATION

The problem of ab initio protein folding is one of the most difficult in modern computational biology. The prediction of residue contacts within a protein provides a more tractable immediate step. Recently introduced maximum entropy-based correlated mutation measures (CMMs), such as direct information, have been successful in predicting residue contacts. However, most correlated mutation studies focus on proteins that have large good-quality multiple sequence alignments (MSA) because the power of correlated mutation analysis falls as the size of the MSA decreases. However, even with small autogenerated MSAs, maximum entropy-based CMMs contain information. To make use of this information, in this article, we focus not on general residue contacts but contacts between residues in β-sheets. The strong constraints and prior knowledge associated with β-contacts are ideally suited for prediction using a method that incorporates an often noisy CMM.

RESULTS

Using contrastive divergence, a statistical machine learning technique, we have calculated a maximum entropy-based CMM. We have integrated this measure with a new probabilistic model for β-contact prediction, which is used to predict both residue- and strand-level contacts. Using our model on a standard non-redundant dataset, we significantly outperform a 2D recurrent neural network architecture, achieving a 5% improvement in true positives at the 5% false-positive rate at the residue level. At the strand level, our approach is competitive with the state-of-the-art single methods achieving precision of 61.0% and recall of 55.4%, while not requiring residue solvent accessibility as an input.

AVAILABILITY

http://www2.warwick.ac.uk/fac/sci/systemsbiology/research/software/

A survey of machine learning methods for secondary and supersecondary protein structure prediction

In this chapter we provide a survey of protein secondary and supersecondary structure prediction using methods from machine learning. Our focus is on machine learning methods applicable to β-hairpin and β-sheet prediction, but we also discuss methods for more general supersecondary structure prediction. We provide background on the secondary and supersecondary structures that we discuss, the features used to describe them, and the basic theory behind the machine learning methods used. We survey the machine learning methods available for secondary and supersecondary structure prediction and compare them where possible.

BetaSearch: a new method for querying β-residue motifs

BACKGROUND

Searching for structural motifs across known protein structures can be useful for identifying unrelated proteins with similar function and characterising secondary structures such as β-sheets. This is infeasible using conventional sequence alignment because linear protein sequences do not contain spatial information. β-residue motifs are β-sheet substructures that can be represented as graphs and queried using existing graph indexing methods, however, these approaches are designed for general graphs that do not incorporate the inherent structural constraints of β-sheets and require computationally-expensive filtering and verification procedures. 3D substructure search methods, on the other hand, allow β-residue motifs to be queried in a three-dimensional context but at significant computational costs.

FINDINGS

We developed a new method for querying β-residue motifs, called BetaSearch, which leverages the natural planar constraints of β-sheets by indexing them as 2D matrices, thus avoiding much of the computational complexities involved with structural and graph querying. BetaSearch exhibits faster filtering, verification, and overall query time than existing graph indexing approaches whilst producing comparable index sizes. Compared to 3D substructure search methods, BetaSearch achieves 33 and 240 times speedups over index-based and pairwise alignment-based approaches, respectively. Furthermore, we have presented case-studies to demonstrate its capability of motif matching in sequentially dissimilar proteins and described a method for using BetaSearch to predict β-strand pairing.

CONCLUSIONS

We have demonstrated that BetaSearch is a fast method for querying substructure motifs. The improvements in speed over existing approaches make it useful for efficiently performing high-volume exploratory querying of possible protein substructural motifs or conformations. BetaSearch was used to identify a nearly identical β-residue motif between an entirely synthetic (Top7) and a naturally-occurring protein (Charcot-Leyden crystal protein), as well as identifying structural similarities between biotin-binding domains of avidin, streptavidin and the lipocalin gamma subunit of human C8.

ASTRO-FOLD 2.0: an Enhanced Framework for Protein Structure Prediction

The three-dimensional (3-D) structure prediction of proteins, given their amino acid sequence, is addressed using the first principles-based approach ASTRO-FOLD 2.0. The key features presented are: (1) Secondary structure prediction using a novel optimization-based consensus approach, (2) β-sheet topology prediction using mixed-integer linear optimization (MILP), (3) Residue-to-residue contact prediction using a high-resolution distance-dependent force field and MILP formulation, (4) Tight dihedral angle and distance bound generation for loop residues using dihedral angle clustering and non-linear optimization (NLP), (5) 3-D structure prediction using deterministic global optimization, stochastic conformational space annealing, and the full-atomistic ECEPP/3 potential, (6) Near-native structure selection using a traveling salesman problem-based clustering approach, ICON, and (7) Improved bound generation using chemical shifts of subsets of heavy atoms, generated by SPARTA and CS23D. Computational results of ASTRO-FOLD 2.0 on 47 blind targets of the recently concluded CASP9 experiment are presented.

CONCORD: a consensus method for protein secondary structure prediction via mixed integer linear optimization

Most of the protein structure prediction methods use a multi-step process, which often includes secondary structure prediction, contact prediction, fragment generation, clustering, etc. For many years, secondary structure prediction has been the workhorse for numerous methods aimed at predicting protein structure and function. This paper presents a new mixed integer linear optimization (MILP)-based consensus method: a Consensus scheme based On a mixed integer liNear optimization method for seCOndary stRucture preDiction (CONCORD). Based on seven secondary structure prediction methods, SSpro, DSC, PROF, PROFphd, PSIPRED, Predator and GorIV, the MILP-based consensus method combines the strengths of different methods, maximizes the number of correctly predicted amino acids and achieves a better prediction accuracy. The method is shown to perform well compared with the seven individual methods when tested on the PDBselect25 training protein set using sixfold cross validation. It also performs well compared with another set of 10 online secondary structure prediction servers (including several recent ones) when tested on the CASP9 targets ( http://predictioncenter.org/casp9/ ). The average Q3 prediction accuracy is 83.04 per cent for the sixfold cross validation of the PDBselect25 set and 82.3 per cent for the CASP9 targets. We have developed a MILP-based consensus method for protein secondary structure prediction. A web server, CONCORD, is available to the scientific community at http://helios.princeton.edu/CONCORD .

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.

Automated protein structure modeling in CASP9 by I-TASSER pipeline combined with QUARK-based ab initio folding and FG-MD-based structure refinement

I-TASSER is an automated pipeline for protein tertiary structure prediction using multiple threading alignments and iterative structure assembly simulations. In CASP9 experiments, two new algorithms, QUARK and fragment-guided molecular dynamics (FG-MD), were added to the I-TASSER pipeline for improving the structural modeling accuracy. QUARK is a de novo structure prediction algorithm used for structure modeling of proteins that lack detectable template structures. For distantly homologous targets, QUARK models are found useful as a reference structure for selecting good threading alignments and guiding the I-TASSER structure assembly simulations. FG-MD is an atomic-level structural refinement program that uses structural fragments collected from the PDB structures to guide molecular dynamics simulation and improve the local structure of predicted model, including hydrogen-bonding networks, torsion angles, and steric clashes. Despite considerable progress in both the template-based and template-free structure modeling, significant improvements on protein target classification, domain parsing, model selection, and ab initio folding of β-proteins are still needed to further improve the I-TASSER pipeline.