Enhancing Protein Conformational Space Sampling Using Distance Profile-Guided Differential Evolution

GraphGPSM: a global scoring model for protein structure using graph neural networks

The scoring models used for protein structure modeling and ranking are mainly divided into unified field and protein-specific scoring functions. Although protein structure prediction has made tremendous progress since CASP14, the modeling accuracy still cannot meet the requirements to a certain extent. Especially, accurate modeling of multi-domain and orphan proteins remains a challenge. Therefore, an accurate and efficient protein scoring model should be developed urgently to guide the protein structure folding or ranking through deep learning. In this work, we propose a protein structure global scoring model based on equivariant graph neural network (EGNN), named GraphGPSM, to guide protein structure modeling and ranking. We construct an EGNN architecture, and a message passing mechanism is designed to update and transmit information between nodes and edges of the graph. Finally, the global score of the protein model is output through a multilayer perceptron. Residue-level ultrafast shape recognition is used to describe the relationship between residues and the overall structure topology, and distance and direction encoded by Gaussian radial basis functions are designed to represent the overall topology of the protein backbone. These two features are combined with Rosetta energy terms, backbone dihedral angles and inter-residue distance and orientations to represent the protein model and embedded into the nodes and edges of the graph neural network. The experimental results on the CASP13, CASP14 and CAMEO test sets show that the scores of our developed GraphGPSM have a strong correlation with the TM-score of the models, which are significantly better than those of the unified field score function REF2015 and the state-of-the-art local lDDT-based scoring models ModFOLD8, ProQ3D and DeepAccNet, etc. The modeling experimental results on 484 test proteins demonstrate that GraphGPSM can greatly improve the modeling accuracy. GraphGPSM is further used to model 35 orphan proteins and 57 multi-domain proteins. The results show that the average TM-score of the models predicted by GraphGPSM is 13.2 and 7.1% higher than that of the models predicted by AlphaFold2. GraphGPSM also participates in CASP15 and achieves competitive performance in global accuracy estimation.

High-accuracy protein model quality assessment using attention graph neural networks

Great improvement has been brought to protein tertiary structure prediction through deep learning. It is important but very challenging to accurately rank and score decoy structures predicted by different models. CASP14 results show that existing quality assessment (QA) approaches lag behind the development of protein structure prediction methods, where almost all existing QA models degrade in accuracy when the target is a decoy of high quality. How to give an accurate assessment to high-accuracy decoys is particularly useful with the available of accurate structure prediction methods. Here we propose a fast and effective single-model QA method, QATEN, which can evaluate decoys only by their topological characteristics and atomic types. Our model uses graph neural networks and attention mechanisms to evaluate global and amino acid level scores, and uses specific loss functions to constrain the network to focus more on high-precision decoys and protein domains. On the CASP14 evaluation decoys, QATEN performs better than other QA models under all correlation coefficients when targeting average LDDT. QATEN shows promising performance when considering only high-accuracy decoys. Compared to the embedded evaluation modules of predicted ${C}_{\alpha^{-}} RMSD$ (pRMSD) in RosettaFold and predicted LDDT (pLDDT) in AlphaFold2, QATEN is complementary and capable of achieving better evaluation on some decoy structures generated by AlphaFold2 and RosettaFold. These results suggest that the new QATEN approach can be used as a reliable independent assessment algorithm for high-accuracy protein structure decoys.

DeepUMQA: ultrafast shape recognition-based protein model quality assessment using deep learning

MOTIVATION

Protein model quality assessment is a key component of protein structure prediction. In recent research, the voxelization feature was used to characterize the local structural information of residues, but it may be insufficient for describing residue-level topological information. Design features that can further reflect residue-level topology when combined with deep learning methods are therefore crucial to improve the performance of model quality assessment.

RESULTS

We developed a deep-learning method, DeepUMQA, based on Ultrafast Shape Recognition (USR) for the residue-level single-model quality assessment. In the framework of the deep residual neural network, the residue-level USR feature was introduced to describe the topological relationship between the residue and overall structure by calculating the first moment of a set of residue distance sets and then combined with 1D, 2D and voxelization features to assess the quality of the model. Experimental results on the CASP13, CASP14 test datasets and CAMEO blind test show that USR could supplement the voxelization features to comprehensively characterize residue structure information and significantly improve model assessment accuracy. The performance of DeepUMQA ranks among the top during the state-of-the-art single-model quality assessment methods, including ProQ2, ProQ3, ProQ3D, Ornate, VoroMQA, ProteinGCN, ResNetQA, QDeep, GraphQA, ModFOLD6, ModFOLD7, ModFOLD8, QMEAN3, QMEANDisCo3 and DeepAccNet.

AVAILABILITY AND IMPLEMENTATION

The DeepUMQA server is freely available at http://zhanglab-bioinf.com/DeepUMQA/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

De novo Protein Structure Prediction by Coupling Contact With Distance Profile

De novo protein structure prediction is a challenging problem that requires both an accurate energy function and an efficient conformation sampling method. In this study, a de novo structure prediction method, named CoDiFold, is proposed. In CoDiFold, contacts and distance profiles are organically combined into the Rosetta low-resolution energy function to improve the accuracy of energy function. As a result, the correlation between energy and root mean square deviation (RMSD) is improved. In addition, a population-based multi-mutation strategy is designed to balance the exploration and exploitation of conformation space sampling. The average RMSD of the models generated by the proposed protocol is decreased by 49.24 and 45.21 percent in the test set with 43 proteins compared with those of Rosetta and QUARK de novo protocols, respectively. The results also demonstrate that the structures predicted by proposed CoDiFold are comparable to the state-of-the-art methods for the 10 FM targets of CASP13. The source code and executable versions are freely available at http://github.com/iobio-zjut/CoDiFold.

A de novo protein structure prediction by iterative partition sampling, topology adjustment and residue-level distance deviation optimization

MOTIVATION

With the great progress of deep learning-based inter-residue contact/distance prediction, the discrete space formed by fragment assembly cannot satisfy the distance constraint well. Thus, the optimal solution of the continuous space may not be achieved. Designing an effective closed-loop continuous dihedral angle optimization strategy that complements the discrete fragment assembly is crucial to improve the performance of the distance-assisted fragment assembly method.

RESULTS

In this article, we proposed a de novo protein structure prediction method called IPTDFold based on closed-loop iterative partition sampling, topology adjustment and residue-level distance deviation optimization. First, local dihedral angle crossover and mutation operators are designed to explore the conformational space extensively and achieve information exchange between the conformations in the population. Then, the dihedral angle rotation model of loop region with partial inter-residue distance constraints is constructed, and the rotation angle satisfying the constraints is obtained by differential evolution algorithm, so as to adjust the spatial position relationship between the secondary structures. Finally, the residue distance deviation is evaluated according to the difference between the conformation and the predicted distance, and the dihedral angle of the residue is optimized with biased probability. The final model is generated by iterating the above three steps. IPTDFold is tested on 462 benchmark proteins, 24 FM targets of CASP13 and 20 FM targets of CASP14. Results show that IPTDFold is significantly superior to the distance-assisted fragment assembly method Rosetta_D (Rosetta with distance). In particular, the prediction accuracy of IPTDFold does not decrease as the length of the protein increases. When using the same FastRelax protocol, the prediction accuracy of IPTDFold is significantly superior to that of trRosetta without orientation constraints, and is equivalent to that of the full version of trRosetta.

AVAILABILITYAND IMPLEMENTATION

The source code and executable are freely available at https://github.com/iobio-zjut/IPTDFold.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Protein Structure Prediction Using Population-Based Algorithm Guided by Information Entropy

Ab initio protein structure prediction is one of the most challenging problems in computational biology. Multistage algorithms are widely used in ab initio protein structure prediction. The different computational costs of a multistage algorithm for different proteins are important to be considered. In this study, a population-based algorithm guided by information entropy (PAIE), which includes exploration and exploitation stages, is proposed for protein structure prediction. In PAIE, an entropy-based stage switch strategy is designed to switch from the exploration stage to the exploitation stage. Torsion angle statistical information is also deduced from the first stage and employed to enhance the exploitation in the second stage. Results indicate that an improvement in the performance of protein structure prediction in a benchmark of 30 proteins and 17 other free modeling targets in CASP.

Unsupervised multi-instance learning for protein structure determination

Many regions of the protein universe remain inaccessible by wet-laboratory or computational structure determination methods. A significant challenge in elucidating these dark regions in silico relates to the ability to discriminate relevant structure(s) among many structures/decoys computed for a protein of interest, a problem known as decoy selection. Clustering decoys based on geometric similarity remains popular. However, it is unclear how exactly to exploit the groups of decoys revealed via clustering to select individual structures for prediction. In this paper, we provide an intuitive formulation of the decoy selection problem as an instance of unsupervised multi-instance learning. We address the problem in three stages, first organizing given decoys of a protein molecule into bags, then identifying relevant bags, and finally drawing individual instances from these bags to offer as prediction. We propose both non-parametric and parametric algorithms for drawing individual instances. Our evaluation utilizes two datasets, one benchmark dataset of ensembles of decoys for a varied list of protein molecules, and a dataset of decoy ensembles for targets drawn from recent CASP competitions. A comparative analysis with state-of-the-art methods reveals that the proposed approach outperforms existing methods, thus warranting further investigation of multi-instance learning to advance our treatment of decoy selection.

TargetDBP+: Enhancing the Performance of Identifying DNA-Binding Proteins via Weighted Convolutional Features

Protein-DNA interactions exist ubiquitously and play important roles in the life cycles of living cells. The accurate identification of DNA-binding proteins (DBPs) is one of the key steps to understand the mechanisms of protein-DNA interactions. Although many DBP identification methods have been proposed, the current performance is still unsatisfactory. In this study, a new method, called TargetDBP+, is developed to further enhance the performance of identifying DBPs. In TargetDBP+, five convolutional features are first extracted from five feature sources, i.e., amino acid one-hot matrix (AAOHM), position-specific scoring matrix (PSSM), predicted secondary structure probability matrix (PSSPM), predicted solvent accessibility probability matrix (PSAPM), and predicted probabilities of DNA-binding sites (PPDBSs); second, the five features are weightedly and serially combined using the weights of all of the elements learned by the differential evolution algorithm; and finally, the DBP identification model of TargetDBP+ is trained using the support vector machine (SVM) algorithm. To evaluate the developed TargetDBP+ and compare it with other existing methods, a new gold-standard benchmark data set, called UniSwiss, is constructed, which consists of 4881 DBPs and 4881 non-DBPs extracted from the UniprotKB/Swiss-Prot database. Experimental results demonstrate that TargetDBP+ can obtain an accuracy of 85.83% and precision of 88.45% covering 82.41% of all DBP data on the independent validation subset of UniSwiss, with the MCC value (0.718) being significantly higher than those of other state-of-the-art control methods. The web server of TargetDBP+ is accessible at http://csbio.njust.edu.cn/bioinf/targetdbpplus/; the UniSwiss data set and stand-alone program of TargetDBP+ are accessible at https://github.com/jun-csbio/TargetDBPplus.

Decoy selection for protein structure prediction via extreme gradient boosting and ranking

Background

Identifying one or more biologically-active/native decoys from millions of non-native decoys is one of the major challenges in computational structural biology. The extreme lack of balance in positive and negative samples (native and non-native decoys) in a decoy set makes the problem even more complicated. Consensus methods show varied success in handling the challenge of decoy selection despite some issues associated with clustering large decoy sets and decoy sets that do not show much structural similarity. Recent investigations into energy landscape-based decoy selection approaches show promises. However, lack of generalization over varied test cases remains a bottleneck for these methods.

Results

We propose a novel decoy selection method, ML-Select, a machine learning framework that exploits the energy landscape associated with the structure space probed through a template-free decoy generation. The proposed method outperforms both clustering and energy ranking-based methods, all the while consistently offering better performance on varied test-cases. Moreover, ML-Select shows promising results even for the decoy sets consisting of mostly low-quality decoys.

Conclusions

ML-Select is a useful method for decoy selection. This work suggests further research in finding more effective ways to adopt machine learning frameworks in achieving robust performance for decoy selection in template-free protein structure prediction.

Two-Stage Distance Feature-based Optimization Algorithm for De novo Protein Structure Prediction

De novo protein structure prediction can be treated as a conformational space optimization problem under the guidance of an energy function. However, it is a challenge of how to design an accurate energy function which ensures low-energy conformations close to native structures. Fortunately, recent studies have shown that the accuracy of de novo protein structure prediction can be significantly improved by integrating the residue-residue distance information. In this paper, a two-stage distance feature-based optimization algorithm (TDFO) for de novo protein structure prediction is proposed within the framework of evolutionary algorithm. In TDFO, a similarity model is first designed by using feature information which is extracted from distance profiles by bisecting K-means algorithm. The similarity model-based selection strategy is then developed to guide conformation search, and thus improve the quality of the predicted models. Moreover, global and local mutation strategies are designed, and a state estimation strategy is also proposed to strike a trade-off between the exploration and exploitation of the search space. Experimental results of 35 benchmark proteins show that the proposed TDFO can improve prediction accuracy for a large portion of test proteins.

CGLFold: a contact-assisted de novo protein structure prediction using global exploration and loop perturbation sampling algorithm

MOTIVATION

Regions that connect secondary structure elements in a protein are known as loops, whose slight change will produce dramatic effect on the entire topology. This study investigates whether the accuracy of protein structure prediction can be improved using a loop-specific sampling strategy.

RESULTS

A novel de novo protein structure prediction method that combines global exploration and loop perturbation is proposed in this study. In the global exploration phase, the fragment recombination and assembly are used to explore the massive conformational space and generate native-like topology. In the loop perturbation phase, a loop-specific local perturbation model is designed to improve the accuracy of the conformation and is solved by differential evolution algorithm. These two phases enable a cooperation between global exploration and local exploitation. The filtered contact information is used to construct the conformation selection model for guiding the sampling. The proposed CGLFold is tested on 145 benchmark proteins, 14 free modeling (FM) targets of CASP13 and 29 FM targets of CASP12. The experimental results show that the loop-specific local perturbation can increase the structure diversity and success rate of conformational update and gradually improve conformation accuracy. CGLFold obtains template modeling score ≥ 0.5 models on 95 standard test proteins, 7 FM targets of CASP13 and 9 FM targets of CASP12.

AVAILABILITY AND IMPLEMENTATION

The source code and executable versions are freely available at https://github.com/iobio-zjut/CGLFold.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

TargetDBP: Accurate DNA-Binding Protein Prediction Via Sequence-Based Multi-View Feature Learning

Accurately identifying DNA-binding proteins (DBPs) from protein sequence information is an important but challenging task for protein function annotations. In this paper, we establish a novel computational method, named TargetDBP, for accurately targeting DBPs from primary sequences. In TargetDBP, four single-view features, i.e., AAC (Amino Acid Composition), PsePSSM (Pseudo Position-Specific Scoring Matrix), PsePRSA (Pseudo Predicted Relative Solvent Accessibility), and PsePPDBS (Pseudo Predicted Probabilities of DNA-Binding Sites), are first extracted to represent different base features, respectively. Second, differential evolution algorithm is employed to learn the weights of four base features. Using the learned weights, we weightedly combine these base features to form the original super feature. An excellent subset of the super feature is then selected by using a suitable feature selection algorithm SVM-REF+CBR (Support Vector Machine Recursive Feature Elimination with Correlation Bias Reduction). Finally, the prediction model is learned via using support vector machine on the selected feature subset. We also construct a new gold-standard and non-redundant benchmark dataset from PDB database to evaluate and compare the proposed TargetDBP with other existing predictors. On this new dataset, TargetDBP can achieve higher performance than other state-of-the-art predictors. The TargetDBP web server and datasets are freely available at http://csbio.njust.edu.cn/bioinf/targetdbp/ for academic use.

Underestimation-Assisted Global-Local Cooperative Differential Evolution and the Application to Protein Structure Prediction

Various mutation strategies show distinct advantages in differential evolution (DE). The cooperation of multiple strategies in the evolutionary process may be effective. This paper presents an underestimation-assisted global and local cooperative DE to simultaneously enhance the effectiveness and efficiency. In the proposed algorithm, two phases, namely, the global exploration and the local exploitation, are performed in each generation. In the global phase, a set of trial vectors is produced for each target individual by employing multiple strategies with strong exploration capability. Afterward, an adaptive underestimation model with a self-adapted slope control parameter is proposed to evaluate these trial vectors, the best of which is selected as the candidate. In the local phase, the better-based strategies guided by individuals that are better than the target individual are designed. For each individual accepted in the global phase, multiple trial vectors are generated by using these strategies and filtered by the underestimation value. The cooperation between the global and local phases includes two aspects. First, both of them concentrate on generating better individuals for the next generation. Second, the global phase aims to locate promising regions quickly while the local phase serves as a local search for enhancing convergence. Moreover, a simple mechanism is designed to determine the parameter of DE adaptively in the searching process. Finally, the proposed approach is applied to predict the protein 3D structure. Experimental studies on classical benchmark functions, CEC test sets, and protein structure prediction problem show that the proposed approach is superior to the competitors.

Reducing Ensembles of Protein Tertiary Structures Generated De Novo via Clustering

Controlling the quality of tertiary structures computed for a protein molecule remains a central challenge in de-novo protein structure prediction. The rule of thumb is to generate as many structures as can be afforded, effectively acknowledging that having more structures increases the likelihood that some will reside near the sought biologically-active structure. A major drawback with this approach is that computing a large number of structures imposes time and space costs. In this paper, we propose a novel clustering-based approach which we demonstrate to significantly reduce an ensemble of generated structures without sacrificing quality. Evaluations are related on both benchmark and CASP target proteins. Structure ensembles subjected to the proposed approach and the source code of the proposed approach are publicly-available at the links provided in Section 1.

Secondary Structure and Contact Guided Differential Evolution for Protein Structure Prediction

Ab initio protein tertiary structure prediction is one of the long-standing problems in structural bioinformatics. With the help of residue-residue contact and secondary structure prediction information, the accuracy of ab initio structure prediction can be enhanced. In this study, an improved differential evolution with secondary structure and residue-residue contact information referred to as SCDE is proposed for protein structure prediction. In SCDE, two score models based on secondary structure and contact information are proposed, and two selection strategies, namely, secondary structure-based selection strategy and contact-based selection strategy, are designed to guide conformation space search. A probability distribution function is designed to balance these two selection strategies. Experimental results on a benchmark dataset with 28 proteins and four free model targets in CASP12 demonstrate that the proposed SCDE is effective and efficient.

Anomaly Detection-Based Recognition of Near-Native Protein Structures

The three-dimensional structures populated by a protein molecule determine to a great extent its biological activities. The rich information encoded by protein structure on protein function continues to motivate the development of computational approaches for determining functionally-relevant structures. The majority of structures generated in silico are not relevant. Discriminating relevant/native protein structures from non-native ones is an outstanding challenge in computational structural biology. Inherently, this is a recognition problem that can be addressed under the umbrella of machine learning. In this paper, based on the premise that near-native structures are effectively anomalies, we build on the concept of anomaly detection in machine learning. We propose methods that automatically select relevant subsets, as well as methods that select a single structure to offer as prediction. Evaluations are carried out on benchmark datasets and demonstrate that the proposed methods advance the state of the art. The presented results motivate further building on and adapting concepts and techniques from machine learning to improve recognition of near-native structures in protein structure prediction.

Building maps of protein structure spaces in template-free protein structure prediction

An important goal in template-free protein structure prediction is how to control the quality of computed tertiary structures of a target amino-acid sequence. Despite great advances in algorithmic research, given the size, dimensionality, and inherent characteristics of the protein structure space, this task remains exceptionally challenging. It is current practice to aim to generate as many structures as can be afforded so as to increase the likelihood that some of them will reside near the sought but unknown biologically-active/native structure. When operating within a given computational budget, this is impractical and uninformed by any metrics of interest. In this paper, we propose instead to equip algorithms that generate tertiary structures, also known as decoy generation algorithms, with memory of the protein structure space that they explore. Specifically, we propose an evolving, granularity-controllable map of the protein structure space that makes use of low-dimensional representations of protein structures. Evaluations on diverse target sequences that include recent hard CASP targets show that drastic reductions in storage can be made without sacrificing decoy quality. The presented results make the case that integrating a map of the protein structure space is a promising mechanism to enhance decoy generation algorithms in template-free protein structure prediction.

Loop Enhanced Conformational Resampling Method for Protein Structure Prediction

Protein structure prediction has been a long-standing problem for the past decades. In particular, the loop region structure remains an obstacle in forming an accurate protein tertiary structure because of its flexibility. In this study, Rama torsion angle and secondary structure feature-guided differential evolution named RSDE is proposed to predict three-dimensional structure with the exploitation on the loop region structure. In RSDE, the structure of the loop region is improved by the following: loop-based cross operator, which interchanges configuration of a randomly selected loop region between individuals, and loop-based mutate operator, which considers torsion angle feature into conformational sampling. A stochastic ranking selective strategy is designed to select conformations with low energy and near-native structure. Moreover, the conformational resampling method, which uses previously learned knowledge to guide subsequent sampling, is proposed to improve the sampling efficiency. Experiments on a total of 28 test proteins reveals that the proposed RSDE is effective and can obtain native-like models.

Balancing multiple objectives in conformation sampling to control decoy diversity in template-free protein structure prediction

Background

Computational approaches for the determination of biologically-active/native three-dimensional structures of proteins with novel sequences have to handle several challenges. The (conformation) space of possible three-dimensional spatial arrangements of the chain of amino acids that constitute a protein molecule is vast and high-dimensional. Exploration of the conformation spaces is performed in a sampling-based manner and is biased by the internal energy that sums atomic interactions. Even state-of-the-art energy functions that quantify such interactions are inherently inaccurate and associate with protein conformation spaces overly rugged energy surfaces riddled with artifact local minima. The response to these challenges in template-free protein structure prediction is to generate large numbers of low-energy conformations (also referred to as decoys) as a way of increasing the likelihood of having a diverse decoy dataset that covers a sufficient number of local minima possibly housing near-native conformations.

Results

In this paper we pursue a complementary approach and propose to directly control the diversity of generated decoys. Inspired by hard optimization problems in high-dimensional and non-linear variable spaces, we propose that conformation sampling for decoy generation is more naturally framed as a multi-objective optimization problem. We demonstrate that mechanisms inherent to evolutionary search techniques facilitate such framing and allow balancing multiple objectives in protein conformation sampling. We showcase here an operationalization of this idea via a novel evolutionary algorithm that has high exploration capability and is also able to access lower-energy regions of the energy landscape of a given protein with similar or better proximity to the known native structure than several state-of-the-art decoy generation algorithms.

Conclusions

The presented results constitute a promising research direction in improving decoy generation for template-free protein structure prediction with regards to balancing of multiple conflicting objectives under an optimization framework. Future work will consider additional optimization objectives and variants of improvement and selection operators to apportion a fixed computational budget. Of particular interest are directions of research that attenuate dependence on protein energy models.

Differential Evolution With Underestimation-Based Multimutation Strategy

As we know, the performance of differential evolution (DE) highly depends on the mutation strategy. However, it is difficult to choose a suitable mutation strategy for a specific problem or different running stages. This paper proposes an underestimation-based multimutation strategy (UMS) for DE. In the UMS, a set of candidate offsprings are simultaneously generated for each target individual by utilizing multiple mutation strategies. Then a cheap abstract convex underestimation model is built based on some selected individuals to obtain the underestimation value of each candidate offspring. According to the quality of each candidate offspring measured by the underestimation value, the most promising candidate solution is chosen as the offspring. Compared to the existing probability-based multimutation techniques, no mutation strategies are lost during the search process as each mutation strategy has the same probability to generate a candidate solution. Moreover, no extra function evaluations are produced because the candidate solutions are filtered by the underestimation value. The UMS is integrated into some DE variants and compared with their original algorithms and several advanced DE approaches over the CEC 2013 and 2014 benchmark sets. Additionally, a well-known real-world problem is employed to evaluate the performance of the UMS. Experimental results show that the proposed UMS can improve the performance of the advanced DE variants.

Sequential search leads to faster, more efficient fragment-based de novo protein structure prediction

Motivation

Most current de novo structure prediction methods randomly sample protein conformations and thus require large amounts of computational resource. Here, we consider a sequential sampling strategy, building on ideas from recent experimental work which shows that many proteins fold cotranslationally.

Results

We have investigated whether a pseudo-greedy search approach, which begins sequentially from one of the termini, can improve the performance and accuracy of de novo protein structure prediction. We observed that our sequential approach converges when fewer than 20 000 decoys have been produced, fewer than commonly expected. Using our software, SAINT2, we also compared the run time and quality of models produced in a sequential fashion against a standard, non-sequential approach. Sequential prediction produces an individual decoy 1.5-2.5 times faster than non-sequential prediction. When considering the quality of the best model, sequential prediction led to a better model being produced for 31 out of 41 soluble protein validation cases and for 18 out of 24 transmembrane protein cases. Correct models (TM-Score > 0.5) were produced for 29 of these cases by the sequential mode and for only 22 by the non-sequential mode. Our comparison reveals that a sequential search strategy can be used to drastically reduce computational time of de novo protein structure prediction and improve accuracy.

Availability and implementation

Data are available for download from: http://opig.stats.ox.ac.uk/resources. SAINT2 is available for download from: https://github.com/sauloho/SAINT2.

Contact

saulo.deoliveira@dtc.ox.ac.uk.

Supplementary information

Supplementary data are available at Bioinformatics online.

Guiding exploration in conformational feature space with Lipschitz underestimation for ab-initio protein structure prediction

Computing conformations which are essential to associate structural and functional information with gene sequences, is challenging due to the high dimensionality and rugged energy surface of the protein conformational space. Consequently, the dimension of the protein conformational space should be reduced to a proper level, and an effective exploring algorithm should be proposed. In this paper, a plug-in method for guiding exploration in conformational feature space with Lipschitz underestimation (LUE) for ab-initio protein structure prediction is proposed. The conformational space is converted into ultrafast shape recognition (USR) feature space firstly. Based on the USR feature space, the conformational space can be further converted into Underestimation space according to Lipschitz estimation theory for guiding exploration. As a consequence of the use of underestimation model, the tight lower bound estimate information can be used for exploration guidance, the invalid sampling areas can be eliminated in advance, and the number of energy function evaluations can be reduced. The proposed method provides a novel technique to solve the exploring problem of protein conformational space. LUE is applied to differential evolution (DE) algorithm, and metropolis Monte Carlo(MMC) algorithm which is available in the Rosetta; When LUE is applied to DE and MMC, it will be screened by the underestimation method prior to energy calculation and selection. Further, LUE is compared with DE and MMC by testing on 15 small-to-medium structurally diverse proteins. Test results show that near-native protein structures with higher accuracy can be obtained more rapidly and efficiently with the use of LUE.

Abstract Convex Underestimation Assisted Multistage Differential Evolution

In differential evolution (DE), different strategies applied in different evolutionary stages may be more effective than a single strategy used in the entire evolutionary process. However, it is not trivial to appropriately determine the evolutionary stage. In this paper, we present an abstract convex underestimation-assisted multistage DE. In the proposed algorithm, the underestimation is calculated through the supporting vectors of some neighboring individuals. Based on the variation of the average underestimation error (UE), the evolutionary process is divided into three stages. Each stage includes a pool of suitable candidate strategies. At the beginning of each generation, the evolutionary stage is first estimated according to the average UE of the previous generation. Subsequently, a strategy is automatically chosen from the corresponding candidate pool to create a mutant vector. In addition, a centroid-based strategy which utilizes the information of multiple superior individuals is designed to balance the population diversity and convergence speed in the second stage. Experiments are conducted on 23 widely used test functions, CEC 2013, and CEC 2014 benchmark sets to demonstrate the performance of the proposed algorithm. The results reveal that the proposed algorithm exhibits better performance compared with several advanced DE variants and some non-DE approaches.