Ranking predicted protein structures with support vector regression

Protein structure prediction is an important problem of both intellectual and practical interest. Most protein structure prediction approaches generate multiple candidate models first, and then use a scoring function to select the best model among these candidates. In this work, we develop a scoring function using support vector regression (SVR). Both consensus-based features and features from individual structures are extracted from a training data set containing native protein structures and predicted structural models submitted to CASP5 and CASP6. The SVR learns a scoring function that is a linear combination of these features. We test this scoring function on two data sets. First, when used to rank server models submitted to CASP7, the SVR score selects predictions that are comparable to the best performing server in CASP7, Zhang-Server, and significantly better than all the other servers. Even if the SVR score is not allowed to select Zhang-Server models, the SVR score still selects predictions that are significantly better than all the other servers. In addition, the SVR is able to select significantly better models and yield significantly better Pearson correlation coefficients than the two best Quality Assessment groups in CASP7, QA556 (LEE), and QA634 (Pcons). Second, this work aims to improve the ability of the Robetta server to select best models, and hence we evaluate the performance of the SVR score on ranking the Robetta server template-based models for the CASP7 targets. The SVR selects significantly better models than the Robetta K*Sync consensus alignment score.     

Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures

In this study, we have developed a statistical mechanics-based iterative method to extract statistical atomic interaction potentials from known, nonredundant protein structures. Our method circumvents the long-standing reference state problem in deriving traditional knowledge-based scoring functions, by using rapid iterations through a physical, global convergence function. The rapid convergence of this physics-based method, unlike other parameter optimization methods, warrants the feasibility of deriving distance-dependent, all-atom statistical potentials to keep the scoring accuracy. The derived potentials, referred to as ITScore/Pro, have been validated using three diverse benchmarks: the high-resolution decoy set, the AMBER benchmark decoy set, and the CASP8 decoy set. Significant improvement in performance has been achieved. Finally, comparisons between the potentials of our model and potentials of a knowledge-based scoring function with a randomized reference state have revealed the reason for the better performance of our scoring function, which could provide useful insight into the development of other physical scoring functions. The potentials developed in this study are generally applicable for structural selection in protein structure prediction.     

Evaluating CASP4 predictions with physical energy functions

Physical energy scoring functions based on implicit solvation models are tested by evaluating predictions from the most recent CASP4 competition. The best performing scoring functions are identified along with the best protocol for preparing structures before energies are evaluated. Ranking of structures with the best scoring functions is compared across CASP4 targets to establish when physical scoring functions can be expected to reliably distinguish structures that are most similar to the native fold in a set of misfolded or unfolded protein conformations. The results are used to interpret previous studies where scoring functions were tested on the standard decoy sets by Park, Levitt, and Baker. We show that the best physical scoring functions can be applied successfully in automated consensus scoring applications where a single best conformation has to be selected from a set of structures from different sources. Finally, the potential for better protein structure scoring functions is discussed with a suggestion for an empirically parameterized linear combination of energy components.     

Predicted residue–residue contacts can help the scoring of 3D models

During the 7th Critical Assessment of Protein Structure Prediction (CASP7) experiment, it was suggested that the real value of predicted residue–residue contacts might lie in the scoring of 3D model structures. Here, we have carried out a detailed reassessment of the contact predictions made during the recent CASP8 experiment to determine whether predicted contacts might aid in the selection of close‐to‐native structures or be a useful tool for scoring 3D structural models. We used the contacts predicted by the CASP8 residue–residue contact prediction groups to select models for each target domain submitted to the experiment. We found that the information contained in the predicted residue–residue contacts would probably have helped in the selection of 3D models in the free modeling regime and over the harder comparative modeling targets. Indeed, in many cases, the models selected using just the predicted contacts had better GDT‐TS scores than all but the best 3D prediction groups. Despite the well‐known low accuracy of residue–residue contact predictions, it is clear that the predictive power of contacts can be useful in 3D model prediction strategies. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Protein model quality assessment prediction by combining fragment comparisons and a consensus C(alpha) contact potential

In this work, we develop a fully automated method for the quality assessment prediction of protein structural models generated by structure prediction approaches such as fold recognition servers, or ab initio methods. The approach is based on fragment comparisons and a consensus C(alpha) contact potential derived from the set of models to be assessed and was tested on CASP7 server models. The average Pearson linear correlation coefficient between predicted quality and model GDT-score per target is 0.83 for the 98 targets, which is better than those of other quality assessment methods that participated in CASP7. Our method also outperforms the other methods by about 3% as assessed by the total GDT-score of the selected top models.     

Assessment of protein model structure accuracy estimation in CASP13: Challenges in the era of deep learning

Scoring model structure is an essential component of protein structure prediction that can affect the prediction accuracy tremendously. Users of protein structure prediction results also need to score models to select the best models for their application studies. In Critical Assessment of techniques for protein Structure Prediction (CASP), model accuracy estimation methods have been tested in a blind fashion by providing models submitted by the tertiary structure prediction servers for scoring. In CASP13, model accuracy estimation results were evaluated in terms of both global and local structure accuracy. Global structure accuracy estimation was evaluated by the quality of the models selected by the global structure scores and by the absolute estimates of the global scores. Residue-wise, local structure accuracy estimations were evaluated by three different measures. A new measure introduced in CASP13 evaluates the ability to predict inaccurately modeled regions that may be improved by refinement. An intensive comparative analysis on CASP13 and the previous CASPs revealed that the tertiary structure models generated by the CASP13 servers show very distinct features. Higher consensus toward models of higher global accuracy appeared even for free modeling targets, and many models of high global accuracy were not well optimized at the atomic level. This is related to the new technology in CASP13, deep learning for tertiary contact prediction. The tertiary model structures generated by deep learning pose a new challenge for EMA (estimation of model accuracy) method developers. Model accuracy estimation itself is also an area where deep learning can potentially have an impact, although current EMA methods have not fully explored that direction.     

ProVal: a protein-scoring function for the selection of native and near-native folds

A low-resolution scoring function for the selection of native and near-native structures from a set of predicted structures for a given protein sequence has been developed. The scoring function, ProVal (Protein Validate), used several variables that describe an aspect of protein structure for which the proximity to the native structure can be assessed quantitatively. Among the parameters included are a packing estimate, surface areas, and the contact order. A partial least squares for latent variables (PLS) model was built for each candidate set of the 28 decoy sets of structures generated for 22 different proteins using the described parameters as independent variables. The C(alpha) RMS of the candidate structures versus the experimental structure was used as the dependent variable. The final generalized scoring function was an average of all models derived, ensuring that the function was not optimized for specific fold classes or method of structure generation of the candidate folds. The results show that the crystal structure was scored best in 64% of the 28 test sets and was clearly separated from the decoys in many examples. In all the other cases in which the crystal structure did not rank first, it ranked within the top 10%. Thus, although ProVal could not distinguish between predicted structures that were similar overall in fold quality due to its inherently low resolution, it can clearly be used as a primary filter to eliminate approximately 90% of fold candidates generated by current prediction methods from all-atom modeling and further evaluation. The correlation between the predicted and actual C(alpha) RMS values varies considerably between the candidate fold sets.     

A structural pattern-based method for protein fold recognition

A method (SPREK) was developed to evaluate the register of a sequence on a structure based on the matching of structural patterns against a library derived from the protein structure databank. The scores obtained were normalized against random background distributions derived from sequence shuffling and permutation methods. 'Random' structures were also used to evaluate the effectiveness of the method. These were generated by a simple random-walk and a more sophisticated structure prediction method that produced protein-like folds. For comparison with other methods, the performance of the method was assessed using collections of models including decoys and models from the CASP-5 exercise. The performance of SPREK on the decoy models was equivalent to (and sometimes better than) those obtained with more complex approaches. An exception was the two smallest proteins, for which SPREK did not perform well due to a lack of patterns. Using the best parameter combination from trials on decoy models, the CASP models of intermediate difficulty were evaluated by SPREK and the quality of the top scoring model was evaluated by its CASP ranking. Of the 14 targets in this class, half lie in the top 10% (out of around 140 models for each target). The two worst rankings resulted from the selection by our method of a well-packed model that was based on the wrong fold. Of the other poor rankings, one was the smallest protein and the others were the four largest (all over 250 residues).     

Princeton_TIGRESS: Protein geometry refinement using simulations and support vector machines

Protein structure refinement aims to perform a set of operations given a predicted structure to improve model quality and accuracy with respect to the native in a blind fashion. Despite the numerous computational approaches to the protein refinement problem reported in the previous three CASPs, an overwhelming majority of methods degrade models rather than improve them. We initially developed a method tested using blind predictions during CASP10 which was officially ranked in 5th place among all methods in the refinement category. Here, we present Princeton_TIGRESS, which when benchmarked on all CASP 7,8,9, and 10 refinement targets, simultaneously increased GDT_TS 76% of the time with an average improvement of 0.83 GDT_TS points per structure. The method was additionally benchmarked on models produced by top performing three‐dimensional structure prediction servers during CASP10. The robustness of the Princeton_TIGRESS protocol was also tested for different random seeds. We make the Princeton_TIGRESS refinement protocol freely available as a web server at http://atlas.princeton.edu/refinement . Using this protocol, one can consistently refine a prediction to help bridge the gap between a predicted structure and the actual native structure. Proteins 2014; 82:794–814. © 2013 Wiley Periodicals, Inc.     

A multiple-template approach to protein threading

Most threading methods predict the structure of a protein using only a single template. Due to the increasing number of solved structures, a protein without solved structure is very likely to have more than one similar template structures. Therefore, a natural question to ask is if we can improve modeling accuracy using multiple templates. This article describes a new multiple-template threading method to answer this question. At the heart of this multiple-template threading method is a novel probabilistic-consistency algorithm that can accurately align a single protein sequence simultaneously to multiple templates. Experimental results indicate that our multiple-template method can improve pairwise sequence-template alignment accuracy and generate models with better quality than single-template models even if they are built from the best single templates (P-value <10(-6)) while many popular multiple sequence/structure alignment tools fail to do so. The underlying reason is that our probabilistic-consistency algorithm can generate accurate multiple sequence/template alignments. In another word, without an accurate multiple sequence/template alignment, the modeling accuracy cannot be improved by simply using multiple templates to increase alignment coverage. Blindly tested on the CASP9 targets with more than one good template structures, our method outperforms all other CASP9 servers except two (Zhang-Server and QUARK of the same group). Our probabilistic-consistency algorithm can possibly be extended to align multiple protein/RNA sequences and structures.     

Refinement of protein termini in template-based modeling using conformational space annealing

The rapid increase in the number of experimentally determined protein structures in recent years enables us to obtain more reliable protein tertiary structure models than ever by template-based modeling. However, refinement of template-based models beyond the limit available from the best templates is still needed for understanding protein function in atomic detail. In this work, we develop a new method for protein terminus modeling that can be applied to refinement of models with unreliable terminus structures. The energy function for terminus modeling consists of both physics-based and knowledge-based potential terms with carefully optimized relative weights. Effective sampling of both the framework and terminus is performed using the conformational space annealing technique. This method has been tested on a set of termini derived from a nonredundant structure database and two sets of termini from the CASP8 targets. The performance of the terminus modeling method is significantly improved over our previous method that does not employ terminus refinement. It is also comparable or superior to the best server methods tested in CASP8. The success of the current approach suggests that similar strategy may be applied to other types of refinement problems such as loop modeling or secondary structure rearrangement.     

Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

RNA molecules play integral roles in gene regulation, and understanding their structures gives us important insights into their biological functions. Despite recent developments in template-based and parameterized energy functions, the structure of RNA--in particular the nonhelical regions--is still difficult to predict. Knowledge-based potentials have proven efficient in protein structure prediction. In this work, we describe two differentiable knowledge-based potentials derived from a curated data set of RNA structures, with all-atom or coarse-grained representation, respectively. We focus on one aspect of the prediction problem: the identification of native-like RNA conformations from a set of near-native models. Using a variety of near-native RNA models generated from three independent methods, we show that our potential is able to distinguish the native structure and identify native-like conformations, even at the coarse-grained level. The all-atom version of our knowledge-based potential performs better and appears to be more effective at discriminating near-native RNA conformations than one of the most highly regarded parameterized potential. The fully differentiable form of our potentials will additionally likely be useful for structure refinement and/or molecular dynamics simulations.     

Princeton_TIGRESS 2.0: High refinement consistency and net gains through support vector machines and molecular dynamics in double‐blind predictions during the CASP11 experiment

Protein structure refinement is the challenging problem of operating on any protein structure prediction to improve its accuracy with respect to the native structure in a blind fashion. Although many approaches have been developed and tested during the last four CASP experiments, a majority of the methods continue to degrade models rather than improve them. Princeton_TIGRESS (Khoury et al., Proteins 2014;82:794–814) was developed previously and utilizes separate sampling and selection stages involving Monte Carlo and molecular dynamics simulations and classification using an SVM predictor. The initial implementation was shown to consistently refine protein structures 76% of the time in our own internal benchmarking on CASP 7‐10 targets. In this work, we improved the sampling and selection stages and tested the method in blind predictions during CASP11. We added a decomposition of physics‐based and hybrid energy functions, as well as a coordinate‐free representation of the protein structure through distance‐binning distances to capture fine‐grained movements. We performed parameter estimation to optimize the adjustable SVM parameters to maximize precision while balancing sensitivity and specificity across all cross‐validated data sets, finding enrichment in our ability to select models from the populations of similar decoys generated for targets in CASPs 7‐10. The MD stage was enhanced such that larger structures could be further refined. Among refinement methods that are currently implemented as web‐servers, Princeton_TIGRESS 2.0 demonstrated the most consistent and most substantial net refinement in blind predictions during CASP11. The enhanced refinement protocol Princeton_TIGRESS 2.0 is freely available as a web server at http://atlas.engr.tamu.edu/refinement/ . Proteins 2017; 85:1078–1098. © 2017 Wiley Periodicals, Inc.     

Template‐free protein structure prediction and quality assessment with an all‐atom free‐energy model

Biophysical forcefields have contributed less than originally anticipated to recent progress in protein structure prediction. Here, we have investigated the selectivity of a recently developed all‐atom free‐energy forcefield for protein structure prediction and quality assessment (QA). Using a heuristic method, but excluding homology, we generated decoy‐sets for all targets of the CASP7 protein structure prediction assessment with <150 amino acids. The decoys in each set were then ranked by energy in short relaxation simulations and the best low‐energy cluster was submitted as a prediction. For four of nine template‐free targets, this approach generated high‐ranking predictions within the top 10 models submitted in CASP7 for the respective targets. For these targets, our de‐novo predictions had an average GDT_S score of 42.81, significantly above the average of all groups. The refinement protocol has difficulty for oligomeric targets and when no near‐native decoys are generated in the decoy library. For targets with high‐quality decoy sets the refinement approach was highly selective. Motivated by this observation, we rescored all server submissions up to 200 amino acids using a similar refinement protocol, but using no clustering, in a QA exercise. We found an excellent correlation between the best server models and those with the lowest energy in the forcefield. The free‐energy refinement protocol may thus be an efficient tool for relative QA and protein structure prediction. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

Refining homology models by combining replica-exchange molecular dynamics and statistical potentials

A protocol is presented for the global refinement of homology models of proteins. It combines the advantages of temperature-based replica-exchange molecular dynamics (REMD) for conformational sampling and the use of statistical potentials for model selection. The protocol was tested using 21 models. Of these 14 were models of 10 small proteins for which high-resolution crystal structures were available, the remainder were targets of the recent CASPR exercise. It was found that REMD in combination with currently available force fields could sample near-native conformational states starting from high-quality homology models. Conformations in which the backbone RMSD of secondary structure elements (SSE-RMSD) was lower than the starting value by 0.5-1.0 A were found for 15 out of the 21 cases (average 0.82 A). Furthermore, when a simple scoring function consisting of two statistical potentials was used to rank the structures, one or more structures with SSE-RMSD of at least 0.2 A lower than the starting value was found among the five best ranked structures in 11 out of the 21 cases. The average improvement in SSE-RMSD for the best models was 0.42 A. However, none of the scoring functions tested identified the structures with the lowest SSE-RMSD as the best models although all identified the native conformation as the one with lowest energy. This suggests that while the proposed protocol proved effective for the refinement of high-quality models of small proteins scoring functions remain one of the major limiting factors in structure refinement. This and other aspects by which the methodology could be further improved are discussed.     

Consistent refinement of submitted models at CASP using a knowledge‐based potential

Protein structure refinement is an important but unsolved problem; it must be solved if we are to predict biological function that is very sensitive to structural details. Specifically, critical assessment of techniques for protein structure prediction (CASP) shows that the accuracy of predictions in the comparative modeling category is often worse than that of the template on which the homology model is based. Here we describe a refinement protocol that is able to consistently refine submitted predictions for all categories at CASP7. The protocol uses direct energy minimization of the knowledge‐based potential of mean force that is based on the interaction statistics of 167 atom types (Summa and Levitt, Proc Natl Acad Sci USA 2007; 104:3177–3182). Our protocol is thus computationally very efficient; it only takes a few minutes of CPU time to run typical protein models (300 residues). We observe an average structural improvement of 1% in GDT_TS, for predictions that have low and medium homology to known PDB structures (Global Distance Test score or GDT_TS between 50 and 80%). We also observe a marked improvement in the stereochemistry of the models. The level of improvement varies amongst the various participants at CASP, but we see large improvements (>10% increase in GDT_TS) even for models predicted by the best performing groups at CASP7. In addition, our protocol consistently improved the best predicted models in the refinement category at CASP7 and CASP8. These improvements in structure and stereochemistry prove the usefulness of our computationally inexpensive, powerful and automatic refinement protocol. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

miREE: miRNA recognition elements ensemble

Background

The accurate prediction of ligand binding residues from amino acid sequences is important for the automated functional annotation of novel proteins. In the previous two CASP experiments, the most successful methods in the function prediction category were those which used structural superpositions of 3D models and related templates with bound ligands in order to identify putative contacting residues. However, whilst most of this prediction process can be automated, visual inspection and manual adjustments of parameters, such as the distance thresholds used for each target, have often been required to prevent over prediction. Here we describe a novel method FunFOLD, which uses an automatic approach for cluster identification and residue selection. The software provided can easily be integrated into existing fold recognition servers, requiring only a 3D model and list of templates as inputs. A simple web interface is also provided allowing access to non-expert users. The method has been benchmarked against the top servers and manual prediction groups tested at both CASP8 and CASP9.

Results

The FunFOLD method shows a significant improvement over the best available servers and is shown to be competitive with the top manual prediction groups that were tested at CASP8. The FunFOLD method is also competitive with both the top server and manual methods tested at CASP9. When tested using common subsets of targets, the predictions from FunFOLD are shown to achieve a significantly higher mean Matthews Correlation Coefficient (MCC) scores and Binding-site Distance Test (BDT) scores than all server methods that were tested at CASP8. Testing on the CASP9 set showed no statistically significant separation in performance between FunFOLD and the other top server groups tested.

Conclusions

The FunFOLD software is freely available as both a standalone package and a prediction server, providing competitive ligand binding site residue predictions for expert and non-expert users alike. The software provides a new fully automated approach for structure based function prediction using 3D models of proteins.     

Scoring function for automated assessment of protein structure template quality

We have developed a new scoring function, the template modeling score (TM-score), to assess the quality of protein structure templates and predicted full-length models by extending the approaches used in Global Distance Test (GDT)1 and MaxSub.2 First, a protein size-dependent scale is exploited to eliminate the inherent protein size dependence of the previous scores and appropriately account for random protein structure pairs. Second, rather than setting specific distance cutoffs and calculating only the fractions with errors below the cutoff, all residue pairs in alignment/modeling are evaluated in the proposed score. For comparison of various scoring functions, we have constructed a large-scale benchmark set of structure templates for 1489 small to medium size proteins using the threading program PROSPECTOR_3 and built the full-length models using MODELLER and TASSER. The TM-score of the initial threading alignments, compared to the GDT and MaxSub scoring functions, shows a much stronger correlation to the quality of the final full-length models. The TM-score is further exploited as an assessment of all 'new fold' targets in the recent CASP5 experiment and shows a close coincidence with the results of human-expert visual assessment. These data suggest that the TM-score is a useful complement to the fully automated assessment of protein structure predictions. The executable program of TM-score is freely downloadable at http://bioinformatics.buffalo.edu/TM-score.     

Model quality assessment using distance constraints from alignments

Given a set of alternative models for a specific protein sequence, the model quality assessment (MQA) problem asks for an assignment of scores to each model in the set. A good MQA program assigns these scores such that they correlate well with real quality of the models, ideally scoring best that model which is closest to the true structure. In this article, we present a new approach for addressing the MQA problem. It is based on distance constraints extracted from alignments to templates of known structure, and is implemented in the Undertaker program for protein structure prediction. One novel feature is that we extract noncontact constraints as well as contact constraints. We describe how the distance constraint extraction is done and we show how they can be used to address the MQA problem. We have compared our method on CASP7 targets and the results show that our method is at least comparable with the best MQA methods that were assessed at CASP7. We also propose a new evaluation measure, Kendall's τ, that is more interpretable than conventional measures used for evaluating MQA methods (Pearson's r and Spearman's ρ). We show clear examples where Kendall's τ agrees much more with our intuition of a correct MQA, and we therefore propose that Kendall's τ be used for future CASP MQA assessments. Proteins 2009. © 2008 Wiley‐Liss, Inc.